L5M Pub 2000 · 2017. 6. 22. · 8 Writing ratios / Simplifying ratios / Sharing in a given ratio N9 9 Equivalent fractions / Writing fractions / Simplifying / Mixed numbers & Improper

$Page 1: L5M Pub 2000 · 2017. 6. 22. · 8 Writing ratios / Simplifying ratios / Sharing in a given ratio N9 9 Equivalent fractions / Writing fractions / Simplifying / Mixed numbers & Improper$
Author: A. W. Stark

Photocopy Masters

A set of activity sheets written utilising MATHEMATICS in the New Zealand CURRICULUM

(Including answers)

Level 5

L5M

This resource unit has been supplied on the understanding that copies of any part of this publication will not be given or sold to teachers or students from other schools or

institutions.

This resource unit may be used as a master, and therefore can be photocopied, only by the school or institution that has purchased this resource unit.

L5M

Level 5 Photocopy Masters

A set of activity sheets written utilising MATHEMATICS in the New Zealand CURRICULUM

(including answers)

L5M

Author: A. W. Stark

P O Box 21304 Edgeware

CHRISTCHURCH 8143 NEW ZEALAND

New contact numbers as from October 2007

(03) 338 0516 or (03) 338 0514

Author: A. W. Stark

Copyright ©1998

A. W. Stark

First Published March 1998

Formatting and publishing by Andrew Stark

Formerly trading as: NOW

trading as:

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Note from the author:

This resource ...

(L5M) Mathematics Level 5

Homework / Assessment Worksheets

has been written utilising the objectives as stated in

Mathematics in the New Zealand Curriculum for Level 5.

The resource L5M has been compiled to complement the series of FIVE resources for Level 5 Mathematics, written utilising the objectives of the five strands for the Mathematics curriculum, (see opposite page for details). L5M can be used on its own or in conjunction with the series of five resources. These Homework / Assessment Worksheets can be utilised in several ways: as a pre-test to assess pupils’ prior knowledge of an objective as a post-test to assess pupils’ understanding of the objective that has been taught as homework or revision worksheets as remedial or extension worksheets Utilising the Homework / Assessment Worksheets contained in the FIVE resources, L5MN, L5MM, L5MG, L5MA & L5MS and the worksheets within the resource L5M, will give you ...

TWO sets of parallel Homework / Assessment Worksheets. Information contained in this resource includes ... a table of contents indicating the strand and objective(s) being covered in each worksheet a list of the Level 5 Mathematics objectives as stated in the curriculum Homework / Assessment Worksheets answers pupil tracking sheets

(03) 338 0516

(03) 338 0514

For more information about these and other resources, please contact ...

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Resource Code:

L5MN

Resource Code:

L5MM

Resource Code:

L5MG

Resource Code:

L5MA

Resource Code:

L5MS

Other specialist Mathematics resources available for Level 5.

About these resources:

Each resource is divided into 8 sections.

Section 1 List of Strand Objectives appropriate to each resource. Table of ‘In-class’ Worksheets / Objectives covered, including the Mathematical Processes objectives.

Section 2: Table of Contents for ‘In-class’ Worksheets. The ‘In-class’ Worksheets generally have the following format: worked example, introducing an objective / skill. one or more Tasks, with graded questions.

Section 3: ‘In-class’ Worksheet PHOTOCOPY MASTERS. Each resource will have between 15 & 24 Worksheets.

Section 4: Teaching Notes / Answers for ‘In-class’ Worksheets

Section 5: Table of Contents for Homework / Assessment Worksheets, including objectives covered.

Section 6: Homework / Assessment Worksheet PHOTOCOPY MASTERS. Each resource will have between 8 & 12 Worksheets. All Homework / Assessment worksheets will contain ‘10 Quick Questions’, written using the Level 4 mathematics objectives, as revision.

Section 7: Answers for Homework / Assessment Worksheets.

Section 8: A Worksheet Tracking Sheet for teachers to record pupil names & worksheets / objectives completed.

A Complete Guide to Statistics

written utilising the objectives as stated in


A Complete Guide to Number



A Complete Guide to Measurement



A Complete Guide to Geometry



A Complete Guide to Algebra



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Table of Contents for the Homework / Assessment Worksheet Masters

Level 5 Mathematics Topics Objective(s)

1 Working with whole numbers / Word problems Revision

2 Number facts / multiples / Factors / Prime numbers / Order of operations / Word problems Revision

3 Squares and square roots / Approximations & Estimations / Rounding off / Decimal places / Significant figures N1 / N2 / N3

4 Decimals / Fractions / Percentages N5

5 Decimal Operations / Estimations N4 / N5

6 Introductions to integers / Multiplication & division squares N6

7 Calculating percentages / Writing percentages / Using percentages N7 / N8

8 Writing ratios / Simplifying ratios / Sharing in a given ratio N9

9 Equivalent fractions / Writing fractions / Simplifying / Mixed numbers & Improper fractions N9

10 Adding & subtracting fractions / Word problems N9

11 Naming 2D geometric shapes / metric measurement units & abbreviations Revision

12 Metric conversions / Word problems Revision

13 Perimeter of simple & compound shapes / Word problems M1 / M2

14 Area of simple & compound shapes / Word problems M1 / M2

15 Area of trapezium / Finding the area of shaded regions / Word problems M1 / M2

16 Naming parts of a circle / Finding the circumference & area of a circle / Word problems M1 / M2

17 Practical problems involving area and perimeter M2

18 Naming 3D shapes / Finding the volume given area of x-section / Finding volumes M1

19 Scale drawings / Similar figures / Word problems M2

20 Analogue & digital time conversions / Intepretation of graphs involving time M3

21 Naming, measuring & drawing angles Revision

22 Angles on a straight line / Angles around a point / Vertically opposite angles Revision

23 Naming triangles / Angles in a triangle Revision

24 Angles & parallel lines G1

25 Naming polygons / Line and rotational symmetry G2

26 Interior angles sum on non-regular polygons / exterior angles G2

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Topic Objective(s)

27 Angle between tangent and radius property / Angles in a semi-circles G3

28 Constructions / Understanding, calculating and plotting compass bearings G4

29 Squares & square roots / Pythagoras theorem / Word problems G5

30 Naming sides / SOHCAHTOA / Trigonometry calculations / Word problems G5

31 Drawing isometric diagrams of 3D shapes built out of blocks G6

32 Naming & drawing vectors / Translation / Word problems G7 / G10

33 Similar figures / Finding missing sides / Finding centres of enlargement / Drawing enlargements / Word problems G8

34 Drawing reflections / Finding mirror lines / Drawing rotations / Finding the centre of rotation / Word problems G9

35 Examples of transformation G11

36 Creating & describing number patterns / Word problems A1

37 Generating number patterns from a rule / Word problems A2

38 Interpretation of everyday graphs A3

39 Naming & plotting co-ordinate points / Word problems A4

40 Plotting integer points / Completing ordered pairs given a rule / Word problems A4

41 Using formulae / Substitution A5 / A10

42 Collecting like terms / Simplify like terms A7

43 Algebra expressions / Writing equations / Solving equations / Word problems A6 / A10

44 Factorising & expanding expressions / Word problems A9

45 Exponent rules A8

46 Solving equations / Rearranging formulae A6 / A10

47 Types of data / Understanding frequency (tally) charts S2 / S4

48 Conducting a survey / Organising & interpreting data presented in a table S1 / S2 / S3

49 Types of ‘averages’ / Calculating the mean, median & mode / Word problems S3

50 Calculating the range & quartiles / Understanding & drawing box and whisker graphs S3 / S5

51 Understanding & drawing column graphs S4

52 Understanding & drawing histogram graphs S4

53 Understanding & drawing pictograms, time series graphs, dot plots & percentage bar graphs S4

54 Understanding pie graphs / Calculating pie graph sectors / Drawing pie graphs S4 / S8

55 Understanding & drawing stem and leaf graphs & scatter graphs S3 / S5

56 Relative frequency & experimental probability / Word problems S9 / 10 / 11

57 Theoretical probability / Using a tree diagram to calculate probabilities S10 / 11 / 12

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Please DO NOT write on the sheets Please DO NOT write on the sheets

N1

L5M

At the top of each Homework / Assessment worksheet for the 5 strand areas, the objective(s) being covered has been indicated. EXAMPLE: For Number, N1 means objective 1, N2 means objective 2, etc.

Number Exploring number [Refer Page 48] Within a range of meaningful contexts, students should be able to: • N1 convert numbers expressed in standard form to ordinary form, and vice versa; • N2 round numbers sensibly; • N3 express the values of square roots in approximate and exact forms; Exploring computation and estimation Within a range of meaningful contexts, students should be able to: • N4 make sensible estimates and check the reasonableness of results; • N5 solve practical problems involving decimals and percentages; • N6 solve problems involving positive and negative numbers, using practical activities or models if needed; • N7 express one quantity as a percentage of another; • N8 increase and decrease quantities by given percentages, including mark up, discount, and GST: • N9 share quantities in given ratios.

Measurement Estimating and measuring [Refer Page 74] Within a range of meaningful contexts, students should be able to: • M1 find perimeter, areas and volume of everyday objects (including irregular and composite shapes) and state the precision (limits) of the answer; • M2 design and use models to solve measuring problems in practical contexts. Developing concepts of rate and change Within a range of meaningful contexts, students should be able to: • M3 interpret and use information about rates presented in a variety of ways, for example, graphically, numerically, or in tables.

Geometry Exploring shape and space [Refer Page 110] Within a range of meaningful contexts, students should be able to: • G1 use the angle properties of parallel lines and explain the reasoning involved; • G2 apply the symmetry and angle properties of polygons; • G3 use the angle between a tangent and radius property, and the angle-in-a-semicircle property; • G4 construct right angles, parallel and perpendicular lines, circles, simple polygons, medians, mediators,altitudes, and angle bisectors; • G5 find the unknown side in a right-angled triangle, using scale drawing, Pythagoras’ theorem, or an appropriate trigonometric ratio; • G6 make isometric drawings of 3-dimensional objects built out of blocks; • G7 solve practical problems which can be modelled, using vectors.

Mathematics in the New Zealand CURRICULUM

Level 5

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Exploring symmetry and transformations Within a range of meaningful contexts, students should be able to: • G8 recognise when 2 shapes are similar, find the scale factor, and use this to find an unknown dimension; • G9 use the symmetry and angle properties of polygons to solve practical problems; • G10 use and interpret vectors which describe translations; • G11 identify and use invariant properties under transformations.

Algebra Exploring patterns and relationships [Refer Page 148] Within a range of meaningful contexts, students should be able to: • A1 generate patterns from a structured situation, find a rule for the general term, and express it in words and symbols; • A2 generate a pattern from a rule; • A3 sketch and interpret graphs which represent everyday situations; • A4 graph linear rules and interpret the slope and intercepts on an integer co-ordinate system. Exploring equations and expressions Within a range of meaningful contexts, students should be able to: • A5 evaluate linear expressions by substitution; • A6 solve linear equations; • A7 combine like terms in algebraic expressions; • A8 simplify algebraic fractions; • A9 factorise and expand algebraic expressions; • A10 use equations to represent practical situations.

Statistics Statistical investigations [Refer Page 186] Within a range of meaningful contexts, students should be able to: • S1 plan and conduct statistical investigations of variables associated with different categories within a data set, or variations of variables over time; • S2 consider the variables of interest, identify the one(s) to be studied, and select and justify samples for collection; • S3 find, and authenticate by reference to appropriate displays, data measures such as mean, median, mode, inter-quartile range, and range; • S4 discuss discrete and continuous numeric data presented in quality displays; • S5 collect and display comparative samples in appropriate displays such as back-to-back, stem-and- leaf, box-and-whisker, and composite bar graphs. Interpreting statistical reports Within a range of meaningful contexts, students should be able to: • S6 use data displays and measures to compare data associated with different categories; • S7 make statements about time-related variation as a result of a statistical investigation; • S8 report on possible sources of error and limitations of an investigation. Exploring probability Within a range of meaningful contexts, students should be able to: • S9 determine probabilities of events based on observations of long-run relative frequency; • S10 determine the theoretical probabilities of the outcomes of an event such as the rolling of a die or drawing a card from a deck; • S11 predict the outcome of a simple probability experiment, test it, and explain the results; • S12 find the probability of a given sequence of events, using tree diagrams.

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B: Number Cross

Across 1. 513 ÷ 9 2. 478 + 283 6. 688 ÷ 8 7. 6121 - 3137 9. 7 × 13 10. 558 ÷ 6 11. 302 - 218 12. 175 + 689 + 126 13. 469 ÷ 7

C: Find the missing numbers Replace each shape with a number. 1. 234 + = 678 = ............... 2. 345 - = 87 = ............... 3. 45 × = 270 = ............... 4. 325 ÷ = 13 = ............... 5. + 224 = 678 = ............... 6. - 235 = 103 = ............... 7. × 57 = 342 = ............... 8. ÷ 13 = 32 = ............... 9. 178 - = 45 = ............... 10. 23 + = 139 = ............... 11. 63 × = 315 = ............... 12. 294 ÷ = 14 = ............... 13. + 194 = 581 = ............... 14. - 437 = 609 = ............... 15. × 47 = 282 = ............... 16. ÷ 19 = 25 = ...............

E: Magic Square

Find the missing

numbers in this magic

square.

12

13

1

14

2

3 4

6 5

6

7 8 7

9 10 9

10 11

A: 10 Quick Questions 1. 569 + 726 = .......................... 2. How many days in 4½ weeks? ................................... 3. 2000 - 795 = ......................... 4. How many months in four years? ............................ 5. 373 × 9 = ................................ 6. How many seconds in 7 minutes? ............................ 7. $4.65 × 7 = ............................ 8. 144 ÷ 12 = ............................... 9. How many weeks in 3 years? .................................... 10. 243 ÷ 9 = ................................

D: Word Problems 1. Rangi went to the shop and bought 37 apples, 19 oranges and 24 kiwi fruit. How many pieces of fruit did he buy? ......................................... 2. Rebecca and Steven have been collecting telephone cards, and together they have 264. If Steven has 172, how many does Rebecca have? ......................................... 3. Alisi bought 12 boxes of matches. If each box contains 47 matches, how many matches does he have altogether? ......................................... 4. Mrs Jones has $112 to share between her 4 grandchildren. How much would each grandchild receive? ......................................... 5. Items in a garge sale sell for $20, $5, $12, $8 and $11. If Sam and Alex are to share this money equally, how much does each person get? .........................................................................................................

This table shows the number and colour of jelly beans in four boxes which Kiri bought.

Box A Box B Box C Box D

Red 25 29 29 26

Blue 19 25 27 25

Green 23 17 16 21

White 21 18 19 19

11

10

7 9

Down 1. 1318 - 766 3. 17 × 4 4. 796 + 845 5. 490 ÷ 5 8. 3213 × 3 9. 1403 - 457 10. 396 ÷ 4

Revision

6. How many white jelly beans in box D? ........................ 7. How many red jelly beans in box A? ............................. 8. How many blue jelly beans in all boxes? ..................... 9. Which box had the most white jelly beans? ............... 10. How many jelly beans in box C? ............................. 11. Which box had the least green jelly beans? .............. 12. How many jelly beans altogether? .............................

Term: Week: To be completed by:

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A: 10 Quick Questions 1. 234 × 23 = ............................. 2. 1450 ÷ 5 = .............................. 3. Find the missing number 45 ÷ = 9 ............................ 4. $4.50 × 7 = ............................ 5. How many sides does a triangle have? ....................... 6. Name this shape ............................ 7. 36018 ÷ 6 = ........................... 8. 123 + 146 = ............................ 9. Find the missing number + 456 = 673 ..................... 10. How many centimetres in one metre? ............................

B: Numbers Facts 1. Write down the even numbers between 60 and 71 .................................................................................... 2. Write down the odd numbers between 44 and 60 .................................................................................... 3. Write down the first 4 multiples of 9 .............................................. 4. Write down the multiples of 6 between 40 and 56 ............................................................. 5. How many multiples of 4 are less than 30? ............................................................. 6. Write down the prime numbers less than 15 .................................................................................... 7. Write down the prime numbers between 25 and 40 . .................................................................................... 8. What are the factors of 15? ............................................................. 9. What are the factors of 24? ............................................................. 10. What are the factors of 32? .............................................................

C: Order of Operations 1. 15 + 8 - 12 = ........................... 2. 19 - 10 + 9 = ......................... 3. 24 ÷ 6 + 13 = .......................... 4. 8 × 7 + 9 = .............................. 5. 17 + 3 × 5 = ............................ 6 60 × 4 - 47 = ......................... 7. 70 - 9 × 6 = ............................ 8. 25 + 7 × 5 = ........................... 9. 39 - 27 ÷ 3 = ......................... 10. 32 ÷ 8 + 11 = .......................... 11. (17 + 23) × 3 = ....................... 12. 5(37 - 17) = ........................... 13. 7(36 - 27) = ........................... 14. 6(26 + 44) = .......................... 15. 8(51 + 19) = ............................ 16. 9 + 3(8 + 12) = ....................... 17. 21 - 2(29 - 23) = .................. 18. 4(6 + 2 × 5) = ......................... 19. 6(18 ÷ 3 + 9) = ....................... 20. 9 + 2(4 + 16) = ....................... 21. 5(7 + 3 × 6) = ......................... 22. 17 - 2(19 - 13) = .................... 23. 8 + 4(21 – 4 × 3) = ................ 24. 27 - 5(6 × 2 - 9) =................. 25. 7(3 + 3 × 9) - 40 = ................ 26. 6(4 × 4 – 7) - 27 = ................

D: Word Problems 1. Angela walks to and from school each day, a total of 4km. How far does she walk in two school weeks? ............................................ 2. Frank bought a piece of wood 330cm long. He cuts 5 pieces, each 60cm long from this piece of wood. How much is left after he has cut the 5 pieces off? .................................................. This table shows the price of tickets sold, and the number of each type sold. 3. How many $15 tickets were sold? ............................ 4. How many tickets were sold altogether? ....................................... 5. What would it cost to buy 7 tickets at $15 each? .................................................. 6. What would it cost to buy 12 tickets at $20 each? ...................... 7. What would it cost to buy 7 tickets at $25 each? ........................ 8. If Steven buys three $15 tickets and four $20 tickets, how much would this cost him? ....................................... 9. If Graham buys five $15 tickets and six $20 tickets, how much would this cost him? ....................................... 10. If Janine has $85 how many $15 tickets can she buy? ................ 11. If Ken has $115 how many $25 tickets can he buy? ...................... 12. If Andrew has $90 and buys 3 $25 tickets, how much change does he have left after buying the tickets? ................................... 13. If Jackie has $150 and buys 7 $15 tickets, how much change does he have left after buying the tickets? ...................................

Price of ticket $15 $20 $25

Total sold 50 30 20


Revision

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A: 10 Quick Questions 1. 21 - 5 × 3 = ............................ 2. 56 ÷ 8 + 12 = .......................... 3. Find the missing number × 12 = 84 = ................. 4. How many sides does a parallelogram have? ........... 5. What would 5 items at $2.75 each cost? ................ 6. How many metres in 4.5 kilometres? ......................... 7. Name this shape ........................ 8. How many minutes in 2½ hours? ............................. 9. List the first 4 multiples of 12 ....................................... 10. List the factors of 18 .................................

Approximations D: Have a Guess? Estimations 1. What is the population of New Zealand? ............. 2. How high is the average doorway? ............... 3. What is the length of your classroom? ................ 4. How many students at your school? .............. 5. How long would it take you to run 100m? ............ 6. How many stars in the sky? ......................... 7. How many metres in a mile? .................. 8. How many yards in a furlong? .....................

B: Squares/Square Roots Find ... 1. 92 .............. 8. 49 .............. 2. 142 .............. 9. 64 .............. 3. 162 .............. 10. 121 .............. 4. 232 .............. 11. 144 .............. 5. 502 .............. 12. 400 .............. 6. 802 .............. 13. 625 .............. 7. 1002 .............. 14. 900 ..............

C: Scientific Notation

Rewrite in standard form. 1. 4700 .......................... 2. 29000 .......................... 3. 689 .......................... 4. 0.009 .......................... 5. 0.063 ..........................

Rewrite as ordinary numbers. 6. 6.4 × 105

............................................ 7. 2.68 × 107

............................................ 8. 7.16 × 10-2

............................................ 9. 9.3 × 10-3

............................................

H: Magic Squares Find the missing numbers in these

magic squares.

E: Rounding Off Numbers

Round off to the nearest 10. 1. 24 ............................ 2. 68 ............................ 3. 113 ............................ 4. 307 ............................ 5. 75 ............................ 6. 138 ............................ 7. 1242 ............................ Round off to the nearest 100. 8. 172 ............................ 9. 246 ............................ 10. 738 ............................ 11. 397 ............................ 12. 1095 ............................ 13. 3252 ............................ 14. 5349 ............................ 15. 4078 ............................

F: Decimal Places Round off to 1 decimal place. 1. 12.44 ............................ 2. 14.76 ............................ 3. 34.82 ............................ 4. 134.73 ............................ 5 452.46 ............................ 6. 193.08 ............................ 7. 415.35 ............................ 8. 309.97 ............................

Round off to 2 decimal places. 9. 2.462 ............................ 10. 7.378 ............................ 11. 13.609 ............................ 12. 196.883 ............................ 13. 158.149 ............................ 14. 237.726 ............................ 15. 300.083 ............................ 16. 410.997 ............................

G: Significant Figures Round off to 1 significant figure. 1. 33 ............................ 2. 76 ............................ 3. 28 ............................ 4. 140 ............................ 5. 42.9 ............................ 6. 86.9 ............................ 7. 286.8 ............................ Round off to 2 significant figures. 8. 428 ............................ 9. 694 ............................ 10. 15.45 ............................ 11. 368.26 ............................ 12. 1420 ............................ 13. 1985 ............................ 14. 6452 ............................ 15. 14499 ............................


16

14

8 6

17

14 16

11

N1 / N2 / N3

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E: Percentages Find the percentage shaded in each diagram.

1. 2. 3. 4. 5.

A: 10 Quick Questions 1. 32 + 3 × 9 = ........................... 2. $2.76 × 13 = .......................... 3. How many days in 14 weeks? ............................ 4. How many metres in 3.5kms? ............................ 5. Write 2.9 × 106 as an ordinary number .................................................. 6. Name this shape ............................ 7. Find the missing number 14 + - 42 = 23 ................... 8. List the factors of 30 ....................................... 9. Round 67 to the nearest ten ............................ 10. Round off 6.25 to one decimal place .......................

C: Decimals / Fractions / Percentages

Complete the table by

converting between

commonly used decimals,

fractions and percentages.

Decimals Fractions Percentages

0.1 1. 2.

3. 4.

5. 6. 33%

0.5 7. 8.

9. 10.

11. 12. 75%

B: Finding Percentages Calculate 1. 10% of $70 ....................... 2. 25% of 160kg .................... 3. 75% of $48 ....................... 4. 50% of $4.50 ..................... 5. 20% of 320cm ................... 6. 60% of 70kg ...................... 7. 33% of $45 .................... 8. 45% of $600 ...................... 9. 15% of 60m ....................... 10. 120% of $80 ......................

D: Word Problems 1. If 57% of a club were girls, what percentage were boys?............. 2. Amanda is in a class of 32 pupils. If 50% were boys, how many were girls? ....................................... 3. 10% of a garden of 140m2 was planted in roses. What was the area planted in roses? ....................................... 4. A body contains 70% water. If Jeremy weighs 50kg, how much of his weight is water? ....................................... 5. A class survey on pets, showed that 80% were cats. If there were 60 pets, how many were cats? .................................. 6. Rangi counted 240 cars going past the school gate. If 60% were going too fast, how many cars was this? ............................ 7 In a class of 24, 25% wanted to take netball as a sport. How many students was this? ....................................... 8. Linwood High School played 20 soccer games during the season, losing only 20%. How many games did they lose? ............ 9. In a school of 730 students, 10% were absent on Monday. How many were absent? ....................................... 10. Calculate 30% of $24.75, round off to nearest cent. ...................


.....................

N5

..................... ..................... ..................... .....................

6. 7. 8. 9. 10.

..................... ..................... ..................... ..................... .....................

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C: Decimals Operations Calculate the following ...

A: 10 Quick Questions 1. 37 - 7 × 4 = ............................ 2. What would 7 items at $8.60 each cost? ................ 3. How many minutes in 14 hours? ................ 4. How many metres in 4.25kms? ................ 5. Find 10% of $65 ................ 6. Name this shape ............................ 7. Find the missing number 75 + - 37 = 47 .................. 8. List the factors of 36 .................................................. 9. Round off 9.67 to one decimal place ................ 10. Find 64 ................

1. 3 computers .................................................. 2. 30 computer disks .................................................. 3. 2000 envelopes .................................................. 4. 5000 sheets of paper .................................................. 5. What is the total cost of setting up the school office? .................................................. 6. What does one computer disk cost? .................................................. 7. What would 45 computer disks cost? ....................................... 8. What would 120 computer disks cost? ....................................... 9. What would it cost to buy 10000 sheets of paper? ........................ 10. What would it cost to buy 15000 sheets of paper? ........................ 11. The school is going to buy 25 computers to set up in a new classroom. What would this cost? ...................................................... 12. If a school has $14000 to spend on computers, how many computers could they buy and how much money would they have left over? ................................. computers $...............................

B: Estimations Have a guess? Without calculating the exact answer.

Estimate answer 1. 19.6 + 4.3 = eg 24 2. 152.9 + 49.4 = .............. 3. 7.7 × 10.3 = .............. 4. 99 ÷ 5.2 = .............. 5. 242 59 .............. 6. 4.3 × 19.5 = .............. 7. 23.7 - 12.3 = .............. 8. 897.5 - 547.2 = .............. 9. 7.3 + 1.9 × 4.1 = .............. 10. 1.7 × 8.9 + 12.1 = ................ 11. 997.5 - 447.2 = ................ 12. 6.9 × 10.3 = ................ 13. 23.8 ÷ 4.1 = ................ 14. 7.3 + 2.3 × 3.1 = ................ 15. 2.432 = ................ 16. 7.872 = ............... 17. 12.092 = ............... 18. 19.532 = ............... 19. 35.78 = ............... 20. 81.128 = ............... 21. 48.7 + 3.262 = ...............

Computers $1550 each

computer disks 10 for $17.50

Envelopes

5 cents each

Paper

$4.50 for 500 sheets


D: How much will it Cost? A school is going to set up a computer in the school office so they can produce newsletters to send home. What will it cost if they buy ...

N4 / N5

52.96 + 8.78

1.

5. 13.68 + 0.897 = ......................... 7. 96.87 - 74.73 = ........................ 9. 42 + 7.3 + 0.384 = ....................

5.063 + 1.734

2. 57.96 - 25.43

3. 6.029 - 4.721

4.

6. 453.98 + 56.532 = ................... 8. 200 - 51.783 = .......................... 10. 27.7 - 8.45 + 4.8 = ...................

15. 43.4 × 0.4 = .............................. 17. 2.430 ÷ 0.5 = ........................... 19. 0.72 ÷ 1.2 = .............................. 21. 0.62 ÷ 0.002 = .........................

16. 2.47 × 0.03 = ........................... 18. 27.36 ÷ 0.9 = ......................... 20. 0.846 ÷ 0.04 = ........................ 22. 0.66 ÷ 0.11 = ............................

7.26 × 8

11. 29.5 × 0.4

12. 4.913 × 0.02

13. 40.6 × 1.2

14.

13. If the newsletters are to be posted home each week, at a cost of 40 cents each, how much would this cost each week, if there are 562 pupils at this school? ............................................

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C: Am I Sick or Well? In our bodies there are good

bugs , and there are bad bugs

. One good bug eats one bad bug.

1. If means +3

what does mean? ........................ Study these bugs.

2. How many bugs? ............

3. How many bugs? ............ 4. Am I sick or well? ................ Use + , - ,and = signs when answering the following; 5. Write a maths sentence to show how you could get your answer for question 4 above. (eg. +6 + -7 = -1) .................................................

B: What is the new Temperature?

Calculate the new temperature. 1. 15oc, then drops 7oc ................. 2. 8oc,then drops 11oc .................. 3. 9oc, then rises 4oc ..................... 4. _7oc, then rises 8oc ................... 5. _3oc, then drops 8oc .................. 6. _5oc, then drops 6oc .................. 7. 0oc, then rises 13oc ................... 8. 0oc, then drops 10oc .................. 9. _5oc, then drops 7oc .................. 10. 3oc, then drops 12oc ................

A: 10 Quick Questions 1. (8 + 43) × 8 = ......................... 2. What would 9 books at $6.75 each cost? ................. 3. How many days in 7.5 weeks? ............................ 4. How many metres in 9.2km? ............................ 5. Find 20% of 140kg .............. 6. Name this shape ...............……............ 7. Find the missing number 35 × = 140 ......................... 8. 4.12 + 0.096 = ...................... 9. 4.12 × 0.06 = ......................... 10. Calculate 122 = ......................

D: Integers Add and Subtract the following 1. 6 + 9 = ................ 2. -4 + 11 = ................ 3. 10 + -6 = ................ 4. -7 + 9 = ................ 5. 11 + -14 = ................ 6. 0 + 9 = ................ 7. 0 + -13 = ................ 8. 5 + -6 = ................ 9. -6 + 12 = ................ 10. 6 + -13 = ................ 11. -5 + 11 = ................ 12. -3 + -6 = ................ 13. -7 - 6 = ................ 14. -14 - 8 = ................ 15. 7 - -11 = ................ 16. 7 - -9 = ................ 17. 6 - -8 = ................ 18. -8 - -9 = ................ 19. -9 - -7 = ................ 20. -11 - -9 = ................ 21. -14 - -7 = ................ 22. -4 - -9 = ................ 23. -8 - -15 = ................ 24. -8 - -5 = ................ 25. 0 - -8 = ................ 26. -8 - -5 = ................

E: Problem Solving Use the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, to make a 3 by 3

Magic Square. Each number is to be used only once.


F: Multiplication & Division Squares Complete these Multiplication and Division squares.

(In 3. +12 ÷ +2 = +6 has been done for you , and entered)

N6

× +2 +6 -1 +4 -3 +5

× -2 -8 +9 +6 -7 -5

1. 2.

÷ +2 +3 -4 +12 +6 +18 -24

÷ +4 -6 -12 -12 +24 -48

3. 4.

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A: 10 Quick Questions 1. 3.14 × 1.2 = ............................ 2. 36.84 ÷ 0.2 = ......................... 3. How many metres in 340 centimetres? ................ 4. 122 + 9 = ................ 5. Write 960000 in standard form ............................ 6. Name this shape .................................... 7. Find the next 2 numbers in the pattern 1, 4, 9, 16, ....................................... 8. What type of triangle is this? ................................................ 9. How many sides does a decagon have? ................ 10. How many minutes in 7.25 hours? ............................

C: What Percentage is it? Calculate the following. 1. Cheryl got 30 out of 50 in a recent maths test. What percentage did she get? .................................................. 2. James spent 6 hours asleep last night. What percentage is that of the whole day? .................................................. 3. The school netball team won 17 games out of 20. What percentage did they lose? .................................................. 4. What percentage of people watched a rugby test on T.V. if 3 out of 4 watched it on television? .................................................. 5. Out of 50 pupils at school, 29 walk to school. What percentage is this? ..................................................

E: How do you spend your day?

Fill out the table of what you do during any school day. Round off the times to the nearest half hour. Calculate the percentage time you spend on each activity as listed. (Does not have to add up to 24 hrs)

Sleeping Eating School TV Sport

Hours spent

%


B: Writing Percentages? Write the following as percentages. 1. 20 out of 40 ................ 2. 10 out of 40 ................ 3. 4 out of 12 ................ 4. 5 out of 15 ................ 5. 10 out of 15 ................ 6. 20 out of 50 ................ 7. 40 out of 50 ................ 8. 10 out of 50 ................ 9. 4 out of 200 ................ 10. 15 out of 20 ................ 11. 36 out of 48 ................ 12. 20 out of 20 ................

2. A house in the street sold for $185000. They had hoped to get 10% more for the house. What would it have sold for then? .........................................

3. A popular take-away bar recently increased its prices by 5%. If a meal had cost $6.00, what would the new price be? .........................................

4. A company offered a group discount of 20%. If the normal price for swimming with the dolphins was $45.00, what would be the discounted price? .........................................

5. In a book sale, all $24.00 and $36.00 books have been reduced in price by 40%. What are the sale prices for these books? .........................................

D: Using Percentages Calculate the following. 1. Ranui bought birthday presents that were going to cost him $55.00, but was given a 10% discount for cash. What did he pay for his presents? ..........................

N7 / N8

6. GST is 12.5%. What would the price be when GST is added to the cost of a new car worth $22,000? .........................................

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B: Writing Ratios Write the following as ratios (do not simplify) 1. There were 11 cats to every 14 dogs. ....................................... 2. There was 1 teacher to every 24 pupils. ....................................... 3. There were 18 patients to every nurse. ....................................... This table shows two Year 9 classes at a school.

A: 10 Quick Questions 1. Find 25% of $80 = .............. 2. 0.25 × 1.2 = ............................ 3. How many minutes in 6.5 hours? ............................ 4. How many kilometres in 4700 metres? ................ 5. Write 0.4 as a percentage ............................ 6. How many sides does a pentagon have? ................ 7. Find the next number 3, 8, 13, 18, ............................ 8. List the first 4 multiples of 11 ............................ 9. Round off 0.264 to two decimal places ................ 10. Calculate 1.52 ................

C: Simplifying Ratios Simplify these ratios by finding the missing numbers. 1. 10 : 14 5 : ............... 2. 21 : 30 7 : ............... 3. 32 : 8 4 : ............... 4. 21 : 49 3 : ............... 5. 25 : 100 1 : ................ 6. 36 : 27 4 : ............... 7. 54 : 9 6 : ............... 8. 12 : 28 3 : ............... 9. 20 : 65 4 : ............... 10. 77 : 22 7 : ............... Simplify these ratios. 11. 20 : 50 ............ : ............ 12. 21 : 9 ............ : ............ 13. 24 : 36 ............ : ............ 14. 55 : 99 ............ : ............ 15. 80 : 50 ............ : ............ 16. 40 : 24 ............ : ............ 17. 35 : 14 ............ : ............ 18. 70 : 100 ............ : ............ 19. 4 : 10 : 20 ...... : ....... : ....... 20. 3 : 9 : 21 ...... : ....... : ....... 21. 8 : 2 : 14 ...... : ....... : ....... 22. 18 : 12 : 6 ...... : ....... : .......

D: Sharing in a given Ratio

1. Share $18 in a ratio of 1 : 2 ....................................... 2. Share $42 in a ratio of 1 : 5 ....................................... 3. Share 54 grams in a ratio of 4 : 5 ....................................... 4. Share 320mls in a ratio of 5 : 3 ....................................... 5. Share $63 in a ratio of 3 : 5 : 1 ................................. 6. Share $60 in a ratio of 2 : 3 : 5 ................................

E: Word Problems 1. The ratio of teachers to pupils on a school trip should be 1 to 9. If there are 27 pupils going on the trip, how many teachers should go? .............................................................

2. Jenny and Steven decided to share 48 lollies between themselves in a ratio of their ages. If Jenny is 9 and Steven is 7, how many lollies does each child get? .............................................................

3. 100 tickets were sold for a concert. If the ratio of tickets sold to children and to adults was 9 to 1, how many children are going to the concert? .........................

4. In a class of 27, Miri was voted most popular by a 5 : 4 majority. How many votes did she get? .......................................

F: Puzzle This pile of 20 cubes is in the corner of a room. There are 2 grey layers and 2 clear layers of cubes. What is the ratio of clear to grey cubes ?


Class 9St Boys 15

Girls 13

Boys 14

Girls 17

Class 9Wt

4. What is the ratio of boys to girls in class 3St? .....................................

N9

5. What is the ratio of girls to boys in class 3Wt? ............................

(Remember to count the ones you cannot see).

...............................

5. Jan has $160. She buys some clothes, some books and some food in a ratio of 5 : 2 : 3. How much did she spend on each item? clothes ................ : books ................. : food ..................

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B: Equivalent Fractions Find the missing numbers to complete these equivalent fractions. 1. 1/2 = /10 = ..............

2. 2/3 = /15 = ..............

3. 3/4 = /40 = ..............

4. 3/11 = /55 = ..............

5. 3/7 = /49 = ..............

6. 3/5 = /40 = ..............

7. 4/5 = /55 = ..............

8. 3/8 = /40 = ..............

9. 6/7 = /35 = ..............

10. 5/9 = /63 = .............. D: Writing Fractions What fraction in each design is shaded?

C: Shade the Diagrams Shade in the fraction given for each diagram. 1. 3/5 2. 1/4 3. 1/3 4. 5/7 5. 3/3

E: Simplifying Fractions

Find the simplest equivalent fraction for these fractions. 1. 8/12 ......................

2. 12/20 ......................

3. 14/18 ......................

4. 100/300 ......................

5. 40/60 ......................

6. 44/99 ......................

7. 15/75 ......................

8. 16/64 ......................

9. 18/27 ......................

10. 14/35 ......................

11. 24/56 ......................

12. 16/36 ......................

13. 36/60 ......................

F: Converting Fractions

Convert these improper fractions to mixed numbers.

1. 13/5 = ........................

2. 17/4 = ........................

3. 26/5 = ........................

4. 56/6 = ........................

5. 68/7 = ........................

6. 50/8 = ........................

7. 71/9 = ........................

8. 80/12 = ........................

Change to improper fractions.

9. 44/5 = ........................

10. 6 1/2 = ........................

11. 3 5/7 = ........................

12. 7 2/3 = ........................

13. 3 5/6 = ........................

14. 6 4/5 = ........................

15. 7 5/9 = ........................

16. 8 3/11 = ........................


1. ..............

2. ..............

3. ..............

4. ..............

5. ..............

A: 10 Quick Questions 1. 1.7 + 15 + 0.074 = .............. 2. 63.9 ÷ 0.3 = ......................... 3. How many weeks in 63 days? ............................ 4. How many millimetres in 57 centimetres? ............... 5. 9 + 2(25 - 4 × 5) = ............. 6. How many years in a century? ............................ 7. Find 20% of $37.50 ............................ 8. What would 7 items at $9.35 each cost? ............. 9. How many minutes between 2:25 p.m. and 5:15 p.m., on the same day? ..................... 10. Calculate 0.72 ....................

N9

6. ..............

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A pile of 20 cubes is stacked in the corner of a room. There are 2 grey layers, 1 clear layer and 1 black layer of cubes. 4. What fraction of the pile is ? ............................ 5. What fraction of the pile is ? ............................ 6. What fraction of the pile is ? ............................ (Remember to count the ones you cannot see)

C: What Fraction? What fraction of each coloured square is in this grid?

A: 10 Quick Questions 1. 9.2 - 5.4 + 0.063 = ............. 2. 31.7 × 0.9 = .......................... 3. Shade 3/4 of this design 4. How many millilitres in 17 litres? ............................ 5. Write 90 in Roman Numerals ............................ 6. 9 + -17 = ............................... 7. Find 75% of $64 ................ 8. Divide $30 in a ratio of 5 : 1 ............................ 9. How many minutes between 9:45 am and 1:20 pm, on the same day? ................ 10. How many sides does a decagon have? ................

B: Adding and Subtracting Fractions Add or subtract these fractions, simplifying if possible.

11. 1/4 + 1/3 = .....................

12. 2/3 + 3/4 = .....................

13. 3/4 + 2/5 = .....................

14. 3/5 + 2/3 = .....................

15. 43/5 + 21/4 = ......................

16. 4/5 - 1/3 = .....................

17. 5/6 - 3/7 = .....................

18. 7/8 - 3/5 = .....................

19. 63/5 - 24/5 = .....................

20. 61/4 - 31/3 = .....................

D: Word Problems Give answers as fractions in their simplest form. 1. Amelia and Joseph share an apple. If Amelia eats 3/5

how much does Joseph eat? ..........................


1. 1/3 + 2/3 = .....................

2. 2/3 + 2/3 = .....................

3. 3/4 + 3/4 = .....................

4. 8/11 + 9/11 = ......................

5. 5/7 + 4/7 = .....................

6. 4/5 - 1/5 = .....................

7. 5/6 - 1/6 = .....................

8. 7/8 - 3/8 = .....................

9. 5/6 - 2/6 = .....................

10. 8/9 - 5/9 = ...................

2. At a party for 20 school friends, 13 were girls and the rest were boys. What fraction were boys? ...............

3. During the May holidays Mr. Chapman painted 4/7 of his house. In the August holidays he painted another 3/7 of the house. How much of the house has been painted so far? .................................................

4. The ‘All Blacks’ won 16 out of their last 20 games. What fraction of the games did they win? .......................

5. In Year 10, 30 out of 150 students will receive a certificate for great results in their exams. What fraction of the year group is this? ..................

6. Paul cuts two lengths of plastic pipe. If one length is 4½ metres and the other is 5¾ metres, what is the total length of pipe he cut? ................................................

N9

1. .................

2.

3.

.................

.................

7. Mrs Jones has 5½ metres of material. If she makes a dress using 2¾ metres, what length of material does she have left? ......................................................... 8. Three TV ads ran for of a minute, of a minute and a minute. Write the total ad time as a mixed number, then convert your answer to seconds. ................. ................... seconds

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C: What Shape is it? Name these shapes using the list below (Use one name twice)

trapezium rhombus hexagon rectangle kite quadrilateral square parallelogram octagon oval arrowhead triangle pentagon circle

A: 10 Quick Questions 1. Find 10% of $47.50 ............................ 2. 53 - 6 × 7 = ........................ 3. Find 64 = .......................... 4. If the temperature was 7oc,then drops 9oc, what is the new temperature? ....................................... 5. 6.9 × 0.005 = ...................... 6. How many seconds in 7.5 minutes? ............................ 7. $4.30 × 13 = ........................ 8. 96 ÷ 1.2 = ........................... 9. How many weeks in 3 years? .................................. 10. Find ½ of $18.50 .................

E: Choose the right unit

Which unit for length, capacity or weight would you use to measure the following? 1. the distance between two countries ......................... 2. the volume of water in a swimming pool .................... 3. a dose of cough medicine ......................... 4. a packet of MM’s ......................... 5. the height of the classroom ......................... 6. the weight of a person .......................... 7. a bucket of water ............. 8. the height of a tree ........ 9. a packet of biscuits ......... 10. the thickness of a match stick ......................... 11. the weight of a feather ......................... 12. the thickness of a tooth pick ......................... 13. a child’s height ....................

D: Metric Measurement In the metric system there are many abbreviations that are used. Match the abbreviations listed with the words below.


1. ................................... 2. .................................. 3. ..................................

4. .................................. 5. .................................. 6. ..................................

7. .................................. 8. .................................. 9. ..................................

10. ................................ 11. ................................. 12. ................................

13. ................................ 14. ................................ 15. ................................

1. cm ..................................... 2. mL ..................................... 3. kL ..................................... 4. mm ..................................... 5. m ..................................... 6. kg ..................................... 7. g ..................................... 8. L ..................................... 9. km ..................................... 10. mg .....................................

gram kilolitre milligram centimetre millimetre litre kilogram metre millilitre kilometre

Revision

B: What does it mean? 1. What do the small lines on each side mean? ......................................................................................... 2. What do the arrows on each side mean? .........................................................................................

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1. 1 m = .......................................... 6. 10 mm = .................................... 2. 1000 g = ................................... 7. 1 km = ........................................ 3. 1 litre = ..................................... 8. 1000 mL = ................................. 4. 1 tonne = ................................... 9. 1 kL = .......................................... 5. 1000 mg = ................................ 10. 1000 m = ...................................

C: Metric Conversions Convert the following. 1. 9cm = .............................. mm 2. 6000m = ......................... km 3. 1.8kg = ................................ g 4. 4m = ................................. cm 5. 270mm = ......................... cm 6. 6300L = ........................... kL 7. 0.78m = ........................... cm 8. 650cm = ............................ m 9. 4tonne = .......................... kg 10. 32mm = ............................. m 11. 4.9m = ............................ mm 12. 855mg =.............................. g 13. 6.9tonne........................... kg 14. 425mL = ............................. L 15. 5.9L = .............................. mL 16. 2.35g = ............................ mg 17. 4250m = ......................... km 18 0.73kg = ............................ g 19 62.7cm = ........................ mm 20. 0.37m = ........................... cm 21. 5.39g = ............................ mg 22. 305mL = ............................. L 23. 0.41 kg = ............................ g 24. 93.7cm = ........................ mm 25. 4570m = ......................... km

D: Add or Subtract these different Metric

Units Answer in centimetres. 1. 1.4m + 47cm = ....................... 2. 3.2m + 38cm + 630mm = ........................ 3. 6.4m - 510cm = .................... 4. 930cm - 1.47m = ................... 5. 1.5m - 620mm + 78cm = ........................ Answer in kgs. 6. 1.3kg + 4500g = .................... 7. 3054g + 3294g = .................. 8. 215g + 937g = ....................... 9. 7460g - 4.7kg = .................... 10. 6.35kg - 4345g = .................

E: Word Problems 1. If 1kg of apples costs $1.45, what does 5kgs cost? ...................... 2. If 1L of milk costs $1.35, what would 7L cost? .............................. 3. A particular shape and size of wood costs $2.60 per metre. How much would 20m cost? ............................ 4. If 10kg of potatoes costs $5.70, what would 1kg cost? .............. 5. If 5kg of meat costs $59.75, what would 1kg cost? ..................... 6. If 12m of timber costs $33.60, what would 1m cost? .................. 7. If 1.5kg of carrots costs $1.95, what would 1kg cost? ................. 8. A 350mL bottle of shampoo costs $5.25. How much does it cost per mL? .......................................... 9. Dried fruit is on sale for $11.50 per kg or it is sold for $1.25 per 100g. Which is the cheapest way to buy the dried fruit ? .........................................................


1 cm 1000 mm 1000 m 1 L 1000 kg 1 km 1 kg 1 g 1000 mL 1000 L

A: 10 Quick Questions 1. 29 - 5 × 4 = ............................ 2. Find the area of a rectangle with a base of 8 cm and a height of 6cm. ....................................... 3. -14 + -13 = ............................ 4. How many months in 2.5 years? ............................ 5. 0.35 × 0.08 = ......................... 6. How many seconds in 4.25 minutes? ............................ 7. $5.65 × 12 = .......................... 8. 4.8 ÷ 1.2 = ............................ 9. Find 25% of $16.40 ............................ 10. ¾ of 280km ..........................

B: The Metric System Match the answers below with the questions for each equivalent metric measurements. (Example: 1 metre = 100 cm)

F: Where do they Go? Place the numbers in the grid. 85, 546, 632, 6652, 7521 8524, 9652, 78523, 98521

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D: Compound Shapes Find the perimeter of these shapes.

B: How far is it around the outside ? Find the perimeter of each shape.

A: 10 Quick Questions 1. 47 - 3 × 12 = ......................... 2. Divide $45 in a ratio of 4 : 5 ............................ 3. 5.3 - 3.653 = ......................... 4. How many metres in 7.25km? ............................ 5. Round off 36.9 to one significant figure ................. 6. How many minutes in 450 seconds? ............................ 7. $3.15 × 6 = ............................ 8. 144 ÷ 0.12 = ........................... 9. What does ‘kL’ stand for? ....................................... 10. Draw a parallelogram

6m

8m

8cm

12m 6m

14.6mm 4mm

14mm

8cm

5cm 7cm

7mm 8.6m

4.4m

5.3m 7.8m

12mm

5mm

11cm

C: Word Problems 1. Rangi and Andrew have a race twice around a soccer field. If the length of the field was 105m and the width was 75m, how far was the race ? .........................................................................

400m

415m

595m

390m

6. For a meeting, 7 square tables, each with sides of 0.9m, are placed as shown. What is the perimeter of this grouping? ................................ ........................................................................................

20mm

8mm

14mm

12.3m

10.5m

4.6m

1.3m

3. ................... .....................................................................

2. ................ ..................................................................

5cm

14cm

5cm 12cm

Term: Week: To be completed by: Term: Week: To be completed by:

4. Mr. Walker is going to build a fence around his section. The section is rectangular with a width of 45m and a length of 68.5m. How far is it around the section? .............................................................................

This is a sketch of a park where a school cross-country race is to be held. 2. How many metres is it for one lap around the outside? .............................. 3. How many laps will they need to run if the race is 7.2 km long? .......................

1. .....................

2. ....................

3. ....................

4. ....................

5. ....................

6. ....................

7. ....................

8. ....................

9. ....................

10. ..................

1. ................. .....................................................................

17cm

8.5cm

8.5cm

M1 / M2

5. Calculate the length of ribbon that is needed to go around the parcel, then add 60cm to allow for a bow to be tied. .......................................................... 25cm 30cm

10cm

2cm

2cm

0.93cm

0.7cm

4. ................... .....................................................................

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C: “If you can paint it, it has Area” Find the areas of these shapes.

B: Find the Areas? Find the approximate areas of each shape by counting squares and part squares.

A: 10 Quick Questions 1. 5(3 + 4 × 5) = ....................... 2. Divide $45 in a ratio of 5 : 4 ............................ 3. 12.5 - 8.853 = ....................... 4. How many kilometres in 5500m? ............................ 5. Round off 23.76 to one decimal place ......................... 6. Find the perimeter of a square with sides of 10cm ............................ 7. Calculate 225 = .............. 8. Solve + 23 = 14 = ............................ 9. 12.4 × 0.014 = ........................ 10. -13 + -14 = ............................

F: Magic Squares Find the missing numbers.

12cm

5cm

8m

9m 20cm

6.5cm

7mm

18mm 6.5cm

8m

12m

D: Compound shapes Find the area of each compound shape.

18 cm

27 cm

14 cm

12 cm

E: Word Problems Wendy is going to paint her bedroom door, but needs to first work out its area, so she can buy enough paint. 1. If the door is 2.00m by 0.95m, what is the area of one side of the door? .............................................................

20 cm

36 cm

14 cm

18 cm

1. ...............

2. ...............

3. ............... 4. ...............

1. ......................................................................

2. ......................................................................

3. ..........................................................................

4. ......................................................................

5 ......................................................................

6. ..........................................................................

1. ..................................................................................................................

2. ..................................................................................................................

2. If the door is to have 2 coats of paint on both sides, what is the total area that has to be painted? ............................................

15

10 6

5

M1 / M2

19

13

18 7

3. If a 500mL tin of paint will paint 7 m2, what volume of paint is required to be able to paint the door? .......................................

4. If a 500mL tin of paint costs $13.25, how many tins will be needed and what will it cost? ............................ tins $..........................

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1. ..................................................................................................................

2. ..................................................................................................................

3. This sketch is of a section of land at the end of a ‘No Exit’ street. Calculate the area. ....................................................................... .......................................................................

2. This diagram shows the cross section of a glass house built against a brick fence. If it is 2.5 metres high at the back, 2 metres at the front and 3 metres from the fence, what is the area of the cross section? ...................................................... ............................................................................................

C: Shaded Area Find the area of the shaded part of each diagram.

D: Word Problems 1. A school swimmng pool has a cross section as shown in the diagram. What is the area of the cross section of the swimming pool? ................................................................ ................................................................

B: Finding the area Use the formula A = ½(a + b)h to find the areas of these trapezia.

A: 10 Quick Questions 1. 1.74 + 2.96 = ........................ 2. Find the next number in the series 2, 10, 18, ............................ 3. How many grams in 3.7kgs? ............................ 4. How many degrees in a triangle? ............................ 5. 0.012 × 0.8 = ......................... 6. Round off 29.635 to 2 d.p. ............................ 7. ½ + ¾ = ............................ 8. 10.8 ÷ 1.2 = ............................ 9. How many weeks in 1.75 years ? ............................ 10. Find the perimeter of a square with sides of 11cm ............................

12m

22m

14m

9mm

10mm 16mm

12mm

2.1cm

3.3cm

1.4cm

2.6cm

2. .......................................... ..........................................

3. .......................................... ..........................................

2.5m 1m

30m

320m

276m

100m

7.7mm

6.8mm

15.4mm

8.4mm

9 cm

12cm

16cm


3. ..................................................................................................................

4. ..................................................................................................................

M1 / M2

13cm

6cm 4cm 7cm

19mm

36mm

1. .......................................... ..........................................

12mm

4. This sketch is of a paddock which is to be planted in grass. Calculate the area of this paddock. ....................................................................... .......................................................................

34m

23m

19m

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D: Word Problems Calculate the area of these shapes. (use = 3.1)

C: Circle Calculations Use C = 2r or C = d and A = r2 to find the both the circumference and area of each circle ( use = 3.1).

B: Which part is it ? Use the list below and the diagram to answer these questions. 1. The point at the middle of a circle is called the .............................................................................. 2. A line from the middle to the outside of the circle is called the ................................. 3. A line passing through the middle of the circle, going from one side to the other is called the ............................................................ 4. The line around the outside of the circle is called the ..................................................................... 5. The area shaded is called a ..................................................... 6. The area shaded is called a ..................................................... 7. Part of the line around the outside is called an ............................... 8. The line in the diagram with the symbol pointing to it, is called a ....................................................................................

A: 10 Quick Questions 1. Calculate the area of a triangle which has a base of 14cm and a height of 17cm ............................ 2. Convert 63mm to cm ............................ 3. Write 47000 in standard form ............................ 4. How many minutes from 1.37 a.m. to 4.19 a.m. on the same day? ..................... 5. 202 - 144 ............................ 6. How many degrees in a 4 sided figure? ...................... 7. $8.35 × 11 = ............................ 8. 42 - 28 ÷ 7 = ......................... 9. 15 + -9 - -5 = ......................... 10. (-7)2 = ............................

circumference sector diameter centre segment arc radius chord

1.

5. Calculate the shaded X-sectional area of this pipe if the inner circle has a radius of 10 cm, and the outer circle has a radius of 20 cm (use = 3.14). ......................................................................................... .........................................................................................

6. Find out the diameter or radius of the world and calculate the circumference of the world at the equator (use = 3.14). .......................................................................................... ..........................................................................................


C = .................... .................. A = ................... ..................

M1 / M2

9 cm

2. C = .................... .................. A = ................... .................. 1.2m

3. C = .................... .................. A = ................... ..................

10 cm

4. C = .................... .................. A = ................... ..................

0.8mm

1.5m

24cm

4. A circle is drawn inside a square so that the sides of the circle just touch the sides of the square. Calculate the area of the shaded region (use = 3.14). .............................................................................................. ..............................................................................................

6cm

40mm

1. 2. 3.

...................................

................................... ................................... ...................................

...................................

...................................

14cm

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A farmer is going to fence a paddock, as shown in the diagram below. The fence is to have 4 wires and posts every 5 metres.

C: What will it Cost?

B: What will it Cost?

20m

10m

6m

5m

3m

This shed is to have a coat of paint (ends. sides and roof). Calculate the 1. area of one side. .......................................... 2. area of both sides. .......................................... 3. area of one end. .......................................... 4. area of both ends. ..........................................

5. area of one side of the roof. ............................................................. 6. area of all of the roof. ............................................................. 7. What is the total area that is to be painted ? (both ends, both sides and all the roof ) .............................................................

The paint used will cover 15 m2 of the shed, with every litre used (15 m2 per litre). 8. Calculate the number of litres needed to paint the shed. ............................................................. 9. If one litre of paint costs $18.50, how much is it going to cost to paint the shed ? ............................................................. 10. Is $1000 enough to pay for the paint ? .......................................

D: Magic Square


A: 10 Quick Questions 1. 8 + -12 = ............................ 2. -9 × -8 = ............................ 3. ¼ of $28.40 = ....................... 4. Divide $72.00 in a ratio of 7 : 2 ............................ 5. 0.48 × 0.09 = ......................... 6. How many grams in 6.25 kilograms? ............................ 7. Find 25% of 360kg ............................ 8. Change 0.6 to a percentage ............................ 9. 23 + 7 × 5 - 12 = ................... 10. Change 8% to a decimal ............................

13 15

19

23

Find the missing

numbers to complete this magic

square.

7. If posts cost $5.60 each, what is the cost of the posts? ............................................................................ 8. What is the total cost of the wire and posts? ...............................................................................................

M2

1. Calculate the length of the sides labelled A, B and C. A = .........................., B = .........................., C = .......................... 2. Calculate the perimeter of the paddock. ............................................................................................................................. 3. How many metres of wire are needed to build the fence? (4 wires in fence) ..................................................................................................... 4. If wire comes in 50m rolls, how many rolls of wire will be needed? ............................................................................................................................. 5. If each wire roll costs $75.00, what will it cost for all the wire? ............................................................................................................................. 6. With posts every 5 metres, how many posts are needed for the fence to go around the paddock? ..........................................................

100m

70m Paddock diagram

90m

150m

90m

150m

A B

C

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C: Volume Find the volume of these shapes given the area of each cross-sectional end and the depth.

A: 10 Quick Questions 1. What is the area of a square with sides of 1.5cm? ............................ 2. How many kilolitres is 4300 litres? ......................... 3. Find 75% of 480mL ............................ 4. How many minutes in 4.25 hours? ............................ 5. 12 × -8 = ............................ 6. 72 + 625 = ............................ 7. 14.4 + 7.6 × 3.6 = .................. 8. 12.1 ÷ 1.1 = ............................ 9. Divide $88.00 in a ratio of 3 : 5 ............................ 10. If 2 + 7 = 23 , find what number the represents = ..............................

D: If you can fill it, it has Volume Calculate the volume of each prism shape.

B: Name these shapes Choose from the list below and name these shapes.

cylinder triangular prism rectangular prism cube pyramid sphere cone

6cm

14cm 8cm

4cm

6cm

9cm

1.5m

1.5m

1.5m

7mm 15mm

9mm 12m

20m 13m

7. Find the volume of a cube with sides of 10cm. .............................. 8. Find the volume of a cube with sides of 6.5m. ............................... 9. Find the volume of a rectangular prism with a base of 9cm, height of 8cm and a depth of 15cm. ....................................... 10. The volume of a rectangular prism is 378m3. If the base is 7m and the depth is 9m, what is the height of the rectangular prism? ....................................... 11. The volume of a rectangular prism is 336m3. If the base is 12m and the height is 7m, what is the depth of the rectangular prism? ....................................... 12. The volume of a rectangular prism is 315m3. If the depth is 14m and the height is 5m, what is the base of the rectangular prism? .......................................

2.5cm


1. .......................... 2. .......................... 3. .......................... 4. ..........................

5. ................................... 6. ................................... 7. ...................................

1 ................................... 2. ................................... 3. ...................................

4. ................................... 5. ................................... 6. ...................................

M1

Area

18m2

7.2m

1. ..................................................

12.5m

Area

0.25m2

2. ..................................................

3. ..................................................

36mm

Area

25mm2

4. ..................................................

1.2cm

Area

1.45cm2

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.......................

3.

27 m

3 m

7. How far would they have to run, in a straight line, if the course started and finished at point A? (A to B to C to D to A) ......................

Use the scale in the diagram, convert these mm distances to metres.

D: Word Problems

3. Edward’s model helicoptor is 4cm long. If it is a 1 : 250 scale model, what is the actual length of the helicopter? ....................................................................................

C: Scale Drawings

B: Similar figures Find the missing sides. (

18cm 6cm

3cm

12mm

4mm

2mm

12m

10m 30m

1m

20m

4m

1.

5m

2m 3m


A: 10 Quick Questions 1. Convert 678 mm to cm ............................ 2. The perimeter of a square is 28cm, what is the area? ............................ 3. 40 ÷ -8 = ............................ 4. How many weeks in three years? ............................ 5. Convert 0.85 to a fraction ............................ 6. How many seconds in 3.75 minutes? ............................ 7. 19m + 628cm = ..................... 8. How many minutes are there from 10.15 a.m. to 3.40 p.m. ............................ 9. 18 - 5 × -3 = ........................... 10. 0.09 × 0.007 = ......................

.......................

2. .......................

1.

.......................

4.

This diagram is of a shed end Using a scale of 1 cm : 100 cm make a scale drawing of the shed, in the box provided.

2. Plans for a house have been drawn with a scale of 1 : 200. If the house is to be 18 metres across the front, how long will this be on the plan diagram? .....................................................................

The diagram shows part of an orienteering map. Measure the distance from 1. A to B (in mm) .................... 2. B to C (in mm) ..................... 3. C to D (in mm) .....................

4. A to B ..................... 5. B to C ..................... 6. C to D .....................

9. Later in the day, the shadow of the tree had changed to be 36m. What would be the new length of Andrew’s shadow ?

......................................................................

8. Andrew is looking at the top of a tree, trying to work out its height. If he is 2m tall, and has a shadow length of 3m, how high is the tree, if it has a shadow of 27m? .........................

M2

6m

18m 9m

.......................

5.

D

C

B

A

10. A 40m power pole has a shadow of 100m. How long would a shadow be for a 30m high tree at the same time of the day? .........................................................

Scale 1 mm : 100m

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E: Word Problems

D: What is the time on these clocks?


1. 3.05 a.m. .......................... 6. 7.14 a.m. .......................... 2. 4.40 p.m. .......................... 7. 12.45 p.m. .......................... 3. 10.23 p.m. .......................... 8. 8.32 p.m. .......................... 4. 3.49 a.m. .......................... 9. 9.12 a.m. .......................... 5. 11.57 a.m. .......................... 10. 5.09 p.m. ..........................

B: What is the time ? Write these a.m. and p.m. times as they would appear on a 24 hour digital clock.

1. 0730 .......................... 6. 1837 .......................... 2. 1523 .......................... 7. 2156 .......................... 3. 2245 .......................... 8. 0528 .......................... 4. 0713 .......................... 9. 2305 .......................... 5. 0043 .......................... 10. 0338 ..........................

C: What time is it now? Convert these 24 hour times to a.m. or p.m.

1. Mary and Jeff began a game of golf at 9.10 a.m. and it finished at 1.48 p.m. How long did the game take ? .....................................................................

2. The dog next door kept Rangi awake one night because of its howling. It started at 8.39 p.m. and stopped at 1.53 a.m. For how long was it howling? ...............................................................................

This is a distance-time graph for a trip along a hilly running track. 4. How far did they run before the first stop? .......................................... 5. For how long did they stop? .......................................... 6. During the next 30 minutes, how far did they run? .......................................... 7. For how long was the second stop? ..............................

8. How far did they run in the last 30 minutes? ......................... 9. What was the average running speed (km/hr) for the entire run? ....................................................................................

M3

17:43

10

0

(km)

D i s t a n c e 5

1 2

3. Jason went into the movies at 8:05 p.m. He left at the end of the movie at 10:17 p.m. If the movie was 1hr 55min long, at what time did it start? ..............................

Time

1. ..................... 2. .....................

3. ..................... 4. .....................

5. ..................... 6. .....................

7. ..................... 8. .....................

A: 10 Quick Questions 1. 745 + = 439 Find ......................... 2. How many metres in 4.15 kilometres? ........................ 3. 7 × -9 = ......................... 4. How millilitres in 2.75 litres? ......................... 5. 4.6 × 0.9 = ......................... 6. How many seconds in 9.5 minutes? ......................... 7. $4.25 × 9 = ......................... 8. 0.84 ÷ 1.2 = ......................... 9. Name this shape ......................... 10. A square has an area of 16m2, what is the perimeter ? .........................

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A: 10 Quick Questions 1. Find 10% of $27.60 ............................ 2. 54 - 12 × 3 = .......................... 3. Find 64 = ............................. 4. If the temperature was 7oC, then drops 9oC, what is the new temperature? ............................ 5. 5.6 × 0.004 = ......................... 6. How many seconds in 6.5 minutes? ............................ 7. $3.60 × 17 = .......................... 8. 10.8 ÷ 0.9 = ............................ 9. How many weeks in 2½ years? ............................ 10. Find ½ of $13.50 .................

F: Drawing angles 1. Draw an angle of 45o

2. Draw an angle of 135o

3. Draw an angle of 210o 4. Draw an angle of 340o

B: What angle is that ? Classify the angles by matching each diagram with a word from the list below.

acute right obtuse straight reflex

C: Which angle is it ? Angles are named using three letters (example: BAC) , a single letter (example: Â) or a mark on a diagram. Study the diagram, then answer the questions.

1. Name the angle marked. ....................... 2. Name the angle marked. ....................... 3. Mark on the diagram BAC 4. Mark on the diagram Ê. 5. Can you mark B on this diagram? ....................... Give a reason ................................... .............................................................

D E

B A

C

D: Guess the angle sizes

Estimate these angles to the nearest 10o (do not measure).

..........................

..........................

..........................

..........................

E: Measure these angles

5. .....................

1. ...................... angle

2. ..................... angle

3. ..................... angle

4. ..................... angle

5. ..................... angle

1.

.......................... 3.

2.

4.

5.

4. .....................

3. .....................

2. .....................

1. .....................

Revision

6. .....................

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C: Missing angles Find the value of the missing angles in these diagrams, using the rules above. The diagrams are not drawn to scale.

B: Which angle rule ? Match the angle rules below, with the diagrams.

A: 10 Quick Questions 1. 27 - 8 × 4 = ............................ 2. Convert 7.2kL to litres ............................ 3. How many seconds in 4.75 minutes? ............................ 4. Find the area of a triangle with a base of 16cm and a height of 9cm. ................ 5. Convert 0.4 to a fraction ............................ 6. Round off 2.076 to 2 d.p. ............................ 7. If 7 books cost $9.45, what does each book cost? ............................ 8. 3.94 × 0.09 = ......................... 9. How many days in 13.5 weeks? ............................ 10. Find 20 % of $14.50 ............................

c

d e

a b

f

g

D: Puzzle How many acute angles in this diagram? .................

Rule Diagram A. Angles at a point add to 3600 ............. B. Vertically opposite angles are equal ............. C. Adjacent angles on a straight line add to 1800 .............

132o 1190

b a 67o

c 124o

d

137o

94o e

540

83o

g

f 97o

36o

h

2j

85o

161o

77o

n 41o

k

m

94o

2p

83o

5u 122o

a = ......................... b = ......................... c = ......................... d = ......................... e = ......................... f = .......................... g = ......................... h = ......................... j = .......................... k = ......................... m = ........................ n = ......................... p = ......................... q = ......................... r = .......................... s = .......................... t = .......................... u = ......................... v = ......................... w = ........................

E: Clock angles Calculate the smaller angle between the hands of a clock, for the given time. 1. 4.00 a.m. .......................... 2. 2.30 p.m. ........................... 3. 8.00 a.m. ........................... 4. 11.30 p.m. ........................... 5. 5.30 a.m. ........................... 6. 02:00 ........................... 7. 07:30 ........................... 8. 15:30 ........................... 9. 22:45 ........................... 10. 12:15 ...........................

129o

92o

117o q

r s

t

v w

137o

Revision

1. 2. 3.

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Revision


E: Puzzle How many obtuse angles in the diagram? .........................

B: Name that triangle Match the list below with the diagrams of these triangles.

A: 10 Quick Questions 1. 5 × -4 + 7 = ............................ 2. Convert 1400mm to metres ............................ 3. How many seconds in 3 hours? ............................ 4. Find the area of a triangle with a base of 18cm and a height of 5cm. ................ 5. Convert 80% to a fraction (simplify) ............................ 6. Round off 7.153 to 1 d.p. ............................ 7. If 9 books cost $8.55, what does each book cost? ............................ 8. Share $63.00 in a ratio of 4 : 3 ............................ 9. What do adjacent angles on a straight line add up to? ............................ 10. Find 75% of $15.80 ............................

1. ........................... triangle

C: Angle rules Match the rules below with the diagrams.

1. 2.

Rules Diagram A. The sum of the interior angles of a triangle adds to 180o ......................... B. The exterior angle is equal to the sum of the interior opposite angles .........................

75o 67o a

b 63o

37o

112o

c

e

88o

d

f

27o

g

k

17o

47o

n m

84o

41o

q p

32o

129o

29o

2r

a = ................ m = ................ b = ................ n = ................ c = ................ p = ................ d = ................ q = ............... e = ................ r = ................ f = ................ s = ................ g = ................ t = ................ h = ................ u = ................ j = ................ v = ................ k = ................ w = ................

a

c

b e d

f

j

h

u v 42o

73o w 65o

2. .......................... triangle

3. .......................... triangle

4. .......................... triangle

6. .......................... triangle

5. .......................... triangle

D: Missing angles Find the value of the missing angles using the rules above. The diagrams are not drawn to scale.

acute scalene obtuse scalene isosceles equilateral

right - angled right - angled isosceles

77o

39o

t s

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G1

D: Missing angles Use the angle rules for parallel lines, and other angle rules to find the values of the missing angles. The diagrams are not drawn to scale.

B: Which line ? Perpendicular, parallel, horizontal or vertical lines.

A: 10 Quick Questions 1. 4 × -8 - 12 = .......................... 2. Convert 365mm to cm ......................... 3. 62 + 144 = ......................... 4. How many sides does a heptagon have?..................

5. 4/5 + 2/5 = ............................

6. Round off 4920 to 2 significant figures ......................... 7. If 4kg of meat cost $47.80 what does 1kg cost? ......................... 8. Share $72.00 in a ratio of 4 : 5 ......................... 9. What is the area of a square with a perimeter of 36m? ......................... 10. Calculate the new price if a 20% discount is taken off $24.00 .........................

Rule Diagram A Co-interior angles add to 180o ............. B Corresponding angles are equal ............. C Alternate angles are equal .............

65o

b

109o

c

93o

e d

g

f 77o

h

123o

j

k

m

n

134o

u v

w 45o

63o x

y z

a = .................. p = .................. b = .................. q = .................. c = .................. r = .................. d = .................. s = .................. e = .................. t = .................. f = .................. u = .................. g = .................. v = .................. h = .................. w = ................. j = .................. x = .................. k = .................. y = .................. m = .................. z = .................. n = ...................

p q

s r t

62o 74o

Look at this picture, then answer the following. On the diagram ... 1. draw around a pair of perpendicular lines, and label it A. 2. draw around some parallel lines and label it B. 3. draw around a line which is horizontal to the ground, label it C. 4. draw around a vertical line, label it D.

C: Which angle rule ? Match the angle rules for parallel lines in the box below, with the diagrams.

a b

1. c

d

2.

e

f 3.

95o

a

a

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C: Order of Symmetry

B: Lines of Symmetry / Rotational Symmetry 1. Name each shape, using the list below.

A: 10 Quick Questions 1. -6 × -3 - 8 = ........................... 2. Convert 57.6cm to mm ............................ 3. 32 + 42 = ........................ 4. How many seconds in 2.5 hours? ........................

5. 3/4 + 1/2 = ..............................

6. Write 230000 in standard form ..................................... 7. If 7 kg of meat cost $48.65 what does 1kg cost? ............................ 8. Share $56.00 in a ratio of 1 : 3 : 4 ................................. 9. Convert 35% to a decimal ............................ 10. Calculate the new price if a 25% discount is taken off $64.00 ............................

a. .................................. b. .................................. c. ..................................

d. ................................. e. .................................. f. ..................................

trapezium arrowhead rectangle rhombus square parallelogram isosceles trapezium kite equilateral triangle hexagon octagon pentagon

g. .................................. h. .................................. i. ..................................

j. .................................. k. .................................. l. ..................................

2. Draw all lines of symmetry on each shape above, (if they have any).

Example: A square has 4 lines of symmetry (mirror lines).

Enter the order of line symmetry for each shape in

Column A in the table opposite.

3. Work out the order of rotational symmetry for each shape, then enter the order in Column B, in the table opposite.

Example: An equilateral triangle has an order of rotational symmetry of 3. Start

1 2 3

Finish

Shape A B

equilateral triangle 3

square 4

rectangle

parallelogram

rhombus

trapezium

isosceles trapezium

kite

arrowhead

pentagon

hexagon

octagon

Rotate for one revolution, and count each time it looks the same, as it did at the start.

G2

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G2

C: Missing angles Use the angle rule below for the exterior angle sum, and the table values above, to calculate the missing angles in these diagrams (not drawn to scale). Other angle rules may also be used where necessary.

A: 10 Quick Questions 1. -9 × -4 - 12 = ......................... 2. 0.078 × 0.063 = .................... 3. Divide $28.00 in a ratio of 4 : 3 ............................ 4. How many minutes in 375 seconds? ............................

5. Convert 37/4 to a mixed number ............................

6. Write 0.0008 in standard form ............................ 7. Convert 5.35kL to litres ............................ 8. Solve 3y + 9 = 24 y = .................... 9. What is the next number in the pattern? 13, 7, 1, ........ 10. Calculate 52 + 12 2

.......................................

B: Interior angles of non-regular polygons Divide the polygons into triangles,from one corner only (labelled with a dot) . Use this to calculate the interior angle sum, based on the number of triangles in each shape, then complete the table.

Example 4 sides 2 triangles 2 × 180o = 360o

4 sides 5 sides 6 sides

7 sides 8 sides

9 sides

10 sides

Angle rule: The sum of the exterior angles of any polygon, no matter how many sides, equals 360o

Example: a + b+ c + d = 360 o

d

a

b

c

a 150o

127o

74o

125o 125o

i

45o 45o 254o 125o 125o

c

d

e

f h

g

78o

87o 92o

b

small angles (s), all the same

all large angles 260o

s

Number of sides

Interior angle sum

4 3600

5

6

7

8

9

10

j

j

132o

270o

270o

j

112o

112o k

134o

85o

96o

52o

98o

131o 49o

m q r

p

o

n

l

a = ................... b = ................... c = ................... d = ................... e = ...................

f = ................... g = ................... h = ................... i = ................... j = ...................

k = ................... l = ................... m = ................... n = ................... o = ...................

p = ................... q = ................... r = ................... s = ...................

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G3

6. Name all the angles in a semi-circle in these 3 diagrams. .............................................. ..............................................

C: Angle in a semi-circle Use the diagram and the information in the box to complete each sentence. 1. Point O is the ..................................... of the circle. 2. Line AC is a ..................................... of this circle. 3. Point B touches the .............................................. of this circle. 4. ABC is said to be the angle in a ........................................................................... 5 An angle in a semi-circle is equal to .....................................

5. Name all the right angles in these 3 diagrams. ........................................... ........................................... ...........................................

Use the diagram and the words in the box to complete each sentence. 1. Point O is the ..................................... of the circle. 2. Line OB is a ..................................... of this circle. 3. Line AC is a ..................................... to this circle. 4. The tangent to a circle and the radius of the circle form a .................................................

B: Angle between a tangent and a radius A: 10 Quick Questions 1. 7 × -8 + 12 = ........................... 2. Convert 1750mm to metres ............................ 3. How many seconds in 3.5 hours? ............................ 4. Find the area of a triangle with a base of 14cm and a height of 12cm. ................ 5. Convert 90% to a fraction (simplify) ............................ 6. Round off 8.375 to 1 d.p. ............................ 7. If 9 books cost $12.15, what does each book cost? ............................ 8. Share $81.00 in a ratio of 4 : 5 ............................ 9. How many degrees in a right-angle?............................ 10. Find 75% of $16.80 ............................

A B

C

O

tangent radius centre right angle

P

O Q

R

A

O

B C

O

E

F

D

O

I H

G

In this diagram, HOI = 65o. 6. What is the size of OHI? ..................... 7. What is the size of OIH? ..................... 8. What is the size of GHO? .....................

diameter 90o semi-circle centre

circumference

A

B

C

O

B C

O

A

E

F

G

O R

S

P

Q

O

In the triangle LMN, MLN = 57o. 7. What is the size of MNL? ..................... 8. What is the size of LMN? .....................

O

M

N L

D: Missing angles Find the size of the angles in these diagrams. Diagrams are not drawn to scale.

c

a b

59o 71o

d

a = .................. b = .................. c = .................. d = ..................

1.

2. e = ............... f = ............... g = ............... h = ...............

43o

32o

e

f

g

O

h

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B: Angles and lines Construct the following. Show construction marks. 1. Bisect ABC.

A: 10 Quick Questions 1. -6 + -4 × 7 = .......................... 2. 15.78 ÷ 0.02 = ...................... 3. 75% of $48 = ...................... 4. How many hours in 6.5 days? ............................ 5. Convert 81/4 to an improper fraction .............. 6. Write 9.6 × 105 as an ordinary number ............................ 7. Convert 0.35km to metres ............................ 8. Solve ½y = 19 y = .................... 9. What is the next number in the pattern 2, 4, 8, ............ 10. Calculate 25 ........................

A

B

C

B C A

4. Bisect line PQ.

Q

P

3. Construct a line through E that is parallel to DF.

E

D F

C: Triangles Accurately draw these triangles. 1.

2. Construct a line through A that is perpendicular to line BC.

A

4.5 cm

2.7 cm

3.2 cm B

C

3. How long is line TS? .................

D: Compass bearings Write the common compass directions, that correspond to the lines drawn below.

Draw and label the following bearings on the compass diagram. 11. 060 label it A 12. 135 label it B 13. 265 label it C 14. 283 label it D

N

N 1. ........... 2. ...........

3. ...........

4. ........... W

5. ...........

6. ........... 18 mm

40 mm R

T

S

2.

Find the bearing of each point from the point X. 7. X to A .................... 8. X to B .................... 9. X to C .................... 10. X to D ....................

N

X

C B

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2. Johnny runs around a triangular field, as shown in the diagram. How far is it across the field (x)? ................................................ 3. How far did he run altogether? ...........................................................

E: Word problems (round to 2 d.p.) 1. A farmer is to make two gates, as in the diagrams. Work out how long to cut each diagonal rod. How long will they be?

2.5m

0.8m

A: 10 Quick Questions 1. 1.2 × 0.8 + 8.4 = ................... 2. 6.72 + 0.7 × 1.4 = ................ 3. ¾ of $52 = ........................... 4. How many grams in 5.23kg? ................ 5. Convert 54/7 to an improper fraction .............. 6. Write 4.8 × 10-3 as an ordinary number ................. 7. Convert 0.73m to cm ............................ 8. Solve ¼x = 9 x = .................... 9. List a prime number between 45 and 55 .............. 10. Calculate 43 ................

C: Pythagoras’ theorem Carefully measure the sides of these triangles (mm), then see if they approximately fit the Pythagoras rule a2 = b2 + c2.

a b

q p d e

q = ...........mm q2 = p2 + r 2

p = ...........mm ............................. r = ............mm .............................

Example

D: Missing sides Use the Pythagoras rule to find the missing sides.

5cm

12cm

A

......................................................................................................................

3. 12 cm

C

15 cm

c r f

16.5 m

h

d = ...........mm d2 = e2 + f 2

e = ...........mm ............................. f = ............mm .............................

B: Squares /square roots Calculate (round to 2 d.p. if answers are not whole numbers). 1. 52 = ................

2. 142 = ...............

3. 42 + 32 = ............

4. 72 + 52 = ............

5. 81 = ................

6. 121 = ...............

7. 58.4 = .............

8. 17.64 = ...........

9. 62 + 52 = ................

10. 72 + 102 = ..............

11. 82 + 42 = ...............

12. 32 + 92 = ................

......................................................................................................................

1.

4. A 6m ladder is 1.5m out from the bottom of a building. How high up the building will the ladder reach? ..............................................

5. A builder needs to calculate the height of a roof, above the ceiling, as shown in the diagram. How high will it be (h)? ..........................................................................

1.5m

6m

6cm

8cm

B

......................................................................................................................

2.

120m

90m

x

4.25m

0.9m

..........................................................................................................................

..........................................................................................................................

30 m

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E: Missing sides Calculate the unknown sides using a trig ratio (round to 2 d.p.).

F: Missing angles Calculate the unknown angles using a trig ratio (round to 1 d.p.).

C: SOHCAHTOA? What does this mean? Fill in the missing words below to complete the trig ratios. 1. Sin = 2. Cos = 3. Tan =

B: Naming sides Name each side of the triangle using the words Opposite, Adjacent and Hypotenuse, for the marked angle A.

(use Opp, Adj and Hyp).

A: 10 Quick Questions 1. List the factors of 27 .................................................. 2. 5(15 ÷ 3 + 6) = .................... 3. Find 33.3.% of $150.90 ............................ 4. How many milligrams in 9.4g? ............................ 5. -8 + 7 - -9 = .......................... 6. Simplify the ratio $2 : 50c ............................ 7. Find the volume of a cube with sides of 5cm ............... 8. Shade in 40% of the shapes

9. Round off 29.234 to 2 d.p. ....................................... 10. Calculate (-3)3 ................

A B

C

D: Calculator or Tables Use the calculator or trig tables to find the value of these trig ratios (round to 4 d.p.). 1. tan 34o ........................ 2. sin 58o ........................ 3. cos 76o ........................ 4. tan 56.8o ........................ 5. cos 23.4o ........................ 6. sin 12.8o ........................ 7. cos 83.1o ........................ 8. tan 34.8o ........................ 9. sin 27.5o ........................

Find the angle Q, using calculator or trig tables (round to 1 d.p.). 10. cos Q = 0.8660 ............... 11. sin Q = 0.7071 ............... 12. tan Q = 11.43 ............... 13. sin Q = 0.2164 ............... 14. cos Q = 0.2588 ............... 15. tan Q = 0.2588 ............... 16. sin Q = 0.8415 ............... 17. cos Q = 0.3714 ............... 18. tan Q = 3.25 ...............

AB = ............... BC = ................ AC = ...............

39o 16cm x

y

1. side x .................................................. .................................................. 2. side y .................................................. ..................................................

1. PQR .................................................. .................................................. 2. QRP .................................................. ..................................................

Q

P R

7cm

10cm

G: Word Problems 1. A ladder is placed against a building as shown in the diagram. What angle ( does the ladder make with the ground? (round to 1 d.p.) ...............................................................................................

16m

h 32o

1.5m

5m

A

2. This diagram shows part of a house plan. How high is the roof peak above the ceiling (h)? (round to 2 d.p.) ...........................................................................

3. This diagram shows part of a house plan. Calculate the angle (B) of the roof. (round to 2 d.p.). ........................................................................

20m

5.9m B

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Top Front Left side Right side Back

1.

2.

B: Drawing on isometric paper Copy each block diagram in the space provided.

D: Drawing view diagrams

Study this diagram of a block structure made from 2 4-pin and 2 8-pin blocks.

1. 2.

= 4 pin blocks = 8 pin blocks

end side top top side

C: Constructing 3D block structures Study the view diagrams and build each block structure.

Draw each block structure above on isometric paper.

1. 2.

Draw the view diagram for the block structure.


A: 10 Quick Questions 1. -8 × -4 - 9 = ........................... 2. Convert 95.3cm to mm ............................ 3. 52 + 122 = ....................... 4. How many seconds in 1.5 hours? ........................

5. 3/4 + 2/3 = ..............................

6. Write 963000 in standard form ..................................... 7. If 9 kg of meat cost $62.55 what does 1kg cost? ............................ 8. Share $56.00 in a ratio of 2 : 1 : 5 ................................. 9. Convert 45% to a decimal ............................ 10. Calculate the new price if a 40% discount is taken off $200.00 .........................

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D: Word Problems This grid shows a map of part of the St. Albans school grounds. Use this to answer these questions. Steven has to run from point A to B to C to D as a warm-up for a sports practice. 1. Draw the vectors, for each part of the run, on the diagram.

2. Write down the translation vectors for each part of the run.

4. Andrew is late for practice so runs directly from A to D. Draw this on the diagram, then write down the translation vector for this run. Is it the same as the answer in question 3 above? ................................

C: Name or draw vectors

Study the vector diagrams, then write the vectors in the form of

B: The shapes moved? Count the squares to move the shapes and draw the new position. 1. Move A, 3 squares to the right and 2 squares up. 2. Move H, 1 square to the left and 3 squares down. 3. Move Z, 2 squares to the right and 3 squares down. 4. Move I, 2 squares to the left and 5 squares up.

A: 10 Quick Questions 1. List the factors of 24 ....................................... 2. -3(3 × 5 - 7) = ..................... 3. Find 120 % of $50.00 ............................ 4. How many centimetres is 567mm? ............................ 5. -12 - -4 + 8 = ...................... 6. Convert 0.63 to a percentage ............................ 7. Find the perimeter of a square with sides of 14cm ............................ 8. What fraction of the shapes is shaded? ...............

9. Round off 0.4576 to 3 d.p. ........................ 10. Calculate (-5)3 ...............

x y

where x = left or right and y = up or down

Draw and label the vectors,

on this grid

A to B =

B to C =

C to D =

= =

3. Add the translation vectors in question 2 above.

+ = + AB BC CD

= AD

= 5 2 = 3

-1 e =

-4 1

f g

= c

b a

= d

D

B

C

A

Field 1 Field 2

a

b c

d

G7 / G10

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E: Drawing enlargements Enlarge each shape by the scale factor given. The centre of each enlargement is marked with a .

B: Similar Figures Find the following pairs of similar shapes and label with the letters as stated, 1. triangles, label them A 2. rectangles,label them B 3. trapeziums, label them C 4. parallelograms, label them D

A: 10 Quick Questions 1. List the factors of 21 ....................................... 2. -4(12 ÷ 3 - 7) = ................... 3. Find 200 % of $72.00 ............................ 4. How many millimetres is 62.9cm? ............................ 5. -15 - -8 + 4 = ...................... 6. Convert 0.08 to a percentage ............................ 7. Find the perimeter of a square with sides of 15cm ............................ 8. What fraction of the shapes are shaded? ............ 9. Round off 0.0215 to 2 s.f. ............................ 10. Calculate (-4)4 ................

C: Missing sides / scale factors for similar figures

Find the missing sides ()

4 mm

10 mm

1. = .............. 2. = .............. Find the scale factors for the enlargements above (object on the left, image on the right) 3. ().............. 4. ()..............

1 m 3 m

9 m

object image

D: Draw lines to find the centre of each

enlargement Mark each centre with a C.

image

1.

object

image

2.

5 mm

object

A'

B'

B

1. Scale factor = 2 2. Scale factor = 2

3. Scale factor = ½

F: Word problems 1. An aerial photo of a building is enlarged by a scale factor of 4. If the building in the photo measured 7.5cm how long is it in the enlargement? .......................

A

2. A map of New Zealand is 32cm wide. How wide is the map after it has been enlarged by a scale factor ¼? .......................................

4. A landscape plan was enlarged by a scale factor of 3. If a rose garden on the enlarged plan is 18cm long, how long was it on the original plan? ........................................

3. A 25cm high road sign is to be enlarged by a scale factor of 2½. How high is the enlarged sign? .................

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F: Word problems A driver of a car sees AMBULANCE the correct way around when looking at it, in the rear-vision mirror. How would the word Ambulance look on the front of the Ambulance, when you are not looking at it using a mirror? 1. .................................................. 2. Write your name as it would look in a mirror. .............................................................

When doing up a nut and bolt, which way (clockwise or anticlockwise), do you have to turn it, to tighten the nut up? 3. ........................................... Is this the same for wood screws and bottle tops? 4. ...........................................

D: Rotation For rotation we need a centre of rotation and an angle of rotation. A positive angle of rotation is anti-clockwise. Rotate the following shapes given the angle, and the centre () of rotation.

C: Draw in the mirror lines for each reflection Draw in all of the lines of symmetry (mirror lines) for each pair of diagrams.

B: Drawing reflections Each figure is reflected in the mirror line (m). Draw the image figure.

A: 10 Quick Questions 1. List the first 4 multiples of 9 ....................................... 2. 5(18 ÷ 6 - 7) = ....................... 3. Find 80 % of $50.00 ........................ 4. How many millimetres is 56.7cm? ............................ 5. -12 + -4 + 8 = ......................... 6. Convert 0.85 to a fraction (simplify) ............................ 7. Find the area of a square with sides of 12cm ............................ 8. What percentage of the shapes is shaded? ........... 9. Round off 2.376 to 2 d.p. ............................ 10. Calculate (-6)3 ................

m m 1.

1. angle of rotation, 90o

angle of rotation,

180o

E: Find the centre and angle of rotation

Mark the centre of rotation with a and find the angle of

rotation (either 90o, 180o, or 270o).

object image

A A'

2.

2.

m

m 3. 4.

1. 2. 3. 4.

A'

A

1.

angle = ....................................

2.

angle = ......................

angle = ......................

3.

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1. Miri drew this kowhaiwhai pattern. What type of transformation does this involve ? .......................................... 2. Draw lines between the repeating pattern above.

3. What type of transformation does this involve ? ...............................................................

Rangi drew a spider’s web. 5. What type of transformation does it best represent? ............................................................. 6. As the spider web gets bigger, are there any points that would appear not to move ? ..................... 7. Draw one more ring to the web, as if the spider was adding to his web.

The leaves of the Hebe plant grow in pairs, and in layers (labelled a to d, this diagram shows four layers of paired leaves). 8. What type of transformation does this represent? ...................................... 9. What is the angle between each pair of leaves? ....................... 10. How is one pair of leaves related to the pair below? ........................................................................ 11. Find out why the Hebe plant has its leaves growing in this pattern. ........................................................................ ........................................................................ 12. Draw in the position of where the next layer of leaves would be.

C: Tile designs Many tile designs involve some form of transformation. Copy the tile patterns to create a design (called tessellating).

a

b

c

d

growing tip

oldest leaf

a

b

c

d

This diagram is looking down on a growing stem.

A: 10 Quick Questions 1. 3.7 × 0.7 + 9.8 = .................... 2. 2.01 + 0.8 × 2.8 = .................. 3. ¾ of $84 = ............................. 4. How many grams in 4.2kg? ............................ 5. Convert 47/8 to an improper fraction ............... 6. Write 3.7 × 10-3 as an ordinary number ................... 7. Convert 0.63m to cm ............................ 8. Solve ¼x = 8 x = ..................... 9. List a prime number between 60 and 70 ............. 10. Calculate (0.4)3 ...............

B: How did they draw that? Look at each drawing and determine if it involves a translation, reflection, rotation, enlargement, or a combination of transformations, then answer the questions that follow.

Steven used the pattern below to draw the pattern on the right.

4. Draw lines between the repeating patterns of Steven’s drawing (lines of symmetry).

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B: Finding number patterns Find the next three numbers in each number pattern,

pattern 1 pattern 2

pattern 4 pattern 5

D: What is the number at the top () ?

Calculate the number at the top of each number pyramid.

41o

A: 10 Quick Questions 1. 40 ÷ 8 –7 = .......................... 2. List the first four multiples of 14 ............................ 3. Find the missing angle ()

4. Find the area of this triangle ()

= ............................... 5. Find 10% of 720kg ............................ 6. Round off 9.538 to 1 d.p. ............................ 7. Evaluate 1/3 + 2/5 = ............................ 8. Convert 21:37 from 24 hr time to a.m. or p.m. time ............................ 9. What fraction is shaded?

10. 0.43 × 6.3 + 8 = .....................

1. 3, 6, 12, .................................... 2. 36, 18, 9, .................................... 3. 4, 11, 18, .................................... 4. 14, 11, 8, .................................... 5. 6, 2, -2, .................................... 6. 5, -10, 20, .................................... and describe in words how each pattern above was generated.

7. No. 1 ........................................................................................................ 8. No. 2 ........................................................................................................ 9. No. 3 ........................................................................................................ 10. No. 4 ........................................................................................................ 11. No. 5 ........................................................................................................ 12. No. 6 ........................................................................................................

C: Classroom desk patterns A teacher wishes to arrange her classroom desks, using one of the patterns below. Draw the next two desk patterns.

pattern 3

Pattern number 1 2 3 4 5 10

Number of desks in each row 2 3 4

Total number of desks needed 4 7

1. Complete this table.

2. Study the numbers in the above table and see if you can work out the relationship between the number of desks in each row, with the number of desks needed to make each pattern. (either answer in words or as a mathematical rule) ............................................................................................... 3. If the teacher has 22 desks, what will be the length of each row, if the teacher uses the pattern above? ....................... 4. If the teacher has 27 desks, what will be the length of each row, if the teacher uses the pattern above and how many desks will be left over? .................................... ................................... 5. How many desks are needed to make the ‘pattern 12’ arrangement of desks? ............................................................. 6. What would be the best pattern to use, if the teacher had 34 desks ( no desks to be left over)? .....................................

A1

= .....................

........................

12 mm

3 mm

5.3 4.6 2.7 6.1 5.7

7.3 9.5

12 9 7 11 9

21 16

1.

2.

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A: 10 Quick Questions 1. 62 ÷ 9 + –7 = ......................... 2. List the first four multiples of 16 .................................................. 3. Find the missing angle () = ............................... 4. Find the area of this square () = ............................... 5. Find 20% of 47.5 km ............................ 6. Round off 0.2739 to 2 d.p. ............................ 7. Evaluate

5/6 – 1/3 = .............................. 8. Convert 17:46 from 24hr time to a.m. or p.m. time ............................ 9. What % is shaded ? ............................ 10. 1.73 × 0.8 – 3.7 = ..................

C: Word problems Paula works for a shop and is paid $5.30 per hour, plus $1.25 per day travelling money. Calculate her daily pay if she worked ... 1. 5 hrs ............................ 2. 6 hrs ............................ 3. 7 hrs ............................ 4. 8 hrs ............................ 5. 9 hrs ............................ 6. 10 hrs ......................... Young children are to be given medicine (mls) using the following rule. Half their age, plus 2mL. Calculate the dose each child would get if the ages were ... 7. 4 yrs ............................ 8. 5 yrs ............................ 9. 6 yrs ............................ 10. 7 yrs ............................ 11. How old is a child who is given 6mL of medicine? ........................... 12. How old is a child who is given 8.5mL of medicine? .....................

The graph opposite shows the total pay for the hours worked. Use the graph to work out the pay for the following hours of work. 13. 4 hrs ........................................ 14. 5 hrs ........................................ 15. 6 hrs ........................................ 16. 7 hrs ........................................ Use the pattern above to work out the pay you would earn in 25 hours. 17. ............................................

112o

7.5 mm

B: Generate the number patterns from the rules Find the first 5 numbers in each pattern given by the word rules. 1. Start with 3, add 4 to each new number .......................................... 2. Start with 10, subtract 6 from each number .................................. 3. Start with 2, double each new number ............................................. 4. Start with 24, halve each number ..................................................... 5. Start with 3, triple each number and then subtract 5 ......................................................................... Replace ‘n’ with the numbers 1 to 5 in each rule, to find the first 5 numbers of each pattern, (the first number has been done). 6. rule = 4n 4, ............................................................... 7. rule = 5n + 3 8, ............................................................... 8. rule = 4n – 1 3, ............................................................... 9. rule = ½n + 5 5½, ............................................................ 10. rule = 5 + n 6, ...............................................................

D: Find out about Pascal’s number triangle

The first four rows have been listed. How is the number pattern created ?

1. .................................................. .................................................. 2. What are the next 3 rows of numbers? .................................................. .................................................. ..................................................

Hours of work (hrs)

0 5 10

40

80

Total pay ($)

0

Wages Graph

A2

1 3 3 1

1 2 1

1 1

1

How many hours did Karen work if she was paid ... 18. $64.00 ............... 19. $128.00 ............... 20. $76.00 ............... 21. $92.00 ............... 22. $110.00 ............... 23. $122.00 ...............

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0 5 10 15

Time (hrs)

60

Graph 1

A: 10 Quick Questions 1. 42 × 5 + –13 = .......................... 2. List the factors of 42 .................................................. 3. Find the missing angle () = ............ 4. Divide $48.00 in a ratio of 5 : 3 ............................ 5. How many grams in 1.35kg ? ............................ 6. Round off 45.764 to 1 d.p. ............................ 7. $50.00 - 4 × $9.60 = ............................ 8. Convert 0.634km to metres ............................ 9. How many in a baker’s dozen? ............................ 10. 16.4 ÷ 0.4 + 5.7 = ..................

63o

B: Wages $ / hr ? Graph 1 shows the wages ($) that Paul could earn over a given period of time (hrs). How many hours would Paul have to work to earn ... 1. $36.00 ...................... 2. $72.00 ...................... 3. $54.00 ...................... 4. $96.00 ...................... 5. $144.00 ...................... How much would Paul earn if he worked for the following hours ? 6. 5 hours ................... 7. 11 hours ................... 8. 14.5 hours ................... 9. 20.5 hours ................... 10. 7.25 hours ................... 11. 9.75 hours ................... 12. Can you describe in words or come up with a rule that could be used to work out how much Paul would earn, no matter how many hours he worked ? ......................................................................... ......................................................................................................................

C: What do the graphs mean ? Graph 2 shows the mood of Hoani as he was watching a movie on T.V. Study the graph, then describe the changes in Hoani’s mood during the movie, between the points listed below, Happy

Sad

Time

B

C D

E F

G Graph 2

A

Time

Graph 3 shows the pulse rate of Marie, who is playing soccer. 6. What has happened to Marie’s pulse rate from A to B? ............................................................................................................... 7. Why do you think the pulse rate changed between A and B? ............................................................................................................... ............................................................................................................... 8. If C is half time, how can you tell ? ............................................ 9. Did Marie run harder in the 1st or 2nd half ? ...........................

Pulse Rate

High

Low

Graph 3

C

A

B

D

E

1. A to B ............................................................................................... 2. B to C............................................................................................... 3. C to D ............................................................................................... 4. D to G ............................................................................................... 5. Did Hoani enjoy the movie ? Give a reason why. ............................ ...............................................................................................

A3

120 W a g e s

($)

Time

10. If Marie did 10 sprints, walking between each one, show on this graph what you think would happen to her pulse rate.

Pulse Rate

High

Low

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A: 10 Quick Questions 1. 102 ÷ 25 + –9 = ....................... 2. List the first four multiples of 17 ....................................... 3. Find the missing angle () = .................... 4. Find the perimeter of this square () = .................... 5. Find 0.25 of 126.4km ............................ 6. Round off 2.3618 to 3 d.p. ............................ 7. Evaluate

3/4 – 2/5 = ............................. 8. Convert 3.075km to metres ............................ 9. What % is shaded? ............................ 10. 1.84 × 0.5 – 6.1 = ...................


E: Plotting points A = (-1,3), B = (6,3), C = (4,-2),

D = (-3,-2) & E = (-1,3) 1. Plot, then join the points A, B, C, D and E with straight lines, in that order. 2. What shape have you drawn? ....................................

D: Where is that point? Below is a map of Heed town.

B: Label the diagram Use the words below to label this diagram of a set of axes.

x - axis y - axis origin

1. ................................

3. ................................

2. ................................

C: Co-ordinates The co-ordinates of a point are a pair of numbers. Written as (x,y), they represent an ordered pair. Study the diagram, then write the ordered pairs for,

x

y

2 -2

-2

2 A

C

B D

Mark on the diagram the following points ... 1. (5, 1) Label it A 2. (-3, 1) Label it B 3. (6,-2) Label it C 4. (-1,-3) Label it D 5. (7,-4) Label it E 6. (-5, 3) Label it F What are the co-ordinates for the following points on the map? 7. The castle by Himmol Lake. 8. The roof of the Abbey. (.......,.......) (.......,.......) 9. The sea monster’s head. 10. Main door in Heed Castle. (.......,.......) (.......,.......) 11. The mermaid on a rock. 12. The biggest single tree. (.......,.......) (.......,.......) 13. The sailing ship 14. The bridge over the river (.......,.......) (.......,.......)

49o

8.2mm

A = (.......,.......)

B = (.......,.......)

C = (.......,.......)

D = (.......,.......)

A4

x

y

2

-2

-2 2

Aria

Heed Castle

The Great Oak

Himmol Lake

y

x

Tiefew Sea

3 0

-3

The Abbey

-6 6

5

0

-5

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2. Graph the points and join with a straight line. 3. Use the graph to find the cost of telephone calls lasting, 7 min ...........& 9 min ............. 4. Use the graph to find how long calls were if they cost ... $6.50 ................................. $9.50 ................................. $14.00 .................................

Cost ($) = $2.00 + $1.50 × T

where $2.00 is a charge for using the operator and T = length of toll call (min). 1. Use the formula above to complete the table

B: Plotting integer points

Plot, then join these (x,y) points with straight lines, in the order given. Label each line with the letter given. 1. (-4,0),(-2,2),(0,4),(2,6) Label A

2. (-4,3),(-1,3),(2,3),(5,3) Label B

3. (-2,1),(0,-1),(2,-3),(4,-5) Label C 4. Label D 5. Label E

A: Quick Questions 1. Find 20% of $75.00 ............................ 2 12 × $0.87 = ......................... 3. Find the missing angle () = ............ 4. Convert 45% to a fraction (simplify) ............................ 5. Write 860000 in standard form ........................................ 6. Round off 5930 to 2 s.f. ............................ 7. Draw in the lines of symmetry on this shape 8. Find the next 3 numbers 3, 7, 11, ........., .........., ........... 9. Express 12 as a % of 48 ............................ 10. Solve 3x + 9 = 24 x = .....................

49o

x 4 4 4 4 y -4 -1 2 5

x -4 -2 0 2 y -4 -2 0 2

C: Completing sets of ordered pairs

Use each rule given to find the y co-ordinate of each ordered pair. The first ordered pair for each rule has been done for you. 1. y = 3x

(1,3), (2, ), (3, ), (4, )

2. y = x + 5 (1,6), (2, ), (3, ), (4, )

3. y = 2x - 4 (1,-2), (2, ), (3, ), (4, )

4. y = ½x + 2 (2,3), (4, ), (6, ), (8, )

5. y = ¼x - 3 (4,-2), (8, ), (12, ), (16, )

6. y = ¼x + 5 (4,6), (8, ), (12, ), (16, )

D: Word problem The “Phone Home” telephone company charges ($) toll call users, using the following formula,

6. Which straight line is vertical ? ................... 7. Which straight line is horizontal ? ................... 8. Try to find the rule for the line in question 1, (write it in the form y = 3x + 2 ) y = ........................

x

-3

-3 3

3

y

0

Time (minutes)

5

10

15

C o s t

($)

5

Time (min) 0 2 4 6 10

Cost ($)

A4

10

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6. If the two parallel sides are 5m and 7m long and distance between them is 4.5m, what is the area of the deck? Deck Area = ...........................................................


A: 10 Quick Questions 1. Find 60% of $80 .................. 2. List the factors of 25 ....................................... 3. Find the missing side ()

4. Find the area of this triangle () = ............................... 5. Convert 0.84 to a fraction (simplify) ............................ 6. 39 - 5 × 9 = ............................ 7. –7 + 8 – –5 = ............................ 8. How many sides does a nonagon have? .................... 9. 6295m = ............................km 10. 0.63 × 3.5 + 2.9 = .................

= .....................

Perimeter = 22cm

7cm

B: Substitution Given that a = 2, b = 7, c = –3 and d = –6 find the value of each expression using substitution (use BEDMAS). 1. 2a + 5 = ........................ 2. 5b – 4 = ........................ 3. 3c + 8 = ........................ 4. 2d + 7 = ........................ 5. 12 – 5a = ........................ 6. ab = ........................ 7. bc = ....................... 8. cd = ........................ 9. d2 = ....................... 10. a2c = ....................... 11. ab2 = ....................... 12. (ab)2 = ....................... 13. abcd = ....................... 14. a + b – c = ....................... 15. 3b – 4d = ....................... 16. c(5a + b) = .......................

9cm

12cm A = ½bh

C: Using formulae / substitution Answer the following by substituting into the given formulae.

A rental van is rented out using the formula Cost of Rental ($) = 50D + 0.50K where D = number of days, K = kilometres driven

4. If the van travels 720 km in 1 week, what has it cost to rent ? (Petrol not included) Cost = .......................................................... 5. If the van rental cost $830 and it travelled 960 km, how long was it rented for ? Days Rented = ...........................................

7. The surface area (S.A.) of a ball or sphere is worked out using the formula S.A. = 4r2. If the ball has a radius (r) = 8 cm and = 3.1, find S.A. Surface Area = ......................................................................

Baked Beans

8. A can of ‘Baked Beans’ is 11 cm high (h), with a radius (r) of 3.75 cm, and a can of ‘Tuna Fish’ is 7cm high with a radius of 5 cm. Using the formula V = r2h, find the volume (V) of each tin, using = 3.1 .(answers 2 d.p.) Baked Beans V = .................... Tuna Fish V = .....................

During the tennis season points for games played were worked out using the formula Total Points = 4W + 2D where W = games won, D = games drawn.

3. Find the points scored by Jimmy who won 12, drew 3 and lost 5 games during the season. Total Points = ....................................

The cost of C.D.’s and tapes is worked out using the formula Cost ($) = 20CD + 15T, 2. If 8 C.D.s and 11 tapes are purchased, what is the cost? Cost = .............................................................

The Jones family are going to have fish & chips for dinner. The Cost ($) = 1.20F + 0.90C, where F = numbers of fish bought and C = number of scoops of chips. 1. Find the cost of their dinner if they buy 7 fish and 3 scoops. Cost = .............................................................

A5 / A10

A wooden deck is built in the shape of a trapezium. The area of a trapezium is worked out using the formula Area = ½(a + b)h, where a & b = lengths of the parallel sides and h = gap between the sides.

a

b

h

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B: How many in each ? These six boxes contain three different coloured Mega Bloks. Each box should have the same number of each colour.

F: Number Puzzle Place the numbers in the grid below. 32, 43, 45, 53, 319, 459, 632, 937,943, 3442, 4921.

A: 10 Quick Questions 1. 66 ÷ 6 + –9 = .......................... 2. Find 2/3 of $27 ................. 3. What do the interior angles of a 5 sided figure add up to? ............................ 4. Write 6.1 × 103 as an ordinary number ................... 5. Convert 0.95 to a fraction (simplify) .............................. 6. 48 - 7 × 8 = .......................... 7. –9 + 6 – –7 = ........................... 8. How many years in a century? ............................ 9. Convert 6320mm to metres ............................ 10. Round off 6.488 to 2 d.p. ............................

C: Collecting ‘like’ terms Add or subtract these ‘like’ terms.

2. Peter had 25 records and 15 tapes. He went to a record shop and traded in 9 records for 7 new tapes. How many of each does Peter have now ? ................................ records + ................................tapes

1. Mary had 17 red and 21 blue marbles. Peter had 25 red and 19 blue marbles. How many of each colour do they have altogether ? ................................ red + ................................ blue

D: Simplify Simplify by collecting like terms. 1. 3k + 12k = ............................ 2. 21w – 14w = ............................ 3. 7r + 4t = ............................ 4. 4p – 9p = ............................ 5. 3x2 + 8x = ............................ 6. 13j + j = ............................ 7. 8f – 9f = ............................ 8. 7h + 6h – 9h = ....................... 9. 15f – 5f – f = ......................... 10. 12g – 6g + 4g = ...................... 11. 5a + 8b – 7b = ....................... 12. 3c – 2d + 7d = ....................... 13. 4g + 2e – 5f = ....................... 14. 8k + 5k – 4g = ....................... 15. 4h + 5h – 7h = ....................... 16. 9k – 13k + 3k = ...................... 17. 14d + 2g + 5d = ..................... 18. 2y + 7x + 5y + 9x = ....................................... 19. 13r – 7r + 8s + 2s = ....................................... 20. 3x2 + 7x + 6x2 – 3x = ....................................... 21. 7h – 5g + 4f + 3 = ....................................... 22. 7h – 5g + 7h + 2g = ....................................... 23. 9x – 6x + 8y + 9y = ....................................... 24. 10r + 6s – 8s + 2r = .......................................

4

5

9

E: Simplify Collect the like terms by adding or subtracting. 1. 5ab + 3ab + 7cd + 4cd = .................................................. 2. 6xy + 4x + 7y + xy = .................................................. 3. 3xy + 7y – 3y – 8xy = .................................................. 4. 14x2 – 7x – 4x2 + 5x = .................................................. 5. 11x2 + 2x + 4xy + y = .................................................. 6. 12x – 6x + 3xy + xy = .................................................. 7. 9x2 + 2x2 – 3y + 6y = .................................................. 8. 7x – 5x + 8xy – 2y 2= ..................................................

A7

............ ............ ..........

............ ............ ..........

1. How many are there of each colour altogether ? 2. How many of each colour should there be in each box ?

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D: Solving equations Solve these equations. The answers will all be whole numbers. 1. 4x = 20 x = .......... 2. 8y = 24 y = .......... 3. 5z = 35 z = .......... 4. ½b = 12 b = .......... 5. x + 9 = 20 x = .......... 6. x – 17 = 20 x = .......... 7. 2y + 3 = 11 y = .......... 8. 3t – 9 = 21 t = .......... 9. 5x + 14 = 39x = .......... 10. ½x + 7 = 19 x = ..........

F: Word problems Write algebra equations for each question, then solve.

C: Algebra equations Algebra expressions become equations if there is an equals sign. Using x to represent the number, write equations for the following, Example: the number added to 15 equals 21, written as x + 15 = 21 (DO NOT NEED TO SOLVE) 1. the number added to 7 equals 13 ....................................... 2. the number minus 12 equals 9 ....................................... 3. twice the number plus 3 equals 17 ....................................... 4. half the number equals 11 ....................................... 5. product of the number and 8 equals 56 .......................................

B: Algebra expressions Using x to represent the number, write expressions for the following. Example: the number plus three would be written as x + 3. 1. seven plus the number ............................ 2. the number minus nine ............................ 3. twice the number ............................ 4. the number times four plus eight ............................ 5. fourteen minus the number ............................ 6. the sum of the number and sixteen ............................ 7. The product of the number and twenty ............................ 8. The product of the number and nine, plus ten ............................

E: Harder equations The answers for these equations with not be whole numbers. 1. 7x = 16 (Show working) ........................... x = ............... 2. 3z – 7 = 25 ........................... z = ............... 3. 2g + 3 = 20 ........................... g = ............... 4. 7y + 9 = 24 ........................... y = ............... 5. 5w – 27 = 25 ........................... w = ...............

1. Mr. West had $100. He took 5 people (p) to lunch and they all had the same meal. After the meal he had $27.50 left . What did each meal cost? Equation: ........ p + ........ = ........ Cost of Meal = ................

2. Rebecca saved most of her weekly pocket money (m) for 6 weeks. At the end of 6 weeks she had $23.00 left, having spent $7.00 on a book. How much pocket money did she receive each week? Equation: ........ m –........ = ........ Pocket Money = ...................

3. Rangi gave half his money (m) to Johnny. Johnny had $29 and now has $50. How much money did Rangi have? Equation: ........... m + ........... = ........... Rangi’s Money = ..............................

A: 10 Quick Questions 1. 56 ÷ 7 + –7 = .......................... 2. Find 2/5 of $30 ................. 3. Find the next 3 numbers in the pattern 10, 6, 2, –2, ....................................... 4. Write 2.7 × 10–2 as an ordinary number ................... 5. Convert 60% to a fraction (simplify) ............................ 6. 42 - 9 × 7 = ............................ 7. –9 + 5 – –3 = ............................ 8. How many years in a decade? ............................ 9. Convert 7856mL to litres ............................ 10. Round off 0.566 to 2 d.p. ............................


A6 / A10

4. James gave a quarter of his money (m) to Abby. Abby had $12 and now has $16. How much money did James have? Equation: ........ m + ........ = ........ Rangi’s Money = .......................................

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B: Word problems 1. 5 people each have a lunch of 2 apples (A), 4 sandwiches (S) and a drink of orange juice (O). This could be written as an algebra expression 5(2A + 4S + O). Use this expression to work out the combined lunch order. ......... A + ......... S + ......... O

2. A school bought 32 triangle, 40 square and 56 circle shapes, which are to be divided into 8 equal groups. Fill in the spaces below to show how this could be done, using algebra.

A: 10 Quick Questions 1. 54 ÷ 6 –7 = .......................... 2. List the first four multiples of 1.5 ....................................... 3. Find the missing angle x x = ............... 4. Find the perimeter of this triangle .................... 5. Find 90% of 320kg ............................ 6. Round off 1.348 to 2 d.p. ............................ 7. How many sides does a pentagon have? ................... 8. Convert 15:37 from 24 hr time to a.m. or p.m. time ............................ 9. Divide $48 in a ratio of 5 : 3 ............................ 10. 4.5 × 0.15 + 7 = .....................

2x

48o

14mm

7mm 15.7mm

C: Expanding brackets Choose from the list below, to help expand these brackets. 1. 4(x + 7) = ........................ 2. 3(x – 4) = ........................ 3. 8(x + 5) = ........................ 4. 4(x – 7) = ........................ 5. 6(3x + 7) = ........................ 6. 7(5x – 9) = ........................ 7. 8(2x + 9) = ........................ 8. x(x + 8) = ........................ 9. x(4x + 3) = ........................ 10. 2x(x – 9) = ........................

Answers (not in order) 16x + 72, 8x + 40, x2 + 8x,

18x + 42, 3x – 12, 4x2 + 3x, 4x + 28, 4x – 28, 35x –63, 2x2 – 18x

E: Expand and simplify Expand, then simplify by collecting the ‘like’ terms 1. 2(x + 4) + 3(x + 3) = ............................................... = ............................................... 2. 5(a + 2) + 7(a + 3) = ............................................... = ............................................... 3. 3(k + 6) + 2(k – 4) = ............................................... = ............................................... 4. 5(h – 4) + 7(h + 6) = ............................................... = ............................................... 5. 7(x – 3) + 4(x – 6) = ............................................... = ...............................................

F: Word problems The diagram shows a wall that Rangi is painting. On Day 1 he painted a square area, with sides x metres long. On Day 2 he painted a 5m section and on Day 3 a 4m section.

1. Write an expression for the area of the wall painted on each day. Day 1 ................. Day 2 ................. Day 3 ................. 2. Write an expression for the Total Area to be painted. Total Area = ........................................................... 3. Factorise your expression for the Total Area. ............... (............... + ...............) 4. If x = 2.5 metres, what area of the wall did Rangi paint each day? Day 1 ................. Day 2 ................. Day 3 ................. 5. What is the total area of the wall? .......................................

D: Factorising Use the list below to factorise (insert brackets) these expressions. 1. 4x + 12 = ..................... 2. 8x + 24 = ..................... 3. 12x – 15 = ..................... 4. 14x + 35 = ..................... 5. 3x2 + 15x = ..................... 6. 5x – 30 = ..................... 7. 18x2 – 6x = ..................... 8. 24x – 48 = ..................... 9. 5x2 + 20 = ..................... 10. 8x2 – 20x = .....................

Answers (not in order) 6x(3x – 1), 3(4x – 5), 7(2x + 5),

4(x + 3), 8(x + 3), 5(x – 6), 24(x – 2), 3x(x + 5), 4x(2x – 5), 5(x2 + 4)

A9

....... + ....... + ....... + ....... + ....... ....... = 8

x m

x m

day 1 day 2

5m

day 3

4m

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A: 10 Quick Questions 1. Find 40% of $65.00 ............................ 2 14 × $0.87 = ......................... 3. What is the perimeter of a square with an area of 36 m2? ............................ 4. Convert 78% to a fraction (simplify) ............................ 5. Write 82000 in standard form ............................ 6. Round off 11460 to 2 s.f. ............................ 7. Draw in all lines of symmetry on this shape 8. Find the next 3 numbers -5, 1, 7, .........., ........., .......... 9. Express 42 as a % of 84 ............................ 10. Divide $36 in a ratio of 3 : 1 : 2 ............................


B: Indices / Exponents / Powers ? Indices (Index), exponents, or powers all mean the same and is the name given to the small numbers written next to other numbers or letters. Example: For 9x3, the 3 is the index / exponent / power. Fill in the gaps in the table below as you convert from index form to expanded form, or from expanded form to index form.

Expanded Form Index Form Expanded Form Index Form w × w × w × w × w × w 1. 5×d×d×d×d×e×e 6.

h × h × h × h × h × h × h 2. 7. 7h3k

3. g4 5k × 6k 8.

g × g × g × g × g × g × g × g × g × g × g × g

4. 4 × d × d × 3 × e × e × e × e × e

9.

5. a3b4 ½ × m × 8 × n × n × n × n 10.

C: Multiplying Simplify, using the index rule for multiplication, (add indices). 1. a3 × a4 = ........................ 2. b7 × b3 = ........................ 3. g5 × g = ........................ 4. y5 × y4 = ........................ 5. c3 × c8 = ........................ 6. k7 × k2 = ........................ 7. 5d × d 4 = ........................ 8. e2 × 4e 7 = ........................ 9. 5p2 × p4 = ........................ 10. 3g × 7g4 = ........................ 11. 5h7 × 4h6 = ........................ 12. 7k3 × 6k5 = ........................ 13. u5v4 × u7v3 = ........................ 14. a6b2 × a5b = ........................ 15. 2v5u3 × 6vu9 = ........................ 16. 9s2r7 × 2s7r3 = ........................ 17. 4y3v2 × 6y9v4 = ........................

E: Exponents Simplify, 1. (x6)2 = ........................ 2. (3x4)2 = ........................ 3. (5x8)3 = ........................ 4. (3a2b6)4 = ........................ 5. 3a (a2)4 = ........................

F: Mixed problems Match each question with the simplified answers below. 1. (2x3)4 = ........................ 2. (4x3)2 = ........................ 3. (5x7)3 = ........................ 4. 5x8 × 6x4 = ........................ 5. 4x3 × 7x9 = ........................

Answers (not in order) 108x13, 7x5, 36x6, 16x12, 4x3, 12x12, 16x6, 40x7, ½x4, 28x12, 125x21, 30x12

D: Dividing Simplify, using the index rule for division, (subtract indices).

x×x×x×x×x x×x×x

y×y×y×y×y×y y×y×y×y×y

= ..................

= ..................

1.

A8

2.

= .................. 18x

6 3.

= .................. 14d

14d 4.

= .................. 18s2

6s 5.

= .................. 10r5

5r3 6.

= .................. 24w7u5

6w3u5 8.

= .................. 4s3k7

16s8k4 9.

= .................. 40a10b5c7

8a4b8c 10.

= .................. 10r8

20r4 7.

= .................. 42x9

6x4 6.

7. 20x7 ÷ 5x4 = ........................ 8. 6x5 ÷ 12x = ........................ 9. 3(2x6)2 = ........................ 10. 4(3x3)2 = ........................ 11. 5x(2x2)3 = ........................ 12. 4x(3x4)3 = ........................

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A: 10 Quick Questions 1. 63 ÷ 7 + –9 =........................... 2. Find 5/6 of $36 ................. 3.

4. Find the missing side of a rectangle if the base is 12 cm and the area 60cm2 ............................ 5. Convert 8% to a fraction (simplify) ............................ 6. 43 - 7 × 6 = ............................ 7. –8 + 9 – –9 = ............................ 8. How many years in ten decades? ............................ 9. Convert 840cm to metres ............................ 10. Round off 5.159 to 1 d.p. ............................

Find the area .........................

14cm

20cm

C: Unknowns both sides Solve these equations, and show your working.

1. 5x + 5 = 2x + 20 .................................................. .................................................. 2. 7x + 12 = 3x + 40 .................................................. .................................................. 3. 2x + 17 = 9x + 2 .................................................. .................................................. 4. 7x – 6 = 4x + 25 .................................................. .................................................. 5. 3x + 8 = 9x – 19 .................................................. ..................................................

D: Equations involving fractions

Solve these equations and show your working.

E: Rearranging formulae Change the subject of each formula by rearranging these equations.

1. If A = bh, what does b = ....................................... ?

2. If A = ½bh, what does h = ....................................... ?

3. If A = ½(a + b)h, what does a = ....................................... ?

4. If A = r2, what does r = ....................................... ? 5. If , what does b = ...........................….......... ?

F: Word problems 1. Part of a fence is a right-angled triangular shape. Rearrange the formula. Area = ½ base × height (A = ½bh) so that

h = .......................................... 2. The area of this fence is 22.5m2, If b =7.5m, what is the height (h) of the fence? .............................................

3. Barry has to design a rectangular box. Rearrange the formula (V = bhd) Volume = base × height × depth so that

d = .......................................... 4. The volume of a box is 90cm3. If b = 5cm and h = 6cm, what is the depth (d) of this box? ..................................................

B: Equations with brackets

Solve these equations, and show your working. 1. 3(x + 4) = 27 .................................................. .................................................. 2. 5(x – 4) = 65 .................................................. .................................................. 3. 3(2x + 3) = 37 .................................................. .................................................. 4. 4(3x – 5) = 34 .................................................. .................................................. 5. 6(x + 7) = 8 .................................................. ..................................................

1.

..............................

..............................

..............................

A6 / A10

= 4 x + 9

5 2.

..............................

..............................

..............................

= 7 x – 4

3

3.

..............................

..............................

..............................

= 5 2x + 8

8 4.

..............................

..............................

..............................

= 6 5x – 3

7

5.

..............................................

..............................................

..............................................

..............................................

= 12 2(x + 5)

3

a + b c

p =

b

h A

b

h d

V

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A: 10 Quick Questions 1. 40 ÷ 8 –6 = .......................... 2. Solve 3x + 5 = 23 x = ................................ 3. Find the missing angle () = .................... 4. Calculate the area of a square that has sides of 9.5cm ............................ 5. Simplify 7x + 6x ............................ 6. Round off 9.052 to 1 d.p. ............................ 7. How many minutes in 4.25 hours? ............................ 8. Convert 2056m to km ............................ 9. $5.49 × 13 = .......................... 10. 0.64 × 1.5 + 18 = ...................

D: What type of data? State if the data is discrete or continuous.

1. Number of students in your class. ............................ 2. The population of New Zealand. ............................ 3. Weight of metal used to build a bicycle. ...................... 4. Money earned in one day by a pupil. ............................ 5. Volume of water in a cup. ............................ 6. Age of students in your class. ............................ 7. The height of trees in a park. ............................ 8. The number of people at a rugby match. ....................... 9. The weight of apples on a tree. ............................

41o

S2 / S4

B: Types of data / frequency tables There are two types of data that can be collected, discrete data and continuous data. Complete these sentences using these words. 1. Data that is obtained by counting is called ............................................................ data. 2. Data that is obtained by measuring is called ............................................................ data. In a Year 9 assessment, grades of 1 to 5 were awarded as shown in this table. Grade 5 is the highest. 3. Organise this data in the frequency table below. Grades Tally F

1

2

3

4

5

2, 4, 2, 3, 5, 4, 2, 3, 4, 4, 5, 3, 2, 5, 4, 5, 3, 1, 4, 3, 4, 3, 1, 4, 2, 4, 5, 2, 1, 5, 4, 4, 3, 4, 5, 2, 5, 4, 2, 1, 5, 4, 5, 3, 4, 3, 5, 4, 5, 3, 5, 1, 5, 4, 4, 1, 3, 2, 4, 3, 1, 4, 5 5, 3, 4, 3, 1, 3, 4, 3, 3 1, 2, 4, 5, 3, 4, 2, 3, 5

Assessment Grades

4. What was the most common grade? .......................

5. How many pupils gained a grade 3 or better? ....................... 6. How many Year 9 students sat the assessment? .......................

C: More frequency tables Continuous data can be organised using a frequency table divided into class intervals.

Native plant seedlings were measured (cm) after 1 year’s growth. The results are displayed in this table.

Height of seedlings (cm)

Tally

F

1 -

5 -

10 -

15 +

5.3, 11.6, 4.9, 13.4, 16.1, 6.9, 14.8, 13.4, 18.4, 11.7, 4.7, 7.2, 8.4, 13.7, 16.4,

19.7, 14.3, 8.9, 7.8, 12.6, 17.0, 9.2, 6.7, 14.3, 15.4, 7.9, 17.8, 7.0, 3.9, 17.1,

13.7, 6.3, 7.9, 14.7, 15.7, 19.4, 11.9, 17.3, 14.7, 8.4, 13.5, 9.1, 15.7, 11.3, 14.1

1. Organise the data into the frequency table. 2. What is the most common class interval? ......................... 3. How many seedlings are discarded, if seedlings less than 5cm are thrown away? ..................... 4. If seedlings 10cm or taller are replanted outside, how many seedlings will be replanted outside? ..................... 5. How many seedlings were measured? .....................

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Describe the ‘average’ pupil based on the height calculation and on the results from these frequency tables.

1. Find the average height (add up all heights, then divide by 14) .........................................… 2. Complete the frequency tables for the other features.

A: 10 Quick Questions 1. 35 ÷ 5 + 7 × 8 = ................... 2 24 × $0.75 = ........................ 3. 4525 mL = ......................... L 4. Convert 0.44 to a fraction (simplify) ........................ 5. How many days in 6½ weeks? ............................ 6. Estimate the answer (do not calculate) 4.9 × 9.9 + 20.3 = ................. 7. Name this shape ............................ 8. Divide $72 in a ratio of 4 : 5 ............. : ........... 9. Simpilify 3x + 6x ............................ 10. Solve 7x – 3 = 22 x = ...........................

B: Find the ‘average’ person ?

The table contains data collected from a survey of Kiri’s class. From this data, your task is to work out the ‘average’ of each feature listed, and then describe the ‘average’ person.

Height (m)

Body Type

Eye Colour

Hair Colour

Shoe Size

1.53 slim brown black 7

1.48 solid blue blonde 5

1.63 slim brown black 6

1.65 medium grey brown 7

1.52 solid brown black 5

1.33 slim grey blonde 4

1.69 solid brown brown 9

1.74 medium blue blonde 10

1.31 medium blue brown 7

1.63 medium hazel brown 8

1.59 solid brown black 8

1.54 slim grey brown 7

1.48 medium hazel black 7

1.69 slim blue brown 8

Eye colour Tally F brown blue hazel grey

Body type Tally F slim

medium solid

Hair colour Tally F black

blonde brown

C: Walk, bicycle, bus, car ?

Andrew walks to school, as do most of his friends, as they live close to the school. Conduct a survey in your class, or of 20 to 30 pupils at your school, as to the way pupils travel to school. Use the table below to help collect the data.

Tally F Walk

Bicycle Bus Car

Other

D: Dogs or cats ? Rangi thinks that cats are the most liked pets, compared to dogs. Is he right ?

Survey at least 30 people as to whether they like dogs, cats, neither or both as pets.

Was Rangi right with his guess ? ............................

Shoe size 4 5 6 7 8 9 10 Tally F

3. ...................................................................................................................... ...................................................................................................................... ......................................................................................................................

S1 / S2 / S3

Tally F

Dogs

Cats

Neither

Both What is the most common way that pupils travel to

school? ...........................................

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E: Word problems 1. During the past week, Rangi has been shearing the following number of sheep each day, 65, 71, 58, 82, 80, 72, 76. Find the average number of sheep shorn each day. ..........................................

A: 10 Quick Questions 1. 0.9 × 8 –4 = ......................... 2. Solve 7x + 11 = 35 x = ................................ 3. Find the missing angle () = .................... 4. Find the perimeter of this square () = .................... 5. Simplify 8x + 4x – 10x ............................ 6. Round off 5.965 to 2 d.p. ............................ 7. How many minutes in 3¾ hours? ............................ 8. Convert 4726mm to metres ............................ 9. $10.60 × ¼ = .......................... 10. 1.4 + 5.9 × 1.3 = .....................

9.7 cm

71o

B: Which average is that? Fill in the gaps with one of the words below. (use one word twice) 1. The .......................... is commonly known as the average. It is worked out using the formula below. 2. The .......................... is the middle data value, once the data values are in order from smallest to biggest. 3. The most common score is called the .......................... There may be more than one, or none at all.

.............................. = Sum of all the data Number of items of data

median mode mean

C: Finding averages Calculate the mean(A), median(B) and mode(C) for the scores below. 1. 8, 10, 13, 13, 16 A = ............ B = ............ C= ............. 2. 6, 10, 14, 16, 21, 23 A = ............ B = ............ C= ............. 3. 2, 3, 5, 6, 4, 2, 4 A = ............ B = ............ C= ............. 4. 4, 7, 9, 10, 10, 6, 8, 10, 8, 2, 2 A = ............ B = ............ C= ............. 5. 3, 4, 4, 7, 5, 10, 13, 16, 16 A = ............ B = ............ C= .............

D: Which average ? Choose which average is best to use, Mean, Median or Mode for the following situations. 1. A shop keeper wishes to know which size shoe he sells the most of. ................ 2. Peter wishes to know what his average mark for his class tests was. ................... 3. The class is to be split into two groups based on their ability using their marks in a test ............................ 4. A golfer played 10 rounds of golf and wants to work out what he can expect to score next time he plays.

...................................

Pass

8. What must he score in his final test, if he is to average 50 % in all 6 tests, as required to pass? .........................................................

2. The bottom half of the field in a golf match is to be dropped before the final round. What is the ‘cut- off’ score, if the following scores were recorded? 64, 68, 69, 70, 72, 74, 74, 75, 75, 76 ............................ 3. What was the most common score for this round of golf? .....................................

4. 5 cars at an auction sold for $87500 altogether. What is the average price of each car? ........................... 5. A sixth car sold for $22300, what is the new average price of the 6 cars? .............................................. 6. 12 cars were sold with an average price of $14250. What was the total value of all cars sold? .......................................

7. Kelly must average 50% in all his class tests to pass Maths this year. If he has scored 55, 60, 43, 37 and 45 % in 5 tests, what is his average so far? ................................................................

S3

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D: Drawing box and whisker graphs A box and whisker graph is so called because of its shape.


C: Calculating the range, median and quartiles

For each list of scores find the range, LQ, median and UQ, and fill in the table with your answers.

1. 4, 6, 6, 6, 7, 9, 9, 10, 16 2. 2, 3, 6, 7, 8, 12, 15, 18, 20 3. 5, 6, 7, 8, 8, 9, 19, 20 ,21, 25 4. 12, 8, 7, 10, 12, 1, 5

A: 10 Quick Questions 1. Find 30% of $75.00 ............................ 2 16 × $0.85 = ......................... 3. Find the missing angle () = .............. 4. Convert 48% to a fraction (simplify) ............................ 5. Write 870000 in standard form ............................ 6. Round off 7830 to 2 s.f. ............................ 7. Draw in the lines of symmetry on this shape

8. Find the next 3 numbers 3, 6, 12, .........., .........., .......... 9. Express 13 as a % of 52 ............................ 10. Solve 5x + 7 = 41 x = ................................

49o

B: Range / quartiles A list of scores can be divided into quartiles and its range calculated. From the words below, fill in the spaces, for the scores as marked.

6. Find the range of the scores listed above. .......................................

1 3 4 8 9 9 14 15 17 21 23

3. ......................................... 4. .........................................

1. .......................................... 2. .........................................

5. .........................................

median highest score upper quartile (UQ) lowest score lower quartile (LQ)

Range LQ Median UQ

1.

2.

3.

4.

5.

5. 2, 6, 12, 1, 8, 17, 9, 8, 10, 1

2. Circle the LQ, median and UQ for the two class tests listed below. Then draw two box and whisker graphs,on the same graph in the space provided.

Scores

Test A Test B 0

10

20 Class Test Results

3. Calculate the range for each test. A = ........... B = ...........

Scores UQ = ........

highest score = ............

lowest score = ............

LQ = ..........

median = .........

0

20

10

S3 / S5

1. The graph below shows the results of a class test, as they might appear using a box and whisker graph. Read off the various scores.

1, 2, 3, 4, 4, 5, 8, 9, 11, 13, 16

4, 5, 7, 8, 9, 13, 15, 16, 17, 18, 19

Test A

Test B

4. Calculate the mean for each test. A = ............ B = ............. 5. Comment on the test results. .............................................................. .....................................................................................................................

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A: 10 Quick Questions 1. Find ¼ of $64 ...................... 2. List the first 4 multiples of 13 ........................... 3. Find the missing side ()

C: Creating a column graph The frequency table shows the number of pupils in Mark’s class who were away from school during one week.

Days away 1 2 3 4 5 No. of pupils (f) 5 3 4 0 2

D: More column graphs In an assessment for Year 10, the following grades were given.

Grades 1 2 3 4 5 Tally

f

Find three things in the above graph, which make it misleading. 1. .................................................. .................................................. 2. .................................................. .................................................. 3. ..................................................

Comment on this statement. More road accidents occur on sunny days than wet days. Therefore it is safer to drive on wet roads. 4. .................................................. .................................................. ..................................................

Perimeter = 34cm

12cm = ...................

B: Column graphs Graph 1 shows the number of children in each family, for the pupils in Rebecca’s class. 1. How many families have 3 children only? ....................................... 2. How many families have at least 2 children? ...............

3. How many families have more than 3 children? ............................ 4. How many pupils have no brothers or sisters? ............................

Number of children 1 2 3 4 5 6

f

2

4

Graph 1

E: Misleading graph

f

B C 50

100

150

A

S4

1. Use the tally chart to complete the frequency table. 2. Draw a column graph for this data. 3. How many pupils scored a grade 3? ................................ 4. Which grade did 15 pupils score? ................................ 5. Pupils who scored a grade 2 or less have to redo the assessment. How many pupils redo the assessment? ..................... 6. If there are two Year 10 classes of equal size, how many pupils in each class? ...........................

Draw a column graph to illustrate this data. (Label each axis clearly)

2, 4, 2, 3, 5, 4, 2, 3, 4, 2, 5, 3, 2, 5, 4, 5, 3, 1, 5, 3, 4, 3, 1, 4, 2, 4, 5, 2, 1, 5, 4, 3, 3, 4, 5, 2, 5, 4, 2, 1, 5, 4, 1, 3, 4, 3, 5, 4, 1, 3, 5, 1,

1, 5, 5, 4, 1, 3, 2, 4, 3, 1, 4, 5

Assessment Grades

Family Size

4. The area of a triangle is 14cm2. If the base is 4cm, what is the height? ...................................... 5. Convert 0.8 to a fraction (simplify) ........................... 6. 23 - 8 × 3 = ........................... 7. –2 + 8 – –9 = ........................... 8. How many sides does a decagon have ? .................... 9. 6532m = ......................km 10. 0.56 × 5.2 + 8.3 = .................

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B: Histograms This graph shows the time taken by runners in the school cross-country race. 1. How many took 20 to 22 minutes ? ................................. 2. How many took longer than 24 minutes ? .............................. 3. How many took less than 16 minutes ? ................................. 4. How many ran the race ? ................................. 5. All runners faster than 18 minutes will run in an interschool race. How many will this be ? .................................


2. Draw the histogram to display this data, labelling your graph. 3. What is the most common group for grass length? ....................... 4. How many grass blades were less than 25mm long? ...................... 5. How many grass blades were 15mm or more long? ................... 6. How many blades of grass were cut and measured? ......................

A: 10 Quick Questions 1. 36 ÷ 9 + –4 = ......................... 2. Solve 5x + 9 = 31 x = ............................ 3. Find the missing angle () = ............................ 4. Find the area of this square () = ................ 5. Simplify 2x + 7x – 10x ............................ 6. Round off 8.27 to 1 d.p. ............................ 7. How many hours in 4.25 days? ............................ 8. Convert 735 metres to km ............................ 9. $8.45 × 13 = ......................... 10. 0.65 × 4.7 + 14 = ...................

47o

2.5mm

5

10

f

C: Creating a histogram The frequency table shows the length of time Shane spent playing a computer game.

Time (minutes) 0 – 1 - 2 - 3 - 4 - 5

F 6 7 5 3 4

1. Use the tally chart below to organise into class intervals.

Length (mm) 10 - 15 - 20 - 25 +

Tally

F

Find four things in the above graph, which make it misleading. 1. .................................................. .................................................. 2. .................................................. .................................................. 3. .................................................. .................................................. 4. .................................................. ..................................................

D: Creating a histogram During a science experiment Miri cut and measured (mm) blades of grass, recording these results.

E: Misleading graph

50

100

200

S4

School X-Country Times

Time (minutes) 14 16 18 20 22 24 26

Draw a histogram to illustrate this data. Remember to label your graph.

19, 12, 16, 11, 18, 21, 25, 28, 24, 14, 23, 27, 21, 16, 26, 10, 15, 18, 17, 24, 12, 26, 18, 23, 17, 11, 15, 16, 22, 12, 18, 28, 24, 17, 16, 14

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1. On what day did Kiri start training? ................. 2. How long did this first run take? ................ 3. How often does she record her time? ...................................... 4. How long did it take her to run the circuit on June 18th? ...................................... 5. On which day did her run take 21 minutes? ....................................... 6. How much faster was she on the 24th of June run, than on her first run of the 12th of June? ...................................... 7. Calculate the average (mean) time for her runs. ..................................................


B: Pictographs The pictograph shows what people thought of a movie, = liked the movie, = the movie was OK, = disliked the movie. 1. How many people liked the movie ? ............................ 2 How many people watched the movie ? ............................ 3. What fraction thought the movie was OK ? ............................ 4. What percentage liked the movie ? ............................

A: 10 Quick Questions 1. What is the area of a square with sides of 4.5cm? ............................ 2. How many kilolitres is 4350 litres? ......................... 3. Find 40% of 420mL ............................ 4. How many minutes in 5.25 hours? ............................ 5. 17 × -9 = ............................ 6. 72 + 625 = ............................ 7. 17.3 + 6.3 × 3.7 = .................. 8. 16.8 ÷ 1.2 = ............................ 9. Divide $96.00 in a ratio of 5 : 7 ............................ 10. If 7x + 9 = 34, find what x = ............................

Each picture = 5 people

Clothes $$$$$

Food $$$

C.D.’s $$$$

Savings

Key: $ = $4.00

D: Dot plots Glen plotted his scores for the ‘10 Quick Questions’ he did each maths period for one week. 1. What was his highest score? .................................

Mon Fri 0

5

10

Sco res

E: % bar graphs James worked out how he spends his time during the day, as follows ...

C: Time series graphs Kiri began training for the school cross-country race. She recorded her times (t = minutes) for a 5km circuit she was running daily, as shown in this line graph.

21

20

Time

June

12th 17th 22nd

2. What was his most common score? .................. 3. What was the average (mean) score for the week? ..................................................

Shade in the bar graph below to show this data. Remember to label your graph and draw a key.

40% Sleeping 25% School 15% T.V. 10% Homework 10% Other

S4

Shanna has $60.00. She spends some of her money as shown in the pictogram. 5. How much has she spent on clothes ................., food ................. and C.D.’s .................? 6. Complete the savings part of the pictogram.

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A: 10 Quick Questions 1. 267 + = 148 Find ............................ 2. How many metres in 4.65 kilometres? ......................... 3. 9 × -12 = ............................ 4. How many millilitres in 3.75 litres? ............................ 5. 1.9 × 0.8 = ............................ 6. How many seconds in 9.5 minutes? ............................ 7. $6.74 × 9 = ............................ 8. 0.96 ÷ 1.2 = ............................ 9. Name this shape ............................ 10. A square has an area of 49m2. What is the perimeter? ............................

C: Pie graph calculations

The DAISY VALLEY HIGH SCHOOL has a roll of 200 students, as follows.

Y9 Y10 Y11 Y12 Y13

50 50 45 30 25

D: Creating pie graphs Cory believes that ‘white cars are the most popular’, so he conducted a survey outside the school gate, collecting the following data, to see if he was right.

B: Pie graphs 1. Five boys and three girls are going to share equally an apple pie. Shade in the pie to show how much of it was eaten by the girls. Brent drew a pie graph to show what he did with $72.00.

APPLE

PIE

1. Complete the frequency column of this frequency table. 2. How many cars did he count? ...................................... 3. Write each colour as a fraction of the total number of cars.

4. Calculate the angle of each pie graph sector, for each colour.

7. Based on his results, Cory says ‘white cars’ are the most popular in N.Z.!’ Is he correct in saying this? ......................................................................................................................

5. Draw the sectors of the pie graph. 6. Shade the graph, and fill in the key below: black blue red white other

black = ............... blue = ..............

red = ............... white = ..............

other = ...............

Colour Tally f black IIII IIII IIII III 18 blue IIII IIII IIII IIII red IIII IIII II

white IIII IIII IIII IIII IIII other IIII IIII IIII I

Total

black = .............................................

blue = .............................................

red = .............................................

white = .............................................

other = .............................................

S4 / S8

Write each Year Group as a fraction of the whole school. Example: Year 9 50/200

1. Y10 = ............. Y11 = ..............

Y12 = ............. Y13 = ..............

Calculate the angle for each of a pie graph needed to display this data. Example: Year 9

50/200 × 360o = 90o

2. Y10 = ............o Y11 = ............o

Y12 = ............o Y13 = ............o

3. What do all the 5 angles for the pie graph add up to? ............................

2. How many sectors is the graph divided into? .................... and each sector = $ ..................... 3. What fraction did he save (S)? ........................ 4. What fraction did he spend on clothes (C)? ........................ 5. How much did he spend on clothes .................... and model aeroplanes (M)? ............................ 6. How much did he save? ............................

C S

M

What Brent did with $72.00

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10m

6m

3 4 5 6

3, 3, 7, 8 4, 5, 7, 8, 9, 9 1, 3, 3, 4, 7 4, 5, 5, 6


A: 10 Quick Questions 1. Find 120% of $60.00 ............................ 2 24 × $0.56 = ........................ 3. Find the value of x x = ................ 4. Convert 7/8 to a percentage ............................ 5. Write 0.0007 in standard form ............................ 6. Round off 7420 to 2 s.f. ............................ 7. Find the area of this shape area = ............... 8. 7 × 8 – 54 ÷ 9 = ..................... 9. 0.476km = ................ metres 10. Solve 3x + 11 = 54 x = ................................

42o 2x

C: Scatter graphs The scatter graph shows the results of 8 pupils who sat both an English (E) and a Maths (M) test, both marked out of 10.

10 5

10

5

M A T H S

ENGLISH

E 4 M 4

D: Scatter graphs 1. Plot this table of data on the graph, as a scatter graph.

A 1 2 3 3 4 4 5 5 6 6

B 1 3 2 4 5 6 6 7 7 9

B

10

A 5 0

stem leaf

Barley Plot A 43, 34, 28, 52, 23, 36, 39, 24, 44,

53, 39, 32, 42, 27, 40, 27, 25

Barley Plot B 52, 35, 29, 50, 45, 42, 32, 36, 42,

53, 47, 41, 42, 59, 37, 41, 37

Sarah was conducting a science experiment involving playing music to barley plants, to see if it affects their growth. The length of the barley grass, measured in millimetres is shown below..

B: Stem and leaf graphs Stem and leaf graphs are so called because of their shape. Example:

2. Draw a back-to-back stem and leaf graph of the results. [Music played only to Barley Plot B]

3. Do Sarah’s results prove anything? Complete the table opposite to help prove if the music has improved the barley plants growth. Comment on the results.

Plot A Plot B

Range

Median

Mean

S3 / S5

1. Complete the table below for the 8 pupils where E = English & M = Maths.

2. How many pupils scored above 7 in the English test and above 6 in the Maths test? ................

1. Complete the set of numbers that this stem and leaf graph represents. 33, 33, 37, ........., ........., ........., ........., ........., ........., ........., ........., ........., ........., ........., ........., ........., ........., ........., .........

2. Does there seem to be a relationship between A and B ? .............................. 3. Why ? ...................................................... ....................................................................

................................................................................................................... ...................................................................................................................

........................................................ .... ........................................................

........................................................ .... ........................................................

........................................................ .... ........................................................

........................................................ .... ........................................................

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A: 10 Quick Questions 1. 35 ÷ 5 + 4 × 7 = ................... 2 31 × $0.36 = ......................... 3. 589mL = ...................... litres 4. Convert 5/8 to a decimal ............................ 5. How many weeks in 66½ days? ............................ 6. Estimate the answer (do not calculate) 9.7 × 5.2 + 4.9 = .................... 7. Name this shape ............................ 8. Divide $24 in a ratio of 3 : 1 : 4 ............................ 9. Simplify 6y – 8y + 3y ............................ 10. Solve ½z – 7 = 9 z = ................................

B: Definitions Complete these definitions by using the words listed below. 1. The rolling of a die, the drawing of a card, etc are called ................................................................................. 2. The result of an experiment is called an ........................... 3. The list of all possible outcomes of an experiment is called the ......................... ......................... . 4. Part of the sample space is called an ................................................

event sample space experiments outcome

C: Listing outcomes 1. If a 6-sided die and a coin are tossed, list all possible outcomes. .................................................. .................................................. 2. A bag contains some red, white and pink jelly beans. If two jelly beans are drawn out, list all possible outcomes. .................................................. ..................................................3. Karen has a part-time job she can do on any 2 school days of the week, but which 2 days? List all possible outcomes. .................................................. .................................................. .................................................. .................................................. ..................................................

D: Finding relative frequencies / probabilities Relative frequency = Experimental Probability (Long-run exp.)

1. A coin is thrown 60 times and heads occurs 32 times. What is the relative frequency of a head occurring? ............................ 2. A die is thrown 200 times and the results are recorded in this table. State the relative frequency of each number occurring.

1 = .......... 2 = ......... 3 = ......... 4 = .......... 5 = ......... 6 = .........

A box of Lego contains the following number of coloured blocks.

Die 1 2 3 4 5 6 f 38 37 28 27 36 34

Relative frequency = Number of times the given event has occurred

Number of trials in the experiment

S9 / S10 / S11

Toss a coin at least 50 times and record your results in this table. 7. Calculate the relative frequency for both heads and tails. 8. Using your answer for the relative frequency for heads in question 3, calculate how many heads could turn up if the coin was tossed 1000 times. ........................................................................

red blue black white green 48 32 64 16 40

3. How many blocks are in the box? ..............................

4. If a block is selected from the box, calculate the relative frequency of selecting each colour of block. red = ................ blue = ............... black = ................ white = ................ green = ................ 5. If the relative frequency of selecting a block is 0.32, which block was selected? ......................................... 6. If the relative frequency of selecting a block is 8%, which block was selected? ...........................................

Tally F Relative Frequency

H T

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Theoretical Probability = Number of ways the event can occur

Number of all possible outcomes

C: What chance ? At a fair, a target was coloured as below for an archery competition. 1. Calculate the chance of hitting each of the coloured rectangles.

D: Tree diagrams Fred has a box of marbles which contains, 6 white, 2 black and 4 yellow. 1. If he draws one marble from the box, find the probability that it is white ..................., black ..................., or yellow .................... . 2. If he replaces the first marble and draws a second marble, have the probabilities for drawing each colour changed ? .......... 3. Fred now draws two marbles, the first being replaced before the second is drawn. Enter the probability values for each colour on the tree diagram. White has been done for you. 4. List all the possible outcomes for two marbles being drawn. (Use W = white, B = black, Y = yellow), Eg: (W,W)

A: 10 Quick Questions 1. 54 ÷ 9 + –7 = .......................... 2. Solve 3x + 9 = 23 x = ................................ 3. What do the interior angles of a pentagon add up to? ............................ 4. Find the volume of a cube with sides of 7cm ............................ 5. Simplify 9x + 3y – 7x ............................ 6. Round off 0.242 to 1 d.p. ............................ 7. How many hours in 2 weeks? ............................ 8. Convert 0.275km to m ............................ 9. $8.75 × 14 = .......................... 10. 7.93 – 5.1 × 1.7 = ...................

= ................ = ..............

= ................ = ..............

.......................................................................... .......................................................................... ..........................................................................5. How many total outcomes are there? ............................... Find the following probabilities. 6. P(white, white) ............................. 7. P(black, black) ............................. 8. P(yellow, yellow) ............................. 9. P(white, black) in that order .................. 10. P(black, yellow) in that order .................. 11. P(yellow, white) in that order .................. 12. P(white, black) in any order ...................... 13. P(yellow, white) in any order .................... 14. P(black, yellow) in any order .................... 15. If the first marble is black and is not replaced, what will be the new probability value of drawing a second black marble? ........................................

1. the number 4 ................... 2. an odd number ................... 3. a factor of 6 ................... 4. the number 7 ................... 5. a number greater than 4 ................................................................

6. a red card ................... 7. a seven ................... 8. a heart ................... 9. a black ace ................... 10. a picture card ................... 11. the 7 of clubs ...................


S10 / S11 / S12

2. How many times would you expect to hit the black rectangles, if you had 75 attempts? ............................ 3. Ben hit the white 31 out of 75 attempts. Was that more then expected? ......... 4. Sam hit the black 53 out of 100 attempts. Was that more then expected? .........

A normal six-sided die is thrown. Find the probability of getting

A card is drawn from a 52 card pack. Find the probability of drawing

B: Calculating probabilities

W

B

Y

W

B

Y

W

B

Y

W

B

Y

Second Draw First Draw

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Homework / Assessment Worksheet Worksheet 1

A: 1. 1295 2. 31.5 days 3. 1205 4. 48 months 5. 3357 6. 420 seconds 7. $32.55 8. 12 9. 156 weeks 10. 27

B:

Worksheet 2

A: 1. 5382 2. 290 3. 5 4. $31.50 5. 3 sides 6. ellipse or oval 7. 6003 8. 269 9. 217 10. 100cm

B: 1. 62, 64, 66, 68, 70 2. 45, 47, 49, 51, 53, 55, 57, 59 3. 9, 18, 27, 36 4. 42, 48, 54 5. 7 multiples 6. 2, 3, 5, 7, 11, 13 7. 29, 31, 37 8. 1, 3, 5, 15 9. 1, 2, 3, 4, 6, 8, 12, 24 10. 1, 2, 4, 8, 16, 32

C: 1. 11 2. 18 3. 17 4. 65 5. 32 6. 193 7. 16 8. 60 9. 30 10. 15 11. 120 12. 100 13. 63 14. 420 15. 560 16. 69 17. 9 18. 64 19. 90 20. 49 21. 125 22. 5 23. 44 24. 12 25. 170 26. 27

D: 1. 40km 2. 30cm 3. 50 tickets 4. 100 tickets 5. $105 6. $240 7. $175 8. $125 9. $195 10. 5 tickets 11. 4 tickets 12. $15 change 13. $45 change

Worksheet 3

A: 1. 6 2. 19 3. 7 4. 4 sides 5. $13.75 6. 4500m 7. hexagon 8. 150 minutes 9. 12, 24, 36, 48 10. 1, 2, 3, 6, 9, 18

B: 1. 81 2. 196 3. 256 4. 529 5. 2500 6. 6400 7. 10000 8. 7 9. 8 10. 11 11. 12 12. 20 13. 25 14. 30

C: 1. 4.7 × 103 2. 2.9 × 104 3. 6.89 × 102 4. 9.0 × 10-3 5. 6.3 × 10-2 6. 640000 7. 26800000 8. 0.0716 9. 0.0093

D: no answer supplied

E: 1. 20 2. 70 3. 110 4. 310 5. 80 6. 140 7. 1240 8. 200 9. 200 10. 700 11. 400 12. 1100 13. 3300 14. 5300 15. 4100 F: 1. 12.4 2. 14.8 3. 34.8 4. 134.7 5. 452.5 6. 193.1 7. 415.4 8. 310.0 9. 2.46 10. 7.38 11. 13.61 12. 196.88 13. 158.15 14. 237.73 15. 300.08 16. 411.00

G: 1. 30 2. 80 3. 30 4. 100 5. 40 6. 90 7. 300 8. 430 9. 690 10. 15 11. 370 12. 1400 13. 2000 14. 6500 15. 14000

5 7 7 6 1

5 9 8 6

2 9 8 4 4

6 9 1

9 3 8 4

9 9 0 6 7

C: 1. 444 2. 258 3. 6 4. 25 5. 454 6. 338 7. 6 8. 416 9. 133 10. 116 11. 5 12. 21 13. 387 14. 1046 15. 6 16. 475

D: 1. 80 pieces of fruit 2. 92 cards 3. 564 matches 4. $28 5. $28 6. 19 white jelly beans 7. 25 red jelly beans 8. 96 blue jelly beans 9. Box A 10. 91 jelly beans 11. Box C 12. 359 jelly beans


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Worksheet 4

A: 1. 59 2. $35.88 3. 98 days 4. 3500m 5. 2900000 6. pentagon 7. 51 8. 1, 2, 3, 5, 6, 10, 30 9. 70 10. 6.3

B: 1. $7.00 2. 40kg 3. $36 4. $2.25 5. 64cm 6. 42kg 7. $15.00 8. $270 9. 9m 10. $96

C: 1. 2. 10% 3. 0.25 4. 25% 5. 0.3. 6. 7. 8. 50% 9. 0.6. 10. 66% 11. 0.75 12. D: 1. 43% 2. 16 girls 3. 14m2 4. 35kg 5. 48 cats 6. 144 cars 7. 6 pupils 8. 4 games 9. 73 pupils 10. $7.43

E: 1. 50% 2. 60% 3. 66% 4. 25% 5. 50% 6. 40% 7. 10% 8. 75% 9. 30% 10. 33%

Worksheet 5

A: 1. 9 2. $60.20 3. 840mm 4. 4250m 5. $6.50 6. (isosceles) trapezium 7. 9 8. 1, 2, 3, 4, 6, 9, 12, 18, 36 9. 9.7 10. 8

B: 1. 24 2. 200 3. 80 4. 20 5. 4 6. 80 7. 12 8. 400 9. 15 10. 30 11. 600 12. 70 13. 6 14. 13 15. 4 16. 64 17. 144 18. 400 19. 6 20. 9 21. 16

C: 1. 61.74 2. 6.797 3. 32.53 4. 1.308 5. 14.577 6. 510.512 7. 22.14 8. 148.217 9. 49.684 10. 24.05 11. 58.08 12. 11.80 13. 0.09826 14. 48.72 15. 17.36 16. 0.0741 17. 4.86 18. 30.4 19. 0.6 20. 21.15 21. 310 22. 6

D: 1. $4650 2. $52.50 3. $100 4. $45 5. $4847.50 6. $1.75 7. $78.75 8. $210 9. $90 10. $135 11. $38750 12. 9 computers, $50 13. $224.80

Worksheet 6

A: 1. 408 2. $60.75 3. 52.5 days 4. 9200m 5. 28kg 6. parallelogram 7. 4 8. 4.216 9. 0.2472 10. 144

B: 1. 8ºc 2. -3ºc 3. 13ºc 4. 1ºc 5. -11ºc 6. -11ºc 7. 13ºc 8. -10ºc 9. -12ºc 10. -9ºc

C: 1. -4 2. +13 3. -15 4. Sick 5. +13 + -15 = -2

D: 1. 15 2. 7 3. 4 4. 2 5. -3 6. 9 7. -13 8. -1 9. 6 10. -7 11. 6 12. -9 13. -13 14. -22 15. 18 16. 16 17. 14 18. 1 19. -2 20. -2 21. -7 22. 5 23. 7 24. -3 25. 8 26. -3

E: F:

8 1 6

3 5 7

4 9 2

× +2 +6 -1 +4 +8 +24 -4 -3 -6 -18 +3 +5 +10 +30 -5

× -2 -8 +9 +6 -12

-48 +54 -7 +14 +56 -63 -5 +10 +40 -45

1. 2.

÷ +2 +3 -4 +12 +6 +4 -3 +18 +9 +6 -4.5 -24 -12 -8 +6

÷ +4 -6 -12 -12 -3 +2 +1 +24 +6 -4 -2 -48 -12 +8 +4

3. 4.


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A: 1. 3.768 2. 184.2 3. 3.4m 4. 147 5. 9.6 x 105 6. cube 7. 25, 36 8. Right angled, scalene 9. 10 10. 435 minutes

B: 1. 50% 2. 25% 3. 33.3% 4. 33.3% 5. 66.6% 6. 40% 7. 80% 8. 20% 9. 2% 10. 75% 11. 75% 12. 100%

C: 1. 60% 2. 25% 3. 15% 4. 75% 5. 58%

D: 1. $49.50 2. $203,500 3. $6.30 4. $36.00 5. $14.40 & $21.60 6. $24,750

Worksheet 7

A: 1. $20.00 2. 0.3 3. 390 minutes 4. 4.7km 5. 40% 6. 5 7. 23 8. 11, 22, 33, 44 9. 0.26 10. 2.25

B: 1. 11 : 14 2. 1 : 24 3. 18 : 1 4. 15 : 13 5. 17 : 14

C: 1. 7 2. 10 3. 1 4. 7 5. 4 6. 3 7. 1 8. 7 9. 13 10. 2 11. 2 : 5 12. 7 : 3 13. 2 : 3 14. 5 : 9 15. 8 : 5 16. 5 : 3 17. 5 : 2 18. 7 : 10 19. 2 : 5 : 10 20. 1 : 3 : 7 21. 4 : 1 : 7 22. 3 : 2 : 1

D: 1. $6, $12 2. $7, $35 3. 24g, 30g 4. 200mL, 120mL 5. $21, $35, $7 6. $12, $18, $30

E: 1. 3 teachers 2. Jenny 27, Steven 21 3. 90 children 4. 15 votes 5. $80, $32, $48

F: 7 : 13

Worksheet 8

A: 1. 16.774 2. 213 3. 9 weeks 4. 570mm 5. 19 6. 100 years 7. $7.50 8. $65.45 9. 170 minutes 10. 0.49

B: 1. 5 2. 10 3. 30 4. 15 5. 21 6. 24 7. 44 8. 15 9. 30 10. 35

C: 1. 2. 3. 4. 5.

D: 1. 3/5 2. 1/2 3. 4/9 4. 2/5 5. 2/5 6. 5/11

E: 1. 2/3 2. 3/5 3. 7/9 4. 1/3 5. 2/3 6. 4/9 7. 1/5 8. 1/4 9. 2/3 10. 2/5

11. 3/7 12. 4/9 13. 3/5

F: 1. 23/5 2. 41/4 3. 51/5 4. 92/6 or 91/3 5. 95/7 6. 62/8 or 61/4 7. 78/9

8. 68/12 or 62/3 9. 24/5 10. 13/2 11. 26/7 12. 23/3 13. 23/6 14. 34/5

15. 68/9 16. 91/11

Worksheet 9


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A: 1. 3.863 2. 28.53 3. 4. 17000mL 5. XC 6. -8 7. $48.00 8. $25:$5 9. 215 minutes 10. 10 sides

B: 1. 1 2. 11/3 3. 11/2 4. 16/11 5. 12/7 6. 3/5 7. 2/3 8. 1/2 9. 1/2 10. 1/3

11. 7/12 12. 15/12 13. 13/20 14. 14/15 15. 617/20 16. 7/15 17. 17/42 18. 11/40

19. 34/5 20. 211/12 C:

1. 12/25 2. 9/25 3. 4/25 4. 3/10 5. 13/20 6. 1/20

D:

1. 2/5 2. 7/20 3. 7/7 = 1 (all of it) 4. 4/5 5. 1/5 6. 101/4 m 7. 23/4 m 8. 21/12 = 125 seconds

Worksheet 10

Worksheet 11

A: 1. $4.75 2. 11 3. 8 4. -2oC 5. 0.0345 6. 450 seconds 7. $55.90 8. 80 9. 156 weeks 10. $9.25

B: 1. all sides with the small mark on them are the same length 2. opposite sides are parallel

C: 1. square 2. rhombus 3. circle 4. rectangle 5. parallelogram 6. pentagon 7. triangle 8. octagon 9. trapezium 10. hexagon 11. quadrilateral 12. kite 13. arrowhead 14. oval 15. quadrilateral

D: 1. centimetre 2. millilitre 3. kilolitre 4. millimetre 5. metre 6. kilogram 7. gram 8. litre 9. kilometre 10. milligram

E: 1. km 2. L or kL 3. mL 4. g 5. m 6. kg 7. L 8. m 9. g 10. mm 11. mg 12. mm 13. cm or m

Worksheet 12

A: 1. 9 2. 48cm2 3. -27 4. 30 months 5. 0.0280 6. 255 seconds 7. $67.80 8. 4 9. $4.10 10. 210km

B: 1. 1000mm 2. 1kg 3. 1000mL 4. 1000kg 5. 1g 6. 1cm 7. 1000m 8. 1L 9. 1000L 10. 1km

C: 1. 90mm 2. 6km 3. 1800g 4. 400cm 5. 27cm 6. 6.3kL 7. 78cm 8. 6.5m 9. 4000kg 10. 0.032m 11. 4900mm 12. 0.855g 13. 6900kg 14. 0.425L 15. 5900mL 16. 2350mg 17. 4.25km 18. 730g 19. 627mm 20. 37cm 21. 5390mg 22. 0.305L 23. 410g 24. 937mm 25. 4.57km

D: 1. 187cm 2. 421cm 3. 130cm 4. 783cm 5. 166cm 6. 5.8kg 7. 6.348kg 8. 1.152kg 9. 2.76kg 10. 2.005kg

E: F: 1. $7.25 2. $9.45 3. $52.00 4. 57c 5. $11.95 6. $2.80 7. $1.30 8. 1.5c 9. $11.50 / kg was the better buy


8 5

9 5

7 8 5 2 3

9 5 4

6 6 5 2

5 1

7 5 2 1

4

6 3 2

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Worksheet 13

A: 1. 11 2. $20:$25 3. 1.647 4. 7250m 5. 40 6. 7.5 minutes 7. $18.90 8. 1200 9. kilolitre 10.

B: 1. 32cm 2. 44cm 3. 20cm 4. 35mm 5. 28m 6. 34mm 7. 32.6mm 8. 36cm 9. 26.1m 10. 36m

C: 1. 720m 2. 1800m 3. 4 laps 4. 227m 5. 210cm 6. 14.4m

D: 1. 64mm 2. 68cm 3. 52.8m 4. 7.26cm

Worksheet 14

A: 1. 115 2. $25:$20 3. 3.647 4. 5.5km 5. 23.8 6. 40cm 7. 15 8. -9 9. 0.1736 10. -27

B: 1. 18 squares 2. 14 squares 3. 15 squares 4. 14 squares

C: 1. 42.25cm2 2. 63mm2 3. 30cm2 4. 48m2 5. 130cm2 6. 72m2

D: 1. 468cm2 2. 540cm2

E: 1. 1.9m2 2. 7.6m2 3. 542.86mL 4. 2 tins, $26.50

F:

11 4 15

14 10 6

5 16 9

12 19 8

9 13 17

18 7 14

Worksheet 15

A: 1. 4.70 2. 26 3. 3700g 4. 180o 5. 0.0096 6. 29.64 7. 1¼ 8. 9 9. 91 weeks 10. 44cm

B: 1. 126cm2 2. 216m2 3. 85.47mm2 4. 117mm2

C: 1. 684 – 144 = 540mm2 2. 6.93 – 1.82 = 5.11cm2 3. 78 – 28 = 50cm2

D: 1. 52.5m2 2. 6.75m2 3. 714m2 4. 65560 + 32000 = 97560m2

Worksheet 16

A: 1. 119cm2 2. 6.3cm 3. 4.7 × 104 4. 162 minutes 5. 388 6. 360o 7. 91.85 8. 38 9. 11 10. 49

B: 1. centre 2. radius 3. diameter 4. circumference 5. sector 6. segment 7. arc 8. chord

C: 1. C = 55.8cm, A = 251.1cm2 2. C = 7.44m, A = 4.464m2 3. C = 31cm, A = 77.5cm2 2. C = 43.4cm, A = 151.9cm2

D: 1. 620mm2 2. 83.7cm2 3. 1.448mm2 4. 576 - 452.16 = 123.84cm2 4. 314 - 78.5 = 235.5cm2 6. Earth has a diameter of 12756km, C = 40053.84km


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Worksheet 17

A: 1. -4 2. 72 3. $7.10 4. $56:$16 5. 0.0432 6. 6250g 7. 90kg 8. 60% 9. 46 10. 0.08

B: 1. 120m2 2. 240m2 3. 15 + 60 = 75m2 4. 150m2 5. 100m2 6. 200m2 7. 590m2 8. 39.3.L 9. $727.66. 10. yes C: D: 1. A = 60m, B = 30m, C = 150m 2. 740m 3. 2960m 4. 60 rolls of wire 5. $4500 6. 740 ÷ 5 = 148 posts 7. $828.80 8. $5328.80

Worksheet 18

A: 1. 2.25cm2 2. 4.3kL 3. 360mL 4. 255 minutes 5. -96 6. 74 7. 41.76 8. 11 9. $33:$55 10. 8

B: 1. cube 2. cone 3. cylinder 4. triangular prism 5. rectangular prism 6. sphere 7. pyramid

C: 1. 129.6m3 2. 3.125m3 3. 900mm3 4. 1.74cm3

D: 1. 3.375m3 2. 216cm3 3. 15.625cm3 4. 672cm3 5. 472.5mm3 6. 1560m3 7. 1000m3 8. 274.625m3 9. 1080cm3 10. 6m 11. 4m 12. 4.5m

Worksheet 19

A: 1. 67.8cm 2. 49cm2 3. -5 4. 156 weeks 5. 85/100 = 17/20 6. 225 minutes 7. 25.58m or 2528cm 8. 325 minutes 9. 33 10. 0.00063

B: 1. 9cm 2. 6mm 3. 36m 4. 5m 5. 27m

C: 1. see diagram at right 2. 9cm 3. 10m

D: 1. 40mm 2. 57mm 3. 30mm 4. 4000m 5. 5700m 6. 3000m 7. 14700m or 14.7km 8. 18m 9. 4m 10. 75m

Worksheet 20

A: 1. 306 2. 4150m 3. -63 4. 2750mL 5. 4.14 6. 570 seconds 7. $38.25 8. 0.7 9. (isosceles) trapezium 10. 16m

B: 1. 0305 2. 1640 3. 2223 4. 0349 5. 1157 6. 0714 7. 0045 8. 2032 9. 0912 10. 1709

C: 1. 7:30 a.m. 2. 3:23 p.m. 3. 10:45 p.m. 4. 7:13 a.m. 5. 12:43 a.m. 6. 6:37 p.m. 7. 9:56 p.m. 8. 5:28 a.m. 9. 11:05 p.m. 10. 3:38 a.m.

D: 1. 5 to 8 or 0755 or 1955 2. 20 past 4 or 0420 or 1620 3. 25 to 2 or 0135 or 1335 4. 20 past 9 or 0920 or 2120 5. 5 past 8 or 0805 or 2005 6. 23 past 7 or 0723 or 1923 7. 19 to 1 or 1241 or 0041 8. 2 to 6 or 0558 or 1758

E: 1. 278 minutes or 4hrs 38 mins 2. 314 minutes or 5hrs 14 mins 3. 8:22 p.m. 4. 4km 5. 10 minutes 6. 2km 7. 20 minutes 8. 3km 9. 4.5 km/hr


13 15 29 35 19 3 9 23 25

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Worksheet 21

A: 1. $2.76 2. 18 3. 8 4. -2oC 5. 0.0224 6. 390 seconds 7. $61.20 8. 12 9. 130 weeks 10. $6.75

B: 1. straight 2. acute 3. right 4. reflex 5. obtuse

C: 1. ACB or BCA 2. ADB or BDA 3. - 4. - 5. No, because there are two angles at point B

D: 1. 150o 2. 20o 3. 325o 4. 30o 5. 125o

E: 1. 125o ± 1o 2. 34o ± 1o 3. 71o ± 1o 4. 330o ± 1o 5. 164o ± 1o 6. 30o ± 1o

Worksheet 22

A: 1. -5 2. 7200L 3. 285 seconds 4. 72cm2 5. 4/10 or 2/5 6. 2.08 7. $1.35 8. 0.3546 9. 94.5 days 10. $2.90

B: A = 2, B = 3, C = 1

C: a = 113o b = 109o c = 124o d = 129o e = 36o f = 83o g = 97o h = 54o j = 57o k = 77o m = 103o n = 62o p = 43o q = 61o r = 51o s = 129o t = 51o u = 31o v = 90o w = 137o

D: 10 acute angles

E: 1. 120o 2. 105o 3. 120o 4. 165o 5. 15o 6. 60o 7. 45o 8. 75o 9. 52.5o 10. 67.5o

Worksheet 23

A: 1. -13 2. 1.4m 3. 10800 seconds 4. 45cm2 5. 80/100 or 4/5 6. 7.2 7. $0.95 8. $36:$27 9. 180o 10. $11.85

B: 1. acute scalene 2. right angled isosceles 3. obtuse scalene 4. right angled 5. isosceles 6. equilateral

C: A = 1, B = 2

D: a = 38o b = 27o c = 31o d = 46o e = 46o f = 63o g = 60o h = 45o j = 45o k = 116o m = 96o n = 55o p = 58o q = 122o r = 50o s = 38o t = 103o u = 65o v = 73o w = 42o

E: 6 obtuse angles

Worksheet 24

A: 1. -44 2. 36.5cm 3. 48 4. 7 sides 5. 6/5 or 11/5 6. 4900 7. $11.95 8. $32:$40 9. 81m2 10. $19.20

C: 1. C 2. B 3. A

D: a = 95o b = 65o c = 71o d = 93o e = 93o f = 77o g = 77o h = 103o j = 57o k = 123o m = 57o n = 57o p = 118o q = 106o r = 62o s = 44o t = 74o u = 134o v = 46o w = 46o x = 45o y = 63o z = 72o


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Worksheet 25

A: 1. 10 2. 576cm 3. 5 4. 9000 seconds 5. 5/4 or 11/4 6. 2.3 x 105 7. $6.95 8. $7:$21:$28 9. 0.35 10. $48.00

B: 1. a = parallelogram b = isosceles trapezium c = square d = rectangle e = rhombus f = trapezium g = kite h = arrowhead i = pentagon j = hexagon k = octagon l = equilateral triangle 2.

C: Shape A B equilateral triangle 3 3

square 4 4 rectangle 2 2

parallelogram 0 2 rhombus 2 2 trapezium 0 1

isosceles trapezium 1 1 kite 1 1

arrowhead 1 1 pentagon 5 5 hexagon 6 6 octagon 8 8

Worksheet 26

A: 1. 24 2. 0.004914 3. $16:$9 4. 6.25 minutes 5. 91/4 6. 8.0 x 10-4 7. 5350L 8. y = 5 9. -5 10. 13

B: 4 sides = 360o 5 sides = 540o 6 sides = 720o 7 sides = 900o 8 sides = 1080o 9 sides = 1260o

10 sides = 1440o

C: a = 9o b = 103o c = 55o d = 90o e = 90o f = 55o g = 70o h = 110o i = 126 j = 24o k = 97o l = 84o m = 128o n = 131o o = 49o p = 82o q = 136o r = 44o s = 28o

Worksheet 27

A: 1. 44 2. 1.75m 3. 12600 sec 4. 84cm2 5. 90/100 = 9/10 6. 8.4 7. $1.35 8. $36:$45 9. 90o 10. $12.60

B: 1. centre 2. radius 3. tangent 4. right-angle 5. ABO, CBO, PQO, RQO, DEO, FEO 6. 90o 7. 25o 8. 90o

C: 1. centre 2. diameter 3. circumference 4. 90o 5. ABC, EFG, RSP, RQP 6. 90o 7. 33o

D: 1. a = 90o b = 31o c = 19o d = 90o 2. e = 90o f = 90o g = 58o h = 47o

Worksheet 28

A: 1. 34 2. 789 3. $36 4. 156 days 5. 33/4 6. 960000 7. 350m 8. y = 38 9. 16 10. 32

C: 1 & 2 check diagrams 3. 44mm ± 1mm

D: 1. NE 2. NW 3. SW 4. E 5. S 6. SE 7. 050 8. 215 9. 140 10. 300 11 to 14 see diagram

A

B

C

D


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Worksheet 29

A: 1. 9.36 2. 7.7 3. $39 4. 5230g 5. 39/7 6. 0.0048 7. 73cm 8. y = 36 9. 47 or 53 10. 64

B: 1. 25 2. 196 3. 25 4. 74 5. 9 6. 11 7. 7.64 8. 4.20 9. 7.81 10. 12.21 11. 8.94 12. 9.49

C: q = 36mm p = 20mm r = 30mm 362 = 1296 & 202 + 302 = 1300, therefore it almost fits the rule d = 42mm e = 30mm f = 30mm 422 = 1764 & 302 + 302 = 1800, therefore it almost fits the rule

D: 1. A2 = 122 + 52 , A2 = 169, A = 13cm 2. B2 = 62 + 82 , B2 = 100, B = 10cm 3. 152 = C2 + 122 , C2 = 225 - 144, C2 = 81, C = 9cm

E: 1. 2.62m, 4.34m 2. 150m 3. 360m 4. 5.81m 5. 6.87m (2 d.p.)

Worksheet 30

A: 1. 1, 3, 9, 27 2. 55 3. $50.30 4. 9400mg 5. 8 6. 4:1 7. 125cm3 8. any 2 shapes 9. 29.23 10. -27

B: AB = Adj, BC = Opp, AC = Hyp

C: Sin x = O/H Cos x = A/H Tan = O/A

D: 1. 0.6745 2. 0.8480 3. 0.2419 4. 1.5282 5. 0.9178 6. 0.2215 7. 0.1201 8. 0.6950 9. 0.4617 10. 30.0o 11. 45.0o 12. 85.0o 13. 12.5o 14. 75.0o 15. 14.5o 16. 57.3o 17. 68.2o 18. 72.9o

E: 1. Cos 39o = x/ 16, x = 12.43cm 2. Sin 39o = Y/ 16, y = 10.07cm

F: 1. Tan Q = 10/7, Tan Q = 1.428, Q = 55o 2. Tan R = 7/10, Tan Q = 0.7, Q = 35o

G: 1. Cos A = 1.5/5, A = 72.5o 2. Sin 32o = h/16, h = 8.48m 3. Sin B = 5.9/20, B = 17.16o

Worksheet 31

A: 1. 23 2. 953mm 3. 13 4. 5400 sec 5. 9/12 + 8/12 = 17/12 = 15/12 6. 9.63 x 105 7. $6.95 8. $14:$7:$35 9. 0.45 10. $120

B: check diagrams

C:


D:


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Worksheet 32

A: 1. 1, 2, 3, 4, 6, 8, 12, 24 2. -24 3. $60.00 4. 56.7cm 5. 0 6. 63% 7. 56cm 8. 2/5 9. 0.458 10. -125

C:

= 4 .2

a = -2 3

b =

-2 -4

c =

3 -2

d e

f g

D: 1. check diagram 2. 4. yes

= 8 1

A to B = 3 13

B to C = -7 10

C to D 3. 4

24

Worksheet 33

A: 1. 1, 3, 7, 21 2. 12 3. $144.00 4. 629mm 5. -3 6. 8% 7. 60cm 8. 3/5 9. 0.022 10. 256

B: C: 1. 8mm 2. 3m 3. scale factor = 2 4. 1/3

D: 1. 2.

A

A

B

B

C

C

D

D C

A'

A

B'

B

C

E:

1. Scale factor = 2 2. Scale factor = 2

3. Scale factor = ½

F: 1. 30cm 2. 8cm 3. 62.5cm 4. 6cm

Worksheet 34

A: 1. 9, 18, 27, 36 2. -20 3. $40 4. 567mm 5. -8 6. 85/100 or 17/20 7. 144cm2 8. 60% 9. 2.38 10. -216

B:

m m 1. 2.

m

m 3. 4.


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C: 1.

2.

3.

4.

D:

2.

1. image

image E: 1. 180o 2. 90o or -270o 3. 270o or -90o

object image

C

A A'

C

A'

A C

F: 1. - 2. - 3. clockwise 4. yes

Worksheet 35

A: 1. 12.39 2. 4.25 3. $63.00 4. 4200g 5. 39/8 6. 0.0037 7. 63cm 8. x = 32 9. 61, 67 10. 0.064

B: 1. translation 3. reflection 5. enlargement 6. centre 8. rotation & enlargement 9. 180o 10. rotated 90o 11. To maximise sunlight 12. Draw leaves above leaves a and b

Worksheet 36

A: 1. 12 2. 14, 28, 42, 56 3. 139o 4. 18mm2 5. 72kg 6. 9.5 7. 11/15 8. 9:37 p.m. 9. 3/6 or 1/2 10. 10.709

B: 1. 24, 48, 96 2. 4.5, 2.25, 1.125 3. 25, 32, 39 4. 5, 2, -1 5. -6, -10, -14 6. -40, 80, -160 7. multiply each new number by 2 8. divide each new number by 2 9. add 7 to each new number 10. subtract 3 from each new number 11. subtract 4 from each new number 12. multiply each new number by -2

C:

2.

4. 7.

5.3 4.6 2.7 3.4 6.1 5.7

9.9 7.3 6.1 9.5 11.8

17.2 13.4 15.6 21.3

30.6 29.0 36.9

59.6 65.9

125.5

12 9 9 7 11 9

21 18 16 18 20

39 34 34 38

73 68 72

141 140

281

pattern 4 pattern 5 1. Pattern number 1 2 3 4 5 10

Number of desks in each row 2 3 4 5 6 11 Total number of desks needed 4 7 10 13 16 31

2. 3 x number of desks in each row subtract 2 or 3x – 2 3. 8 desks 4. 9 desks & 2 left over 5. 37 desks 6. pattern 11

D:


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x

-3

-3 3

3

y


Worksheet 37

A: 1. -3 2. 16, 32, 48, 64 3. 68o 4. 56.25mm2 5. 9.5km 6. 0.27 7. 3/6 or 1/2 8. 5:46 p.m. 9. 66.6.% 10. -2.316

B: 1. 3, 7, 11, 15, 19 2. 10, 4, -2, -8 3. 2, 4, 8, 16, 32 4. 24, 12, 6, 3, 1.5 5. 3, 4, 7, 16, 43 6. 4, 8, 12, 16, 20 7. 8, 13, 18, 23, 28 8. 3, 7, 11, 15, 19 9. 5.5, 6, 6.5, 7, 7.5 10. 6, 7, 8, 9, 10

C: 1. $27.75 2. $33.05 3. $38.35 4. $43.65 5. $48.95 6. $54.25 7. 4mL 8. 4.5mL 9. 5mL 10. 5.5mL 11. 8yrs 12. 13yrs 13. $32 14. $40 15. $48 16. $56 17. $200 18. 8hrs 19. 16hrs 20. 9.5hrs 21. 11.5hrs 22. 13.75hrs 23. 15.25hrs

D: 1. add the two number above, write the answer below 2. 1 4 6 4 1

Worksheet 38

A: 1. 67 2. 1, 2, 3, 6, 7, 14, 21, 42 3. 63o 4. $30:$18 5. 1350g 6. 45.8 7. $11.60 8. 634m 9. 13 10. 46.7

B: 1. 6hrs 2. 12hrs 3. 9hrs 4. 16hrs 5. 24hrs 6. $30 7. $66 8. $87 9. $123 10. $43.50 11. $58.50 12. Total money earned (M) = 6 times the number of hours worked (H), M = 6H

C: 1. starts out neither sad nor happy then becomes happier 2. starts happy then becomes sad 3. stayed sad 4. starts sad, becomes happy and then becomes very happy 5. Hoani enjoyed the movie as he was more happy at the end of the movie than at the start 6. pulse rate has gone up 7. running around 8. pulse rate goes down 9. first half as pulse rate was higher 10.

Worksheet 39

A: 1. -5 2. 17, 34, 51, 68 3. 131o 4. 32.8mm 5. 31.6km 6. 2.362 7. 15/20 -

8/20 = 7/20 8. 3075m 9. 40% 10. -5.18

B: 1. y - axis 2. origin 3. x - axis

C: A = (1,2), B = (-1, -2), C = (-2, 1), D = (1, -2)

D: 1 to 6 check graph 7. (3, 3) 8. (-3, 3) 9. (-7, -3) 10. (2, -3) 11. (-5, -1) 12. (½, 2) 13. (-½, -4½) 14. (1, -½)

E: 1. check graph 2. parallelogram

Worksheet 40

A: 1. $15 2. $10.44 3. 49o 4. 45/100 = 9/20 5. 8.6 x 105

6. 5900 7. 8. 15, 19, 23 9. 25% 10. x = 5

B: 1 to 5 see graph 6. line D 7. line B 8. y = x + 4

C: 1. (1,3), (2,6), (3,9), (4,12) 2. (1,6), (2,7), (3,8), (4,9) 3. (1,-2), (2,0), (3,2), (4,4) 4. (2,3), (4,4), (6,5), (8,6) 5. (4,-2), (8,-1), (12,0), (16,1) 6. (4,6), (8,7), (12,8), (16,9)

A

B

C

D

E

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D: 1. 2. check graph 3. $12.50 & $15.50 4. 3 mins, 5 mins, 8 mins Time (min) 0 2 4 6 10

Cost ($) 2 5 8 11 17

Worksheet 41

A: 1. $48 2. 1, 5, 25 3. 4cm 4. 54cm2 5. 84/100 or 21/25 6. -6 7. 6 8. 9 sides 9. 6.295km 10. 5.105

B: 1. 9 2. 31 3. -1 4. -5 5. 2 6. 14 7. -21 8. 18 9. 36 10. -12 11. 98 12. 196 13. 252 14. 12 15. 45 16. -51

C: 1. $11.10 2. $325 3. 54 points 4. $710 5. 7 days 6. 27m2 7. 793.6cm2 8. 479.53cm3 542.50cm3

Worksheet 42

A: 1. 2 2. $18 3. 540o 4. 6100 5. 95/100 or 19/20 6. -8 7. 4 8. 100 9. 6.32m 10. 6.49

B: 1. 30 24 12 2. 5 4 2

C: 1. 42 red + 40 blue 2. 16 records + 22 tapes

D: 1. 15k 2. 7w 3. 7r + 4t 4. -5p 5. 3x2 + 8x 6. 14j 7. -f 8. 4h 9. 9f 10. 10g 11. 5a + b 12. 3c + 5d 13. 4g + 2e - 5f 14. 13k - 4g 15. 2h 16. -k 17. 19d + 2g 18. 7y + 16x 19. 6r + 10s 20. 9x2 + 4x 21. 7h - 5g + 4f + 3 22. 14h - 3g 23. 3x + 17y 24. 12r - 2s

E: 1. 8ab + 11cd 2. 7xy + 4x + 7y 3. 4y - 5xy 4. 10x2 - 2x 5. 11x2 + 2x + 4xy + y 6. 6x + 4xy 7. 11x2 + 3y 8. 2x + 8xy - 2y2

Worksheet 43

A: 1. 1 2. $12 3. -6, -10, -14 4. 0.027 5. 60/100 or 3/5 6. -21 7. -1 8. 10 9. 7.856L 10. 0.57

B: 1. 7 + x 2. x - 9 3. 2x 4. 4x + 8 5. 14 - x 6. x + 16 7. 20x 8. 9x + 10

C: 1. x + 7 = 13 2. x - 12 = 9 3. 2x + 3 = 17 4. ½x = 11 5. 8x = 56

D: 1. 5 2. 3 3. 7 4. 24 5. 11 6. 37 7. 4 8. 10 9. 5 10. 24

E:

1. 22/7 2. 102/3 3. 81/2 4. 21/7 5. 102/5

F: 1. 5p + 27.50 = 100, $14.50 2. 6m - 7 = 23, $5.00 3. ½m + 29 = 50, $42.00 4. ¼m + 12 = 16, $16.00

Worksheet 44

A: 1. 16 2. 1.5, 3.0, 4.5, 6.0 3. 66o 4. 36.7mm 5. 288kg 6. 1.35 7. 5 8. 3:37 p.m. 9. $30:$18 10. 7.675

B: 1. 10 + 20 + 5 2. 32 + 40 + 56 = 8(4 + 5 + 7)

C: 1. 4x + 28 2. 3x - 12 3. 8x + 40 4. 4x - 28 5. 18x + 42 6. 35x - 63 7. 16x + 72 8. x2 + 8x 9. 4x2 + 3x 10. 2x2 + 18x

D: 1. 4(x + 3) 2. 8(x + 3) 3. 3(4x - 5) 4. 7(2x + 5) 5. 3x(x + 5) 6. 5(x - 6) 7. 6x(3x - 1) 8. 24(x - 2)

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9. 5(x2 + 4) 10. 4x(2x - 5)

E:

1. 2x + 8 + 3x + 9 = 5x + 17 2. 5a + 10 + 7a + 21 = 12a + 31 3. 3k + 18 + 2k - 8 = 5k + 10 4. 5h - 20 + 7h + 42 = 12h + 22 5. 7x - 21 + 4x - 24 = 11x - 45

F: 1. Day 1 = x2 Day 2 = 5x Day 3 = 4x 2. x2 + 5x + 4x 3. x(x + 9) 4. Day 1 = 6.25m2 Day 2 = 12.5m2 Day 3 = 10m2 5. 28.75m2

Worksheet 45

A: 1. $26 2. $12.18 3. 24m 4. 78/100 = 39/50 5. 8.2 x 104 6. 11000 7. 8. 13, 19, 25 9. 50% 10. $18:$6:$12

B: 1. w6 2. h6 3. gxgxgxg 4. g12 5. axaxaxbxbxbxb 6. 5d4e2 7. 7xhxhxhxk 8. 30k2 9. 12d2e5 10. 4mn4

C: 1. a7 2. b10 3. g6 4. y9 5. c11 6. k9 7. 5d5 8. 4e9 9. 5p6 10. 21g5 11. 20h13 12. 42k8 13. u12v7 14. a11b3 15. 12v6u12 16. 18s9r10 17. 24y12v6

D: 1. x2 2. y 3. 3x 4. 1 5. 3s 6. 2r2 7. ½r4 8. 4w4 9. ¼s-5k3 10. 5a6b-3c6

E: 1. x12 2. 9x8 3. 125x24 4. 81a8b24 5. 3a9

F: 1. 16x12 2. 16x6 3. 125x21 4. 30x12 5. 28x12 6. 7x5 7. 4x3 8. ½x4 9. 12x12 10. 36x6

11. 40x7 12. 108x13

Worksheet 46

A: 1. 0 2. $30 3. 280cm2 4. 5cm 5. 8/100 = 2/25 6. 1 7. 10 8. 100 years 9. 8.4m 10. 5.2

B: 1. 3x + 12 = 27, 3x = 15, x = 5 2. 5x – 20 = 65, 5x = 85, x = 17 3. 6x + 9 = 37, 6x = 28, x = 42/3 4. 12x – 20 = 34, 12x = 54 x = 41/2 5. 6x + 42 = 8, 6x = -34, x = -52/3

C: 1. 3x = 15, x = 5 2. 4x = 28, x = 7 3. 7x = 15, x = 21/7 4. 3x = 31, x = 101/10 5. 6x = 27, x = 41/2

D: 1. x + 9 = 20, x = 11 2. x – 4 = 21 , x = 25 3. 2x + 8 = 40, 2x = 32, x = 16 4. 5x – 3 = 42, 5x = 45, x = 9 2x + 10 = 36, 2x = 26, x = 13

E: 1. b = A/h 2. h = 2A/b 3. a = 2A/h – b 4. r = A/ 5. b = pc – a

F: 1. h = 2A/b 2. 6m 3. d = V/bh 4. 3cm


Worksheet 47

A: 1. 11 2. 6 3. 139o 4. 90.25cm2 5. 13x 6. 9.1 7. 255 min 8. 2.056km 9. $71.37 10. 18.96

B: 1. discrete 2. continuous 3. 4. Grade 4 5. 60 pupils 6. 80 pupils

C: 2. 10 - 3. 3 seedlings 4. 28 seedlings 1. 5. 45 seedlings

D: 1. discrete 2. discrete 3. continuous 4. discrete 5. continuous 6. continuous 7. continuous 8. discrete 9. continuous

Grade 1 2 3 4 5

F 9 11 19 24 17 80

Height 1 - 5 - 10 - 15 +

F 3 14 16 12 45

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Worksheet 48

A: 1. 63 2. &18 3. 4.525L 4. 44/100 = 11/25 5. 45.5 days 6. 70 7. octagon 8. $32:$40 9. 9x 10. 34/7

B: 1. 1.56m 2. 3. The ‘average’ pupils is 1.56m tall, is of slim to medium build with brown eyes, brown hair and has a shoe size of 7.

Eye colour F brown 5 blue 4 hazel 2 grey 3

Body type F slim 5

medium 5 solid 4

Hair colour F black 5

blonde 3 brown 6

Shoe size 4 5 6 7 8 9 10 F 1 2 1 5 3 1 1

Worksheet 49

A: 1. 3.2 2. 33/7 3. 71o 4. 38.8cm 5. 2x 6. 5.97 7. 225 minutes 8. 4.726m 9. $2.65 10. 9.07

B: 1. mean, mean 2. median 3. mode

C: 1. A = 12, B = 13, C = 13 2. A = 15, B = 15, C = no mode 3. A = 3.7, B = 4, C = 2 & 4 4. A = 6.9, B = 8, C = 10 5. A = 8.7, B = 7, C = 4 & 16

D: 1. mode 2. mean 3. median 4. mean or mode

E: 1. 72 sheep 2. 73 or higher 3. 74 & 75 4. $17500 5. $18300 6. $171000 7. 48% 8. 60%

Worksheet 50

A: 1. $22.50 2. $13.60 3. 49o 4. 48/100 = 12/25 5. 8.7 x 105 6. 7800 7. 8. 24, 48, 96 9. 25% 10. 64/5

B: 1. lowest score 2. highest score 3. lower quartile 4. upper quartile 5. median

C:

Range LQ Median UQ

1. 12 6 7 9.5

2. 18 4.5 8 16.5

3. 20 7 8.5 20

4. 11 5 8 12

5. 16 2 8 10

Test A Test B 0

10

20 Class Test Results

D: 1. HS = 19, UQ = 15, median = 8, LQ = 4, LS = 1 2. See graph opposite Test A: LQ = 3, M = 5, UQ = 11 Test B: LQ = 7, M = 13, UQ = 17 3. A = = 15, B = 15 4. A = 6.9, B = 11.9 5. Test B result were better in all aspects except, but the range was the same as Test A.

Worksheet 51

A: 1. $16 2. 13, 26, 39, 52 3. 5cm 4. 7cm 5. 8/10 = 4/5 6. -1 7. 15 8. 10 9. 6.532km 10. 11.212

B: 1. 5 families 2. 9 families 3. 9 families 4. 3 pupils

C:

Number of Days Away

1 2 3 4 5

Number of

pupils (F)

0

5

Pupils absent in Mark’s class

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D: 1. 3. 13 pupils 4. Grade 5 5. 20 pupils 6. 32 pupils

E: 1. no titles or labels on axes 2. vertical scale not constant 3. different colours and widths of columns 4. It does not mean it is safer to drive on wet roads, as more people drive on sunny days.

Grades 1 2 3 4 5 f 10 10 13 16 15

15

10

5

0

Number of

pupils (F)

Grades

Grades scores Year 10 Assessment

1 2 3 4 5

Worksheet 52

A: 1. 0 2. 42/5 3. 133o 4. 6.25mm2 5. -x 6. 8.3 7. 102hrs 8. 0.735km 9. $109.85 10. 17.055

B: 1. 8 runners 2. 5 runners 3. 3 runners 4. 35 runners 5. 9 runners

C: D: 10

5

Number of

turns (F)

Time (minutes)

Computer Game Times

1 2 3 4 5 0

1. 2. see graph 3. 15 - 4. 30 blades 5. 28 blades 6. 36 blades

15

5

Number of

grass blades

(F)

Length of blades of grass

Science Experiment results

10 15 20 25+ 0

10

Length 10 - 15 - 20 - 25 + f 10 10 13 16

E: 1. No scales on horizontal axis 2. width and colour of columns vary 3. No title 4. vertical scale not even

Worksheet 53

A: 1. 20.25cm 2. 4.35km 3. 168mL 4. 315 min 5. -153 6. 74 7. 40.61 8. 14 9. $40:$56 10. 34/7

B: 1. 35 people 2. 100 people 3. 2/5 4. 35% 5. clothes =$20, food = $12, C.D.’s = $16 6. $ $ $

C: 1. 12th June 2. 21 minutes 20 seconds 3. every 3rd day 4. 20 minutes 30 seconds 5. 15th June 6. 1 minute 20 seconds faster 7. 20 minutes 42 seconds

D: 1. 9 2. 8 3. 7.6

E: Key: S = sleeping, Sc = school, TV = television, HW = homework, O = other S S S S Sc Sc TV H O

Worksheet 54

A: 1. -119 2. 4650m 3. -108 4. 3750mL 5. 1.52 6. 570 seconds 7. $60.66 8. 0.8 9. (isosceles) trapezium 10. 28m

B: 1. 2. 8 sectors, $9 3. 3/8 4. 1/4 5. clothes = $18, model aeroplanes = $27 6. $27

C: 1. Y10 = 50/200, Y11 = 45/200, Y12 = 30/200, Y13 = 25/200, 2. Y10 = 90o, Y11 = 81o, Y12 = 54o,

Y13= 45o 3. 360o

D: 1. 9 2. 8 3. 7.6

G

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D: 1. 2. 90 cars

3. black = 18/90, blue = 20/90, red = 12/90, white = 24/90, other = 16/90 4. black = 72o, blue = 80o, red = 48o, white = 96o, other = 64o

5. 6. check key 7. Of all car colours, white cars were the most common colour. However, of the 90 cars counted, only 24 were white car.

Colour black blue red white other

F 18 20 12 24 16 90

black blue

red

white

other

Worksheet 55

A: 1. $72 2. $13.44 3. x = 21o 4. 87.5% 5. 7.0 x 10-4 6. 7400 7. 60m2 8. 50 9. 476m 10. 141/3

B: 1. 33, 33, 37, 38, 44, 45, 47, 48, 49, 49, 51, 53, 53, 54, 57, 64, 65, 65, 66 2. 3. 4. While the range values are the same,

Plot B barley plants had a higher median &

mean, therefore the music had improve barley plant growth

C: D: 1. 2. 3 1. check graph 2. yes 3. all points are

almost in a straight line

5 ,7 ,7 ,4 ,3 ,8 2 9

2 ,9 ,9 ,6 ,4 3 5, 2, 6, 7, 7

0 ,2 ,4 ,3 4 5, 2, 2, 7, 1, 2, 1

3 ,2 5 2, 0, 3, 9

Plot A Plot B Range 30 30

Median 36 41 Mean 38 45

Worksheet 56

A: 1. 35 2. $11.16 3. 0.589L 4. 0.625 5. 9.5 weeks 6. 55 7. trapezium 8. $9:$3:$12 9. y 10. z = 32

B: 1. experiment 2. outcome 3. sample space 4. event

C: 1. H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 2. RR, RW, RP, WW, WP, PP 3. MTu, MW, MTh, MF, TuW, TuTh, TuF, WTh, WF, ThF

D: 1. 32/60 2. 1 = 38/200, 2 = 37/200, 3 = 28/200, 4 = 27/200, 5 = 36/200, 6 = 34/200

3. 200 blocks 4. red = 48/200 or 0.24, blue = 32/200 or 0.16, black = 64/200 or 0.32, white = 16/200 or 0.08, 3

green = 40/200 or 0.2 5. black 6. white

Worksheet 57

A: 1. -1 2. 42/3 3. 540o 4. 343cm3 5. 2x + 3y 6. 0.2 7. 336hrs 8. 275m 9. $122.50 10. -0.74

B:

1. 1/6 2. 3/6 = 1/2 3. 4/6 = 2/3 4. 0 5. 2/6 = 1/3 6. 26/52 = 1/2

7. 4/52 = 1/13 8. 13/52 = 1/4 9. 2/52 = 1/26

10. 12/52 = 3/13 11. 1/52

C: D: 1. 1. W = 6/12 = 1/2, B = 2/12 = 1/6, Y = 4/12 = 1/3

2. no 3. see tree diagram 4. (W,W), (W,B), (W,Y), (B,W), (B,B), (B,Y), (Y,W), (Y,B), (Y,Y) 5. 9 outcomes

2. 24 times 6. 1/4 7. 1/36 8. 1/9 9. 1/12 10. 1/18 3. no 11. 1/6 12. 1/6 13. 1/3 14. 1/9 4. yes 15. 1/11

= 11/25 = 8/25

= 4/25 = 2/25

W

B

Y

W

B

Y

W

B

Y

W

B

Y

Second Draw First Draw

E 4 5 6 7 7 8 9 10 M 4 5 5 6 9 8 9 7

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Worksheet Objectives

19 M2

18 M1

17 M2

16 M1 / M2

15 M1 / M2

14 M1 / M2

13 M1 / M2

12 Rev

11 Rev

10 N9

9 N9

8 N9

7 N7 / N8

6 N6

5 N4 / N5

4 N5

3 N1/N2/N3

2 Rev

1 Rev

Tracking Sheet: Homework / Assessment Activity

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38 A3

37 A2

36 A1

35 G11

34 G9

33 G8

32 G7 / G10

31 G6

30 G5

29 G5

28 G4

27 G3

26 G2

25 G2

24 G1

23 Rev

22 Rev

21 Rev

20 M3


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57 S10 / S11

56 S9 / S10

55 S3 / S5

54 S3 / S8

53 S3

52 S2 / S3

51 S2 / S3

50 S3

49 S3

48 S1/S2/S3

47 S2 / S4

46 A6 / A10

45 A8

44 A9

43 A6 / A10

42 A7

41 A5 / A10

40 A4

39 A4


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Documents

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