Levels 3 to 6 eBook - Jebel Ali Maths · Levels 3 to 7 eBook Questions Level 3 Contents ..... (i) Level 4 Contents ..... (ii) Level 5 Contents ... Ordering Decimals

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Levels 3 to 7eBook QuestionsLevel 3 Contents ................. (i)

Level 4 Contents ................. (ii)

Level 5 Contents ................. (iii)

Level 6 Contents ................. (iv)

Level 7 Contents ................. (v)

APP Record Sheet .............. (vi)

Level 3 Certificate ............... (vii)

Level 4 Certificate ............... (viii)

Level 5 Certificate ............... (ix)

Level 6 Certificate ............... (x)

Level 7 Certificate ............... (xi)

Worksheets ......................... 1A to 134

Extras - Weights .................. 135A to 135C

Extras - Balances ................ 136A to 136E

Extras - Congruent Halves .. 137A to 137E

Extras - Circles .................... 138A to 138H

M atchathsWM atchathsW

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Number

N1..... Place Value .......................................................1A, 1BN2..... Negative Numbers.............................................2A, 2BN3..... Introduction to Fractions ....................................3A, 3BN4..... Money ...............................................................4A, 4B

Calculating

C1..... Mental Addition ..................................................5A, 5BC2..... Mental Subtraction ............................................6A, 6BC3..... Addition of Integers ...........................................7A, 7BC4..... Subtraction of Integers ......................................8A, 8BC5..... Multiplication by 2, 3, 4, 5 and 10 ......................9A, 9BC6..... Division by 2, 3, 4, 5 and 10 ..............................10A, 10B

Shape, Space and Measure

S1 ..... Reflective Symmetry of 2D Shapes ...................11A, 11BS2 ..... Recognising Nets ..............................................12A, 12BS3 ..... Reflecting Shapes .............................................13A, 13BS4 ..... Metric Units .......................................................14A, 14BS5 ..... Time ..................................................................15A, 15B

Handling Data

D1..... Reading Bar Charts and Pictograms .................16A, 16B, 16CD2..... Drawing Bar Charts and Pictograms .................17A, 17B

Level 3

N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2

LEVEL 3

Page

Page (i)

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Number

N5..... Number Patterns ...............................................18A, 18BN6..... Square Numbers ...............................................19A, 19BN7..... Multiples ............................................................20A, 20BN8..... Factors ..............................................................21A, 21BN9..... Multiplication and Division by 10 and 100 .........22A, 22BN10... Fractions and Percentages................................23A, 23BN11 ... Ordering Decimals .............................................24A, 24BN12... Basic Ratio ........................................................25A, 25B

Calculating

C7..... Addition .............................................................26A, 26BC8..... Subtraction ........................................................27A, 27BC9..... Short Multiplication ............................................28A, 28BC10... Short Division ....................................................29A, 29BC11 ... Multiplication of Decimals ..................................30A, 30BC12... Problems, Without a Calculator .........................31A, 31BC13... Problems, With a Calculator ..............................32A, 32B

Algebra

A1 ..... Formulae Expressed in Words ..........................33A, 33BA2 ..... Coordinates in First Quadrant ...........................34A, 34B


S6 ..... Making 3D Models .............................................35A, 35B, 35C, 35DS7 ..... Reflection in Diagonal Lines ..............................36A, 36B, 36C, 36D, 36ES8 ..... Translation .........................................................37A, 37BS9 ..... Rotation .............................................................38A, 38BS10 ... Reading Scales .................................................39A, 39BS11 ... Perimeter ...........................................................40A, 40BS12 ... Areas .................................................................41A, 41B

Handling Data

D3..... Discrete Data.....................................................42A, 42BD4..... Grouping Data ...................................................43A, 43BD5..... Mode, Median and Range .................................44A, 44B

LEVEL 4

Level 4

N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5

Page

Page (ii)

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Number

N13... Mult. and Div. of Decimals by 10 and 100 .........45A, 45BN14... Rounding ...........................................................46A, 46BN15... Ordering Negative Numbers ..............................47A, 47BN16... Ordering Fractions.............................................48A, 48BN17... Simplification of Fractions .................................49A, 49BN18... Understanding Ratios ........................................50A, 50B

Calculating

C14... Long Multiplication .............................................51A, 51BC15... Long Division .....................................................52A, 52BC16... BODMAS...........................................................53A, 53BC17... Fraction of an Amount .......................................54A, 54BC18... Directed Numbers .............................................55A, 55BC19... Ratio Questions in Context ................................56A, 56BC20... Direct Proportion ...............................................57A, 57BC21... Real Life Tables .................................................58A, 58B

Algebra

A3 ..... Algebraic Expressions .......................................59A, 59BA4 ..... Coordinates in Four Quadrants .........................60A, 60BA5 ..... Horizontal and Vertical Lines .............................61A, 61BA6 ..... Function Machines ............................................62A, 62B


S13 ... Symmetries of 2D Shapes.................................63A, 63BS14 ... Measuring and Drawing Angles .........................64A, 64B, 64C, 64D, 64E, 64FS15 ... Angle Facts .......................................................65A, 65BS16 ... Area of Rectangles ............................................66A, 66B

Handling Data

D6..... Probability..........................................................67A, 67BD7..... The Mean Average ............................................68A, 68B

LEVEL 5

Level 5

N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7

Page

Page (iii)

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Number

N19... Fractions, Decimals and Percentages ................... 69N20... Improper Fractions and Mixed Numbers ............... 70N21... Prime Numbers, HCF and LCM ............................ 71

Calculating

C22... Percentage of an Amount ...................................... 72C23... Percentage Increase and Decrease ...................... 73C24... Addition and Subtraction of Fractions.................... 74C25... Multiplication & Division of Integers by Fractions .. 75

Algebra

A7 ..... Substitution............................................................ 76A8 ..... Trial and Improvement........................................... 77A9 ..... Algebraic Simplification ......................................... 78A10 ... Linear Equations ................................................... 79A11 ... Generate a Number Sequence ............................. 80A12 ... Finding the nth Term.............................................. 81A13 ... Straight Line Graphs.............................................. 82A14 ... Distance - Time Graphs ......................................... 83A15 ... Real Life Graphs ................................................... 84


S17 ... Properties of Quadrilaterals ................................... 85S18 ... Nets of 3D Shapes ................................................ 86A, 86BS19 ... Constructions ........................................................ 87S20 ... Geometric Problems.............................................. 88S21 ... Corresponding and Alternate Angles ..................... 89S22 ... Enlargement .......................................................... 90A, 90BS23 ... Similar Shapes ...................................................... 91S24 ... Area of a Triangle .................................................. 92A, 92BS25 ... Area of a Parallelogram......................................... 93S26 ... Volume of a Cuboid ............................................... 94S27 ... Surface Area of a Cuboid ...................................... 95S28 ... Circumference of a Circle ...................................... 96S29 ... Area of a Circle...................................................... 97A, 97B

Handling Data

D8..... Bar Charts and Frequency Diagrams .................... 98D9..... Scatter Graphs ...................................................... 99D10... Pie Charts.............................................................. 100D11 ... Two-Way Tables .................................................... 101D12... Surveys ................................................................. 102D13... Further Probability ................................................. 103

LEVEL 6

Level 6

N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28

A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

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Page (iv)

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Number

N22... Rounding to 1 Significant Figure ........................... 104

Calculating

C26... Percentage Increase and Decrease ...................... 105C27... Addition and Subtraction of Fractions.................... 106C28... Multiplication and Division of Fractions ................. 107C29... Numbers Between 0 and 1 (Mult. & Div.) .............. 108C30... Estimating Answers ............................................... 109C31... Using a Calculator ................................................. 110

Algebra

A16 ... Further Algebraic Simplification ............................. 111A17 ... Expanding Brackets .............................................. 112A18 ... Factorisation .......................................................... 113A19 ... Solving Difficult Equations ..................................... 114A20 ... Rearranging a Formula ......................................... 115A21 ... Trial and Improvement........................................... 116A, 116BA22 ... Inequalities ............................................................ 117A23 ... Solving Inequalities ............................................... 118A24 ... Understanding Straight Line Graphs ..................... 119A25 ... Regions ................................................................. 120A26 ... Simultaneous Equations Graphically ..................... 121A27 ... Simultaneous Equations Algebraically ................... 122A28 ... nth Term of Quadratic Sequences ......................... 123A29 ... Graphs of Quadratic and Cubic Functions ............ 124A, 124B, 124C


S30 ... Pythagoras’ Theorem ............................................ 125A, 125B, 125CS31 ... Areas of Compound Shapes ................................. 126A, 126B, 126CS32 ... Volumes of Prisms................................................. 127S33 ... Surface Area of Triangular Prisms ......................... 128S34 ... Loci ........................................................................ 129S35 ... Enlargement by a Negative Scale Factor .............. 130S36 ... Bounds .................................................................. 131S37 ... Compound Measures ............................................ 132

Handling Data

D14... Averages from Tables ............................................ 133A, 133BD15... Relative Frequency ............................................... 134

LEVEL 7

Page

C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26

Level 7

Page (v)

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Secure Level 3

Secure Level 3 withsome Level 4 features

Secure Level 4


Secure Level 5


Secure Level 6

Name: _________________________

Year: ______ Class: ______

Teacher: ________________

APP Record Card

Date

Page (vi)

Level 3


Level 4


Level 5


Level 6


A14 A15S29S17 S18

D8 D9 D10 D11 D12 D13

Level 7



Secure Level 7

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LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3

MathematicsLevel 3

Certificate

This is to certify that _______________________

has successfully achieved Level 3 in Mathematics.

Class: ____________________

Date: ___________ Signed: ____________

Page (vii)

Level 3


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MathematicsLevel 4

Certificate



Class: ____________________

Date: ___________ Signed: ____________

Level 4


LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3

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MathematicsLevel 5

Certificate



Class: ____________________

Date: ___________ Signed: ____________

Level 5


LEVEL 7

LEVEL 6

LEVEL 5

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LEVEL 3

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MathematicsLevel 6

Certificate



Class: ____________________

Date: ___________ Signed: ____________

Level 6


A14 A15S29S17 S18

D8 D9 D10 D11 D12 D13

LEVEL 7

LEVEL 6

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MathematicsLevel 7

Certificate



Class: ____________________

Date: ___________ Signed: ____________

LEVEL 7

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LEVEL 5

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LEVEL 3


Level 7

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Level 3


N1Place Value

1) Put the following numbers in the place value table.

a) 2415

b) 607

c) 9380

d) 2004

2) Write the following numbers in figures.

a) six hundred and sixty seven

b) two thousand one hundred and fifty six

c) nine hundred and fourteen

d) four thousand and seventy one

3) Write the following numbers in words.

a) 5432

b) 811

c) 3620

d) 9090

4) a) What is the value of the 2 in thenumber 1250?

b) What is the value of the 6 in thenumber 6924?

Page 1A

1000Thousands

100Hundreds

10Tens

1Units

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Level 3


N1Just For Fun

1) Match the words with the correct numbers.

2) Here are four number cards.

a) What is the biggest three digit numberyou can make with these cards?

b) What is the biggest even number youcan make with all four cards?

3) a) Write a whole number that is bigger thanone thousand but smaller than onethousand one hundred.

b) Write the number eleven thousand elevenhundred and eleven.

Page 1B

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Level 3


N2Negative Numbers

-5-4-3-2-10123456789

101112C

-5-4-3-2-10123456789101112C

-5-4-3-2-10123456789

101112C

-5-4-3-2-10123456789101112C

-5-4-3-2-10123456789101112C

-5-4-3-2-10123456789

101112C

A B C D E F

A

B

C

D

E

F

-3 °C rises 8 °C 5 °C

falls 6 °C

rises 3 °C

-4 °C

rises 8.5 °C

-4.5 °C

Thermometer Temperatureat 3.00 A.M

Temperaturechange over

next five hours

Temperature at8.00 A.M.

The thermometers A to F show the temperature at 3:00 A.M.in six different cities.Use them to fill in the table below.The first one has been done for you.

Page 2A

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Level 3


N2Just For Fun

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Player A Player B

Start point

3) Place a counter on 0.Player A and B take turns in rolling a dice.Whatever scores player A gets, he/she alwaysmoves this many squares to the left.Whatever scores player B gets, he/she alwaysmoves this many squares to the right.Player A wins if he/she needs to move to asquare which is less than -8.Player B wins if he/she needs to move to asquare which is more than 8.

1) Place these numbers in order of size, smallest to largest.

a) 6, -1, 2, 5

b) 4, 7, -5, 3, -2

c) -1, -4, 0, 3, 9, -2

d) 1, -3, 4, -6, 8, -9, -4

e) -8, -4, -10, -6, -3, -7, -12

f) 6, 7.5, -3.5, -4, 8.5, -5.5, -2.5, -3

2) a) What is special about the temperature 100 °C?

b) What is special about the temperature 0 °C?

Page 2B

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Level 3


1) Find three equivalent fractions to each of thefollowing:

a) b) c)

d) e) f)

2) Fill in the missing number in each of theseequivalent fractions.

a) = b) = c) =

d) = e) = f) =

g) = h) = i) =

13

3) Complete the following equivalent fraction series.

a) = = = = =

b) = = = = =

14

15

25

34

58

23

15

3119 20 22

13

5 27

10 49

8

25

57

910

814250

12

26

520

615

1250

30035

50

N3

Page 3A

Introduction to Fractions

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Level 3


Just For Fun

Use the diagram below to help you fill in themissing numbers.

a)

b)

c)

d)

1) Here are six number cards.

a) Choose two of these six cards

to make a fraction that is

equivalent to .

b) Choose two of these six cards


equivalent to .

2)

2 4 6 8 10 12

16

14

13

= +

1216

16

= –

212

16

+ =

16

13

+ =14

+

112

16

112

112

13 1

4

112

N3

Page 3B

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Level 3


Money

1) Write the following amounts of money usinga £ sign and numbers.

a) Three pounds and thirty seven pence.

b) Twenty four pounds and fifty pence.

c) Two hundred and five pounds.

d) Nine pounds and sixty pence.

e) Nine pounds and six pence.

f) Forty eight pence.

2) Write the following amounts of money in words.

a) £2.78

b) £6.07

c) £5.40

d) £0.24

3) Work out the following on a calculator and write theanswers correctly:

a) £115.23 ÷ 23

b) £100.80 ÷ 14

c) 71p × 10

d) £6.40 – £3.83 + £2.10

e) £14.83 + £6.17

N4

Page 4A

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Level 3


Three men went into a second-hand shop to buy atelevision.

It was priced in the window at £30.

Each of them handed over £10 to the shop assistant.

As the assistant opened the till, the manager had a quietword with him, “that TV is in the sale and is only £25now, you will have to give them £5 back.”

The assistant was very lazy and couldn’t be bothered tocount out the right change for each man.

Instead, he took 5 £1 coins out of the till.

He put two of them in his own pocket and gave eachman £1 back.

Here’s the problem:

The men have now paid £9 each for the TV.

The assistant has kept £2 for himself.

3 × £9 = £27.

£27 + £2 = £29.

But £30 was handed over in the first place.

WHERE IS THE MISSING £1?

N4Just For Fun

Page 4B

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Level 3


C1Mental Addition

For each set of questions, time how long it takes to getthe answers.You must work out the answers in your head - you can’tdo any working on paper.

1) 23 + 35

2) 17 + 13

3) 45 + 46

4) 38 + 44

5) 71 + 54

6) 38 + 46

7) 27 + 68

8) 64 + 77

9) 64 + 99

10) 87 + 96

Set A

1) 42 + 56

2) 23 + 56

3) 37 + 25

4) 68 + 26

5) 83 + 65

6) 59 + 37

7) 42 + 39

8) 57 + 68

9) 99 + 48

10) 68 + 94

Set B

1) 62 + 24

2) 38 + 22

3) 17 + 34

4) 52 + 29

5) 82 + 63

6) 28 + 36

7) 88 + 17

8) 67 + 56

9) 42 + 98

10) 78 + 93

Set C

For any set of questions:45 seconds or less: Maths teacher standard46 to 89 seconds: Extremely fast90 to 149 seconds: Fast150 to 209 seconds: Reasonable210 seconds or more: A bit more practise needed

Page 5A

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Level 3


C1Just For Fun

This is a game for two people.

The player who goes first will say either 1 or 2, it istheir choice.

The other player must now add on either 1 or 2 andsay what the total is.

The first player now adds on 1 or 2 and says what thetotal is.

The game continues like this (always adding 1 or 2)until one of the players gets to 21.

The player who gets to 21 is the winner.

Here is a game between Ben and Sara as anexample:

Ben goes first and says 2.Sara adds 2 and says 4Ben adds 1 and says 5Sara adds 1 and says 6Ben adds 2 and says 8Sara adds 1 and says 9Ben adds 2 and says 11Sara adds 2 and says 13Ben adds 2 and says 15Sara adds 1 and says 16Ben adds 2 and says 18Sara adds 1 and says 19Ben adds 2, says 21 and wins.

Play the game a few times and see if you can find any way ofmaking sure you win.

If you go second, with the right tactics you can always win.

If you go first and the other person doesn’t know the trick youcan usually win as well.

Page 5B

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Level 3


C2Mental Subtraction

For each set of questions, time how long it takes to getthe answers.You must work out the answers in your head - you can’tdo any working on paper.

1) 75 – 71

2) 98 – 93

3) 84 – 32

4) 68 – 24

5) 79 – 47

6) 38 – 29

7) 67 – 48

8) 54 – 39

9) 94 – 36

10) 72 – 25

Set A

1) 57 – 52

2) 78 – 71

3) 56 – 13

4) 78 – 27

5) 66 – 31

6) 84 – 38

7) 76 – 29

8) 43 – 17

9) 62 – 26

10) 51 – 24

Set B

1) 39 – 34

2) 67 – 62

3) 83 – 42

4) 88 – 34

5) 76 – 25

6) 63 – 39

7) 46 – 28

8) 54 – 48

9) 72 – 27

10) 72 – 38

Set C

For any set of questions:45 seconds or less: Maths teacher standard46 to 89 seconds: Extremely fast90 to 149 seconds: Fast150 to 209 seconds: Reasonable210 seconds or more: A bit more practise needed

Page 6A

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Level 3


C2Just For Fun

This is a good trick.This page tells you how to do the trick.The next page gives you the secrets.

Let your friend see you writing on a piece ofpaper. Don’t let them see what you are writ-ing, though.Fold the piece of paper to hide what you havewritten and place it on the table.Now ask your friend to write a number wherethe first digit is bigger than the third digit.Let’s say they write 723.Ask them to write the number back-to-frontunderneath the first number they wrote.

Ask them to subtract the bottom number fromthe top.

Now tell them to write their answer back-to-front underneath it.

Now ask them to add the two numberstogether.

Tell them to unfold the paper on the desk.They will find that you correctly predicted theirfinal answer.

723327

723327396

–

723327396693

–

723327396693

–

+1089

Page 6B

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Level 3


1) 51 + 36

2) 41 + 27

3) 231 + 25

4) 446 + 38

5) 569 + 84

6) 316 + 262

7) 596 + 472

8) 657 + 847

9) 62 + 38 + 517

10) 216 + 32 + 518 + 74

=

=

=

=

=

=

=

=

=

=

C3Addition of Integers

Page 7A

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Level 3


C3Just For Fun

2 3

4

6 8*1) 5 8

2

8 4*2)

7 9

4*3) 3

8*4)

1 2 7 1 6 0*

*5) 2 6

3 5*6)

4

6 4*7) 6

4 6*8)

7 5 1 1 3 6 3*

*8*1 9 2

*

** *

+ +

+ +

+ +

+ +

Work out whatthe must be.*

6 1 8

Page 7B

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Level 3


1) 35 – 12

2) 58 – 27

3) 93 – 46

4) 258 – 37

5) 681 – 79

6) 420 – 68

7) 743 – 471

8) 361 – 278

9) 800 – 692

10) 1450 – 785

C4Subtraction of Integers

=

=

=

=

=

=

=

=

=

=

Page 8A

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Level 3


C4Just For Fun

4 5

2

2*1) 7 9

5

3*2)

6 7

*3) *6 1

4)

4 1 2 5

*

*5) *6) 3 5

2 6

9

6 3*7) *8)

5 9 6

5 6 5 1 8 7

*

6 3

* *

**

*

– –

– –

– –

– –

Work out whatthe must be.*

8 2

* *

*

1 6

Page 8B

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Level 3


C5

× 5 4 2

2

4 12

20

3

× 10 4 5 3

3

2 8

1 3

5 25

1) Fill in the missing numbers in theminitables below.

a) b)

2) Work out

a) 2 × 17 = ____ b) 24 × 5 = ____

c) 10 × 9 = ____ d) 4 × 62 = ____

e) 37 × 3 = ____ f) 2 × 81 = ____

g) 5 × 32 = ____ h) 3 × 19 = ____

i) 26 × 4 = ____ j) 11 × 10 = ____

Page 9A

Multiplication by 2, 3, 4,5, and 10

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Level 3


C5Just For Fun

1) a) Use the table to fill in the gaps below.

21 × 14 = ____

12 × ____ = 228

____ × 15 = 315

286 ÷ 22 = ____

b) Give two different pairs of numbers.

____ × ____ = 252

____ × ____ = 252

× 11 12 13 14 15

18 198 216 234 252 270

19 209 228 247 266 285

20 220 240 260 280 300

21 231 252 273 294 315

22 242 264 286 308 330

2) Julia says:

“Multiply any number by five. The answer must be an odd number.”

Is she correct?Circle Yes or No

Explain how you know.

_______________________________________

Yes / No

Page 9B

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Level 3


C6

2) Work out

a) 46 ÷ 2 = ____ b) 39 ÷ 3 = ____

c) 65 ÷ 5 = ____ d) 62 ÷ 4 = ____

e) 47 ÷ 3 = ____ f) 11 ÷ 10 = ____

g) 92 ÷ 4 = ____ h) 57 ÷ 3 = ____

i) 90 ÷ 5 = ____ j) 83 ÷ 10 = ____

1) Work out

a) 16 ÷ 2 = ____ b) 30 ÷ 5 = ____

c) 21 ÷ 3 = ____ d) 40 ÷ 4 = ____

e) 35 ÷ ____ = 7 f) 24 ÷ ____ = 8

Page 10A

Division by 2, 3, 4,5, and 10

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Level 3


C6Just For Fun

1) Here is part of the 45 times table.Use the table to help you fill inthe missing numbers.

a) 315 ÷ 7 = ____

b) 135 ÷ 45 = ____

c) 270 ÷ ____ = 45

d) ____ × 45 = 405

e) 495 ÷ 45 = ____

f) ____ × 45 = 900

g) 450 ÷ 30 = ____

2) Joe says:

“Divide any number by three. The answer must be an even number.”

Is he correct?Circle Yes or No

Explain how you know.

_______________________________________

Yes / No

1 × 45 = 45

2 × 45 = 90

3 × 45 = 135

4 × 45 = 180

5 × 45 = 225

6 × 45 = 270

7 × 45 = 315

8 × 45 = 360

9 × 45 = 405

10 × 45 = 450

Page 10B

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Level 3


Look at each shape, read the descriptionand then draw in all the lines of symmetry.

S1

1) RectangleTwo lines of symmetry

2) SquareFour lines of symmetry

3) Isosceles triangleOne line of symmetry

4) Equilateral triangleThree lines of symmetry

5) Regular pentagonFive lines of symmetry

6) Regular hexagonSix lines of symmetry

Page 11A

Reflective Symmetryof 2D Shapes

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Level 3


S1Just For Fun

1) Shade in five more littletriangles so that the figurehas one line of symmetry.

2) Shade in just three morelittle triangles so that thefigure has one line ofsymmetry.

Page 11B

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Level 3


S2Recognising Nets

Cuboid

Triangle-basedpyramid

Square-basedpyramid

Cube

Draw two lines from each label.One line should go to the correct 3-Dshape.The other one should go to the net ofthe 3-D shape.

Page 12A

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Level 3


There are exactly eleven different nets of a cube.

Below, you can see two of them.

See how many of the other nine you can find.

1) 2)

3) 4)

6) 7)

9) 10)

5)

8)

11)

S2Just For Fun

Page 12B

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Level 3


In all four questions, reflect the shadedshape in the dotted mirror line.

1)

3)

2)

4)

S3Reflecting Shapes

Page 13A

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Level 3


S3Just For Fun

3)

2)1) Reflect every line in the dottedmirror line.

Use the grid to help you reflectRobbie Rabbit in the dotted mirrorline.

Reflect the shape in the verticalmirror line.Then, reflect both shapes in thehorizontal mirror line.

4) Reflect the shape in the verticalmirror line.Then, reflect both shapes in thehorizontal mirror line.

Page 13B

© Mathswatch Ltd

Level 3


S4

1) a) How many millimetres are in a centimetre?

b) How many centimetres are in a metre?

c) How many metres are in a kilometre?

d) Work out how many millimetres are in a metre.

2) How many grams are in three kilograms?

3) How many millilitres are in a five litres?

4) In the table, work out what each item should bemeasured in.

Your choices are mm, cm, m, km, g, kg, ml or l.

Amount of lemonade in a bottle

Mass of a lemonade bottle

Width of a lemonade bottle

Distance to the moon

Mass of a wasp

Length of a wasp

Amount of blood in a human body

Metric Units

Page 14A

© Mathswatch Ltd

Level 3


S4Just For Fun

The ship is in a harbour.

There are ten rungs visible on theship’s ladder and they are 30 cm apart.

The tide is coming in and the water isrising at the rate of 20 cm per minute.

How many rungs will be visible after 9minutes?

2)

Average capacity ofair breathed in a day

Blood vessels in a humanbody laid end-to-end

Mass of MountEverest

Length of airways in thelungs laid end-to-end

Mass ofthe Earth

Capacity of allwater on Earth

5 980 000 000 000 000 000 000 000 kg

1460 000 000 000 000 000 000 litres

2 400 km

11 000 litres

3 041 409 000 000 000 kg

100 000 km

A

B

C

D

E

F

U

V

W

X

Y

Z

Try to match up A to F with U to Z1)

Page 14B

© Mathswatch Ltd

Level 3


S5 Time

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

1) Write these times as 24 hour clock times

a) b) c) d)

a.m. p.m. p.m. p.m.

a) b) c) d)09:40 18:10 13:35 23:55

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

2) Draw these times on the clock faces.Underneath the clocks write whether the time is a.m. or p.m.

3) Peter wants to watch a programme which begins at 8.00 p.m.

It is now 4.30 p.m.

How much time will Peter have to wait?

4) Susie is going to watch a programme which begins at 20:30and lasts for one hour and forty five minutes.

What time will it finish?

121

2

3

4

567

8

9

1011

Page 15A

© Mathswatch Ltd

Level 3


S5Just For Fun

1) Here is a train timetable for trains going fromLondon Euston to Crewe.

a) How many trains stop at Tamworth?

b) If Tom gets to London Euston at 15:30 howlong will he have to wait for a train to take him

to Crewe?

c) How many minutes does the 09:38London Euston train take to get to Northampton?

d) How many minutes does the 14:23 Lichfield traintake to get to Crewe?

e) How long does the 17:48 London Euston traintake to get to Crewe in hours and minutes?

London Euston 09:38 12:49 15:46 16:49 17:17 17:48

Northampton 10:25 -------- -------- -------- -------- --------

Rugby 10:47 13:47 -------- -------- -------- --------

Nuneaton 11:00 14:01 -------- -------- -------- --------

Atherstone -------- 14:07 -------- -------- -------- --------

Polesworth -------- 14:12 -------- -------- -------- --------

Tamworth 11:15 14:17 15:53 -------- 18:24 --------

Lichfield 11:22 14:23 -------- 18:03 -------- 19:00

Rugeley -------- 14:33 -------- -------- -------- --------

Stafford -------- 14:44 -------- -------- -------- --------

Crewe 12:00 15:09 17:31 18:41 19:07 19:34

2) You have two egg-timers.

One takes 11 minutes for the sand to run throughand the other takes 7 minutes.

You want to boil an ostrich egg for 15 minutes.

How can you measure exactly 15 minutes withyour two egg-timers?

11 minute timer7 minute timer

Page 15B

© Mathswatch Ltd

Level 3


D1

Red

Blue

Yellow

Green

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1

2

3

4

5

6

0

Favourite colour

Numberof

children

Bar chart to show favouritecolour of all pupils in class 5A

a) How many children chose green as their favourite colour?

b) Which was the least favourite colour in the class?

c) How many more children chose blue than red?

d) How many children are in class 5A?

Page 16A

Reading Bar Chartsand Pictograms

© Mathswatch Ltd

Level 3


D1

An art gallery uses a pictogram to show the numberof paintings sold over a 5 week period.

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Week 2

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Week 3

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Week 5

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Key: = 4 paintings

a) How many paintings were sold in week 1?

b) In which week was the least number ofpaintings sold?

c) How many paintings were sold in week 3?

d) How many paintings were sold in week 4?

e) How many more paintings were sold in week 2compared with week 5?

f) How many paintings were sold altogether in thefive weeks?

Page 16B

Reading Bar Chartsand Pictograms

© Mathswatch Ltd

Level 3


D1Just For Fun

300

250

200

150

100

50

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Ann Ben Jane Cara Dave Carl

Ma

rks

Science123456123456123456123456123456123456

Maths English

Six students sat exams in English, Maths and Science.Each exam was marked out of 100.Their teacher made a bar chart of their results.

a) Which student got the highest total mark?

b) Who got the highest English mark?

c) One student got the same mark for all threesubjects. Write down the name of this student.

d) What mark did Ann get for Maths?

e) One student had their lowest mark for English.Who was it?

Page 16C

© Mathswatch Ltd

Level 3


D2

1) The beginners class in a Judo club has 24 membersand each of them has either a white, yellow, orange,green or blue belt.

The table below shows how many of each belt there are.

On squared paper, draw a bar chart to show thisinformation.

2) All year 6 pupils in a school were each given a newpencil case as a leaving present.

The pupils chose which colour they would like and this isshown in the table below.

Draw a pictogram to show this information.

Let represent 4 pencil cases.

Colour of belt Frequency

White 3

Yellow 5

Orange 7

Green 3

Blue 6

Colour of pencil case Frequency

Red 17

Green 4

Black 10

Yellow 15

Blue 8

Page 17A

Drawing Bar Chartsand Pictograms

© Mathswatch Ltd

Level 3


D2Just For Fun

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A B C D Eo

1

2

3

4

5

6

7

8

9

Exam grades for History and Geography

Exam grades

Fre

quen

cy

1) A class of 30 pupils took a History exam and a Geography exam.The comparative bar chart below shows how many of each gradethe class gained for both subjects.

a) Which subject had more grade A results?

b) How many more grade D results were there inGeography compared to History?

123456123456123456123456123456

History GeographyKey:

Meal Class A Class B

Fish 3 9

Curry 8 2

Pizza 7 5

Stew 5 7

Frequency2) One Tuesday a record was kept of which mealsstudents in Class A and Class B bought in theschool dining hall.

The results can be seen in the table.

Draw a comparative bar chart to showthis information.

Page 17B

© Mathswatch Ltd

Level 4


N5

Page 18A

Number Patterns

3, 5, 7, 9, 11, 13, ?, ?, ?

a) Describe the number pattern.

b) What are the next three terms?

It goes up in 2s

15, 17, 19

Example

1) For each number pattern:

a) Describe the pattern

b) Work out what the next three terms are

(i) 2, 4, 6, 8, 10, 12, ?, ?, ?

(ii) 1, 4, 7, 10, 13, 16, ?, ?, ?

(iii) 5, 12, 19, 26, 33, 40, ?, ?, ?

(iv) -2, 3, 8, 13, 18, 23, ?, ?, ?

(v) 36, 33, 30, 27, 24, 21, ?, ?, ?

(vi) -12, -8, -4, 0, 4, 8, ?, ?, ?

(vii) 100, 91, 82, 73, 64, 55, ?, ?, ?

(viii) 7, 8.5, 10, 11.5, 13, 14.5, ?, ?, ?

2) For both of the following number patterns:

a) Describe the pattern

b) Work out what the next three terms are

(i) 1, 4, 9, 16, 25, 36, ?, ?, ?

(ii) 1, 3, 6, 10, 15, 21, ?, ?, ?

© Mathswatch Ltd

Level 4


N5

Page 18B

Just For Fun

1) Work out the next two terms for each ofthe following number patterns:

a) 3, 8, 15, 24, 35, ?, ?

b) 4, 14, 36, 76, 140, ?, ?


a) 1, 2, 4, 8, 16, 32, ?, ?

b) 2, 7, 22, 67, 202, ?, ?


a) 1, 1, 2, 3, 5, 8, 13, 21, ?, ?

b) 1, 2, 3, 6, 11, 20, 37, 68, ?, ?

4) Work out the next two terms for each ofthe following :

a) O, T, T, F, F, S, S, ?, ?

b) J, F, M, A, M, J, J, ?, ?

This number pattern begins with a 1.After that, every row can be workedout from the row above it.Can you work out the rule and find outwhat the question marks should be inthe last row?

This is a very difficult question andnot many succeed.

6)1

1 12 1

1 2 1 11 1 1 2 2 13 1 2 2 1 1

1 3 1 1 2 2 2 11 1 1 3 2 1 3 2 1 1

3 1 1 3 1 2 1 1 1 3 1 2 2 1? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

5) Choose any number between 1 and 20.

If your number is even, halve it andwrite down the answer.If your number is odd, multiply it bythree and add one. Write down theanswer.

Look at your answer and follow thesame rules:If it is even you halve it and write downthe answer.If it is odd you multiply by three andadd one and write down the answer.

Only stop when you get to one.

Try more starting numbers (of any size).

Do they all go to one?

What about if you use 27 as thenumber to start with?

© Mathswatch Ltd

Level 4


N6

Page 19A

Square Numbers

1 2 3 4 5 6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72

73 74 75 76 77 78 79 80 81 82 83 84

85 86 87 88 89 90 91 92 93 94 95 96

97 98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115 116 117 118 119 120

121 122 123 124 125 126 127 128 129 130 131 132

133 134 135 136 137 138 139 140 141 142 143 144

Shade the twelve squares with square numbers in them.

© Mathswatch Ltd

Level 4


Just For FunN6

Page 19B

We call the numbers1, 4, 9, 16, 25 . . . . .square numbers because we canarrange their number of dots intosquares.

a) Can you work out what specialname is given to the numbers1, 3, 6, 10, 15, . . .?

b) If you choose one of these specialnumbers and add it to the nextone, what do you get every time?

Can you see why?

1 4 9 16 25

© Mathswatch Ltd

Level 4


N7

Page 20A

Multiples

1) a) Write down the first five multiples of 3.

b) Write down the first five multiples of 7.

c) Write down the first five multiples of 4.

2) 6, 12, 18, 24, 30 are the first five multiplesof which number?

3) What are the eighth, ninth and tenth multiples of 11?

4) Put the correct numbers in these circles.Be careful of the overlaps.

First eight multiplesof 3 in this circle

First eight multiplesof 4 in this circle

© Mathswatch Ltd

Level 4


Just For FunN7

Page 20B

The sieve of Eratosthenes

Just follow these steps:

a) Cross out 1.

b) Shade in the square with 2 in it.Now cross out all other multiples of 2.

c) Shade in the 3 square.Cross out all other multiples of 3(some will already be crossed out).

d) Shade in the 5 square.Cross out all other multiples of 5.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

e) Shade in the 7 square.There should be just threeother multiples of 7 whichhaven’t already been crossed out.Cross them out.

f) Shade in every square that hasn’tbeen crossed out.

g) Write out the numbers in everyshaded square.

h) The numbers you have written downhave a special name. What is it?

© Mathswatch Ltd

Level 4


N8

Page 21A

Factors

1) Write down all the factors of:

a) 6

b) 8

c) 10

d) 12

e) 20

f) 21

2) 100 has nine factors.

What are they?

3) The numbers 2, 3, 5 and 7all have exactly two factors.

Find the next four numberswith only two factors.

4) The numbers 1, 4, 9 and 16 allhave an odd number of factors.

Find the next three numberswhich have an odd number offactors.

Factors of 24 inthis circle

Factors of 40 inthis circle

5) Put the correct numbers in the circles.Be careful of the overlaps.

© Mathswatch Ltd

Level 4


Just For FunN8

Page 21B

A

B

C

Place all the whole numbers from 1 to 60 in thediagram below.However, you must stick to these four rules:

1) In the rectangle you must have every wholenumber from 1 to 60

2) In circle A you must have all the factors of 60

3) In circle B you must have all the factors of 45

4) In circle C you must have all the factors of 36

Factors of 60

Factors of 45

Factors of 36

Numbers from 1 to 60

© Mathswatch Ltd

Level 4


N9

Page 22A

1) 75 × 100

2) 102 × 10

3) 9 × 1000

4) 450 ÷ 10

5) 3800 ÷ 10

6) 9700 ÷ 100

7) 60 × 1000

8) 7000 ÷ 100

9) 210 × 1000

10) 1050000 ÷ 1000

=

=

=

=

=

=

=

=

=

=

Multiplication and Divisionby 10 and 100 (and 1000)

© Mathswatch Ltd

Level 4


Just For FunN9

Page 22B

7 000 000

700 000

70 000

7 000

700

Place Approximate population

London

Glasgow

Barnsley

Penkbridge

High Bickington

The table shows the approximatepopulations of five different places.

Complete these sentences:The population of Barnsley is about 10 times

bigger than the population of .............................

The population of ............................. is about 100times bigger than the population of Barnsley.

The population of Glasgow is about ........ times

bigger than the population of Penkbridge.

The population of Barnsley is about 10 timessmaller than the population of .............................

The population of ............................. is about 100times smaller than the population of Barnsley.

The population of High Bickington is about ........times smaller than the population of Penkbridge.

© Mathswatch Ltd

Level 4


N10

Page 23A

Fractions and Percentages

1) What fraction of the following shapes is shaded?

a) b) c)

d) e) f)

2) Shade the shapes according to the given fractions.

a) b) c)57

13

25100

3) What percentage of the shapes below are shaded?

a) b) c)

© Mathswatch Ltd

Level 4


Just For FunN10

Page 23B

1) of this shape is shaded.

a) What fraction of this diagram is shaded?

b) What fraction of this diagram is shaded?

2)

13

These rectangles have been split into fourequal pieces.

Split each of these rectangles into four equal piecesin different ways.

© Mathswatch Ltd

Level 4


N11

Page 24A

1) a) 0.47 b) 0.407 c) 7.04 d) 47.4 ____ ____ ____ ____

From the following list, match the correct way ofreading each of the above numbers.

A- seven point four F- seven zero fourB- zero point forty seven G- forty seven point fourC- zero point four zero seven H- four seven fourD- four seven point four I- four seven point zeroE- seven point zero four J- zero point four seven

2) Arrange the numbers in order of size, starting withthe smallest.

a) 1.8 0.8 8 8.1___ ___ ___ ___

b) 0.08 1.16 0.12 1.09___ ___ ___ ___

c) £4.04 £4.40 £4.14 £0.41___ ___ ___ ___

d) 3.11 3.1 3 3.011 3.001___ ___ ___ ___ ___

e) 0.2 0.022 0.202 0.222 0.22___ ___ ___ ___ ___

f) 6.06 60.06 6.606 66.06 6.066___ ___ ___ ___ ___

Ordering Decimals

© Mathswatch Ltd

Level 4


N11

Page 24B

Just For Fun

I am a decimal number.I have two figures before the decimal point andtwo figures after the decimal point.I read the same forwards as backwards.I have no zeros.My first digit is bigger than my second digit.The sum of my digits is 8.

What number am I?

4 7 3 1 .

1)

2)

3)

Here are some number cards.

a) What is the smallest number you canmake?

b) What is the largest number you canmake?

Each card can be used once, all cards must be used,the decimal point card cannot be at the end of a number.

The times, in seconds, for the seven runnersin a 100m race were:

9.96 10.03 9.92 10.26 10.37 9.99 10.00

What was the time of the winner?

© Mathswatch Ltd

Level 4


N12

Page 25A

1) For each of the three grids below, write down theratio of shaded squares to unshaded squares.

Simplify the ratios if possible.

a) b) c)

2) Shade in squares for each grid to give the correct ratios.

Shaded Unshaded

5 : 7

Shaded Unshaded

1 : 2

Shaded Unshaded

5 : 1

a) b) c)

3) The instructions on a lemonsquash bottle are as follows:

a) If you put 20 ml of squash in a glass, how muchwater would you need?

b) If you had used 200 ml of water, how muchsquash should be in the drink?

c) If you want to make 500 ml of squash drink,how much squash should be used and howmuch water?

1 part squash to4 parts water

Basic Ratio

© Mathswatch Ltd

Level 4


Just For FunN12

Page 25B

DragianVesuvian

1) Here we have a fine exampleof a Vesuvian and a Dragian.

If you count carefully you cansee that the ratio of teeth is 5 : 7

a) What is the ratio of feet?

b) What is the ratio of eyes?

c) What is the ratio of fingers?

Check that you have given allratios in the simplest form.

2) Look at this picture ofVesuvians and Dragians andwork out the following:

a) The ratio of Vesuvians toDragians.

b) The ratio of Vesuvian feet inthe picture to Dragian feet inthe picture.

c) The ratio of Vesuvian eyes inthe picture to Dragian eyes inthe picture.

3) In another picture of Vesuvians and Dragians we onlyknow two things:

Firstly, there are more Vesuvians than Dragians.Secondly, there are 46 teeth altogether in the picture.

Work out how many Vesuvians and Dragians there arein the picture.

© Mathswatch Ltd

Level 4


C7

Page 26A

1) 1524 + 4273

2) 7452 + 216

3) 24578 + 1215

4) 591 + 372 + 85

5) 9876 + 55 + 1039

6) 59.1 + 37.2

7) 24.75 + 9.98

8) 94.78 + 104.9

9) 309 + 12.5 + 631.4

10) 105 + 7.32 + 51.8 + 2804

=

=

=

=

=

=

=

=

=

=

Addition

© Mathswatch Ltd

Level 4


Just For FunC7

Page 26B

a)

1)1 1 12 2 23 3 34 4 45 5 5 +

+ = 4.6

+ = 11.26b)

a) replace three of the digits with zerosso that the answer is 1411

b) replace three of the digits with zerosso that the answer is 1513

c) replace three of the digits with zerosso that the answer is 1626

d) replace three of the digits with zerosso that the answer is 1583

In the sum on the right

2)

3.61

3.2

2.975

7.65

2.35

1.006

1.3

3.58

6.72

2.25

Choose a number from a box and a number from a

loop to make the totals in a) and b).

© Mathswatch Ltd

Level 4


C8

Page 27A

1) 14562 – 1251

2) 6652 – 716

3) 42160 – 39215

4) 2300 – 934

5) 475.83 – 81.6

6) 68.1 – 27.3

7) 24.75 – 0.098

8) 94.78 – 36

9) 3564 – 1971.6

10) 800 – 237.62

=

=

=

=

=

=

=

=

=

=

Subtraction

© Mathswatch Ltd

Level 4


Just For Fun

Page 27B

C8

Complete the boxes and the circles:

2010

– 1962

– 750

– 806.5

– 21.65

– 26.261

– 1002

– 38.1

1875

1658.8

81

661

© Mathswatch Ltd

Level 4


C9

Page 28A

=

=

=

=

=

=

=

=

=

=

1) 3 × 13

2) 55 × 4

3) 9 × 64

4) 92 × 5

5) 7 × 87

6) 342 × 8

7) 6 × 208

8) 745 × 4

9) 289 × 7

10) 113 × 9

Short Multiplication

© Mathswatch Ltd

Level 4


Just For Fun

Page 28B

C9

20 3

** 27

1) Here are some items available from a

local shop:

Work out the cost of:

a) 5 jackets

b) 6 MP3 players

c) 4 pairs of trainers

d) 7 televisons

Jacket: £17 Trainers: £56 MP3 player: £32 Television: £499

2) Work out what the must be.

a) b)

**

*×

*answer: * **

**× 5

72

© Mathswatch Ltd

Level 4


C10

Page 29A

1) 786 ÷ 2

2) 465 ÷ 5

3) 448 ÷ 8

4) 552 ÷ 6

5) 801 ÷ 9

6) 5976 ÷ 8

7) 9080 ÷ 5

8) 17801 ÷ 7

9) 18054 ÷ 6

10) 374877 ÷ 9

=

=

=

=

=

=

=

=

=

=

Short Division

© Mathswatch Ltd

Level 4


Just For Fun

Page 29B

C10

1) Here are some items available from a local

shop:

Work out the unit price of each item knowingthat:

7 watches cost £336,

5 cameras cost £380,

4 camcorders cost £1260,

6 laptops cost £7794.

2) a) If 3 chairs cost £17.40,

how much would one of them cost?

£_____

b) If 7 shirts cost £34.93,

how much would one of them cost?

£_____

Watch: £ ____ Camera: £ ____ Camcorder: £ ____ Laptop: £ _______

© Mathswatch Ltd

Level 4


C11

Page 30A

=

=

=

=

=

=

=

=

=

=

1) 4 × 1.2

2) 6.5 × 3

3) 9 × 18.7

4) 3.6 × 5

5) 7 × 8.2

6) 6 × 1.39

7) 9.2 × 8

8) 8.35 × 4

9) 3.62 × 7

10) 25.3 × 9

Multiplication of Decimals

© Mathswatch Ltd

Level 4


Just For FunC11

Page 30B

1) Here are some items available from alocal shop:

Work out the cost of:

a) 7 lollies,

b) 3 bottles of milk,

c) 2 loaves of bread,

d) 5 boxes of chocolates.

Milk: £1.20 Bread: £0.65 Lollies: £0.30 Chocolates: £3.99

2) Rulers cost £0.25 each.Pens cost £0.45 each.Kelly buys 3 rulers and 5 pens.

Work out how much she pays.

© Mathswatch Ltd

Level 4


C12

Page 31A

1) Which four coins make a total of 77p?

2) Six bars of metal each weigh 2.75 kg.How much do they weigh altogether?

3) At a party for 171 people, 9 guestssat at each table.How many tables were there?

4) Coke cans cost 43p each.How many cans you buy with £6?

5) Olivia went to a cafe.She ordered:

2 sausagesBaked beans3 coffee1 juice

She paid with a £5 note.Work out how much change she got.

Menu

Problems Withouta Calculator

Fried eggs 30pBaked beans 45pSausages 38p

Coffee 65pTea 72pJuice 50p

© Mathswatch Ltd

Level 4


C12

Page 31B

Just For Fun

A bus starts at Birmingham and makes three stopsbefore reaching London.At Birmingham, 37 people get on.At Rugby, 13 people get off and 6 get on.At Willen, 9 people get off and 15 get on.At Luton, 24 people get off and 8 get on.How many people are on the bus when itreaches London?

A mug and a plate together cost £2.90.The mug cost 40p more than the plate.

How much does the plate cost?

1)

2)

3)

4)

Cheese is on offer at £3.26 per kilogram.Emma buys half a kilogram.

How much change does she receive froma £10 note?

A man is 27 cm taller than his son, who is8 cm shorter than his mother. The man was born42 years ago and is 1.78 m tall.

How tall is his wife?

© Mathswatch Ltd

Level 4


C13

Page 32A

1) There are 7 people in a team.How many teams can you make from131 people?

2) A motorist bought 26 litres of petrol at£1.19 per litre.a) How much did it cost?b) What change did he get from £50?

3) A museum trip is organised for 57members of a youth club. They go inminibuses that can each seat up to15 people.It costs £42.50 for each minibus and £172for the group to access the museum.How much will the trip cost per person?

4) Mars Bars cost 35p. Skittles cost 45p.Gillian bought 5 bags of Skittles andsome Mars Bars.She paid with a £5 note and received30p change.How many Mars Bars did she buy?

Problems With a Calculator

© Mathswatch Ltd

Level 4


C13

Page 32B

Just For Fun

1) Three consecutive integers have a sum of 105.What are they?

2) Using the brackets keys of your calculator,

work out the following.

a) 164 – (27 + 56) =

b) 44.8 ÷ (15.4 – 9.8) =

c) (19.8 – 3.3) ÷ (31.2 – 16.2) =

d) (8 × 14.4) ÷ (11.1 – 4.7) =

3) If you start with 16 and press the square root key ofyour calculator ( ) twice, the answer given is 2.

If you start with 81 and press the square root key ofyour calculator ( ) twice, the answer given is 3.

Complete the following sentences:a) If you start with 1296 and press the square root

key of your calculator twice,the answer given is_____ .

b) If you start with _____ and press the square rootkey of your calculator twice, the answer given is 5 .

16

16

© Mathswatch Ltd

Level 4


A1

Page 33A

Multiply by 2 Add 3Input Output

3) a) If Simon puts 7 into the number machine, what numbercomes out?

b) If 100 goes in, what comes out?

c) If 5½ goes in, what comes out?

d) If 2.25 goes in, what comes out?

e) If 25 comes out, what number was put in?

f) If 8 comes out, what number was put in?

g) If x goes in, what comes out?

2) It costs 4p per copy on the school photocopier.

a) How much would it cost to make 15 single-sidedcopies?

b) Jane has to make 6 copies of a documentwhich is double-sided (writing on both sides).

How much will it cost?

c) Ted copies a single-sided document but forgetshow many copies he has made.

Rather than counting them he simply looks atthe bill and works it out from there.

The bill was for £2.20.

How many copies had he made?

Single-sidedcopies

4p each

1) A vintage car hire firm charges £70 for the first day’shire followed by £55 per day for all other days.

a) How much would it cost to hire a car for 2 days?

b) How much would it cost to hire a car for 9 days?

c) When Sue hires a car it costs her £345.

How many days did she hire the car for?

Formulae Expressed in Words

© Mathswatch Ltd

Level 4


Just For FunA1

Page 33B

1) Choose any number.

Add three to it.

Multiply your result by two.

Add six to it.

Halve your answer.

Subtract your original number.

You should be left with six.Try to find out why you are always left with six.

Input Output

1 __

4 __

10 __

2.5 __

-3 __

__ 30

__ 48

__ -18

x __

Input Output

3 __

10 __

-4 __

__ or __ 54

x __

4) Copy the table on the right.

Use this function machine to complete thetable.

Multiply byitself

Add 5Input Output

Input Output

1 __

4 __

10 __

2.5 __

-3 __

__ 30

__ 48

__ -18

x __

2) 3)

© Mathswatch Ltd

Level 4


A2

Page 34A

×

×

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

×

×

×

×

×

×

××

A

B

C

D

E

F

G

H

I

J

x

y1) Write down the

coordinates of thecrosses labelledA to J.

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

x

y

2) Put crosses at the followingpoints and label them with thecorrect letters.

A (3, 7)

B (8, 4)

C (2, 5)

D (6, 0)

E (2.5, 3)

F (0, 6.5)

G (5.5, 7.5)

H (8, 8)

Coordinates in First Quadrant

© Mathswatch Ltd

Level 4


Just For FunA2

Page 34B

Sue has hidden an ostrich on the grid on the left -it is at (6, 5) and is labelled O.

Jack guesses the hiding place by shouting outcoordinates.

Sue marks them on her grid and then tells Jackhow far away he is from the hiding place.

Jack’s first guess is (2, 3).Sue tells him this is 6 away from the ostrich.

a) Why does she tell him his guess is 6 away?

b) He then guesses (4, 6) and she tells him it is3 away. Why?

c) How far away is (8, 8)?

d) How far away is (6, 4)?

e) Which guess would be the furthest away?

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

x

y

×O

×

1)

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

x

y

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

x

y

2) Play “Find the Ostrich” with a friend. You both need two grids like the ones below:

a) You hide an ostrich on your left hand grid, your friend hides an ostrich on his/herleft hand grid. (Coordinates must be whole numbers)

b) Choose who guesses first.

c) When your friend guesses, tell him/her how far away the guess is.

d) When you guess, mark the guess on the right hand grid.When you are told how far away it is, write it next to your guess.

e) The first one to find the ostrich is the winner.

Hide an ostrich on this grid Mark your guesses on this grid

×

×

×

© Mathswatch Ltd

Level 4


S6

Page 35A

1234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678

1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567

1234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789

Making 3D Models

Print this page onto card.Cut out the net and score along all the dotted lines with a compass point.Put glue on the shaded tabs, fold and stick to make a TETRAHEDRON.

© Mathswatch Ltd

Level 4


S6 Making 3D Models

Page 35B

123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456

1234512345123451234512345123451234512345123451234512345123451234512345123451234512345123451234512345123451234512345123451234512345

123456789012345678901234567123456789012345678901234567123456789012345678901234567123456789012345678901234567123456789012345678901234567

123456789012345678901234567123456789012345678901234567123456789012345678901234567123456789012345678901234567123456789012345678901234567

1234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456

1234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456

1234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456

Print this page onto card.Cut out the net and score along all the dotted lines with acompass point.Put glue on the shaded tabs, fold and stick to make a CUBE.

© Mathswatch Ltd

Level 4


S6 Making 3D Models

Page 35C

1234567890123456789012345678901212312345678901234567890123456789012123123456789012345678901234567890121231234567890123456789012345678901212312345678901234567890123456789012123

12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 1234567890123456789

123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789

12345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789

123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234

Print this page onto card.Cut out the net and score along all the dotted lineswith a compass point.Put glue on the shaded tabs, fold and stick to makean OCTAHEDRON.

© Mathswatch Ltd

Level 4


Just For FunS6

Page 35D

12345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123

12345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123

12345678901234567890121234567890123456789012123456789012345678901212345678901234567890121234567890123456789012

12345678901234567890121234567890123456789012123456789012345678901212345678901234567890121234567890123456789012

1234567890123456789012123456789012345678901212345678901234567890121234567890123456789012

Print this page onto card.Cut out, score and glue each net to make two 3D shapes.

You now have a two-piece jigsaw.Can you fit both pieces together to make a TETRAHEDRON.

When you can do it, challenge other people to try.

© Mathswatch Ltd

Level 4


S7

Page 36A

In all four questions, reflect the shadedshape in the dotted mirror line.

1)

3)

2)

4)

Reflection in Diagonal Lines

Just For FunS7

Page 36B

How to use reflections to draw a Rangoli Pattern

Step 1:On the grid on page 36E,draw ANY three lines in thetop right section.You can see my three linesin this grid.

Step 2:Reflect your lines in thevertical mirror line.

vertical mirror line

Level 4


Rangoli Patterns

© Mathswatch Ltd

Just For FunS7

Page 36C

Level 4


Rangoli Patterns

How to use reflections to draw a Rangoli Pattern

Step 3:Reflect the completepattern in the horizontalmirror line.

Step 4:Choose one of the diagonalmirror lines.First reflect the top sectionin this line and then reflectthe bottom section in thesame line.

horizontal mirror line

Your Rangoli design can becoloured to give a strikingpattern.They can also be placed sideby side as on page 36D.

© Mathswatch Ltd

Just For FunS7

Page 36D

Level 4


Rangoli Patterns

Six Rangoli Patterns Placed Together

© Mathswatch Ltd

Just For FunS7

Page 36E

Level 4


Rangoli Patterns

© Mathswatch Ltd

© Mathswatch Ltd

Level 4


S8

Page 37A

Translation

Translate the shape 5 squaresto the right and 2 squares up.

1) Translate the shape 3 squaresto the left and 2 squares down.

2)

Translate the shape with vector3) -43

Translate the shape with vector4) 4-5

© Mathswatch Ltd

Level 4


Page 37B

Just For FunS8

A with vector

B with vector

C with vector

D with vector

E with vector

F with vector

G with vector

H with vector

I with vector

03

-20

5-1

20

-1-3

4-2

-3-2

23

1-4

Use tracing paper and translate the following shapes.

A

C

D

E

F

GB

HI

© Mathswatch Ltd

Level 4


S9

Page 38A

Rotate the shape 90° about thecross.

1) 2)

3) 4)

Rotate the shape 90° about thecross.

Rotate the shape 180° aboutthe cross.

Rotate the shape 90° clockwiseabout the cross.

Rotation

© Mathswatch Ltd

Level 4


Just For FunS9

Page 38B

1

2

A

a) Rotate triangle A 90° clockwise about cross 1.Label your new triangle B.

b) Rotate triangle B 90° clockwise about cross 2.Label your new triangle C.

c) How many degrees would you need to rotate triangle A toget to triangle C?

d) Mark with a cross the centre of rotation to get from A to C.

© Mathswatch Ltd

Level 4


S10

Page 39A

Reading Scales

ml.50

100

150

A

B

1)

2)

Miles

Kilometres0

0 10 20 30

10 20 30 40 50

Use the scale to convert

a) 10 miles to km.

b) 40 km to miles.

c) 16 miles to km.

d) 8 km to miles.

3)

C

a) If water comes up to arrow A, howmuch will there be in thecontainer?

b) About how much water will therebe if it comes up to arrow B?

a) If milk comes up to arrow A, howmuch milk will there be in thecontainer?

b) How much milk will there be ifit comes up to arrow B?

c) Draw arrow C to show 140ml ofliquid.

0.5L1L1.5L2L2.5L3L3.5L4L

A

B

© Mathswatch Ltd

Level 4


Just For FunS10

Page 39B

You have eight genuinegold coins and one fakegold coin.Each genuine coin weighsone ounce.The fake coin weighsslightly less but notenough to detect by hand.You are allowed to use thebalance pans just twice todetect the false coin.How do you find the fake?

You have a 3 pint jug and a 5 pint jug and asmuch water from a tap as you like.How can you use the two jugs to measure outexactly 4 pints of water?

1)

2)

3 Pints5 Pints

© Mathswatch Ltd

Level 4


S11

Page 40A

Perimeters

1) Find the perimeter of thisrectangle on the cm grid.

2) Find the perimeter of thisshape on the cm grid.



© Mathswatch Ltd

Level 4


Just For FunS11

Page 40B

A

Perimeter = 16Area = 7 squares

On the dotty grid you can see a shape which has a perimeterof length 16 and an area of 7 squares.

Keeping the perimeter always 16, draw 9 more shapes whichhave areas of 8, 9, 10, 11, 12, 13, 14, 15 and 16 squares.

© Mathswatch Ltd

Level 4


S12

Page 41A

1) Find the area of the rectangleon this centimetre grid.



Areas

© Mathswatch Ltd

Level 4


Just For FunS12

Page 41B

1) Draw three different-shapedrectangles with an area of 12cm2

on the centimetre grid.

2) Find the area of thesquare on thiscentimetre grid.

3) Find the area of thesquare on thiscentimetre grid.

This is a difficult question

© Mathswatch Ltd

Level 4


D3

Page 42A

Discrete Data

Blue Green Red Yellow

1) 30 students were asked which of the four coloursthey liked best.The results are listed below:

Red Green Blue Red Yellow Red Green Red

Green Yellow Red Blue Blue Red Green Blue

Red Green Green Yellow Blue Red Blue

Green Red Red Red Blue Green Green

Record these results in a tally chart.

2) Peter asked all the pupils in his class how many childrenthere were (including themselves) in each of their families.

These are the results:

1, 3, 2, 2, 2, 1, 3, 2, 3, 4, 2, 1, 1, 4, 2, 6, 3, 2,

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

Show these results in a tally chart.

3) A teacher asked the pupils in her class to put stickers onthe board to show which pets they had. The stickers wereof dogs, cats, hamsters, goldfish and snakes.

Draw a tally chart to show how many of each petthere were.

© Mathswatch Ltd

Level 4


Just For Fun

Page 42B

D3

This is the first paragraph of a book.

However, it is written in code where each letter has beenreplaced by a different letter.

Can you decode the paragraph?

There is a little bit of help at the bottom of the page.

Some helpWhen you decode the paragraph you will findthat:‘e’ is the most common letter.‘a’ is the second most common followed by‘o’ third most common, then‘n’ and ‘r’then ‘t’then ‘s’.

Imjz zsmop mck dj m wmo-kww gmjh qbsos gdush

mj kcos kw brcs loklkoqdkjp.

Bdp wmukrodqs kttrlmqdkj vmp qk tmlqros lkko

lsmpmjqp mjh imfs qbsi vkof wko woss kj bdp

gmjh. Bs vmpj’q usoz jdts.

Qbs jmis kw qbs kcos vmp Gmjts.

© Mathswatch Ltd

Level 4


D4

Page 43A

1) Here are the Maths test marks for two mixedability Year 7 classes.

Complete the frequency table to show all the results.

Mark Tally Frequency

20 and under

21 - 30

31 - 40

41 - 50

51 - 60

61 - 70

over 70

43 16 68 49 31 24 83 61 55 40 72 44 45 23 48 33 2081 63 58 41 50 59 46 35 24 13 66 99 53 47 66 48 5133 35 40 64 50 31 37 42 35 54 97 24 33 48 53 42

Class interval Tally Frequency

14 s < 16

16 s < 18

18 s < 20

20 s < 22

<

<

<

<

2) A group of students measured their hand span (s) inin centimetres. Here are their results:

Complete the frequency table to show all the results.

Grouping Data

14.720.016.721.618.217.918.1

19.019.916.014.419.121.816.4

17.915.918.019.116.521.118.9

© Mathswatch Ltd

Level 4


Just For FunD4

Page 43B

Sally, the organiser of a slimming club, keeps data on howmuch weight (w), in kg, her 60 members have lost over theprevious twelve months.

She organises the data in a two-way table.

a) Complete the two-way table.

b) How many members of the club were women?

c) How many women lost between 5 and 10 kg?

d) How many men lost less than 20 kg?

e) How many men lost 5 kg or more?

f) How many men and women lost 15 kg or more?

Men Women Total

0 < w < 5 2 6

5 < w < 10 14

10 < w < 15 7

15 < w < 20 2 10

20 < w < 25 11 14

Total 18

© Mathswatch Ltd

Level 4


D5

Page 44A

Tim Sue Ben Tom Dev Ned Kim

1) a) In this group of seven people, which one hasthe median average height?

b) What are the names of the people who arebelow the median average height?

c) To find the range of the heights you wouldneed to measure the height of two people.Which two?

2) A class of students were asked how many petsthey own.

The answers were as follows:

1, 0, 1, 2, 1, 5, 2, 0, 1, 2, 3, 1, 4

2, 3, 1, 2, 2, 0, 1, 1, 2, 1, 3, 2

a) Find the median average number of pets per student.

b) Which number of pets is the mode?

c) What is the range of the answers?

3) Twenty children were asked what their favourite colour was.

Their answers were:

Blue, Red, Yellow, Red, Green, Red, Green, Blue, Red, Blue

Green, Blue, Red, Blue, Yellow, Red, Blue, Orange, Red, Red

a) Which colour is the modal average?

b) Why can’t we find the median colour?

Mode, Medianand Range

© Mathswatch Ltd

Level 4


Just For FunD5

Page 44B

1) The heights of 18 plants, to the nearest cm, are as follows:

15, 19, 16, 12, 13, 15, 20, 18, 16, 14, 12, 18, 16, 16, 17, 15, 15, 15

a) Find the modal height of the plants.

b) Find the median height of the plants.

c) Find the range of the heights.

87815

2) You are told that the median score onthese four cards is 9.5

Work out what the number is on thebottom card.

9123) We have six cards with numbers on

them and we know the following:

the modal average is 3

the median average is 5

the range is 11

Work out the numbers on the other four cards.

Score Frequency

1 2

2 3

3 3

4 4

5 4

6 7

4) Sue rolls a dice 23 times and puts herscores into a table.

a) What is Sue’s modal score?

b) What is Sue’s median score?

c) What is the range of Sue’s scores?

© Mathswatch Ltd

Level 5


N13

Page 45A

1) 3.6 × 10

2) 82.9 × 100

3) 0.5 × 1000

4) 47 ÷ 10

5) 106.4 ÷ 10

6) 9.9 ÷ 100

7) 6.2 × 1000

8) 70 ÷ 1000

9) 0.035 × 10000

10) 0.01 ÷ 100

Multiplication and Divisionby 10 and 100

=

=

=

=

=

=

=

=

=

=

© Mathswatch Ltd

Level 5


Just For Fun

Page 45B

N13

1)

2) Using the fact below:

365 × 17 = 6205

Work out the following

a) 36.5 × 17 = ____ d) 3650 × 1.7 = ____

b) 36.5 × 1.7 = ____ e) 62.05 ÷ 17 = ____

c) 365 × 170 = _____ f) 6.205 ÷ 36.5 = ____

Fill in the missing box in each case.

a) f)

b) g)

c) h)

d) i)

e) j)

1)

12 540 5.4

7.5 0.6 0.006

83.1 8310 73.7

0.9 900 ×10 0.18

662 66.2 ×1000 104

×100

÷10

÷100

© Mathswatch Ltd

Level 5


N14

Page 46A

Rounding

2) Round the following numbers to 1 decimal place.

a) 4.21 f) 578.48

b) 53.43 g) 79.035

c) 31.59 h) 3443.77052

d) 8.827 i) 26.9999

e) 0.653 j) 99.961

1) Using a calculator, work out the following.Give your answers to the nearest 10.

a) 24 × 14

b) 383 × 43

c) 4088 ÷ 56

d) 265364 ÷ 326

e) (42000 + 768) ÷ 54

© Mathswatch Ltd

Level 5


Just For Fun

Page 46B

N14

Round each of the numbers on the calculators to(i) 1 d.p.(ii) 2 d.p.(iii) the nearest whole number.

4.762181)

(i) ___

(ii) ___

(iii) ___

0.5239872)

(i) ___

(ii) ___

(iii) ___

4870.10553)

(i) ___

(ii) ___

(iii) ___

4)(i) ___

(ii) ___

(iii) ___

1.6371285)

(i) ___

(ii) ___

(iii) ___

17.490386

6)(i) ___

(ii) ___

(iii) ___

19799.992

© Mathswatch Ltd

Level 5


N15

Page 47A

The temperature is-2 °C and then rises

by 6.5 °C.

A

1 °C colder thanfreezing point.

B

The temperature is-6 °C then rises by

8 °C before falling by5 °C.

C

102 °C cooler thanboiling point.

D

1) Work out the value of each card and then place the cards inorder from lowest to highest.

You have £5 in thebank but write acheque for £9.

E

Tim owes you £5.Sam owes you £3.You owe Ben £12.Tom owes you £2.

F

You owe threepeople £0.50 each.

H

You owe five people£1.25 each but

someone owes you£3.50

I

You owe sevenpeople £2 each but

six people eachowe you £1.50

J

You have £10 in thebank but then write

cheques for £6,£2.50, £5 and £1.

G

2) Work out the value of each card and then place the cards inorder from lowest to highest.

Ordering Negative Numbers

© Mathswatch Ltd

Level 5


Just For FunN15

Page 47B

5 2

1)These two cards each have a numberon the back as well as on the front.

Eric shuffles the cards quite a fewtimes and lays them on the table.

He then adds the numbers he cansee.

He discovers there are four differenttotals.

They are: 3, 5, 7 and 9.

Can you work out what numbers areon the back of each card?

12 8

2)

The totals with these cards are:

11, 13, 20 and 22.


5 9

3)


2, 7, 9 and 14.


12 7

4)


2, 3, 19 and 20.


© Mathswatch Ltd

Level 5


N16

Page 48A

Ordering Fractions

1) Put the following fractions in order of size startingwith the smallest.

You can use the grids to help if you wish.

34

56

23

712


You can use the grids to help if you wish.

1320

35

34

710


712

12

58

1324


25

310

13

16

© Mathswatch Ltd

Level 5


Just For FunN16

Page 48B

1730 2

5

4760

1524

38

712

129

20

23

715

34

13

Smallest

Largest

Place the fractions on thecards in order of size fromsmallest to largest.

© Mathswatch Ltd

Level 5


N17

Page 49A

Simplification of Fractions

1) Cancel each of these fractions to theirsimplest form:

a) b) c)

d) e) f)

26

510

312

216

927

2080

2) Cancel each of these fractions to theirsimplest form:

a) b) c)

d) e) f)

414

3070

1634

2442

2745

2836

3) Cancel down fully each of these fractions:

a) b) c)

d) e) f)

3355

7296

4590

75100

40180

68116

© Mathswatch Ltd

Level 5


Just For FunN17

Page 49B

Here are six number cards.

a) Choose two of these six cards


equal to .

b) Choose two of these six cards


equal to .

c) Choose three of these six cards


equal to .

d) Choose three of these six cards

to make the smallest

possible fraction.

2 5 9 7 4 11

4599

112144

28175

© Mathswatch Ltd

Level 5


N18

Page 50A

1) Draw ten 4 by 3 rectangles and label them a to j

Shade in the rectangles in the following ratios.

The first answer is

Shaded : Unshaded

1 3

1 2

1 5

5 7

1 1

1 11

2 4

0.5 2.5

0.2 1

9 15

a

b

c

d

e

f

g

h

i

j

a

The three shaded squarescould have been any threeof the squares.

2) Write the following ratios intheir simplest form:

a) 8 : 12

b) 6 : 10

c) 15 : 10

d) 16 : 4

e) 18 : 16

f) 25 : 15

g) 45 : 15

h) 18 : 27

i) 24 : 30

j) 36 : 48

3) Find the missing numbers inthese ratios:

a) 1 : 4 = 2 :

b) 1 : 5 = 6 :

c) 2 : 7 = 8 :

d) 5 : 4 = 15 :

e) 2 : 3 = : 12

f) 9 : 5 = : 35

g) 3 : = 18 : 30

Understanding Ratios

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Level 5


Just For FunN18

Page 50B

A

1

2

3

4

5

6

7

B

A B

A B

BA

A B

BA

A B

= water= orangeWhich is orangier: A or B?

You must give convincingreasons for each of youranswers

© Mathswatch Ltd

Level 5


C14

Page 51A

1) 17 × 32

2) 24 × 62

3) 13 × 156

4) 1.5 × 22

5) 7.6 × 2.1

6) 4.5 × 9.99

7) 528 × 16

8) 19.7 × 6.3

9) 34 × 466

10) 0.35 × 0.12

=

=

=

=

=

=

=

=

=

=

Long Multiplication

© Mathswatch Ltd

Level 5


Just For FunC14

Page 51B

1)

2)

Work out what the must be.*1 5

27 0

1 3 5 00

×******

3

4800

6120

80 *****

*answer: * ** *

×

0

25450

40 ****

*answer: 13775

× *00 ************

47

3 39 0

3

×**** **

A school organises a trip to a museum.

They set off in 13 minibuses, each minibus containing24 pupils who will each pay to go into the museum.

Entrance to the museum costs £1.20 per person.

a) How many people made the trip?

b) What was the total cost?

a)

c)

b)

d)

© Mathswatch Ltd

Level 5


C15

Page 52A

Long Division

=

=

=

=

=

=

=

=

=

=

1) 288 ÷ 12

2) 285 ÷ 15

3) 425 ÷ 25

4) 784 ÷ 56

5) 79.2 ÷ 22

6) 5.89 ÷ 19

7) 893 ÷ 38

8) 9.87 ÷ 47

9) 330.2 ÷ 13

10) 35259 ÷ 92

© Mathswatch Ltd

Level 5


Find the missing digits.

a) b)3

Just For FunC15

Page 52B

1)

2)

a) If 48 luxurious pens cost £768,how much would one of them cost?

b) If 25 tee shirts cost £77.50,how much would one of them cost?

c) If 53 mobile phones cost £2 119.47,how much would one of them cost?

Cans of juice cost 24p each.

Wendy has £8.65 to spend.

a) What is the maximum number of cans Wendycan buy?

b) How much change does she get?

3)

14 0 4 2 2 22

© Mathswatch Ltd

Level 5


C16

Page 53A

BODMAS

1) Work out the following:

a) 3 × 6 – 2

b) 7 + 2 × 3

c) 5 + 3 × 4 – 1

d) (7 + 1) × 3

e) 5 – 3 × 2

f) 9 – 35 ÷ 5

g) 3 × 2 + 7 + 5 × 4

h) 20 – 9 ÷ 3 + 1

i) 2 × (15 – 10) ÷ 5

j) 7 + 2 – 3 × 4

k) 10 ÷ (2 + 3)

l) 10 ÷ 5 – 8 ÷ 2

m) 7 × (5 – 2) + 10

n) 48 ÷ (2 + 3 × 2)

o) 4 × 12 ÷ 8 – 6


a) 32 – 23

b) 25 – (3 – 1)2

c) 8 × 7 – 16

d) 36 ÷ 22 – 3 × 3

e) 53 – (3 × 15 – 25)

f) ((9 + 1) × 4) ÷ 2

3) Place brackets in thefollowing questions tomake the answers correct.

a) 3 × 5 – 1 = 12

b) 10 + 2 × 3 = 36

c) 7 × 5 – 2 × 2 = 42

d) 24 ÷ 6 – 2 = 6

e) 3 + 2 × 6 ÷ 10 = 3

f) 5 × 5 – 3 ÷ 4 + 1 = 2

4) If x = 3 and y = 7, work out the following:

a) 2x – y

b) 3y + x2

c) y2 – x2

d) (x + y)2 – x3

e) 5(y – x) + (y + x) ÷ 2

f) 10xy – (2y – x)2

© Mathswatch Ltd

Level 5


Just For FunC16

Page 53B

1) Use the numbers 6, 3, 2 and 1 plus the operations +, –, ×, ÷to make the numbers 0 to 9.

The numbers must be used in the specified order (6, 3, 2, 1).

They cannot be put together as in 63 for example.

Signs can be used as many times as you like. Brackets canalso be used.

0 = 6 – 3 – 2 – 1 5 = 6 ÷ 3 + 2 + 1

1 = 6 – 3 × 2 + 1 6 = 6 + 3 – 2 – 1

2 = 6 – 3 – 2 + 1 7 = 6 + 3 ÷ 2 + 1

3 = 6 + 3 ÷ 2 + 1 8 = 6 + 3 – 2 + 1

4 = 6 – 3 + 2 – 1 9 = 6 – 3 × 2 + 1

2) Use four 4s plus the operations +, –, ×, ÷ to make thenumbers 0 to 9.

All four 4s must be used. 4s cannot be put together as in 44.

Signs can be used as many times as you like. Brackets canbe used.

A possible answer for 0 could be 4 ÷ 4 – 4 ÷ 4

0 = 5 =

1 = 6 =

2 = 7 =

3 = 8 =

4 = 9 =

© Mathswatch Ltd

Level 5


C17

Page 54A

1) Find the following:

a) 13

of 24 b) 23

of 24

c) 15

of 30 d) 35

of 30

e) 18

of 40 f) 58

of 40

2) Work out:

a) 710

of £30 b) 37

of £84

c) 45

of £1.50 d) 1120

of £19

e) 29

of £10.98 f) 813

of £31.85

3) Julie has £4.50 pocket money every week.

If she spends of it on a magazine and ofit on a dance lesson, how much of the pocketmoney does she have left?

25

13

4) Paul has £7.80 pocket money each week.

He always saves of it.

With the remaining money he spends oncomics and the rest on sweets.

(i) How much does he save?

(ii) How much is spent on comics?

(iii) How much does he spend on sweets?

58

13

Fraction of an Amount

© Mathswatch Ltd

Level 5


Just For FunC17

Page 54B

12

a)1) of 23( )of 60

34

b) of 12( )of 80

12

c) of 49

of 42of 34

2) If 34

a) of a number is 60, what is the number?

If 37

b) of a number is 21, what is the number?

If 49

c) of a number is 12.3, what is the number?

3) If 12

of 15

of a number is 6, what is the number?

4) If 12

of 13

of 14

of 15

of a number is 2.5, what is the number?

5) If 35

of 12

of 23

of a number is 3.8, what is the number?

Find

Find

Find

© Mathswatch Ltd

Level 5


C18

Page 55A

Directed Numbers

1) The temperature is 3°C at midnightand then falls 8 degrees by 6 a.m.

What is the temperature at 6 a.m?

2) Tim has only £8 in his bank accountbut writes a cheque for £15.

If the cheque is cashed, how muchwill Tim have in his account?

3) Sue owes £7 to one friend and £6 toanother friend.

She writes this in her diary as (-7) + (-6)

a) How much does she owe altogether?

b) What is (-7) + (-6)?

4) Sue still owes £7 to one friend and £6to another friend but her motherdecides to take away the £6 debt bypaying it off.

Sue writes this as (-7) + (-6) – (-6)

a) How much does Sue owe now?

b) What is (-7) + (-6) – (-6)?

5) Work out the answers to

a) 6 – 14

b) 2 – 12

c) -1 – 6

d) -3 – 5

e) -7 – 15


a) 2 – (-3)

b) 6 – (-5)

c) -3 – (-6)

d) -7 – (-2)

e) -20 – (-18)


a) 5 + (-2)

b) 8 + (-6)

c) 3 + (-8)

d) -4 + (-3)

e) -8 + (-4)

-1 0 1 2 3 4 5 6 7 8-2-3-4-5-6-7-8


a) 4 – (+1)

b) 7 – (+5)

c) 1 – (+3)

d) -6 – (+1)

e) -1 – (+6)

© Mathswatch Ltd

Level 5


Just For FunC18

Page 55B

1) Each magic square below has a magic number writtenabove it.

You must fill in the blank squares so that the rows,columns and diagonals add up to the magic number.

10

4 0

-2 9

2

515

-22

-9

-10

Magic Number is

12Magic Number is

15Magic Number is

-27

2) Work out which numbers should go in the squares tomake the sums correct.

a) 7 + = 9

b) 7 + = 5

c) 2 – = -6

d) 4 – = 7

e) -5 – = 4

f) + 6 = 4

g) – 9 = -12

h) – 14 = -30

a) b) c)

© Mathswatch Ltd

Level 5


C19

Page 56A

Ratio Questionsin Context

1) Share out £20 between Bill and Suein the ratio 3 : 2.

2) Divide £60 between Jack and Jillin the ratio 7 : 3.

3) Debbie and Dave share 200 Smartiesin the ratio 1 : 4. How many Smartiesdo they each get?

4) Alec, Tony and Sara share £720 inthe ratio 1 : 2 : 3. How much do theyeach get?

5) If Dave and Sue share £30 in theratio 2 : 3, how much more thanDave does Sue get?

6) Divide £12 between Mick andSharon in the ratio 5 : 3.

7) Pete and Sandra work part-time in arestaurant. They share the tips in theratio 3 : 5.If Pete gets £30 at the end of theweek, how much will Sandra get?

8) Vicky and John share some sweetsin the ratio 2 : 7.If Vicky ends up with 12 sweets, howmany will John have?

9) Len makes some concrete bymixing cement, sand and gravel in theratio 1 : 4 : 3.If he uses 8 bags of sand, how manybags of cement and gravel will he use?

10) An old television has a width and heightin the ratio 4 : 3. If the width is 48 cm,what is the height?

© Mathswatch Ltd

Level 5


Just For FunC19

Page 56B

1) Which one of these regularpolygons has the number ofdiagonals and the number ofsides in the ratio 2 : 1?

A B C D

2) Two numbers are in the ratio 7 : 3.If you take one of the numbers away from theother one you get an answer of 24.What are the two numbers?

3) In a class of 30 pupils the ratio of boys to girlsis 2 : 3.If 6 girls (but no boys) join the class what isthe new ratio of boys to girls?

4) Sue, Ted and Ben all have theirbirthday on the 1st January.

In 2010, Sue, Ted and Ben haveages in the ratio 2 : 3 : 4.

a) If Ted is 15 years old, how oldare Sue and Ben?

b) When Sue, Ted and Ben are allfive years older, what will be theratio of their ages? Write theanswer in its simplest form.

c) In which year was the ratio ofSue, Ted and Ben’s age 1 : 2 : 3?

d) How old was Ben when the ratioof the three ages was 1 : 3 : 5?

e) On what date was the ratio ofSue and Ben’s age 1 : 41?

© Mathswatch Ltd

Level 5


C20

Page 57A

Direct Proportion

1) 4 litres of orange juice cost £3.20.

a) What is the cost of 8 litres?

b) How much would 20 litres cost?

c) How much would you pay for 6 litres?

d) What is the cost of 5 litres?

2) 15 voice minutes cost 45p.

What is the cost ofa) 30 voice minutes?

b) 150 voice minutes?

3) If £1 is worth 1.12 euros, how many euroswould you get for £150?

4) Use direct proportion to solve the followingproblems:

a) 5 litres of water cost £3.00.How much would 9 litres cost?

b) A recipe for two people uses 90 g of flour.How much flour is needed for 5 people?

c) 20 blank CD-Roms cost £3.20.How much do 75 CD-Roms cost?

d) A litre of water costs 62p.What is the cost of 2.5 litres of water?

e) 3 kg of cheese costs £7.50What is the cost of 6.5 kg of cheese?

f) 2 litres of smoothie contains 900 ml oforange juice.How much orange juice is in 8.5 litres ofsmoothie?

g) A 120 ml carton of yoghurt contains12 g of sugar.How much sugar would be in a 200 mlcarton of yoghurt?

© Mathswatch Ltd

Level 5


Just For FunC20

Page 57B

Miles Kilometres

5 8

10

24

32

50

1)a) Use direct proportion to complete

this conversion table.

b) The distance between London andBirmingham is 120 miles.Use the table to work out thisdistance in kilometres.

c) The distance between London andParis is 460 kilometres.Use the table to work out thisdistance in miles.

3) A jar has 200 sleeping flies in it and the lid is firmly on.

The weight of the jar, when empty is 1 kg.

The weight of the jar and sleeping flies is 1.9 kg (1900 g).

a) If all the flies are the same weight, what is the weightof one fly?

b) Tina shakes the jar so that all the flies are now awakeand flying around.What will the weight of the jar of flies be, now?

2) Here are three offers for voice minutes on a mobile phone.

In which of the offers are the numbers in direct proportion?In each case, explain your answer.

Minutes Cost

1 £0.04

5 £0.20

40 £1.60

A

Minutes Cost

2 £0.24

10 £1.00

100 £7.00

B

Minutes Cost

10 £0.70

50 £3.50

60 £4.20

C

© Mathswatch Ltd

Level 5


C21

Page 58A

Real Life Tables

London

195300

330

Nottingham100

159

Manchester

56 Liverpool

All distances are in miles.

1)

a) Write down the distance between London and Nottingham.

b) Write down the names of the two cities which are(i) The furthest apart.

(ii) The least distance apart.

c) Peter travels from London to Manchester where he collects a parcel.He then delivers the Parcel in Nottingham before returning to London.Work out the total distance travelled by Peter.

Stockport 05:26 06:16 06:55 07:15 07:55

Stoke 05:55 06:45 07:24 - -

Stafford 06:12 - 07:41 - 08:41

Euston 08:09 08:26 - 09:11 10:06

2) Here is part of a railway timetable

a) Rosie wants to travel from Stockport to Euston. She mustarrive in Euston before 09:00.

(i) What is the latest time she could depart from Stockport?

(ii) How long will her journey last?

b) James gets to Stockport station at 07:00.How long will he have to wait for the next train to Stafford?

c) Alex travels to Euston.She gets on the 07:24 train from Stoke.How long will her journey take?

© Mathswatch Ltd

Level 5


Just For FunC21

Page 58B

1)

Emma lives in Doncaster.She has to drive to Peterborough to pick up her friend, David, and then continue on toLondon to attend a graduation ceremony which begins at 11 am.The ceremony will last two hours and she will then return to Doncaster with David.

a) How far does Emma travel in order to get to London with David?

b) If Emma averages 50 mph on the return trip, at what time would she be backin Doncaster?

Stevenage48

165

Peterborough

130 Doncaster

All distances are in miles.

210 170 45 York

London

2275

195

235

Chester

Wrexham16 minutes

Gobowen35 minutes

Shrewsbury55 minutes

Welshpool76 minutes

Wellington69 minutes

Newtown90 minutes

Telford75 minutes

Wolverhampton90 minutes

2) The train route diagram show the times it takesto travel from Chester to other major stationson the line.

Use the information in the diagram to completethe following

timetables.

Wolverhampton 16:42

Wellington

Shrewsbury

Gobowen

Wrexham

Chester

Telford

Chester 04:22

Gobowen

Shrewsbury

Welshpool

Newtown

Wrexham

© Mathswatch Ltd

Level 5


A3

Page 59A

1) Write down the expression you will have ifyou think of a number (let x be the number)and then:

a) add three to it

b) double it

c) multiply it by three and then subtract four

d) multiply it by itself

e) divide it by two

f) divide it by two and then add one

g) add three to it and multiply the resultby two

h) multiply it by five, add four, divide theresult by two

2) Say what the following expressionsmean in words.

a) x + 6

b) x – 7

c) 8x

d) 4x + 2

e)

f) 6(x + 7)

g) 4(3x – 1)

x5

3) If s = 2v, work out the value of swhen v = 7

4) If y = 3t + 4, work out the value of ywhen t = 5

5) If g = 2t – 1, work out the value ofg when t = 9

6) If f = 2(t + 8) and t = 3, find thevalue of f

7) If d = 3(2e – 3) and e = 5, findthe value of d

8) If c = 4 and d = 3, find thevalue of:

a) 2c

b) 2c – d

c) cd

d) 5c + 2d

e) 10cd

f) 2(c + d)

g) 5(3c – 2d)

What expression do I have ifI think of a number, double itand then add three?

Answer: 2x + 3

Say what the expression 4x + 17means in words.

Answer: Take a number, multiplyit by four and then add seventeen.

Algebraic Expressions

© Mathswatch Ltd

Level 5


Just For FunA3

Page 59B

The body mass index (BMI) is a measure used to show if an adult isat a healthy weight. It doesn’t apply to children, only adults.

Here is a formula for calculating BMI

A person with BMI between 18.5 and 25 is at a healthy weight.

A person with BMI less than 18.5 is underweight.

A person with BMI between 25 and 30 is overweight.

A person with BMI over 30 is obese.

BMI = (weight in kg) ÷ (height in m) ÷ (height in m)

Here are the heights and weights of the four people above.They are in no particular order.

a) Work out the BMI for each height and weight and put them in the table.Give your answers to the nearest whole number.

b) Match each height, weight and BMI with the correct person.

c) For each person, decide whether he/she is underweight, healthy,overweight or obese - write the answer next to each person.

d) A woman is 1.65 m tall and weighs 45.6 kg.She worries that she is overweight.Is she right?

Height (m) 1.74 1.82 1.62 1.62

Weight (kg) 70 57 55 74

BMI

© Mathswatch Ltd

Level 5


A4

Page 60A

1) Write down thecoordinates of thecrosses labelledA to J.

2) Put crosses at the followingpoints and label them with thecorrect letters.

A (-5, 3)

B (2, -4)

C (-2, -6)

D (5.5, 3)

E (0, 0)

F (-3, 0)

G (-6, -5)

H (0, -5)

10-1-2-3-4-5-6 2 3 4 5 6

1

-1

-2

-3

-4

-5

-6

2

3

4

5

6

x

y

B

E

H

AF

J

I

C

D

×

×

×

× ×

×

××

×10-1-2-3-4-5-6 2 3 4 5 6

1

-1

-2

-3

-4

-5

-6

2

3

4

5

6

x

y

×

G

y

y

x

Coordinates in FourQuadrants

© Mathswatch Ltd

Level 5


Just For FunA4

Page 60B

10-1-2-3-4-5-6 2 3 4 5 6

1

-1

-2

-3

-4

-5

-6

2

3

4

5

6

x

y

×

×

×

×

×

×

y = 2x + 1

(2, 5)

(1, 3)

(0, 1)

(-1, -1)

(-2, -3)

(-3, -5)

For every point on the line if youmultiply the x coordinate by 2 andthen add 1 you always get the ycoordinate.This is why we call the line y = 2x + 1

2) Plot the following points on thegrid, draw a line through thepoints and try and work out thename of the line.

a) (6, 6), (5, 5), (4, 4), (3, 3), (2, 2)(1, 1), (0, 0), (-1, -1), (-2, -2)(-3, -3), (-4, -4), (-5, -5), (-6, -6)

b) (6, 3), (4, 2), (2, 1), (0, 0), (-6, -3)

c) (4, 5), (3, 3), (2, 1), (1, -1), (-1, -5)

d) (5, 6), (5, 5), (5, 4), (5, 3), (5, 2)(5, 1), (5, 0), (5, -1), (5, -2), (5, -6)

WEARCLEAN

POTOOOOOOOO

O _ E R _ T _ O _ XMASCARA

must get heremust get heremust get here

HOROBODDR doo

1) Below there are seven well-known phrases or expressions.Expression (a) is “Clean underwear”.Try and work out the other six.

(a)(b) (c) (d)

(e) (f)

(g)

Every question on this pagecan be answered if you justsee them in the right way.

© Mathswatch Ltd

Level 5


A5

Page 61A

Horizontal & Vertical Lines

-8 -7 -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6 7 8

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

x

y

1) Draw the following lines on theaxes to the right:

a) x = 3

b) x = -4

c) y = 1

d) x = 7.5

e) y = -3

f) y = 4.5

-8 -7 -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6 7 8

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

x

y

2) Name all the lines drawn on theaxes on the left.

Line a is: ______________

Line b is: ______________

Line c is: ______________

Line d is: ______________

Line e is: ______________

Line f is: ______________

a

bc

d

e

f

© Mathswatch Ltd

Level 5


Just For FunA5

Page 61B

O 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

x

y

1) (i) Plot the points(0, 1)(1, 2)(2, 3)(3, 4)(4, 5)(5, 6)

(ii) Draw a line throughthese coordinates.

(iii) Name the line.

2) (i) Plot the points(0, 0)(1, 2)(2, 4)(3, 6)(4, 8)(5, 10)



3) (i) Plot the points(0, 1)(1, 3)(2, 5)(3, 7)(4, 9)(5, 11)



© Mathswatch Ltd

Level 5


A6

Page 62A

Function Machines

1) Find the output for each of these function machines.

× 53a)

+ 57b)

× 2 – 36c)

+ 5 ÷ 313d)

÷ 2 – 710e)

– 4 × 2.57f)

2) Find the input for each of these function machines.

– 5 8a)

÷ 4 25b)

× 2 – 1 19c)

÷ 5 + 8 18d)

– 7 ÷ 2 3.5e)

× 19 – 4 -4f)

© Mathswatch Ltd

Level 5


Just For FunA6

Page 62B

x

× 2– 7

× 5

– 7

– 2 10x - - - - - -

÷ 2– 5

- - -

- - -

- - -

x5 + 6

× 3

+ 1

× 2- - -

- - - - - + 3

- - -

- - -

4x + 1

- - - - - - - - - -

5x – 7- - - - - - - - - -

- - - - - - - - - -

- - - - - - - - - -

Complete the diagram below. Every time you see dashes like thisyou need to write the correct number or expression.

One of them (5x – 7) has already been done for you.

- - - - - - - - - -,

- - - - - - - - - -,

© Mathswatch Ltd

Level 5


S13

Page 63A

a) b)c) d)

e) f) g)

h)

1) For figures a to h, work out

i) The order of rotational symmetry.

ii) How many lines of symmetry it has.

2) Shade in six more triangles sothat this figure has rotationalsymmetry order 3

Symmetries of 2D Shapes

© Mathswatch Ltd

Level 5


Just For FunS13

Page 63B

a) Shade in one squareso that this shape hasrotational symmetry oforder 2.

1) b) Shade in a differentsquare so that thisshape has rotationalsymmetry of order 2.

2) Shade three more squaresso that the grid has rotationalsymmetry of order 4.

CHLOEBAXTER

3) The diagram shows a poster whichChloe has on her wall.When Chloe was standing on her head,looking in a mirror on the opposite wallat the poster on the wall behind her,how many letters could still be read thenormal way?

© Mathswatch Ltd

Level 5


S14

Page 64A

a

e fg

d

c

b

1) Each of the angles below can be described as an acuteangle, an obtuse angle, a reflex angle or a right angle.

Decide which each of them are.

2) a) Draw a triangle which has three acute angles.

b) Draw a triangle which has one obtuse angleand two acute angles.

c) Draw a quadrilateral (4-sided shape) whichhas one reflex angle and three acute angles.

d) Draw a quadrilateral which has one rightangle, one acute angle and two obtuse angles.

e) Draw a quadrilateral which has two obtuseangles and two acute angles.

Measuring and Drawing Angles

© Mathswatch Ltd

Level 5


S14

Page 64B

a

b

c

d

e

Use a protractor to measure theangles below.


© Mathswatch Ltd

Level 5


S14

Page 64C

a

c

d

e

Use a protractor to measure theangles below.

b


© Mathswatch Ltd

Level 5


S14

Page 64D

Draw the angle where you see the dot.Here is an example:

40° 40°

70°a) 135°b)

28°c)

171°d)


© Mathswatch Ltd

Level 5


S14

Page 64E

Draw the angle where you see the dot.

340°a) 305°b)

245°c)

193°d)


© Mathswatch Ltd

Level 5


Just For FunS14

Page 64F

a) Measure, very carefully, angles A, B and C.

b) Add the angles together.

c) What do they add up to?

d) Tear or cut along the wavy lines.

e) Fit the angles together to form a straight line.

1)

a) Draw some more triangles.Don’t forget ones like these

b) For each triangle, label the angles A, B and C.It doesn’t matter which is which.

Fill in the table below.

2)

Triangle 1

Angle A Angle B Angle CAll three anglesadded together

Triangle 2

Triangle 3

Triangle 4

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Tear or cut here

A

B C

© Mathswatch Ltd

Level 5


S15

Page 65A

50°35°

a

42° b

c

65°

70°

70°80°

85°

d

55°

e

120°

58°f

g

h

1) Work out the size of angles a to h.

Angle Facts

© Mathswatch Ltd

Level 5


Just For FunS15

Page 65B

110°

x

A B

CD

E

ABCD is a rhombus (all four sides the same length)

ABE is an isosceles triangle in which BA = BE

Angle AED = 110°

Work out the size of angle x

Question 1 is tricky.Question 2 is very challenging - some teachers struggle

68°

a 34°

b123°c

Find angles a, b and c1)

2)

© Mathswatch Ltd

Level 5


S16

Page 66A

Areas of Rectangles

1) Find the areas of the following four rectangles.

9 cm

4 cm

5 m

3 m

9.6 cm

2.8 cm

12 m

3.5 m

a) b)

c)

d)

2) Find the lengths of the missing sides.

Area = 24 cm26 cm

?

Area = 96 cm2

12 cm

?Area =

253.44 cm2

13.2 cm

?

b)a) c)

© Mathswatch Ltd

Level 5


Just For FunS16

Page 66B

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10 cm

14 cm

8 cm

6 cm

1) Find the area of the shaded section.

2) Find the area of the shape below.

15 cm

6 cm

10 cm

7 cm

© Mathswatch Ltd

Level 5


D6

Page 67A

1) Estimate a probability (decimal) to go with these:

a) You will be on time for school on the nextschool day.

b) It will snow sometime this week.

c) Your teacher will smile at least once tomorrow.

d) You will have a disagreement with one of your friends.

e) England will win the World Cup in 2018.

f) England or France will win the World Cup in 2018.

2) Work out an exact probability (as a fraction)for these events:

a) If you flip a coin you will get a ‘head’.

b) If you flip two coins you will get two ‘heads’.

c) If you roll a dice you will get a 6.

d) If you roll two dice you will get two 6’s.

e) If you flip a coin and roll a dice you will geta ‘head’ and a 6.

f) If you flip three coins you will get three ‘heads’.

g) If you flip three coins you will get two ‘heads’and a tail in any order.

h) If you flip three coins you will get at leastone ‘head’.

i) If you roll two dice and add the scorestogether you will get a total of 4.

Probability

© Mathswatch Ltd

Level 5


Just For FunD6

Page 67B

To play this game you needthe following:

two dice.

18 counters each torepresent the 36 horses.

a big copy of the diagramon the left.

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

R I V E R

Player A puts 18 horses on this side

Player B puts 18 horses on this side

Rules of the game:

Each player places their eighteen countersbehind any numbers of their choice. (Youcan see an example below when Sophie andAlex play the game).

Roll the dice and add the scores together.

If any player has a horse behind the totalscore, he/she can move the horse to theother side.

Keep rolling the dice and movingthe horses whenever you can.

The winner is the first one to getall their horses to the other side.

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

R I V E R

Sophie

Alex

Tactics matter in thisgame.The person whoarranges their horses inthe best way willusually win.Play at least 3 times.

© Mathswatch Ltd

Level 5


D7

Page 68A

The Mean Average

1) a) Move blocks around so thatthe heights of the five towersare the same.

b) What is the mean averagenumber of blocks in eachtower?

2) a) Move blocks around so thatthe heights of the five towersare the same (you may haveto cut some blocks).

b) What is the mean averagenumber of blocks in eachtower?

3) In a spelling test, the results for the class (out of 10) are:

3, 6, 8, 8, 4, 1, 7, 6, 2, 9, 3, 8, 4, 1, 1, 3, 5 and 2

a) Work out the mean average score for the class.

b) How many children had a score below the mean average?

4) Two Year 6 classes had a ‘times table test’ which wasmarked out of 20.

The marks in David’s class were:

14, 12, 19, 20, 20, 15, 14, 12, 13, 3, 18, 19, 16, 14, 12, 6

Harry was in the other class and the marks were:

9, 12, 17, 17, 16, 14, 18, 20, 8, 13, 16, 14, 18, 8

Use the mean average to work out which class didbetter in the test.

© Mathswatch Ltd

Level 5


Just For FunD7

Page 68B

878

52

1) If the mean average number on thesefive cards is 6, what is the number on thebottom card?

2) If the mean average number on theseeight cards is 4.25, what is the numberon the bottom card?

845

26

4

7 3

3) John rolled a dice thirty times andput the results into this table.

Work out his mean average score.

Score Frequency

1 4

2 3

3 5

4 6

5 4

6 8

4) What is the mean averagenumber of arms per personin Britain?

5) Can you find out the meannumber of children perfamily in the UK?

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

N19

Page 69

Fraction Decimal Percentage

50%

40%

0.25

0.7

11013

Fraction Decimal Percentage

35%

5%

0.6

0.6

68100

1350

1) Complete the tables.

a) b)

2) Put these fractions, decimals and percentagesin order, smallest to largest.

a) , 49%, , 0.55

b) 27%, 0.2, ,

c) , 95%, 0.99,

d) , 0.6, , 30%

e) 0.125, 10%, , 0.09

12

3514

310

910

97100

13

23

11100

3) Chris says that is halfway between 0.5 and 100%.

Is Chris correct? You must explain your answer.

34

4) Emily says that 0.2 is halfway between 10% and .

Is Emily correct? You must explain your answer.

35

Fractions, Decimalsand Percentages

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 70

N20Improper Fractions and

Mixed Numbers

54

127

165

83

209

4712

307

253

758

1009

2) Convert the following mixed numbers to improper fractions.

a) f)

b) g)

c) h)

d) i)

e) j)

35

23

27

14

35

311

58

19

45

34

1

2

5

3

11

10

7

9

6

12

3) Put these numbers in order, lowest to highest.

a) 3.5, 3 ,

b) 7 , 7.14,

c) 1 , 98%, , 1

15

113

14

345

54

110

1) Convert the following improper fractions to mixed numbers.

a) f)

b) g)

c) h)

d) i)

e) j)

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 71

N21Prime Numbers,HCF and LCM

1) Split up the following numbers into the product of their prime factors.

a) 12 d) 120

b) 45 e) 550

c) 72 f) 1296

2) Find the Highest Common Factor (HCF) of the following numbers.

a) 4 and 6 d) 300 and 525

b) 8 and 16 e) 374 and 918

c) 36 and 48 f) 45, 90 and 105

3) Find the Lowest Common Multiple (LCM) of the following numbers.

a) 8 and 12 d) 4, 6 and 8

b) 30 and 45 e) 24 and 84

c) 15 and 18 f) 72 and 96

4) The bells at Kings School ring every 6 minutes.

At Queens School the bells ring every 5 minutes.

At Princess School the bells ring every 9 minutes.

All three bells ring together at 8.30 am.

When is the next time the bells of the three schools will ring together?

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 72

C22Percentage

of an Amount


a) 50% of 80

b) 50% of 48

c) 50% of 15

d) 25% of 120

e) 25% of 90


a) 10% of 150

b) 10% of 26

c) 50% of 12

d) 25% of 12

e) 75% of 12


a) 10% of £40

b) 5% of £40

c) 15% of £40

d) 5% of £70

e) 15% of £380


a) 20% of £50

b) 45% of £9

c) 80% of £11

d) 35% of £6

e) 65% of £824

5) Jamie received £26 pocket money last week.

He spent it as follows: 10% on sweets,

25% on magazines

15% on games

How much did Jamie have left?Show your working.

6) Tony had £40 saved up and gave 35% of it to his younger sister, Ella.

Ella gave 20% of what she was given to her younger brother, Ben.

Ben gave 30% of what he was given to his younger brother, Tim.

Tim spent 75% of what he was given on buying a toy for his hamster, Hammy.

How much was the toy for Hammy?

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 73

C23

3) Increase the following numbers by 10%

a) 40 e) 75

b) 140 f) 505

c) 810 g) 12

d) 320 h) 123

4) Decrease the following numbers by 10%

a) 20 e) 25

b) 160 f) 445

c) 80 g) 13

d) 190 h) 7


a) Increase £400 by 5% e) Increase 250 m by 50%

b) Decrease £120 by 15% f) Decrease £820 by 75%

c) Decrease 500 km by 20% g) Increase 60 kg by 60%

d) Increase 96 kg by 10% h) Decrease £26 by 35%

6) A shop is having a sale and all prices are reduced by 25%.

a) Work out the sale price of an item normally priced at £18.40

b) Work out the sale price of an item normally priced at £99

2) Describe how you would decrease a number by 10%.

Percentage Increaseand Decrease

1) Describe how you would increase a number by 10%.

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 74

C24Addition and Subtraction

of Fractions

1) Work out the following, simplifying youranswers where possible.

a) e)

b) f)

c) g)

d) h)

27

37+ =

38

18+ =

79

29 =

16

23+ =

16

23+ =

45

12 =

1415

35 =

7

9

18 18+ =

6 6+ =

15 15 =

2) Work out the following, simplifying youranswers where possible.

a) f)

b) g)

c) h)

d) i)

e) j)

38

48+ =

12

13+ =

12

25+ =

510

110 =

911

511 =

57

35 = 3

812+ =

512

16+ =

56

14 =

45

110 =

89

56 =

2) Write the missing numbers in each of these fraction sums.

a)

b)

c)

d)

13 6+ =

85 15 =

37

12 =

15 14 =

+

1

1

1

1

© Mathswatch Ltd

Level 6


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Page 75

C25Multiplication and Division of

Integers by Fractions

1) Work out the following, giving your answers in their simplest forms

a) 3 × e) 4 ×

b) 7 × f) 10 ×

c) 2 × g) × 6

d) 9 × h) × 3

14

17

45

13

49

38

89

215


a) of £40 e) of 30 cm

b) of 20 km f) of £16

c) of 120 kg g) of 7000 g

d) of £99 h) of £500

12


a) 3 ÷ e) 10 ÷

b) 7 ÷ f) 8 ÷

c) 12 ÷ g) 3 ÷

d) 9 ÷ h) 15 ÷

14

12

13

15

23

45

57

23

15

14

19

25

78

47

34

4) An industrial machine takes of an hour to produce a very special tool.

How long would it take the machine to produce 12 of the tools?

34

5) A road is 20 km long. Road signs are to be installed every ofa kilometre. How many signs will be needed?

23

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Level 6


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Page 76

A7 Substitution

1) Using a = 3, work out

a) a + 5 d) 2a + 1

b) 7 – a e) 13 –

c) 6a f) a2 + 2a – 20

a3

2) Using x = 5 and y = 2, work out

a) x – y d) 5y – 5x

b) y – x e) x2 + 3y

c) 3x + 2y f) – xy4xy

3) Using a = 3, b = 1 and c = -2, work out

a) a + b + c d) ab – c

b) 2b + c e) ac + 5b

c) c – a + b f) c2 – 2ab

4) Using x = 3, work out

a) x2 – 2x

b) 2x2 + x + 1

c) x3 – 2x2 – 5

5) If = 3.142 and r = 9, work out

a) 2 r

b) r 2

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Level 6


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Page 77

A8 Trial and Improvement

1) Using a trial and improvement method,solve the equation x2 – x = 56

You must show ALL your working.

3) Using a trial and improvement method,solve the equation x3 + 2x = 72


2) Using a trial and improvement method,solve the equation x2 + 4x = 21


4) Using a trial and improvement method,solve the equation x3 – 3x = 110


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Level 6


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Page 78

A9Algebraic Simplification

1) Simplify these expressions

a) 3a + 4a = f) 3r – 2r + 4r =

b) b + 4b = g) 5t – 3t + t + 2t =

c) 5x – x = h) 7p – p + 2p – 5p =

d) 6d + 3d – 2d = i) -4y + 2y – y + 4y =

e) 2k + k + k – 3k = j) -2c + c – 3c – c =


a) a + b + a + b = f) 6x – 4y + 7y – 2x =

b) 3a + 2a + 4b + b = g) 2k – 3l – k + 10l =

c) 7x + 2y + x + 3y = h) 3m + 5n + 7m – 7n =

d) 5r + 6p – 2r – 3p = i) v – 4w – 5v – 2w =

e) 4c + 8d – 3c + d = j) -3x – y – 3y – x =


a) 7xy – 2xy = f) 6m + 2pr – m + 3rp =

b) 5cd + 3dc = g) 10a2d + 2y – 3da2 + y2 =

c) x2 + 4x2 + 2x2 = h) bz2 + 4t3 – 3t3 – 5zb2 =

d) 9y3 + y – 2y3 = i) 2r2b + 5r2 – r + 6br2 =

e) 3ab + 7ab – 2a = j) 8x3y + 2w – 5w – 3yx3 =

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Level 6


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Page 79

A10Linear Equations

1) Solve

a) x + 5 = 8 f) 2x = 14

b) x + 7 = 9 g) 3x = 30

c) x – 3 = 12 h) = 8

d) x – 6 = 10 i) = 7

e) 2 + x = 5 j) = 8

2) Solve

a) 5x + 2 = 17 f) + 3 = 7

b) 3x – 1 = 17 g) – 2 = 4

c) 2x + 10 = 20 h) – 1 = 9

d) 4x – 7 = 29 i) + 5 = 11

e) 4 + 2x = 14 j) + 6 = 8

x2x5

2x53x2

4x5

3) Using the statement: “I think of a number, double it,and subtract 1. I get 7.”

a) Form an equation.

b) Solve the equation to find the number that was thought of.

4) Using the statement: “I think of a number, multiply it by 7,and add 3. I get 80.”



5) Using the statement: “I think of a number, multiply it by 2,divide the result by 3 and then subtract 5.I get 5.”



x2x5

4x3

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Level 6


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Page 80

A11Generate a Number

Sequence

1) Write the first five terms of each sequence

a) Start at 1 and add 5 d) Start at 8 and subtract 4

b) Start at 30 and subtract 4 e) Start at -10 and add 6

c) Start at 11 and add 9 f) Start at 4 and subtract 3

2) For each sequence, describe the rule and find the next two terms

a) 5, 7, 9, 11, ___, ___ d) -1, 2, 5, 8, ___, ___

b) 11, 16, 21, 26, ___, ___ e) 6, 2, -2, -6, ___, ___

c) 22, 19, 16, 13, ___, ___ f) -42, -35, -28, -21, ___, ___

3) Here is a pattern made up of sticks

a) Write the pattern as a number sequence.

b) Describe the rule.

c) Find the next five terms of the sequence.

4) For each sequence, find the first 5 terms and the 10th term.

a) 3n – 1

b) n + 2

c) 5n + 2

d) 4n – 7

e) 10n + 9

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Level 6


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Page 81

A12

Pattern 1 Pattern 2 Pattern 3

1)

a) Draw pattern 4

b) How many lines would be in Pattern 6?

c) How many lines would be in Pattern n?

2) Work out the nth term of the following number patterns.

a) 2, 4, 6, 8, . . . .

b) 3, 5, 7, 9, . . . .

c) 5, 8, 11, 14, . . . .

d) 1, 5, 9, 13, . . . .

e) 12, 22, 32, 42, . . . .

f) 2, 8, 14, 20, . . . .

g) 3, 4.5, 6, 7.5, . . . .

3) Write down the first four terms and the 10th term of the followingnumber patterns.

a)

b)

c)

d)

e)

f)

g)

n 3n

n 3n + 2

n n – 3

n 2n + 5

n 3n – 7

n 5n + 3

n 4n – 1

Finding the nth Term

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Level 6


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Page 82

A13Straight Line Graphs

-5 -4 -3 -2 -1 O 1 2 3 4 5

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

12

13

x

y

x -2 -1 0 1 2 3 4 5y

1) a) Complete the table of values for y = 3x – 2

b) Plot the graph of y = 3x – 2

c) Use your graph to estimate the value of xwhen y = 2

d) Use the graph to estimate the value of xwhen y = -4

-3 -2 -1 O 1 2 3 4

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

y

x

2) a) Plot the graphof y = 2x – 4

b) Plot the graphof x + y = 1

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Level 6


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Page 83

A14

The graph, above, shows Jade’s journey by scooter from herhouse to university with some stops along the way.

a) How long did the journey take?

b) How many breaks did Jade take throughout her journey?

c) At what time did Jade take her first break?

d) How long did the first break last?

e) What was Jade’s average speed between 3 pm and 4 pm?

f) What was Jade’s average speed between 4.30 pm and 5 pm?

g) What was Jade’s average speed between 5.30 pm and 7 pm?

Distancein miles

3 4 5 6 7 80

10

20

30

40

50

60

70

80

pm pm pm pm pm pmTime

Distance - Time Graphs

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Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

2) The graph below shows three different mobile phone tariffs.

Tariff 1Pay as you go50p per minute.

Tariff 2£15 per month and30p per minute

Tariff 3£40 per month,100 free minutes then10p per minute

a) Match each tariffwith its graph, A, B or C

b) Every month, Jamesneeds about 90 minstalk time.Work out which tariff wouldbe best for him. Explain your answer.

c) Tariff 4 is announced. This is £10 per month, 40 free minutes then 30p per minute.Draw a line on the graph to show this tariff.

Page 84

A15 Real Life Graphs

1) Use the conversion graph below to convert :

a) 80 km to miles

b) 35 miles to km

c) 40 km to miles

d) 60 miles to km

e) 100 miles to km

f) 140 km to miles

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

0Kilometres

Miles

0 20 40 60 80 100 120 140 1600

10

20

30

40

50

60

Costin £

Monthly used minutes

A

BC

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Level 6


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Page 85

S17Properties of Quadrilaterals

a) b) c)

d) e) f) g)

1) Write down the names of the quadrilaterals a) to g)

8 cm

14 cm

9 cm

A

12 cm

8 cm

9 cm

B

16 cm

10 cm

C

Number of linesof symmetry

Order of rotationalsymmetry AreaShape

A

B

C

2) Fill in the table for quadrilaterals A, B and C.

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Level 6


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S17 S18

Page 86A

S18 Nets of 3D Shapes

a) Draw a net of this cube. b) Draw a net of this cuboid.

3 squares

3 squares

3 squares

2 squares1 square

4 squares

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Level 6


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Page 86B

S18 Nets of 3D Shapes

Draw a net of this triangular prism.

12 squares

5 squares13 squares

4 squares

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Level 6


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Page 87

S19 Constructions

1) Using only a ruler, protractor and pencil, draw the following diagrams accurately.

For each diagram measure and write down the side you are asked for.

a)

A B

C

7 cm

40° 65°

Measure length AC

25°120°

6 cmA B

C

Measure length AC

b)

110°

80°

4 cm

3.5 cm

A

D

C

B

Measure length CDc)

A B

C

DE

F

3 cm

3 cm

3 cm

3 cm

3 cm

Measurelength CD

d)

120°120°

120°

120° 120°

2) Using only a ruler, pencil, compasses and protractor as needed, draw thefollowing diagrams accurately.

For each diagram, measure and write down the angle you are asked for.

6 cm

4.5 cm7 cmr

A B

C

a)Measureangle r

8 cm

5 cm5 cm

sA B

C Measureangle sb)

A B

C

t

3 cm

5 cm7.5 cmMeasure

angle t

c)d)

A B

C

D

E

7 cm

4 cm5 cm

2 cm5 cm

80° 70°

Measureangle uu

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Level 6


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Page 88

S20In every question below, calculate the missing angles indicated by theletters. None of the diagrams are drawn accurately.

46° 78°

a

29°

35°

b

41°

c 57°

d

50°

e

235°

f50°

g

74°85°

40°

h

24°

64° e

f 35° g

h

40°

ji 55°

l

k

44°a 115°

b53°

c

38°

d

72°

115°e

125° 72°f 143° 45°

g

20°

32°

h36°

148°

65°

a

145°

73°

b 68° 54°

c32°

d

1)

2)

3)

Geometric Problems

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 89

S21

a

bc

e

fg

d58°

Corresponding andAlternate Angles

28°b

d

105°f

153°

79°

h

i

jk

l

mn

o64° 70°

p q

r s

t

a

61°

72°

64°

71°

a

bc

d

e

80°

24°

37°

a

In every question below, calculate the missing angles indicated by theletters. None of the diagrams are drawn accurately.

1)

124°c

2)

e

137°

3)

4)

45°

40°

b

c

de

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 90A

S22 Enlargement

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Enlarge the following shapes with scale factor 2, using the dot as the centre of enlargement.

a) b)

c) d)

e) f)

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Level 6


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Page 90B

Enlargement

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Scale factor 3 Scale factor 3

Scale factor 4 Scale factor 0.5

a) b)

c) d)

A

B

C

D

2) Use dots to mark on the grids the positions of the centres of enlargement.

a) b)

1) Enlarge the following shapes using the dots as the centres of enlargement.

S22

© Mathswatch Ltd

Level 6


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Page 91

S23Similar Shapes

1) In each of the following questions, the two shapes aremathematically similar.

Work out the lengths of the missing sides.

a) b)

c) d)

12 cm

?

4 cm

7 cm

4 cm

?

8 cm

10 cm

8.2 cm

7 cm

?

9.8 cm

4.2 cm

?10 cm

2 cm16.6 cm

?

2) a) Work out the length of CD.

b) Work out the length of AE.

A

B

CD

E

5 cm

3 cm

10 cm

4 .5 cm

© Mathswatch Ltd

Level 6


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Page 92A

S24Area of a Triangle

1) Find the areas of the following triangles

a) b) c) d)

8 cm 5 cm

6 cm 7 cm 1 cm

0.6 cm

13 cm 15 cm


a) b)

c)

12 cm

5 cm

13cm

2.8 cm

1.3 cm2.5 cm

30 cm

40 cm

50 cm


a) b)

13 cm

8 cm 8.6 cm6.4 cm

26.4 cm

18.2 cm

c)

d)

14 cm

20 cm

e) 36 cm

28 cm

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Level 6


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Page 92B

S24Area of a Triangle

16 cm

20 c

m

5 cm

3 cm

7 cm

6 cm

14 cm

22 c

m

20 cm

26 c

m

4 cm

5 cm

9 cm 6 cm

5 cm 8 cm

7 cm

7 cm

2) Find the areas of the following shaded parts of rectangles

a) b) c)

6 cm

wArea = 12 cm2

8 cm

x

Area =18 cm2

Area =12.5 cm2

y

4 cm

1) Find the lengths w, x, y and z

Area = 40.5 cm2

z z

3) The two squares are drawn on 1 cm square grids.Find the areas of the squares.

a) b)

a) b)

c)

d)

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Level 6


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Page 93

S25

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1) Find the areas of the five parallelograms on this cm square grid.

a) b)

c)

d)

e)

2) Find the areas of these four parallelograms

8.4 cm

3.6 cm

19 cm

19.8 cm

13 cm

12.3 cm 20 cm

18 cm

22 cm

a) b)

c)

d)

Area of aParallelogram

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 94

S26

20 cm10 cm

15 cm

19 cm

7 cm

11 cm

30 cm

22 cm

14 cm

15 cm6 cm8 cm

4.2 cm1.6 cm

2.1 cm

19 cm8 cm

?

20 cm

7 cm

9 cm

6 cm

3 cm1) Find the volume of the following:

a) b)

c) d)

2) Find the height of this cuboid

Volume = 1140 cm3

3) The cuboid below is made out ofsteel and has a rectangular hole allthe way through it.

If 1 cm3 of steel has a mass of 8 g,what is the mass of the cuboid?

Volume of a Cuboid

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 95

S27

20 cm10 cm

15 cm

19 cm

7 cm

11 cm

4.2 cm1.6 cm

2.1 cm

23 cm8 cm

9.5 cm

1) Find the surface area of the following:

a) b)

c) d)

30 cm

22 cm

14 cm

15 cm6 cm8 cm

20 cm

7 cm

9 cm

6 cm

3 cm

3) The shape below consists of acuboid glued onto another cuboid.

If the whole shape - including thebase - is painted, work out thearea which will be painted.

2) The cuboid below is made out ofsteel and has a rectangular hole allthe way through it.

All the surfaces are paintedincluding the base and the sides ofthe rectangular hole.Work out the area which will bepainted.

Surface Area of a Cuboid

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 96

S28Circumference of a Circle

8 cm6.5 cm

9.4 cm

14 cm 9.6 cm16.7 cm

1) Find the circumference of the following circles

a) b) c)

d) e) f)

60°

The circumference of the earth isapproximately 40000 km.

If you had a piece of string which was 6.3 mlonger than 40000 km and put it around theearth, how far away from the earth, all the wayround, would the extra 6.3 m allow it to be?

a) 0.1 mm b) 1 mm c) 1 cm d) 1 m

2) Find the perimeter of the following

10 cm

11 cm

12 cm18 cma) b) c)

d) 3)

.

In all questions, take to be 3.142π

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 97A

S29 Area of a Circle


8 cm6.5 cm

9.4 cm

14 cm 9.6 cm16.7 cm

1) Find the areas of the following circles

a) b) c)

d) e) f)

60°

2) Find the areas of the following

10 cm

11 cm

12 cm18 cma) b) c)

d)

130°

e)

.

5 cm

.

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 97B

S29 Area of a Circle

32 cm16 cm

= 2 cm

24 cm

A square touching acircle at four points

14 cm

14 cm

18 cm

In each question, find the area of the shaded section.

a) b)

c) d)

e)f)


© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 98

D8Bar Charts and

Frequency Diagrams

1) A group of pupils were askedfor their favourite colour.Here are the results.

Draw a suitable chart toshow this information.

Colour Frequency

Red 8

Blue 10

Purple 9

Green 4

Yellow 7

Time in mins Frequency

5

6

12

11

10

0 < t < 10

10 < t < 20

20 < t < 30

30 < t < 40

40 < t < 50

2) A group of people were given a puzzle to solve.The time taken by each individual to complete the puzzlewas recorded in the table below.

Draw a suitable chart to showthis information.

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 99

D91) The heights and weights of some children are shown in the table, below.

a) Plot the informationfrom the table.

b) Describe the correlationbetween height and weight.

c) Draw a line of best fit.

d) Estimate the weight of achild of similar age to thegroup above with a heightof 155 cm.

Height(cm)

Weight(kg)

132

34

145

40

150

43

140

35

175

60

168

54

177

62

162

51 57

162

51

165

58

149

40

150

41

135

33

159

44

160

50

170

2) The scatter graph below relates car engine sizes to their fuel consumption in mpg.

a) Describe the correlationshown by the data.

b) A car has an mpg of 25.Estimate the engine size.

0 1 2 3 40

10

20

30

40

50

60mpg

Engine size (litres)

130 140 150 160 170 18030

40

50

60

70

Height (cm)

Scatter Graphs

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 100

D10Pie Charts

1) The table on the right shows how far 90 visitorsto a museum have travelled.

Draw a pie chart to show this information.

Distance

Within the city

Within 30 milesof the city

Over 30 milesfrom the city

Overseas

Frequency

13

9

20

48

.

2) The table shows the land usage of a farm.

Draw a pie chart to show this information.

Land usage Area(hectares)

Arable

Pasture

Woodland

Waste

80

70

50

40.

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

2) A survey was done by a school to find out how people travel to the school.

Altogether, 100 people were asked and the results can be seen below.

a) Complete the two-way table.

b) How many people cycle to school?

c) How many female pupils go to school by taxi?

Page 101

D11 Two-Way Tables

1) 160 pupils in a school are asked to choose a new colour for theschool tie. They can only choose from Blue, Green or Red.

Some of the results are shown in this two-way table.

Complete the two-way table.

Blue Green Red Total

30 85

14

65 42 160

Male

Female

Total

Walk Car Cycle Taxi Bus Total

12 3 6 1

1 5 6 20

12 6 32

4 2 7 2 23

25 19 20 12 100

Male pupils

Female pupils

Male teachers

Female teachers

Total

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 102

D12Surveys

2) Beth wants to find out two things:the types of books people prefer to readhow much time, on average, they spend reading books

a) Design two suitable questions for Beth to use in her questionnaire.

b) She decides to ask her questions to the first ten people going into thepublic library on a Saturday morning.

Give one reason why this might not be a good way to carry out the survey.

1) Lesley wants to find out the types of food people like best.She is going to ask people to choose between Italian Food,French Food, Indian Food and Chinese Food.

Design a suitable table for a data collection sheet she coulduse to collect this information.

© Mathswatch Ltd

Level 6


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 103

D131) A counter is taken at random from set 1 followed by another counter

at random from set 2.

a) Write down all the possible pairs of counters that may be chosen.

b) What is the probability that 3B will be picked?

c) What is the probability that any pair of counters will be chosenexcept 3B?

d) What is the probability that the pair of counters chosen willinclude an odd number?

Further Probability

1 2

3

A

B

C

D

Set 1 Set 2

2) The two spinners on the right are spun and theirscores added together to give a total.

a) Draw a possibility space to show all the totals.

b) What is the probability of scoring a total whichis bigger than 5?

1

2 34 3

4 5

6

3) Every Tuesday the main school dinner is eitherSausages, Chicken, Pizza or Tuna.

Use the table below to work out the probability thatthe main dinner will be Pizza next Tuesday.

School dinner Sausages Chicken Pizza Tuna

Probability 0.24 0.18 ? 0.47

© Mathswatch Ltd

Level 7


N22Rounding to

1 Significant Figure

1) Round the following to 1 significant figure.

a) 478 cm

b) 450 cm

c) 449 cm

d) 12761 m

e) 28481 km


a) 673.8 cm

b) 4017.9 kg

c) 246.83 m

d) £45.38

e) 20482.1 kg


a) 0.26 ml

b) 0.043 g

c) 0.0671 m

d) 0.000256 km

e) 0.3822 m


a) 962 m

b) 0.923 cm

c) 0.971 cm

d) 0.096 km

e) 0.00985 km


a) £631428

b) 0.00573 g

c) £3614.68

d) 0.493 ml

e) £968

Page 104

© Mathswatch Ltd

Level 7


C26

Page 105

Percentage Increaseand Decrease

1) a) Increase £400 by 16%

b) Increase £750 by 24%

c) Increase £2000 by 38%

d) Increase £14500 by 19%

e) Increase £16.50 by 30%

2) a) Decrease £700 by 32%

b) Decrease £36 by 14%

c) Decrease £1970 by 40%

d) Decrease £3000 by 12.5%

e) Decrease £3124 by 16.25%

3) A sports shop reduces the price of all its trainersby 15% in the Spring sale.Before the sale, one pair of trainers cost £74.How much are they after the reduction?

4) Tim took up weightlifting.In his first session he could bench-press 45 kg.Four weeks later he could bench-press 22% more.How much could he now lift to the nearest kg?

5) If a manager of a shop reduces the price of a£1500 piano by 15% and then, four weeks later,increases the reduced price by 15%, how muchdoes it now cost?

© Mathswatch Ltd

Level 7


C27Addition and Subtraction

of Fractions

1) Work out

a)

b)

c)

d)

e)

13

+ 12

35

+ 14

27

+ 35

12

+ 29

310

+ 37

2) Work out

a)

b)

c)

d)

e)

23

+ 16

35

+ 310

12

+ 45

56

+ 35

712

+ 34

3) Work out

a)

b)

c)

d)

e)

23

+ 34

12

+ 57

25

+ 12

710

+ 15

34

+ 56

4) Work out

a)

b)

c)

d)

e)

12

+ 15

34

+ 23

16

+ 13

29

+ 23

12

+ 310

1

2

3

1

2

2

1

3

2

4

1

1

1

1

2

5) Work out

a)

b)

c)

d)

e)

23

12

34

23

45

34

56

23

34

38

6) Work out

a)

b)

c)

d)

e)

34

45

16

23

29

56

12

78

7) Work out

a)

b)

c)

d)

e)

12

12

25

110

23

1115

34

58

23

49

8) Work out

a)

b)

c)

d)

e)

4

1

1

2

5

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

1

2

3

2

6

2

1

1

1

3

cm

34

2 cm

9) Find the perimeter of the rectangle below.Give your answer as a mixed number.

cm

cm

10) Find the perimeter of the triangle below. Give your answer as a mixed number.

11) If a length of copper tubing is 20 cm long and Jim

cuts off a piece that is 17 cm long, what is the length

of the copper tubing left over?

14

3 13

12

34

45

12

29

56

38

56

5

17

3

4

1

2

5

+

–

+

–

–

1

1

2

2

8

12

1

58

cm58

1

35

Page 106

© Mathswatch Ltd

Level 7


C28Multiplication and Division

of Fractions

1) Work out

a)

b)

c)

d)

e)

12

× 34

23

× 45

1011

× 23

49

× 25

47

× 19

2) Work out

a)

b)

c)

d)

e)

23

× 35

37

× 56

89

× 610

12

× 89

710

× 521

3) Work out

a)

b)

c)

d)

e)

12

× 89

23

× 67

611

× 18

25

× 1011

34

× 89

4) Work out

a)

b)

c)

d)

e)

12

× 15

34

× 23

16

× 25

29

× 15

47

× 1315

1

2

1

4

3

2

3

4

2

3

2

2

2

1

1

5) Work out

a)

b)

c)

d)

e)

23

12

34

23

25

34

37

611

34

38

6) Work out

a)

b)

c)

d)

e)

34

15

47

79

14

67

35

910

12

38

7) Work out

a)

b)

c)

d)

e)

12

12

25

110

13

1115

34

58

23

49

8) Work out

a)

b)

c)

d)

e)

23

34

25

12

2

3

1

2

5

1

4

5

3

2

14

4

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

1

1

2

2

1

3

1

1

1

4

cm

34

2 cm

9) Find the area of the rectangle below.Give your answer as a mixed number.

12

1 cm

12

2 cm

10) Find the area of the triangle below. Give your answer as a mixed number.

11) Jim has a length of copper tubing which is 85 cm long.

He wants to cut it into pieces which are 4 cm long.

If there is no wastage, how many pieces will Jim get?

34

14

3 13

Page 107

© Mathswatch Ltd

Level 7


Page 108

C29Numbers Between 0 and 1(Multiplication and Division)

1) Work out the answers to the following:

a) 24 × 0.2

b) 13 × 0.4

c) 60 × 0.7

d) 243 × 0.2

e) 0.6 × 700


a) 314 × 0.02

b) 836 × 0.001

c) 800 × 0.006

d) 418 × 0.003

e) 411 × 0.09


a) 0.2 × 0.4

b) 0.1 × 0.03

c) 0.02 × 0.06

d) 0.08 × 0.003

e) 0.05 × 0.08


a) 62 × 0.14

b) 2.7 × 2.5

c) 613 × 0.042

d) 42.3 × 1.8

e) 228 × 0.063


a) 6 ÷ 0.2

b) 8 ÷ 0.1

c) 9 ÷ 0.3

d) 4 ÷ 0.02

e) 7 ÷ 0.002


a) 62 ÷ 0.2

b) 51 ÷ 0.3

c) 4.56 ÷ 0.04

d) 22.5 ÷ 0.05

e) 14.7 ÷ 0.007


a) 7.24 ÷ 0.2

b) 8.13 ÷ 0.3

c) 1.512 ÷ 0.07

d) 0.16 ÷ 0.008

e) 0.0732 ÷ 0.04


a) 0.718 ÷ 0.2

b) 0.0141 ÷ 0.003

c) 0.24 ÷ 0.012

d) 1.625 ÷ 0.0013

e) 47.1 ÷ 0.15

© Mathswatch Ltd

Level 7


Page 109

C30EstimatingAnswers

1) Estimate the value of:

a) 21 × 34

b) 42 × 56

c) 17 × 62

d) 29 × 78

e) 66 × 96


a) 510 × 724

b) 86 × 2146

c) 753 × 184

d) 48 × 6315

e) 3642 × 1356


a)

b)

c)

d)

e)

6119

7643

36278

73896

416781


a)

b)

c)

d)

e)

35712 × 23

92434 × 13

172 × 411430

625 × 4316 × 38

972 × 36817 × 23 × 18


a) 8 ÷ 0.12

b) 6 ÷ 0.24

c) 5 ÷ 0.49

d) 7 ÷ 0.012

e) 23 ÷ 0.18


a)

b)

c)

d)

e)

215 × 380.183

18.3 × 31.20.017

405 × 2740.488

46 × 6.20.135

24 × 5100.53

© Mathswatch Ltd

Level 7


Page 110

C31Using a Calculator

1) Using a calculator, work out the value of:

a) 24 + 16 ÷ 4

b) 3 + 8 ÷ 2 × 3

c) 60 × 2 – 20 ÷ 4

d) (2 + 7 × 8) × 4

e) (3 + 7) × (8 – 2)


a) 63 – (24 + 35)

b) (37 – 26) ÷ 104

c) 28 ÷ 23 × 52

d) 53 × 35

e) 220 – 38


a) 256 × 24 – 169

b) 365 × 365

c) 550 – 21

d) 28 + 34 – 13

e) 46 × 28 ÷ (32 – 1)


a)

b)

c)

7 + 4 × 818 – 5

63 – 23

(32 + 7) ÷ 2

d)

e)

62 × 24 + 23

43 + 32 + 33

284 – 29 – 112(3 + 17) × 100

729 + 2164

© Mathswatch Ltd

Level 7


Page 111

A16Further Algebraic

Simplification

1) Simplify the following

a) 6 × x

b) 2 × x × y

c) 6 × x × 3 × y

d) s × t × u

e) 7 × s × 2 × t × u


a) x × x × x × x

b) t × t × t × t × t × t × t

c) g × g

d) x × x × x × y × y × y × y

e) x × y × x × y × y


a) x × x2

b) y3 × y4

c) x2 × x3 × x

d) g × g × g2 × g4

e) x2 × x3 × x4 × x5


a) 3x2 × 2x3

b) 5x × 4x2

c) 6y3 × 2y4

d) 9x2 × x3

e) 4x3 × 2x × 3x2


a) 3x2y3 × 2x3y4

b) 2xy4 × 3x2y

c) 5x3y4 × 2x2y2

d) 2x2y × x4y2

e) 3x3y × 2xy2 × 3x2y2


a) x8 ÷ x2

b) 9y6 ÷ 3y2

c) 14y3 ÷ 2y2

d) 20x5 ÷ 4x

e) 16x8 ÷ 8x2


a)

b)

c)

d)

e)

12x6

3x2

20x3

2x

5x4

x2

6x5

3x3

300x9

10x2


a)

b)

c)

d)

e)

12x3y4x

15x4y3

3xy

20x3y5

4x2y3

14x2y2

7xy

30x2y3z6

3xy2z4

9) Find the value of

a) 40

b) 60

c) 120

d) z0

e) x0

© Mathswatch Ltd

Level 7


Page 112

A17Expanding Brackets

1) Expand

a) 2(x + 3)

b) 2(x – 4)

c) 5(2x + 1)

d) 7(3x – 1)

e) 4(2a + 7)

2) Expand

a) 2x(3x + 1)

b) 3x(4x – 2)

c) 2x(x + 1)

d) 3x(2x – y)

e) 5x(3x + 2y)

3) Expand and simplify

a) 2(x + 3) + 4(x + 1)

b) 3(2x + 1) + 2(5x + 2)

c) 4(x + 1) + 3(3x + 4)

d) 6(2x + 3) + 5(x + 2)

e) 4(3x + 2) + 5(2x + 1)


a) 2(5x + 3) + 3(x – 1)

b) 3(4x + 5) + 2(3x – 4)

c) 5(2x – 1) + 3(2x + 5)

d) 2(3x – 4) + 3(x + 2)

e) 3(2x – 1) + 4(3x – 2)


a) 3(x + 2) – 2(x + 3)

b) 4(2x + 3) – 3(2x + 1)

c) 5(3x – 2) – 2(x – 2)

d) 2(5x – 1) – 4(2x – 3)

e) 3(2x + 7) – 2(3x + 2)


a) (x + 2)(x + 2)

b) (x + 3)(x + 5)

c) (x + 7)(x + 1)

d) (x + 4)(x + 3)

e) (x + 7)(x + 2)


a) (2x + 1)(3x + 2)

b) (4x + 3)(2x + 1)

c) (3x + 4)(3x + 2)

d) (5x + 2)(5x + 7)

e) (2x + 10)(2x + 4)


a) (x + 5)(x – 3)

b) (x – 2)(x + 4)

c) (x – 6)(x – 2)

d) (x + 7)(x + 3)

e) (x – 8)(x – 2)


a) (2x – 1)(3x + 4)

b) (5x – 2)(3x – 1)

c) (3x + 4)(2x – 3)

d) (5x – 1)(5x – 2)

e) (4x + 2)(3x – 5)

Expand and simplify

a) (x + 5)2

b) (x – 2)2

c) (2x + 3)2

d) (3x – 1)2

e) (4x + 3)2

10)

© Mathswatch Ltd

Level 7


Page 113

A18Factorisation

1) Factorise the following

a) 6x – 2

b) 8x + 14

c) 6x + 9

d) 10x – 5

e) 12x + 18


a) x2 + x

b) t2 – t

c) x3 + x

d) x5 – x2

e) a7 + a4


a) 3x2 + 6x

b) 8x3 – 2x

c) 12a2 + 4a3

d) 20x4 – 6x2

e) 7x3 + 8x


a) 6x2y4 + 4xy3

b) 4x3y4 + 2x2y2

c) 10x4y3z – 5xy5z

d) 16a2b3c4 + 3ab2c3

e) 9x2y4z – 6xy2z


a) 10x + 4

b) x4 – x2

c) 9x5 – 12x2

d) 12x2y3 + 4xy2

e) 24x3yz4 – 10xz2

© Mathswatch Ltd

Level 7


Page 114

A19Solving Difficult Equations

1) Solve the following

a) 2x + 3 = 19

b) 3x – 2 = 13

c) 5x – 1 = 9

d) 3 + 2x = 23

e) 12 – 3x = 9


a) 2(3x – 1) = 22

b) 3(x + 7) = 18

c) 4(5x – 2) = 12

d) 66 = 6(2x + 3)

e) 20 = 5(x – 6)


a)

b)

c)

d)

e)

x – 62 = 3

x + 83 = 5

2x – 13 = 5

6x + 12 = 8

7x – 35 = 5


a) 2x + 7 = x + 12

b) 4x – 5 = 2x + 3

c) 7x + 2 = 3x + 26

d) 6x – 7 = 4x – 5

e) 3x + 4 = x – 7


a) x – 6 = 2x – 13

b) 3x + 4 = 5x – 8

c) 4x + 17 = x – 4

d) 5 – 2x = x – 7

e) 2x – 1 = 14 – 3x


a) 2(3x – 1) = 4x + 7

b) 3(x + 4) = 2(x – 5)

c) 5(2x – 3) = 3(3x + 4)

d) 2(2x – 1) = 5(2x – 4)

e) 2(2x + 3) = 5(x + 3)


a)

b)

c)

d)

e)

2(x + 1)3

= 6

4(2x – 3)5

= 4

2(4x – 5)3

= x + 10

3(5x + 4)2

= 7x – 8

2(x + 7)34 – x =

© Mathswatch Ltd

Level 7


Page 115

A20Rearranging a Formula

1) Rearrange to make x the subjectof the formula

a) y = x – 2

b) y = x + 7

c) y = x + t

d) y = 5x + 3

e) y = 2x – 4


a) 3x + 2 = y

b) 4x – 1 = y

c) ax – 3 = y

d) ax + m = t

e) x + y = t


a) y = x + t – v

b) ax – c = y

c) y = ax – tv + c

d) y + x = ct

e) c + ax + t = y + m


a)

b)

c)

d)

e)

5x – 24 = y

ax + cm = y

x – 45

y =

t + mxyk =


a)

b)

c)

d)

e)

y = 3x42x5y = – 8

cxty = + m

y = abx + c

mxt + c = y


a) y = 4(x + t)

b) y = a(x – m)

c) at(c + x) = y

d) y + m = a(c + x)

e) t – v = m(x – y)


a)

b)

c)

d)

e)x + 2

3 = y

x – u4 = y

x + ab = c

3(x + 2)c = y

a(x + b)c = d

t(x + c)d = e + f

© Mathswatch Ltd

Level 7


Page 116A

A21Trial and Improvement

1) The equation x2 + 3x = 37has a solution between 4 and 5.

Use a trial and improvement method to find this solution.Give your answer to one decimal place.


2) The equation x2 – 4x = 6has a solution between 5 and 6.



© Mathswatch Ltd

Level 7


Page 116B

A21Trial and Improvement

2) The equation x3 – 2x = 9has a solution between 2 and 3.



1) The equation x3 + 3x = 114has a solution between 4 and 5.



© Mathswatch Ltd

Level 7


Page 117

A22Inequalities

-5 -4 -3 -2 -1 0 1 2 3 4 5

1) Represent the inequalities on the number lines.

a) x < 3

b) -1 < x < 4

c) -3 < x < 3

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

2) Write down the inequalities shown below

a)

b)

c)

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

3) If x is an integer, what are thepossible values of x?

a) -4 < x < 2

b) -3 < x < 1

c) 1 < x < 5

d) -3 < x < 4

e) -7 < x < -4

© Mathswatch Ltd

Level 7


Page 118

A23Solving Inequalities

1) Solve

a) 2x – 1 > 7

b) 3x + 4 < 19

c) 5x – 7 < 18

d) 2x + 9 > 5

e) 4x + 11 < 14

2) Solve

a)

b)

c)

d) 12 > 2x – 1

e) 20 < 5 + 5x

x3 < 7

x5 – 1 > 3

2x3 + 4 < 9

3) Solve

a) 2(5x – 1) < 18

b) 3(4x + 2) > 60

c) 42 > 2(6x + 15)

d) 4(1 + x) < 12

e) 8(2x – 1) >12

4) Solve

a) 2x + 7 < x + 9

b) x – 6 > 3x – 18

c) 4x + 3 < 2x – 9

d) 2x – 4 > 7x – 34

e) 2(x + 3) < x – 1

© Mathswatch Ltd

Level 7


Page 119

A24Understanding

Straight Line Graphs

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

1) Find the gradients ofthe lines A to F.

A

BC

D

E

F

O 1 2 3 4 5

2

4

6

8

10

12

14

16

18

20

x

y

2) Find the gradients ofthe lines G to K.

G

HI

J

K

-4 -3 -2 -1 O 1 2 3 4 5 6

-4

-3

-2

-1

1

2

3

4

5

6

x

y

3) Find the equations oflines A and B.

-4 -3 -2 -1 O 1 2 3 4 5 6

-4

-3

-2

-1

1

2

3

4

5

6

x

y

4) Find the equations oflines C, D and E.

A

B

C

D

E

© Mathswatch Ltd

Level 7


A25Regions

Page 120

1) a) Shade the region represented by x < -1

b) Shade the region represented by x > 3

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

2) a) Shade the region represented by y < -1

b) Shade the region represented by y > 2

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

3) Shade the region represented by -3 < x < 2

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

4) Shade the region represented by 1 < y < 4

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

5) Shade the region where -1 < x < 3and -4 < y < -2

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

6) Shade the region where -3 < x < 2and -1 < y < 4

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

© Mathswatch Ltd

Level 7


A26Simultaneous Equations

Graphically

Page 121

1) a) Complete the table of values for y = x + 2

b) Draw the graph of y = x + 2

c) Complete the table of values for x + y = 7

d) Draw the graph of x + y = 7

e) Use your graph to solve the simultaneousequations y = x + 2 and x + y = 7

O 1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8

x 0 1 2 3 4

y

y

x

-6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6

-6

-5

-4

-3

-2

-1

1

2

3

4

5

62) Using a graphical method, solve the

simultaneous equations

y = 2x – 3 and y = 6 – x

y

x

3) Solve the simultaneous equations y = x + 6 and y = 3 – x

4) Solve the simultaneous equations y = x – 14 and y = 2 – 3x

x 0 1 2 3 4

y

© Mathswatch Ltd

Level 7


A27Simultaneous Equations

Algebraically

Page 122

1) Solve 3x + y = 11

4x – y = 3

2) Solve 2x – 5y = 3

4x + 5y = 21

3) Solve x – 2y = 3

3x + 2y = 5

4) Solve x + 3y = 10

x + y = 6

5) Solve 3x + 2y = 3

2x + 2y = 5

6) Solve 5x – 3y = 23

2x – 3y = 11

7) Solve 3x – 2y = 6

x + y = 7

8) Solve 6x + y = 10

2x – 3y = 10

9) Solve 2x + 7y = 11

3x – 2y = 4

10) Solve 4x + 3y = 9

5x + 2y = 13

11) Solve 2x + 3y = -7

7x – 2y = -12

12) Solve 3x – 2y = 5

9x + 5y = -7

13) In the first week of opening, a zoo sold200 adult tickets and 300 child tickets. Thetakings for that week were £2600.

In the second week, 500 adult tickets weresold and 400 child tickets were sold. Thetakings for the second week were £5100.

Form two equations and solve them tofind the price of an adult ticket and theprice of a child ticket.

14) If you multiply Sid’s age by four and Tony’sage by five and add the answers togetherit comes to 259 years.

However, if you multiply Sid’s age byseven and then take away two timesTony’s age the answer is 120 years.

Form two equations and solve them to findthe ages of Sid and Tony.

15) If nine rats and seven ferrets cost £116.75and four rats and six ferrets cost £88, howmuch would five rats and four ferrets cost?

16) If a mouse and a goldfish cost £1.10 andthe mouse costs £1 more than the goldfish,how much does the goldfish cost?

© Mathswatch Ltd

Level 7


A28nth Term of Quadratic

Sequences

Page 123

1) Find the nth term of

a) 1, 4, 9, 16, 25, . . . .

b) 2, 5, 10, 17, 26, . . . .

c) 0, 3, 8, 15, 24, . . . .


a) 1, 4, 9, 16, 25, . . . .

b) 2, 8, 18, 32, 50, . . . .

c) 0.5, 2, 4.5, 8, 12.5, . . . .


a) 3, 9, 19, 33, 51, . . . .

b) 1, 7, 17, 31, 49, . . . .

c) 11, 41, 91, 161, 251, . . . .

4) For the following nth terms,find the first three terms and the tenth term

a) n2 + 4

b) n2 – 3

c) n2 + 10

d) n2 + 2n

e) n2 – n

5) For the following nth terms,find the first three terms and the tenth term

a) 4n2

b) 2n2 + 3n

c) 3n2 – 2n

d) n2 + n + 1

e) 2n2 + 4n – 3

© Mathswatch Ltd

Level 7


A29Graphs of Quadratic and

Cubic Functions

Page 124A

x -2 -1 0 1 2

y -1 2

31) a) Complete the table of values for y = x2 – 2

b) Draw the graph of y = x2 – 2

-2 -1 O 1 2 3

-3

-2

-1

1

2

3

4

5

6

7

c) Use the graph to estimate thevalues of x when y = 1

2) a) Complete the table of values for y = 4x2

b) Draw the graph of y = 4x2

c) Use the graph to estimate thevalue of y when x = 1.5

-2 -1 O 1 2-2

2

4

6

8

10

12

14

16

y

x

x

y

x -2 -1 0 1 2

y 4 16

© Mathswatch Ltd

Level 7



Cubic Functions

Page 124B

x -2 -1 0 1 2

y -1 8

31) a) Complete the table of values for y = x2 + 2x

b) Draw the graph of y = x2 + 2x

c) Use the graph to estimate thevalues of x when y = -0.5

2) a) Complete the table of values for y = x2 – 2x + 1

b) Draw the graph of y = x2 – 2x + 1

c) Use the graph to estimate thevalue of y when x = 2.5

y

x

x

y

x -2 -1 0 1 2

y 4 1

-2 -1 O 1 2 3-1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

3

-2 -1 O 1 2 3

1

2

3

4

5

6

7

8

9

10

11

12

13

© Mathswatch Ltd

Level 7



Cubic Functions

Page 124C

x -2 -1 0 1 2

y -3 9

1) a) Complete the table of values for y = 2x2 + 2x – 3

b) Draw the graph of y = 2x2 + 2x – 3

c) Use the graph to estimate thevalues of x when y = -2

2) a) Complete the table of values for y = x3 + x

b) Draw the graph of y = x3 + x

y

x

x

y

x -2 -1 0 1 2

y -2 10

-2 -1 O 1 2

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

-2 -1 O 1 2

-10

-8

-6

-4

-2

2

4

6

8

10

© Mathswatch Ltd

Level 7


S30Pythagoras’ Theorem

Page 125A

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1) Use Pythagoras’ theorem to work out the areas of squares A and B.

AB

2) Use Pythagoras’ theorem to work out the areas of squares C and D.

Area25 cm2

Area100 cm2

CArea

841 cm2

Area441 cm2

D

© Mathswatch Ltd

Level 7


S30Pythagoras’ Theorem

Page 125B

1) Find the lengths of the sides of these three squares.

a) b) c)

Area529 cm2 Area

210.25 cm2

Area152.7696 cm2

2) Find the lengths of the sides labelled a to d.

8 cm

15 cm

a

12 cm

35 cmb

29 cm

21 cm

c25 cm

24 cm

d

© Mathswatch Ltd

Level 7


Pythagoras’ Theorem

Page 125C

1) Calculate the lengths of the sides a to f, giving each answer to 1 decimal place.

12 cm

7 cm 18 cm 13 cm

6.4 cm

12 cm

a

b

c

13.8 cm3.7 cm

9.6 cm

4.5 cm

15.8 cm

18.3 cm

d

ef

2) Calculate the lengths of the sides a and b, giving each answer to 1 decimal place.

17 cm

10 cm13 cm

15 cm

a

b

3) Find the height of this isosceles triangle.Give your answer to 1 decimal place.

13 cm

16 cm

4) Find the area of this isosceles triangle.

25 cm

14 cm

S30

© Mathswatch Ltd

Level 7


Page 126A

S31Areas of

Compound Shapes

1) Find the areas of the following shapes:

7 cm

4 cm

12 cm

6 cm

8 cm

9 cm

a) b) c)

d) e)

16 cm10 cm


14 cm

13 cm

5 cm

9 cm

20 cm17 cm

18 cm

6 cm

12 cm

7 cm 7 cm

5 cm 3 cm4 cm

a) b)

c)

Take to be 3.142

© Mathswatch Ltd

Level 7


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Page 126B

S31Areas of

Compound Shapes


7 cm

9 cm

4 cm

5 cm

12 cm

5 cm9 cm

13 cm

11 cm

9 cm6 cm

6 cm

2) Find the areas of the shaded parts of the following:

a) b) c)

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14 cm

8 cm

11 cm

5 cm15 cm

11 cm

7 cm

8 cm

15 cm

6 cm

24 cm

Take to be 3.142 when needed.a) b)

c)d)

15 cm

© Mathswatch Ltd

Level 7


Page 126C

S31Areas of

Compound Shapes

Find the areas of the shapes below:

Take to be 3.142

16 cm

22 cm12 cm

20 cm

20 cm

23 cm

a)

b)

c)

© Mathswatch Ltd

Level 7


Page 127

S32Volumesof Prisms

Find the volumes of the prisms, below.Take to be 3.142 for questions c and d.

5 cm

6 cm

8 cm

3 cm

8 cm

10 cm

4 cm

5 cm19 cm

23 cm

12 cm

13 cm

2 cm

9 cm

10 cm

6.4 cm

25.7 cm

30 cm

a) b)

c) d)

e) f)

© Mathswatch Ltd

Level 7


Page 128

S33Surface Area

of Triangular Prisms

1) Find the total surface area of this triangular prism.

10 cm

12 cm 13 cm

20 cm

2) Find the total surface area of this triangular prism.

7.2 cm

6.5 cm9.7 cm

3) Find the total surface area of this triangular prism.You will need to use Pythagoras’ theorem at somestage to get the answer.

10.2 cm

14 cm

24 cm

23 cm

© Mathswatch Ltd

Level 7


Page 129

S34Loci

1) Draw the locus of all the points that are 1.2 cm away from the line AB.

A B

2) Draw the locus of all the points that are 1.5 cm away from the rectangle ABCD.

3) Radio signals can be heard within a 4.5 km radius of transmitter A and a 5.5 km radiusof transmitter B. Show, by shading, the area where radio signals can be heard from bothtransmitters at the same time. Use a scale of 1 cm represents 1 km.

A B

© Mathswatch Ltd

Level 7


Page 130

S35Enlargement by a

Negative Scale Factor

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

1) Enlarge line AB with scale factor -2 andpoint (7, 6) as the centre of enlargement.

A

B

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

2) Enlarge line AB with scale factor -3 andpoint (3, 4) as the centre of enlargement.

A

B

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

3) Enlarge triangle ABC with scale factor -2and point (7, 6) as the centre of enlargement.

A

B

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

A

B

4) Enlarge triangle ABC with scale factor -1.5and point (4, 5) as the centre of enlargement.

C

C

© Mathswatch Ltd

Level 7


Page 131

S36Bounds

1) The length of a bracelet is 24 cm measured tothe nearest centimetre.

a) Work out the lower bound of the length ofthe bracelet.

b) Work out the upper bound of the length ofthe bracelet.

2) The length of a snake is 80 cm measured tothe nearest 10 centimetres.

a) Work out the lower bound of the length ofthe snake.

b) Work out the upper bound of the length ofthe snake.

3) The weight of a necklace is 145 g measured tothe nearest 5 grams.

a) Work out the lower bound of the weight ofthe necklace.

b) Work out the upper bound of the weight ofthe necklace.

4) The length of a line is given as 17.2 cmmeasured to the nearest tenth of a centimetre.

a) Work out the lower bound of the length ofthe line.

b) Work out the upper bound of the length ofthe line.

5) A rectangle has a length of 80 cm and a width of60 cm, both measured to the nearest 10 cm.

a) Work out the lower bound of the area ofthe rectangle.

b) Work out the upper bound of the perimeterof the rectangle.

6) A right-angled triangle has lengths as shown, allmeasured to the nearest centimetre.

a) Work out the lower bound of the area ofthe triangle.

b) Work out the upper bound of the area ofthe triangle.

80 cm

60 cm

12 cm

5 cm

© Mathswatch Ltd

Level 7


Page 132

S37Compound Measures

1) A car travels at 60 mph for 3 hours.How far does the car travel?

2) A cyclist cycles for 4 hours and covers a distance of 48 miles.What was her average speed in miles per hour?

3) How long would it take a train which travels at an average speedof 80 mph to cover a distance of 400 miles?

4) A runner runs at a speed of 12 km/h for 3 hours and 15 minutes.How far does he run?

5) An aeroplane flies at an average speed of 510 mph.How long would it take to fly a distance of 2720 miles?

6) If a worm travels a distance of 8.25 m in 2 hours and 45 minutes, work outhis average speed in metres per hour.

7) 12.5 cm3 of mercury has a mass of 170 g.Work out the density of mercury.

8) Platinum has a density of 21.4 g/cm3.What is the mass of 35 cm3 of platinum?

9) A quantity of ice had a mass of 62.56 g.Knowing that ice has a density of 0.92 g/cm3, work out how muchice there was, in cm3.

15000 cm3 of nitrogen has a mass of 18.765 g.Work out the density of nitrogen in g/cm3.

15000 cm3 of gold has a mass of 289.5 kg.Work out the density of gold in g/cm3.

10)

11)

© Mathswatch Ltd

Level 7


Page 133A

D14Averages from Tables

1) Sally conducted a survey to see how many sandwiches each pupilbrought to school in her class per day.The results can be seen in the table.

a) What is the modal number of sandwiches brought to school?

b) What is the median number of sandwiches brought to school?

c) Work out the mean number of sandwiches brought to school.Give your answer to 1 decimal place.

24

2) 50 hippos were captured over the course of a year and weighed.The results can be seen in the table, below.

Work out an estimate for the mean weight of a hippo.Give your answer to 1 decimal place.

22.9 w < 3.2<

Weight of hippoin tonnes

Frequency

5

9

15

12

7

1.4 w < 1.7<

1.7 w < 2.0<

2.0 w < 2.3<

2.3 w < 2.6<

2.6 w < 2.9<

No. ofsandwiches

Frequency

1

5

6

12

0

1

2

3

© Mathswatch Ltd

Level 7


Page 133B

D14Averages from Tables

Jenny had a theory that if asked to guess the length of a line, childrenunder the age of 10 would overestimate the length but adults wouldunderestimate the length.

To help her decide if she was correct she asked 100 under-10s and100 adults to guess the length of a 34 cm line.

The results can be seen in the two tables, below.

Use the results in the tables to see if Jenny was correct.Show all your workings.

Estimate oflength in cm

Frequency

4

11

24

39

22

20 l < 24<

24 l < 28<

28 l < 32<

32 l < 36<

36 l < 40<

Children under the ageof 10 estimates

Estimate oflength in cm

Frequency

2

6

16

62

14

20 l < 24<

24 l < 28<

28 l < 32<

32 l < 36<

36 l < 40<

Adult estimates

© Mathswatch Ltd

Level 7


Page 134

D15Relative Frequency

1) Peter bought an unfair dice from a Joke Shop.He didn’t know how the dice was biased and so he rolled it100 times and noted down which numbers came up.

He found that the number 6 occurred 8 times.

a) What is the relative frequency of getting a six?

b) If Peter rolls the dice 400 times, estimate how many6s he will roll.

2) Mary had a bag containing four different colour marbles.She chose a marble, noted its colour and then replaced it,80 times.

The results can be seen in this table.

a) Estimate the probability that a blue marble will bechosen on the next pick.

b) If a marble is chosen and replaced 280 times,estimate how many times you would expect tochoose a red marble.

ColourNo. of times

chosen

12

24

18

26

Red

Blue

Green

Yellow

3) Benford’s law says that if you look at real-life sources ofdata (heights of mountains, populations of countries, etc)the number 1 will be the first digit with relative frequency 0.3

If you go through any newspaper and write down the first 20numbers you come across, about how many of the numberswould you expect to begin with a ‘1’.

© Mathswatch Ltd

Using and Applying Maths

Weights QuestionsLevel 3

1kg 2kg 3kg7kg

1) You have one 1 kg weight, one 2 kg weight,one 3 kg weight and one 7 kg weight.

Using any combination of the weights,which total weights can you make?

This worksheet is to bedone after watching theWeights Q1 video clip.

Page 135A

© Mathswatch Ltd

3) a) Which set of five weights would givethe most possibilities? List them all.

b) What about if you had six or sevenweights? (please don’t list thepossibilities)

What do you notice?

Can you make a generalisation?

? ??

??

2) Which set of four weights would give us themost possibilities with no gaps?

List all the possibilties and how you wouldmake them.

??

??



This worksheet is to bedone after watching theWeights Q2 and Q3video clip.

Page 135B

© Mathswatch Ltd

4) This time you can put weights on one sideof the scales and weights on the other sideto give a net weight.

Using these rules, which set of fourweights would give us the mostpossibilities with no gaps?

? ??

?

Can you give a generalrule for more weights?

5kg

9kg

This gives a netweight of 4 kg

This gives a netweight of 14 kg

12kg7kg

1kg4kg



This worksheet is to bedone after watching theWeights Q4 video clip.

Page 135C

© MedianThese worksheets should be usedtogether with the Balances video clip.

Extras

Balances 1

1) 2)

3) 4)

5) 6)

Page 136A


1) 2)

3) 4)

6)5)

Extras

Balances 2

Page 136B


1) 2)

3) 4)

Extras

Balances 3

Page 136C


1) 2)

6)

Extras

Balances 4

Put numbers in the circles sothat the numbers in thetriangles (total of numbers incircles) are as small aspossible.

4)3)

5)

All numbers must be wholenumbers and greater than 0.

Page 136D


Extras

Balances 5

1)

2)

Smallest possible

Highest possible

6

5

All numbers must be wholenumbers and greater than 0.

Page 136E

© Mathswatch Ltd

These worksheets should be usedtogether with the Congruent Halvesvideo clip.

1)2)

3) 4)

5)

6)

Show how to cut each shape intotwo identical pieces.

Extras

Congruent Halves

Page 137A

© Mathswatch Ltd


7) 8)

9)

10)


Extras

Congruent Halves

Page 137B

© Mathswatch Ltd


11)

12)13)


Extras

Congruent Halves

Page 137C

© Mathswatch Ltd


14) 15)

16)

17)


Extras

Congruent Halves

Page 137D

© Mathswatch Ltd


18)

19)20)


Extras

Congruent Halves

Page 137E

© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.

Extras

Circles

Object Circumference Diameter C ÷ D

(138A)

Page 1


Find the circumference ofthe circles below

C = × D

13cm

= 3.142

9cm

15.6cm

1) 2)

3)

Extras

Circles

(138B)

Page 2


2cm

5cm

1.8cm

7.5c

m

1)

2)

3)

4)

C = × D

= 3.142

C = 2 × × r

Extras

Circles

Find the circumference ofthe circles below

(138C)

Page 3


Circles with radius 5cm

(138D)

Page 4


Circle with radius 5cm

(138E)

Page 5


Find the area of the circlesbelow

4cm

11cm

1.3cm

9.6c

m

1)

2)

3)

4)

A = × r × r= 3.142

Extras

Circles

(138F)

Page 6


Find the area of the circlesbelow

24cm 17cm

16.9cm

1) 2)

3)

Extras

CirclesA = × r × r

= 3.142

(138G)

Page 7


Find the area of the shadedsections

13cm

30cm

30cm 11cm

12cm 15.6cm 19.2cm

53cm

23cm

1)

2)

3)

11cm

Extras

CirclesA = × r × r

= 3.142

(138H)

Page 8

Documents

Levels 3 to 6 eBook - Jebel Ali Maths · Levels 3 to 7 eBook Questions Level 3 Contents ..... (i) Level 4 Contents ..... (ii) Level 5 Contents ... Ordering Decimals