New Century Maths Year 8 Chapter 1

Number

Working with numbers

1

In previous years you have been introduced to new numbers and have found some interesting facts about familiar numbers.

Now you will take a fresh look at some of that work and at the use of calculators.

apply a range of mental strategies to aid computation revise operations on whole numbers, integers, decimals and fractions divide two-digit and three-digit numbers by a two-digit number apply order of operations to simplify expressions round numbers and estimate answers estimate and calculate squares, cubes, other powers, square roots and

cube roots explore the properties of the square and square root of products:

(ab)2 and

mental calculation To operate with numbers in your head, without usingpen and paper, or calculator.

order of operations The rules for calculating an expression containing mixed operations, such as 14 2 4 + 1.

decimal places The places after the decimal point in a number. square root The positive value which, if squared, will give the number

required, for example because 72 = 49. cube root The value which, if cubed, will give the number required,

for example because 23 = 8. improper fraction A fraction whose numerator is larger than its

denominator, for example . mixed numeral A numeral consisting of a whole number and a fraction,

for example 1 .

Can you think of a simple way of evaluating 182?

What about ?

In this chapter you will:

ab

Wordbank

49 7=

83 2=

74---

34---

Think!

49 9

WORK ING W I TH NUMBERS 3

CHAPTER 1

4

N EW CENTURY MATHS 8

Mental calculation shortcuts

In the Skillbank sections of

New Century Maths 7

, you were provided with a variety of strategies for mental calculation to simplify numerical expressions. Some of them are shownin the table on the next page.

1 Find the answers to these without using a calculator:a 6 9 b 7 4c 43 + 20 d 17 + 25e 5 8 f 9 9g 42 7 h 36 4i 64 8 j 16 9k 6 6 l 45 9

2 Round 2870 to the nearest hundred.3 Rewrite these integers in ascending order:

6, 0, 9, 7, 1, 5, 3, 34 Find the highest common factor of:

a 12 and 8 b 20 and 25 c 6 and 185 Find:

a 52 b 82

c 152 d

e f 43

g 33 h

i j6 Find the lowest common multiple of:

a 6 and 10 b 2 and 5 c 3 and 47 Convert each of these fractions to a decimal.

a b c

8 Rewrite these numbers in ascending order:1.805, 1.085, 1.85, 1.05, 1.058, 1.508

9 Complete these pairs of equivalent fractions:

a

b

c

10 Convert each of these decimals to a common fraction in its simplest form.a 0.003 b 0.8 c 0.05

36

100

83

13 1253

25---

14---

38---

23---

4?---=

45---

?40------=

58---

?32------=

Start up

Worksheet 1-01

Brainstarters 1

Skillsheet 1-01

Factors anddivisibility

WORK ING W I TH NUMBERS 5 CHAPTER 1

Skill Examples

Multiplying by a multiple of 10 5 80 = 5 8 10 = 40 10 = 400Changing the order when adding or multiplying

15 + 37 + 18 + 45 + 22 = (15 + 45) + (18 + 22) + 37= 60 + 40 + 37 = 137

7 4 5 = 7 (4 5) = 7 20 = 140Adding and subtracting 8 or 9 43 + 29 = 43 + 30 1 = 73 1 = 72

67 18 = 67 20 + 2 = 47 + 2 = 49Doubling and halving numbers 47 2 = double 40 + double 7 = 80 + 14 = 94

144 = half of 140 + half of 4 = 70 + 2 = 172

338 = half of 320 + half of 18 = 160 + 9 = 169

Multiplying and dividing by 4 or 8

17 8 Double 17 = 34, double 34 = 68, double 68 = 136.17 8 = 136.

560 4 Half 560 = 280, half 280 = 140.560 4 = 140

Estimating answers 43 + 125 + 66 + 32 40 + 130 + 70 + 30= (130 + 70) + (40 + 30)= 270

635 18 640 20 = 64 2 = 32Multiplying and dividing by 5, 15, 20, 25, 50

18 5 = 9 2 5 = 9 10 = 90300 25 = 300 100 4 = 3 4 = 12

Multiplying by 9, 11, 99, 101 17 11 = 17 10 + 17 1 = 170 + 17 = 18725 9 = 25 10 25 1 = 250 25 = 225

Commonly used fractions and decimals

0.25 24 = 24 = 6

36 = 36 = ( 36) 2 = 12 2 = 24

12---

12---

14---

0.6 23---13---

1 Use the mental calculation shortcuts shown in the table above to evaluate each of the following expressions.a 0.1 130 b 58 + 19c 68 2 d 8 60e Estimate 26 + 71 + 146 + 19 + 14 f 26 + 71 + 146 + 19 + 14g 16 5 hi 6 25 4 j 600 25k 168 4 l 32 11m 3 70 n 16 + 48o 140 5 p 0.5 38q Estimate 88 + 43 + 27 + 7 + 102 r 88 + 43 + 27 + 7 + 102

2 Use mental calculation shortcuts to evaluate these:a 7 1000 b 14 15 c 400 50 d 232 e 74 28f 392 8 g 16 25 h 4 7 5 i 46 9 j 27 4k 0.25 44 l 80 5 m 22 8 n 300 20 o 16 101p 0.75 20 q 3 8 2 r 5 900 s 12 50 t 15 + 39u 15 8 v 27 99 w 28 + 35 x 63 2 y 826

0.3 24

12---

12---

Exercise 1-01

6 NEW CENTURY MATHS 8

The four operationsThe four basic operations of arithmetic are:

+ addition subtraction multiplication division

We will now review these operations.

Example 1

Complete this number grid:

Solution

Simplify 504 18.

SolutionMethod 1: Long division Method 2: Preferred multiples

2 818 ) 5 0 4 18 into 50 goes 2 18 ) 5 0 4

3 6 1 8 0 10 times1 4 4 18 into 144 goes 8 3 2 4

1 4 4 1 8 0 10 times 0 1 4 4

9 0 5 times 5 4

5 4 3 times 0 28 times

504 18 = 28

5 14

8

12

+

5 14

8

12

+

13

17

22

26

5 14

8

12

+

13

17

22

26

5 + 8

5 + 12

14 + 8

14 + 12

Example 2


1 Copy and complete the following number grids:

2 Find the answers to the following:a 285 + 633 b 581 + 1023 c 3417 + 45d 688 35 f 899 389 g 1436 802h 158 7 i 601 36 i 246 25

3 Find the answers to the following:a 780 12 b 512 16 c 525 35d 672 42 e 756 21 f 364 52

a + 17 23 48 95

35

46

77

81

Exercise 1-02

b top row minus left-hand column

d top row divided by left-hand column

59 68 91 112

38

43

57

34

120 180 135

3

5

15

c 12 15 20 37

8

10

18

33

Example 1

Example 2


IntegersIntegers are the positive and negative whole numbers and zero. You have previously learned the rules for operating with integers using the number line. Negative numbers can be enteredinto a calculator using the sign change key or .

Working mathematicallyReasoning and communicating: Doubling numbersCalculators always carry out calculations in the same way. People, however, can use calculator answers to discover patterns and relationships between numbers.1 a Use a calculator to double each of these numbers. (Write the answers.)

2358 4229 7490 63 236 180b Choose your own numbers to double and write the answers.

2 Use your answers from Question 1 to explain what happens to numbers when you double them.a What happens to the number of digits?b What happens to the number of zeros at the end?

3 Double these numbers and write the answers.9 99 999 9999 99 999 etc.a Can you see a pattern in the answers?b How long before your calculator breaks the pattern? What does your calculator do?

4 What do you notice if you triple some numbers?

Worksheet 1-02

Integer review+/ ()

Example 3

1 Find the answer to 1 + 5.

Solution

On a calculator: 1 5 The answer is 4.

2 Find the answer to 3 2.

Solution

On a calculator: 3 2 The answer is 5.

-2 -1 0 1 2 3 4 5

+/ + =

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

+/ =

Skillsheet 1-02

Integers

Skillsheet 1-03

Integers usingdiagrams


Adding a negative number is the same as subtracting its opposite. Subtracting a negative number is the same as adding its opposite. positive positive = positive

positive negative = negativenegative positive = negativenegative negative = positive(The above is also true for dividing with integers.)

When multiplying or dividing two numbers which have the same sign, the answer is positive.

When multiplying or dividing two numbers which have different signs, the answer is negative.

+

+

+

+

Example 4

Find the answer to 4 (2).Solution4 (2) = 4 + 2 (subtracting a negative number is the same as adding its opposite)

= 6On a calculator: 4 2 The answer is 6.

Find the answer to:a 3 5 b 6 (2)Solutiona 3 5 = 15 b 6 (2) = 3

On a calculator: On a calculator: 3 5 6 2

The answer is 15. The answer is 3.

+/ =

Example 5

+/ = +/ +/ =

1 Find the answers to the following:a 3 10 b 6 13 c 12 3 11 d 2 7

2 Find the answers to the following:a 5 + (-8) b 6 (4) c 12 (5) d 15 + 3e 6 15 f 7 + 8 g 13 + 13 h 6 5 4i 18 + 10 3 j 7 + 3 + 8 k 18 15 + 3 6 l 2 12 3 + 18

Exercise 1-03Example 3

Example 4

SkillBuilder 3-03


Rounding and estimationThere are many situations in which it is impractical or impossible to give an exact answer.If the length of a wall is measured or calculated to be 4.831 metres, we may approximate it to 4.83 m or 4.8 m.In Year 7, we looked at rounding a number to a certain number of decimal places.

3 Work out answers to each of the following:a 5 4 b 3 (6) c (4) (8)d 26 (13) e 15 (3) f 14 2g 5 (9) h 10 7 i 12 (4)j 64 (4) k 25 (5) l 75 (5)m 18 (2) (3) n (2) (2) 7 o (5)2

4 Find the answers to the following:a 11 7 4 b 8 + 3 5 c 3 2 + 5d 12 (3) + 4 e 8 4 (2) f 6 3 8g 25 + 10 15 h 8 (3) 5 i 6 (2) (1)

5 We have a number of ways of saying add, such as plus and increase. Find other words which mean to subtract and to multiply.

Example 5

SkillBuilder 3-15

Worksheet 1-03

Estimationgame

To round a decimal: cut the number at the required decimal place look at the digit immediately to the right of the specied place if this digit is 0, 1, 2, 3 or 4, leave the number in the specied place unchanged if the digit is 5, 6, 7, 8 or 9, add 1 to the number in the specied place

Example 6

Round 5.261 correct to one decimal place.

Solution5.2 61

cut The next digit is 6, so add 1 to the 2 in the tenths place, to give 3.So 5.261 is 5.3 (correct to one decimal place).

Round 4.8239 correct to two decimal places.

Solution4.82 39

cut The next digit is 3, so the number 2 does not change.So 4.8239 is 4.82 (correct to two decimal places).

Example 7


Order of operationsYou should remember when carrying out calculations that there is a certain order in whichthe operations are done.

Scientic calculators are also programmed to perform calculations using the order of operations rules.

a Estimate the answer to 6.03 12.16 53.99b Use your calculator to nd the exact answer, then round it to two decimal places.

Solutiona 6.03 12.16 53.99 6 12 54 = 72 54 = 18.

Estimated answer = 18.

b On a calculator: 6.03 12.16 53.99 gives 19.3348.Rounded answer = 19.33 (correct to two decimal places).

Note: Most scientic calculators have a FIX mode that rounds the number on its display to a given number of decimal places. You may like to investigate the FIX mode.

Example 8

=

1 Round each of these, correct to one decimal place.a 3.851 b 4.0736 c 0.3333 d 7.34 e 15.0801 f 3.991

2 Round each of these, correct to three decimal places.a 9.7043 b 13.45671 c 0.08281d 53.09423 e 68.91093 f 100.003011

3 Round each of these, correct to the number of decimal places shown in the brackets.a 38.055 [2] b 99.005 [1] c 86.539 [1] d 3.0983 [3]e 4.70771 [4] f 3.198 [2] g 32.999 [1] h 19.769312 [4]

4 For each of these questions, make an estimate of the answer and then use your calculator to evaluate the answer to the number of decimal places shown in brackets.a 1.9 5.3 + 8.66 [1] b (19.75 14.3) 5.1 [2] c 301.603 98.5 [2]d 7.092 10.382 [1] e 9.92 4.71 [1] f 3.61 2.08 11.431 [2]


Example 7

Example 8

Spreadsheet 1-01

Roundingdecimals

Worksheet1-04

Order ofoperations

puzzleThe order of operationsFirst: Grouping symbols (innermost brackets rst)Second: or (working left to right)Third: + or (working left to right)

Skillsheet 1-04

Order ofoperations


Example 9

Find answers for each of the following:a 6 + 5 2 b 18 (2 + 1) c 5 2 + 3 9 d 2 [25 (24 8)]Solutiona 6 + 5 2 = 6 + 10 b 18 (2 + 1) = 18 3

= 16 = 6On a calculator: On a calculator:6 5 2 18 2 1

c 5 2 + 3 9 = 10 + 27= 37

On a calculator: 5 2 3 9

d 2 [25 (24 8)] = 2 [25 3]= 2 22= 44

On a calculator:2 25 24 8

Evaluate:

a b

Solution

a Divide 8 by all of 39 23.

On a calculator: 8 39 23

The answer is 0.5 or .

b Divide all of 8 + 16 by all of 12 8.

On a calculator: 8 16 12 8

The answer is 6.

+ = ( + ) =

+ =

( ( ) ) =

Example 10

839 23------------------

8 16+12 8---------------

839 23------------------

( ) =12---

8 16+12 8---------------

( + ) ( ) =

1 Calculate:a 8 + 5 2 b 7 2 3c 6 5 2 d 12 6 3e 3 6 + 2 5 f 7 + 15 3g 34 18 3 h (34 29) 6i 15 (20 2) j 5 10 + 16 2



k 3 6 2 5 l 26 (14 + 12)m (38 14) (7 + 5) n (7 10) 20 5o 72 (4 + 16) 7 p 14 [3 + 2 2]q [(38 14) 6] 4 r 48 (29 + 3) + (26 5 4)s 6 [22 (4 2)] + 1 t [36 (2 4)] [3 (5 + 2) + 7]

2 Simplify each of the following. Give your answers to one decimal place where necessary.

a b c

d e f

g h i

15 5+5 8---------------

19 5+18 6---------------

45 2100 10+---------------------

-6614 4+---------------

41 13-15 8+------------------

4 5 2+16 10 4+---------------------------

28 5 3( )[ ]56 30( ) 2----------------------------------

7 11 2( )30 7 2( ) 1[ ]-------------------------------------------

96 3 218 3 2+------------------------

Example 10

CAS 1-01

BODMAS

The abacusThe abacus is often called the first computer.It was invented by the Chinese in the 14thcentury and it is still used today to add, subtract,multiply, divide and to solve mathematicalproblems involving fractions and square roots.The word abacus comes from the Greek wordabax meaning calculating board. The abacusis composed of three sections: the upper beads,the lower beads and the horizontal centre barcalled the beam. Only the beads which have been moved to touch the two sides of the beam represent numbers. Each vertical row of beads represents a power of 10 (that is 10 000, 1000, 100, 10, 1). The beads below the beam represent one unit of that row. The beads above the beam represent five units of that row.

Study the examples shown:

10

0

(One 10 unit bead and one 5 unit bead)Abacus showing 15

(One 500 unit bead, one 10 unit bead, one 5 unit bead and two 1 unit beads)Abacus showing 517

10000

0

100

10

1

Represent 23, 56 and 466 on an abacus.

Just for the record

An abacus uses place valueto represent numbers.


DecimalsAddition and subtractionMake sure you keep place-value columns correct by placing the decimal points underneath each other.

Multiplication and division

Worksheet 1-05

Decimal review

Example 11

Evaluate:a 2.1 + 44.3 + 13.25 b 13.85 5.6Solutiona 2.1 + 44.3 + 13.25

2.144.3

+ 13.2559.65

b 13.85 5.613.85

5.68.25

Skillsheet 1-05

Decimals

Example 12

1 Evaluate:a 12 0.1 b 5.31 1.3 c 6.25 5SolutionMultiply without decimal points rst. Then make sure you have the same number of decimal places in the answer as there were at the start of the question.a 12 0.1 b 5.31 1.3

(question has one decimal place) (question has three decimal places)Multiplying without decimal points: Multiplying without decimal points:

12 1

12Answer: 1.2 (answer has one decimal place)

c 6.25 5 = 1.251.25

5) 6.252 Simplify 12.4 0.04.

SolutionWhen dividing by a decimal fraction, make the decimal fraction a whole number by moving the decimal point the appropriate number of places to the right.In this case: 0.04 4Move the decimal point in the other number the same number of places: 12.4 1240.Divide the new rst number by the new second number: 12.4 0.04 = 1240 4 = 310.

531 13159353106903

Answer: 6.903 (answer has three decimal places)


Number grids

1 Write each of these as a fraction in its simplest form:a 0.3 b 0.07 c 0.03 d 0.009e 0.4 f 0.82 g 0.35 h 0.026

2 Work out these calculations:a 1.3 + 0.8 b 42.51 + 3.6 c 18.4 6.9d 3.92 0.49 e 3.6 0.46 f 12 + 0.56 + 3.4g 20.03 1.06 h 12.56 9.88 i 4.123 + 71.05 + 6.3j 65.001 13.06 k 9 0.004 l 3.671 1.289

3 Find the answers to the following:a 4.2 3 b 12.61 2 c 24.8 4d 18.5 0.5 e 1.3 0.6 f 0.06 0.4g 6.24 1.2 h 0.12 1.2 i 238 1.4j 0.87 12 k 0.252 2.1 l 1.7 1.5

Exercise 1-06

Example 11

Example 12

1 Complete each of these number grids by nding the missing numbers.(Round decimals to two places, when required.)

b top row minusleft-hand column

e top row divided by left-hand column

2 Complete each of these number grids, rounding answers to two decimal places.

b top row minusleft-hand column

26 17.6

5.4

11.93

20.14 0.81

0.5

0.07

12.8 28.7

15.9

3.8

a + 4.1 2.07

9.36

18

c 8.6 2.1

0.6

5.8

d 2.04 12.11

70.07

0.65

a + 1.6

1.11

4.7 18.2

c

36.12 94.6

5.9 24.78

Exercise 1-07


3 Select an operation (+, , , or ) to use with each of these number grids. Find a set of numbers that will correctly ll the grid each time.

d 0.8 e

0.1512 2.5 40

0.7 3.528 0.8 4

a b c

45 15 9 21 60

18 24 48 48

Time before and time after1 Examine these examples.

a What is the time 4 hours and 25 minutes after 6:30pm?6:30pm + 4 hours = 10:30pmCount: 6:30, 7:30, 8:30, 9:30, 10:3010:30pm + 25 minutes = 10:55pm.

b What is the time 7 hours and 40 minutes after 11:45am?11:45am + 7 hours = 6:45 pmCount: 11:45, 12:45, 1:45, 2:45, 3:45, 4:45, 5:45, 6:456:45pm + 40 minutes = 6:45pm + 15 minutes + 25 minutes = 7:00pm + 25 minutes

= 7:25pm.or

c What is the time 10 hours and 15 minutes after 1850 hours?1850 hours + 10 hours = 0450 hours (next day).Count: 1850, 1950, 2050, 2150, 2250, 2350, 0050, 0150, 0250, 0350, 04500450 hours + 15 minutes = 0450 hours + 10 minutes + 5 minutes

= 0500 hours + 5 minutes = 0505 hours.or

2 Now nd the time of day.a 3 hours 20 minutes after 9:05am b 5 hours 40 minutes after 7:30pmc 4 hours 35 minutes after 6:15pm d 11 hours 10 minutes after 11:45ame 2 hours 45 minutes after 0325 hours f 7 hours 5 minutes after 1705 hoursg 8 hours 30 minutes after 12:40am h 4 hours 55 minutes after 10:20pmi 6 hours 25 minutes after 0435 hours j 2 hours 15 minutes after 2050 hoursk 9 hours 50 minutes after 2:30pm l 3 hours 10 minutes after 8:25am

11:45am 12:00noon 7:00pm 7:25pm

15 minutes 7 hours 25 minutes = 7 hours 40 minutes

1850 hours 1900 hours 0500 hours 0505 hours


Skillbank 1A

SkillTest 1-01

Time beforeand after


PowersRemember that powers are used as a shorthand way of writing repeated multiplication.We write 2 2 2 2 as 24.

Squares can be found on the calculator using the key.Other powers can be found on the calculator using the power key or .

3 Examine these examples.a What is the time 3 hours and 15 minutes before 11:20am?

11:20am 3 hours = 8:20am Count back: 11:20, 10:20, 9:20, 8:208:20am 15 minutes = 8:05am.

b What is the time 2 hours and 40 minutes before 7:20pm?7:20pm 2 hours = 5:20pm Count back: 7:20, 6:20, 5:205:20pm 40 minutes = 5:20pm 20 minutes 20 minutes = 5:00pm 20 minutes

= 4:40 pm.or

c What is the time 8 hours and 45 minutes before 1115 hours?1115 hours 8 hours = 0315 hoursCount back: 1115, 1015, 0915, 0815, 0715, 0615, 0515, 0415, 0315 (or 11 8 = 3).0315 hours 45 minutes = 0315 hours 15 minutes 30 minutes

= 0300 hours 30 minutes = 0230 hoursor

4 Now nd the time of day:a 1 hour 15 minutes before 7:20pm b 4 hours 40 minutes before 11:20amc 3 hours 20 minutes before 3:30pm d 5 hours 35 minutes before 8:25ame 2 hours 10 minutes before 1455 hours f 3 hours 45 minutes before 0740 hoursg 5 hours 25 minutes before 4:15am h 9 hours 30 minutes before 9:45pmi 4 hours 20 minutes before 2005 hours j 2 hours 15 minutes before 0615 hoursk 3 hours 55 minutes before 5:30pm l 4 hours 40 minutes before 12:00 noon

4:40pm 5:00pm 7:00pm 7:20pm




Skillsheet 1-06

IndicesExample 13

Evaluate 53.Solution53 = 5 5 5

= 125

x 2

x y ^


Example 14

Use your calculator to nd:a 142 b 64 c 25

Solutiona On a calculator: 14 gives the answer 196.

142 = 196.b On a calculator: 6 4 gives the answer 1296.

64 = 1296.c On a calculator: 2 5 gives the answer 32.

25 = 32.

x 2 =

x y =

x y =

1 Evaluate each of the following:a 52 b 23 c 62 d 34 e 71 f 15g 82 h 44 i 103 j 92 k 35 l 63

2 Find the missing power each time.a 2 = 8 b 3 = 27 c 10 = 100d 4 = 4096 e 5 = 125 f 3 = 243

3 Calculate:a 3 22 b 2 32 c 22 32 d 52 6e 43 2 f 43 22 g 45 53 h 32 52i 62 82 j 24 + 2 k 33 32 l 53 + 25

4 a Find (2 3)2.b Find: i 22 ii 32c Does (2 3)2 = 22 32? Explain your answer.

5 a Find: i (4 5)2 ii 42 iii 52b Does (4 5)2 = 42 52? Explain your answer.

6 Use what you found in Questions 4 and 5 to complete this pattern:(3 8)2 = .

7 Write three examples of your own to show that (ab)2 = a2b2.8 Copy and complete the following:

a 182 = (6 3)2 b 222 = (2 11)2 c 302 = ( 10)2

= 62 = = = = =


Example 14


Square roots and cube rootsThe square root of a given number is the positive value which, if squared, will give that number.The cube root of a given number is the value which, if cubed, will give that number.

d 162 = (2 )2 e 282 = ( 7)2 f 152 = ( )2= = =

= = =

Working mathematicallyApplying strategies and reasoning: Crossnumber puzzleChoose the correct clue from each pair and complete the puzzle.Across1. 37 6 or 37 22. 22 3 or 23 33. 6543 or 54324. 282 or 2925. 5 16 1 or 5 16 + 19. 457 9 or 579 4

10. 27 or 2811. 33 25 or 33 2212. 82 52 or 72 5214. 29 + 3 or 29 3

Down1. 63 or 53 10. 123 or 2314. 87 or 78 12. 840 24 or 840 356. 122 or 152 13. 11 12 or 13 147. 72 or 92 15. 16 3 or 16 68. 72 32 or 62 32 16. 25 13 or 52 13.

1 6 12 15

2 10

3 8

9 13 16

4 7 14

5 11

Skillsheet 1-07

Square rootsand cube roots

( )

3( )

Example 15

Find the square root of 36.Solution

because 62 = 6 6 = 36 On a calculator: 36

Find the cube root of 125.Solution

because 53 = 5 5 5 = 125 On a calculator: 125

36 6= =

Example 16

1253 5= 3 =


Example 17

Estimate the value of .SolutionThere is no exact answer for the square root of 40, because there isnt a number which, if squared, equals 40 exactly. Instead, we estimate and nd a number whose square is close to 40.Looking at the square numbers, 52 = 25, 62 = 36, 72 = 49, we can tell that must lie somewhere between 6 and 7. Because 40 is closer to 36 than to 49, the square root must be closer to 6.As an estimate, .On the calculator, the answer is 6.324555..., a more accurate answer than our estimate above.

40

40

40 6.3=

1 Copy and complete the following table:

2 Between which two numbers does lie? (Choose one from the answers given.)A 40 and 41 B 9 and 10 C 79 and 81 D 8 and 9

3 Between which two numbers does lie? (Choose from the answers given.)A 22 and 23 B 5 and 6 C 6 and 7 D 8 and 9

4 Between which two whole numbers does lie?5 Give estimates for each of the following.

a b c d e f6 Find the square root of:

a 4 b 121 c 81 d 900e 784 f 256 g 289 h 1089

7 Find the cube root of:a 8 b 343 c 2197 d 216e 512 f 1728 g 8000 h 2197

8 Give the answer to each of these to one decimal place:

a b c d

e f g h

9 a Find .

b Find: i ii

c We know that . Does ? Explain your answer.

Number 1 2 3 4 5 6 7 8 9 10 11 12Number squared 16Number cubed 512

80

45

31

56 105 210 1003 5763 8003

37 1003 502 6.53

4953 2000 1.1 11033

36

4 9

36 4 9= 36 4 9=

Exercise 1-09

Example 17

Example 15

Example 16


Fractions

Fractions can be entered into a calculator using the fraction key: .

Some types of fractions proper: the numerator is smaller than the denominator. For example , ,

improper: the numerator is larger than the denominator. For example , ,

mixed numeral: a whole number and a common fraction. For example 1 , 4

10 a Find: i ii iii

b We know that . Does ? Explain your answer.

11 Use what you found in Questions 9 and 10 to complete each of the following:a = b =

= = = =

c = d = = = = =

e = f = = 9 5 = 6 7= =

12 Write three examples of your own to show that .

13 Evaluate each of the following. (Give answers to one decimal place where necessary.)a b c

d e f

225 25 9

225 25 9= 225 25 9=

64 16 4 484 121

900 100 324 81

2025 1764

ab a b=

3 3 2 3+ 7 2

1449

------------- 113 2 43 43 43

numerator denominator

27---

Skillsheet 1-08

Fractions

Skillsheet 1-09

Fractions anddecimals

ab/c

12---

512------

781200------------

53---

115------

12374---------

35---

78---

Example 18

Change these improper fractions into mixed numerals:a b

Solutiona = 7 2 b = 27 4

= 3 = 6

On a calculator: 7 2 On a calculator: 27 4

72---

274------

72---

274------

12---

34---

ab/c = ab/c =


Pressing ( or ) converts a mixed numeral into an improper fraction.

Example 19

Change these mixed numerals into improper fractions:a 2 b 4

Solution

a 2 = b 4 =

= =

On a calculator: On a calculator:

2 1 3 4 2 5

13---

25---

2 3 4 513---

6 1+3------------

25---

20 2+5---------------

73---

225------

ab/c ab/c = d/c ab/c ab/c = d/c

d/c SHIFT ab/c 2nd F ab/c

Example 20

Simplify these fractions:a b

SolutionTo simplify fractions, we divide the numerator and the denominator by a common factor.a = b = or =

= = =

=

On a calculator: 10 25 On a calculator: 36 60

1025------

3660------

1025------

10 525 5---------------

3660------

36 660 6---------------

3660------

36 1260 12------------------

25---

6 210 2---------------

35---

35---

ab/c = ab/c =

1 Write each of these improper fractions as a mixed numeral:a b c d

e f g h

2 Write each of these mixed numerals as an improper fraction:a 3 b 4 c 5 d 5

e 6 f 7 g 10 h 15

3 Arrange these fractions in order, starting with the smallest., , , , ,

4 Simplify the following:a b c d e f

g h i j k l

32---

113------

94---

115------

203------

4711------

10021---------

7315------

12---

13---

14---

23---

34---

15---

17---

34---

14---

34---

18---

38---

58---

78---

510------

412------

1226------

1824------

1525------

1734------

3248------

60100---------

4477------

150310---------

2135------

1816------


Example 19

Example 20


Operations with fractionsAddition and subtractionTo add or subtract fractions, the fractions must have common denominators.

5 Copy and complete each of the following:a = b = c =

d = e = f =

g = h = i =

12--- 6------

23--- 12---------

45---

16---------

1560------

1------ 8------

34---

2128------ 4------

24---------

610------

54---------

915------ 30---------

1510------

Example 21

Evaluate:a + b c 1 + 4 d 3 1

Solutiona + b

= + =

= + =

= =

= 1

On a calculator: On a calculator:1 3 5 6 5 7 2 3

c 1 + 4

= 1 + 4 + +

= 5 + +

= 5

On a calculator: 1 2 3 4 1 5

d 3 1

= 3 1 +

= 2 +

= 2

On a calculator: 3 3 4 1 1 2

13---

56---

57---

23---

23---

15---

34---

12---

13---

56---

57---

23---

2 12 3------------

56---

3 53 7------------

7 27 3------------

26---

56---

1521------

1421------

76---

121------

16---

ab/c + ab/c = ab/c ab/c =

23---

15---

23---

15---

1015------

315------

1315------

ab/c ab/c + ab/c ab/c =

34---

12---

34---

12---

34---

24---

14---

ab/c ab/c ab/c ab/c =

Worksheet 1-06

Fractionreview

Worksheet1-07

Fractagons


Multiplication and divisionTo multiply fractions, multiply the numerators together and multiply the denominators together. Convert any mixed numerals to improper fractions rst.To divide by a fraction, multiply by its reciprocal. Convert any mixed numerals to improper fractions rst.

Example 22

Evaluate:a b 1 3 c d 2 1

Solutiona b 1 3

= =

=

= 5


3 5 2 7 1 1 2 3 5

c d 2 1

= =

= =

= 1 =

= 1


4 5 2 3 2 1 2 1 1

3

35---

27---

12---

25---

45---

23---

12---

13---

35---

27---

12---

25---

635------

32---

175------

5110------

110------

ab/c ab/c = ab/c ab/c ab/c =

45---

23---

12---

13---

42

5-----321-----

52---

43---

65---

52---

34---

15---

158------

78---

ab/c ab/c = ab/c ab/c ab/c ab/c

=

1 Evaluate:a + b + c +

d + e + f

g h 1 i 2

j 2 1 k 2 + 1 l 3 1m 4 + 1 n 2 o 3 + 1

2 a b c d

15---

35---

38---

18---

25---

310------

23---

15---

37---

23---

35---

14---

12---

14---

12---

34---

13---

25---

56---

12---

13---

16---

13---

23---

25---

34---

34---

58---

15---

34---

12---

13---

25---

37---

34---

12---

25---

34---


Example 22

SkillBuilder 2-052-17Adding andsubtractingfractions


e 1 2 f 3 g 1 h 3 1

i 8 j 2 k + l 2

3 a 8 b 15 c 24

d 60 e 33 f 21

12---

14---

45---

23---

13---

12---

14---

111------

14---

38---

1116------

23---

14---

12---

34---

12---

35---

12---

15---

34---

35---

23---

47---

SkillBuilder 2-24

Multiplying mixed fractions

Time differences1 Examine these examples.

a What is the time difference between 11:40am and 6:15pm?From 11:40am to 5:40pm = 6 hoursCount: 11:40, 12:40, 1:40, 2:40, 3:40, 4:40, 5:40From 5:40am to 6:00pm = 20 minutesFrom 6:00pm to 6:15pm = 15 minutes5 hours + 20 minutes + 15 minutes = 6 hours 35 minutesor

b What is the time difference between 8:30pm and 1:20am?From 8:30pm to 12:30am = 4 hours Count: 8:30, 9:30, 10:30, 11:30, 12:30From 12:30am to 1:00am = 30 minutesFrom 1:00am to 1:20am = 20 minutes4 hours + 30 minutes + 20 minutes = 4 hours 50 minutesor

11:40am 12:00noon 6:00pm 6:15pm


8:30pm 9:00pm 1:00am 1:20am


Skillbank 1B

SkillTest 1-02

Time differences


Applying number

c What is the time difference between 1645 hours and 2320 hours?From 1645 hours to 2245 hours = 6 hours (22 16 = 6)From 2245 hours to 2300 hours = 15 minutesFrom 2300 hours to 2320 hours = 20 minutes6 hours + 15 minutes + 20 minutes = 6 hours 35 minutesor

2 Now nd the time difference between:a 11:10am and 7:40pm b 6:20pm and 12:00 midnightc 4:45pm and 8:10pm d 2:30am and 10:55ame 1:05pm and 12:30am f 9:35am and 11:15amg 0425 hours and 0935 hours h 1440 hours and 2025 hoursi 7:55am and 3:50pm j 2:45pm and 10:10pm



1 Michael went shopping and bought the following items: an exercise book at $2.70,two pens at $1.60 each, a drink at $1.50 and a packet of chips for $2.65.a How much did Michael spend in total?b If Michael paid with a $20 note, how much change did he receive?

2 Jessicas car holds 45 litres of petrol. If the price of petrol is 92.6 cents per litre,how much will Jessica need to pay to ll the tank?

3 Traci needs to build a wooden rectangle similar to the one shown. How much timber would be left from a 3.4 m length of timber?

4 Lendal spent of his pocket money. If his pocket money is $14, how much does he have left?

5 A mobile phone plan charges $20 per month plus $0.18 for each phone call. How much will Thao need to pay if she made 92 calls in one month?

6 Katy, Josh and Kylie shared a $500 000 lotto win. How much did they each receive?

7 In 1912, Donald Lippincott from the USA ran 100 m in 10.6 seconds while, in 2002, Tim Montgomery, also from the USA, ran 100 m in 9.78 seconds.a If he could maintain the same speed, how far (to the nearest metre) could Donald have

run in one minute?b How far could Tim have run in one minute?c After one minute, how far ahead of Donald would Tim be?

0.8 m

0.5 m

34---

Exercise 1-12


Calculator talkDid you know that your calculator can talk? Not out loud, but it can give you written messages. Try this calculation on it:

623 411 213 303 + 1296 4 579 288 16Turn it upside down to read the word. (Hint: You should not eat your food like this!)

8 Copy these shopping dockets and ll in the missing sections:a b

9 From a jar containing 160 lollies, Lindy takes of the lollies and shares them equally among her four children. How many lollies does each child receive?

10 Elly made a dress for herself and the expenses were: 3 metres of material at $15.60 per metre. 2 metres of lace at $1.85 per metre. 2 metres of ribbon at $1.05 per metre. 6 buttons at 35 cents each.Elly saw a similar dress for sale at $126.50. How much did Elly save by making the dress herself?

11 Calculate the area of each of these triangles.a b

12 Danielle uses half a sheet of contact to cover her books, and Christina uses two-fths of the same sheet of contact. What fraction of the original sheet remains?

Fruity Fruit Shop2 kg of potatoes

at $2.15 per kg1 kg of carrots

at $2.99 per kg5 kg of oranges

at $3.55 per kg

TotalAmount tendered: $50

Change

12--

3 sponge cakesat $3.88 each

6 1.25 L bottles of lemonadeat $1.65 each

1 loaf of sliced breadat $2.55

1 2 L carton of milkat $2.85

2 videos at $29.99 each


Change

38---

12---

14---

11.1 cm

23.6 cm

33.7 m

20.4 m

Worksheet1-08

Magic squares

Worksheet1-09

Cross numberpuzzles


1 Turn your calculator upside down and make a list of the numbers that match these letters:O I Z E h S g L B G D

2 What number would make your calculator display these words?a hEEL b SLIDE c OhIO d gLOSS

3 Find the answers by turning your calculator upside down after each of the following calculations:a 121 217 8550 is liked by all children.b The number that multiplies by itself to give 196 says Gday.c The 5 77 8 is a very difcult instrument to play.d 8.0808 20 tells you what Father Christmas said to the child who pulled his beard.e Some people like to eat a pickled 52 043 71.f (12 500 0.625 5 6000 + 152) 4 is the name of an exciting word game.

4 Find the word answers to these questions:a What is made in the factory where Mavis is the manager?

(343 409 534) 2 13 + 295b The waves and tides have damaged many of these:

(145 420.4 12 0.24 + 910 500) 16c This is how Drew told his Mum he would avoid detention for not doing his homework:

(864.5 3.5 20 + 0.9) 19 .d High on the cliff overlooking the beach was the:

(17 967 15 680) 16 + 1146 Vue hotel.5 Do each question on your calculator. Turn it upside down to read the answer to the

given clue.

Question Cluea 9 22 (45 654 45 463) Good bookb 202 7 73 137 Greetingsc 13 456 704 123 456 31 Delightd 3 17 73 101 137 Tainte 8237 41 Cricket legendf (43 505 + 43 210) 123 000 One onlyg 13 003 823 200 Defeated feministh 14 (659 2 + 1) 29 Snake talki 1667 7 3 Not tightj (123 456 + 10 421) 4 Top brassk 8922 + 20 132 + 6285 Silly birdsl (300 + 67) 67 2 Mutiny captainm 9 (123 456 + 173 807) 50 Beat himn 4 131 (11 000 733) The mindo 5 49 358 005 12 345 Dirtyp 0.12 0.37 (2 53 151 + 1) For tortureq 0.73 1.01 1.37 0.4 Santa Clausr 0.01 (692 + 62) 7 0.7 Find outs (1 + 62 11) 9 Alternative

Exercise 1-13

Skillsheet 1-10

Spreadsheets


t 2 205 459 32 372 33 Tree bitsu 79 (822 + 9) TV awardsv (777 + 10) 7 0.082 Top manw 2 (1702 41) Accountsx (72.62 + 3.31) 0.5 0.7 3 Bad businessy (1.12 2.32 + 0.0178) 241 50 By the sea shore

1 Calculate the answers to three decimal places:

a b

c d

2 Solve this crossnumber puzzle using these four pieces of information as a guide: p + q = 680 f + k = 342 k = 161 k + m = 193Across1. 1 less than 11 down3. k5. p + q + k + f6. k + m 808. p + q k + 102

10. k + 102012. 2k + 2m + 1513. m

Down1. Equals 1 across2. q + k + f + p3. 4m 74. m + k7. p + q + f + 2k8. 2f + 2k9. f 70

11. A dozen

5.62 1.83+ 15

-------

23

-------

6.2 5.411.01 6.04+------------------------------3

5.92 8.12+13.6 2.04---------------------------

1 2 3 4

5

6 7

8 9

10 11

12 13

Power plus


3 Make your own calculator talking puzzles.Step 1: Enter a number into the calculator so that it spells a word when the calculator is

turned upside down.5508 spells BOSS

Step 2: Create a string of operations starting with your number:[(5508 500) 8 + 374] 32 = 31.25

Step 3: Write the reverse operation string which will be your talking clue:(31.25 32 374) 8 + 500

Step 4: Make up a question, riddle or rhyme:What do you call a gorilla armed with a machine gun?

Create a calculation and a word problem that makes your calculator give these talking answers:

a ShELLOIL b hOLES c hELLOd EggShELLS e ShEBOIL f two of your own invention

4 Scientic notation (standard form)Scientic notation is a special way of representing very large or very small numbers. This is how your calculator handles this problem:

Screen means 2.56 104that is 2.56 10 10 10 10

= 25 600

Screen means 1.678 103that is 1.678 10 10 10

= 0.001 678a Can you see a quick way of writing the answer each time?b Write each of the following calculator displays as an ordinary number:

i ii

iii iv

v vi

vii viii

ix x

5 Write each of these in scientic notation:a 12 000 b 345 000 000c 0.007 d 4000e 0.0005 f 0.000 41g 1 000 000 h 0.000 335i 0.000 000 011 1 j (1.2 104) (6 103)

6 a What is the largest number that can be displayed on your calculator?b What is the smallest?

2.56 04

1.678 -03

2.4 04 4.55 05

9.33 -02 6.667 02

9.6 -06 8.9 -06

1.001 -02 5.698 07

2.4 08 5.7011 -03

Worksheet 1-10

Scientificnotation


Topic overview What parts of this chapter did you remember from last year? Are there parts of this chapter that you still dont understand?

Discuss any problems with your teacher or a friend. Copy and complete this topic overview which has been started for you.

Check your work with other students and your teacher.

Language of mathscalculator cube cube root decimaldecimal place denominator division estimateevaluate factor tree fraction improper fractioninteger long division mixed numeral numeratoroperation order of operations power proper fractionround simplify square square root

1 What are the four arithmetic operations?2 If you round a decimal to the nearest hundredth, how many decimal places is this?3 What are the order of operations rules?4 What type of numeral can an improper fraction be converted to?5 How do you write the cube root of 64?6 What is the cube root of 64?

Worksheet 1-11

Numbers crossword

2

8 7 6

5

41

0

9

3

-3-2

-1 0 1 2 3

Denominators

Numerators

+

Powers

.

.

....

..

.

3

+/a bc/

NUMBERS

FRAC

TION

S

OPERATIONS

CALCULATOR

DEC

IMA

LS

INTEGERS


1 Evaluate each of these expressions without using a calculator.a 7 30 b 0.25 16c 44 29 d 53 9e 2 154 f 18 15g 0.1 400 h 25 11i 920 20 j 612 4k l 8 18m 120 15 n 0.5 100o 23 50 p 37 8

2 a Estimate the answer to 45 + 73 + 11 + 160 + 25.b Find the exact answer to 45 + 73 + 11 + 160 + 25 without using a calculator.

3 Copy and complete the following number grids:

4 Evaluate each of these expressions without using a calculator.a 48 + 126 + 56 b 109 + 53 + 1002c 783 52 d 652 388e 27 12 f 44 17g 231 28 h 1347 6i 812 7 j 840 12k 396 18 l 2139 23m 103 + 2099 + 56 n 236 15o 4803 178 p 759 11

a + 16 21 39 88

27

59

81

103

c 7 13 29 61

6

13

21

35

Chapter 1 Review

Ex 1-01

Topic testChapter 1

0.6 60

Ex 1-01

b top row minus left-hand column

d top row divided by left-hand column

56 68 99 101

2

48

51

55

36 108 180

4

9

18

Ex 1-02

Ex 1-02


5 Evaluate:a 4 + 6 b 13 18c 5 (2) d 11 20e 3 8 f 2 7g 24 (2) h 15 (5)i 36 9 j 24 (6) (2)k 10 5 + 20 l (2) (2) (2)m 28 7 (2) n 12 3 (5)o 13 15 6 p 18 (3) (6)

6 Round each of these numbers correct to the number of decimal places shown in the brackets.a 0.473 [1] b 13.1051 [2]c 98.0873 [3] d 69.97 [1]e 0.952 [2] f 6.0738 [3]g 100.099 [1] h 12.309 16 [4]

7 Evaluate:a 22 5 2 b 4 2 5c 12 + 16 4 8 d (13 + 8) 11e 16 8 + 23 f 16 8 5 15g 80 [(4 + 5) 8] h 56 (3 + 5 5)i 40 18 3 2 j (36 2) (21 9)k (84 10) 6 4 l [38 + (6 5)] [4 (5 4)]

8 Evaluate these expressions, giving your answers rounded to two decimal places.

a b

c d

e f

9 Evaluate:a 2.51 + 6.8 b 13.3 + 0.82 + 5.6c 37.4 6.9 d 8 0.03e 2.6 4 f 3.5 0.5g 4.2 0.2 h 0.071 1.3i 0.26 0.8 j 9.6 0.12k (2.5)2 l 32.13 5.1m 12.5 3.01 n (1.1)2o 16.4 0.3 3

10 Calculate:a 73 b 64 c 115d 42 5 e 25 4 f 43 34

Ex 1-03

Ex 1-04

Ex 1-05

Ex 1-05

8 315 4---------------

33 2 517 6------------------------

438 15 1469 13+( ) 7---------------------------------

22 8 6( )24 3 8+-----------------------------

72 -4 16+( )38 16( ) 6----------------------------------

-14 5 2 2+( )11 6( ) 6-----------------------------------------

Ex 1-06

Ex 1-08


11 Copy and complete:202 = (____ 5)2

= ____2 52

= ____ ____= ____

12 Calculate:

a b c d

e f g h

13 Without using a calculator, write an estimate for .14 Copy and complete the following:

=

= ____ ____= ____

15 Convert each of these improper fractions to a mixed numeral.a b c d

e f g h

16 Convert each of these mixed numerals to an improper fraction.a 4 b 3 c 6 d 11

e 7 f 8 g 15 h 3

17 Reduce these fractions to their simplest form.a b c d

e f g h

18 Evaluate:a + b c + d +

e f 1 + g 2 + 1 h 1

i j k l 119 a Tamara earns $579.50 for working 38 hours a week. How much does she earn each

hour?b A light aircraft can climb 320 metres every minute. If it climbed for 4.5 minutes

after take-off, what height did it reach?c One Friday, the manager of a store added together all the sales gures of the staff.

They were: Mario $1230, Sue $957.60, Theo $883.50, Frank $1448.40, Samantha $1101.What was the total of the sales gures?

Ex 1-08

Ex 1-09

81 400 273 -1253

2.25 -13 10 000 3 3

Ex 1-09 31

Ex 1-09

3136 ___ 49

Ex 1-10

154------

225------

73---

7811------

3310------

265------

417------

6613------

Ex 1-10

12---

23---

34---

25---

23---

12---

45---

58---

Ex 1-10

68---

1214------

1836------

2848------

3070------

1313------

90130---------

5226------

Ex 1-11

27---

37---

910------

210------

13---

15---

47---

12---

78---

23---

12---

34---

15---

12---

58---

67---

45---

23---

67---

58---

16---

13---

711------

12---

Ex 1-12


d A gardener took 300 watermelons to market and sold three-quarters of them for $2.30 each. The rest were sold for $1.90 each.

i How many watermelons were sold for $2.30 each?ii Calculate the total amount received by the gardener.

e Mark is paid $6.75 per hour. How much does he earn if he works for 16 hours?f A petrol tanker holds 20 000 L of fuel. If of the tank is emptied, how much fuel is

left in the tank?g Copy this shopping docket and ll in the missing sections.

14---

2 shirts at $49.95 each

3 belts at $35.90 each

4 pairs of socks at $6.99 each


Change

Student textImprint pageTable of contentsPrefaceHow to use this bookHow to use the CD-ROMAcknowledgementsSyllabus reference grid1 Working with numbersMental calculations shortcutsThe four operationsIntegersRounding and estimationOrder of operationsDecimalsNumber gridsPowersSquare roots and cube rootsFractionsOperations with fractionsApplying numberCalculator talkTopic overviewChapter review

2 AlgebraFrom words to algebraic expressionsSubstitution and evaluationAdding and subtracting algebraic termsMultiplying and dividing algebraic termsAdding and subtracting algebraic fractionsMixed problems: a reviewExpanding algebraic expressionsFactorising algebraic termsFactorising algebraic expressionsFactorising with negative termsIndex lawsIndex laws: mixed problemsTopic overviewChapter review

3 Geometrical figuresAngle geometryAngles and parallel linesClassifying trianglesThe angle sum of a triangleThe unknown angle in a triangleAn exterior angle of a triangleClassifying quadrilateralsThe angle sum of a quadrilateralAngle sum of a convex polygonConstructing perpendicular and parallel linesConstructing triangles and quadrilateralsBisecting intervals and anglesTopic overviewChapter review

4 PercentagesPercentages as fractionsFractions as percentagesPercentages as decimalsDecimals as percentagesOrdering fraction, decimals and percentagesPercentages of quantitiesExpressing quantities as percentagesPercentages greater than 100Percentage increasePercentage decreaseProfit and lossUsing percentagesThe unitary methodSimple interestTopic overviewChapter review

Mixed revision 15 ProbabilityThe language of chanceNumerical probabilityComplementary eventsExperimental probabilityTopic overviewChapter review

6 Graphing linear equationsGraphing patterns on the number planeGraphing linear equationsFinding the equation of a lineComparing linear equationsIntersecting linesTopic overviewChapter review

7 The circleThe circleThe radius and the diameterCircumference of a circleWhat is pi?Calculating the circumferenceArea of a circleComposite areasPerimeter and area of a sectorTopic overviewChapter review

Mixed revision 28 Pythagoras theoremSquares, square roots and surdsRight-angled trianglesDiscovering Pythagoras theoremApplying Pythagoras theoremMixed problemsTesting right-angled trianglesPythagorean triadsPerimeter and area problems using Pythagoras theoremTopic overviewChapter review

9 Collecting and presenting dataTypes of dataCollecting data: sample or census?Organising and displaying dataMisuse of graphsGrouped dataFrequency histograms and polygonsDot plotsStem-and-leaf plotsTopic overviewChapter review

10 Ratios and ratesIntroducing ratiosEquivalent ratiosSimplifying ratiosRatios with fractions and decimalsApplying ratiosDividing quantities in a given ratioRatios and the unitary methodScale drawingsMap scalesRatesUsing ratesSpeed (a special rate)Travel graphsConverting unitsTopic overviewChapter review

11 Area and volumeAccuracy in measurementAreas of composite shapesArea of a parallelogramArea of a rhombusArea of a trapeziumSurface areaVolume of a prismVolume of a cylinderTopic overviewChapter review

Mixed revision 312 Equations and inequalitiesWhat is an equation?Solution by inspectionSolving equations using guess, check and improveOne-step equationsSolving word problemsTwo-step equationsMore fraction equationsEquations with variables on both sidesEquations with grouping symbolsUsing equationsEquations and formulasInequalitiesInequalities and the number lineSolving inequalitiesMultiplying and dividing inequalities by negative numbersTopic overviewChapter review

13 Analysing dataSummarising dataMeasures of location: mean, mode and medianAnalysing frequency tablesAnalysing dot plots and stem-and-leaf plotsAnalysing dataScatter diagramsPredictions using scatter diagramsPredictions using samplesInterquartile rangeTopic overviewChapter review

14 Congruent and similar figuresCongruenceTransformationsCongruent figuresDrawing congruent figuresTests for congruent figuresUsing congruence testsSimilar figuresThe scale factorFinding side lengths in similar figuresScale drawingsSimilar trianglesTopic overviewChapter review

Mixed revision 4General revisionAnswersIndex

GlossaryABCDEFG HI JK LMNOPQRSTU VW X Y Z

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New Century Maths Year 8 Chapter 1