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Contents

(Higher tier only material appears bold)

7 Transformations, constructions and loci

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

Congruent triangles Rotational symmetry Transformations Combinations of transformations Bisectors Defining a locus Loci problems Plans and elevations

55 56 57 62 63 64 65 67

2 Fractions, ratio and proportion 13

Algebraic manipulation

2.1 One quantity as a fraction of another 2.2 Adding, subtracting and calculating with fractions 2.3 Multiplying and dividing fractions 2.4 Fractions on a calculator 2.5 Increasing and decreasing quantities by a percentage 2.6 Expressing one quantity as a percentage of another

8.1 Basic algebra 69 8.2 Factorisation 72 8.3 Quadratic expansion 73 8.4 Expanding squares 76 8.5 More than two binomials 76 8.6 Quadratic factorisation 77 8.7 Factorising ax2 + bx + c 78 8.8 Changing the subject of a formula 79

3 Statistical diagrams and averages

3.1 3.2 3.3

Statistical representation Statistical measures Scatter diagrams

20 22 25

Number and sequences

How to use this book

Basic number

1.1 Solving real-life problems 1.2 Multiplication and division with decimals 1.3 Approximation of calculations 1.4 Multiples, factors, prime numbers, powers and roots 1.5 Prime factors, LCM and HCF 1.6 Negative numbers

4.1 Patterns in number 4.2 Number sequences 4.3 Finding the nth term of a linear sequence 4.4 Special sequences 4.5 General rules from given patterns 4.6/4.7 ( Finding) The nth term of a quadratic sequence

Ratio and proportion

5 6 7 10 10 12

13 13 14 16 17

26 26 27 28 30 31

5.1 Ratio 5.2 Direct proportion problems 5.3 Best buys 5.4 Compound measures 5.5 Compound interest and repeated percentage change 5.6 Reverse percentage (working out the original amount)

6 Angles

6.1 6.2 6.3 6.4 6.5 6.6 6.7

41 42 44 46 47 48 50

Angle facts Triangles Angles in a polygon Regular polygons Angles in parallel lines Special quadrilaterals Scale drawings and bearings

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32 34 35 36 39

9 Length, area and volume

9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

Circumference and area of a circle Area of a parallelogram Area of a trapezium Sectors Volume of a prism Cylinders Volume of a pyramid Cones Spheres

81 82 83 84 85 86 87 89 90

Linear graphs

10.1 Drawing linear graphs from points 10.2 Gradient of a line 10.3 Drawing graphs by gradient-intercept and cover-up methods 10.4 Finding the equation of a line from its graph 10.5 Real-life uses of graphs 10.6 Solving simultaneous equations using graphs 10.7 Parallel and perpendicular lines

98 100

Right-angled triangles

101

11.1 Pythagoras’ theorem 11.2 Finding the length of a shorter side 11.3 Applying Pythagoras’ theorem in real-life situations 11.4 Pythagoras’ theorem and isosceles triangles 11.5 Pythagoras’ theorem in three dimensions 11.6 Trigonometric ratios 11.7 Calculating angles 11.8 Using the sine and cosine functions 11.9 Using the tangent function

101 102

91 92 94 96 97

103 104 105 107 107 108 110

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11.10 Which ratio to use 11.11 Solving problems using trigonometry 11.12 Trigonometry and bearings 11.13 Trigonometry and isosceles triangles

110 111 113 115

12 Similarity

116

12.1 12.2

116 119

Similar triangles Areas and volumes of similar shapes

13 Exploring and applying probability

122

13.1 Experimental probability 13.2 Mutually exclusive and exhaustive outcomes 13.3 Expectation 13.4 Probability and two-way tables 13.5 Probability and Venn diagrams

124 125 127 128

14 Powers and standard form

130

122

14.1 Powers (indices) 130 14.2 Rules for multiplying and dividing powers 131 14.3 Standard form 132

15 Equations and inequalities

135

15.1 Linear equations 135 15.2 Elimination method for simultaneous equations 137 15.3 Substitution methods for simultaneous equations 137 15.4 Balancing coefficients to solve simultaneous equations 138 15.5 Using simultaneous equations to solve problems 138 15.6 Linear inequalities 139 15.7 Graphical inequalities 141 15.8 Trial and improvement 143

16 Counting, accuracy, powers and surds

144

16.1 Rational numbers, reciprocals, terminating and recurring decimals 144 16.2 Estimating powers and roots 145 16.3 Negative and fractional powers 146 16.4 Surds 147 16.5 Limits of accuracy 149 16.6 Problems involving limits of accuracy 150 16.7 Choices and outcomes 152

17 Quadratic equations

153

17.1 Plotting quadratic graphs 17.2 Solving quadratic equations by factorisation 17.3 Solving a quadratic equation by using the quadratic formula 17.4 Solving quadratic equations by completing the square 17.5 The significant points of a quadratic curve 17.6 Solving one linear and one non-linear using graphs 17.7 Solving quadratic equations by the method of intersection

153

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154 155 156 157 158

17.8 Solving linear and non-linear simultaneous equations algebraically 17.9 Quadratic inequalities

160 161

18 Sampling and more complex diagrams

162

18.1 Sampling data 18.2 Frequency polygons 18.3 Cumulative frequency graphs 18.4 Box plots 18.5 Histograms

162 163 165 166 168

171

Combined events

19.1 Addition rules for outcomes of events 171 19.2 Combined events 172 19.3 Tree diagrams 174 19.4 Independent events 176 19.5 Conditional probability 178

Properties of circles

180

20.1 20.2 20.3 20.4

Circle theorems Cyclic quadrilaterals Tangents and chords Alternate segment theorem

180 181 183 184

21 Variation

186

21.1 21.2

186 188

Direct proportion Inverse proportion

22 Triangles

190

22.1 Further 2D problems 22.2 Further 3D problems 22.3 Trigonometric ratios of angles between 0° and 360° 22.4 Solving any triangle 22.5 Using sine to calculate the area of a triangle

190 191 193 194 198

23 Graphs

199

23.1 23.2 23.3 23.4 23.5 23.6 23.7

199 201 204 205 206 207 208

Distance–time graphs Velocity–time graphs Estimating the area under a curve Rates of change Equation of a circle Other graphs Transformations of the graph y = f(x)

24 Algebraic fractions and functions

211

24.1 Algebraic fractions 24.2 Changing the subject of a formula 24.3 Functions 24.4 Composite functions 24.5 Iteration

211 211 212 213 214

Vector geometry

215

25.1 25.2

Properties of vectors Vectors in geometry

215 217

159

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How to use this book Welcome to Collins Edexcel GCSE Maths Higher Practice Book. This book follows the structure of the Collins Edexcel GCSE Maths 4th edition Higher Student Book, so is ideal to use alongside it.

A sycamore tree is 40 cm tall. It grows at a rate of 8% per year. A conifer is 20 cm tall. It grows at a rate of 15% per year. How many years does it take before the conifer is taller than the sycamore?

The population of a small town is 2000. It is falling by 10% each year. The population of a nearby village is 1500. It is rising by 10% each year.

Colour-coded questions

After how many years will the population of the town be less than the population of the village?

Each week, a boy takes out 20% of the amount in his bank account to spend. After how many weeks will the amount in his bank account have halved from the original amount?

Know what level of difficulty you are working at with questions ranging from more accessible (green), through intermediate (blue) to more challenging (pink).

5.6 Reverse percentage (working out the original amount) Homework 5J 1

Find what 100% represents in each situation. a 20% represents 160 g

b 25% represents 24 m

a 40% represents 28 kg

c 5% represents 42 cm

Find what 100% represents in each situation. b 30% represents £54

c 15% represents 6 hours

VAT is a government tax added to goods and services. With VAT at 17.5%, what is the pre-VAT price of these goods? Jumper

£14.10

Socks

£1.88

Trousers

£23.50

Use of calculators

Paula spends £9 each week on CDs. This is 60% of her weekly allowance. How much is Paula’s weekly allowance?

Alan’s weekly pay is increased by 4% to £187.20. What was Alan’s pay before the increase?

Questions when you could use a calculator are marked with a icon.

Jon’s salary is £23 980. This is 10% more than he earned two years ago. Last year his salary was 3% more than it was two years ago. a How much was his salary last year? b By what percentage did he salary increase last year?

Twice as many people visit a shopping centre on Saturdays as on Fridays. The numbers visiting on both days increases by 50% in the week before Christmas. How many more visit on this Saturday than on this Friday? Give your answer as a percentage.

A man’s savings decreased by 10% in one year and then increased in the following year by 10%. He now has £1782. How much did he have two years ago?

5 Ratio and proportion and rates of change: Ratio and proportion

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A runner sets off at 8 am from point P to jog along a trail at a steady pace of 12 km/h. One hour later, a cyclist sets off from P on the same trial, at a steady pace of 24 km/h. After 30 minutes, the cyclist gets a puncture that takes her 30 minutes to fix. She then sets off at a steady pace of 24 km/h. At what time did the cyclist catch up with the runner?

Hints and tips Drawing a distance–time graph is a straightforward method of answering this question. Remember that the cyclist doesn’t start until 9 am.

Calculate the average speed of each journey. 50

b 250

250

200

30 20 10 0

30 20 10

1 1 Time (hours) Time (hours)

Distance (miles)

Distance (km)

These are provided where extra guidance can save you time or help you out.

Distance (miles)

Distance (km)

Hints and tips

150

100

50 0

1 1 2 2 Time (hours) Time (hours)

This graph shows a car’s journey from London to Brighton and back again. The car leaves at 8 am and returns at 3 pm. 50

Distance (miles)

40 30 20 10 0

Time

a For how long does the car stop in Brighton? b Was the car travelling faster from London to Brighton or on the return journey from Brighton to London? Describe how you can tell this from the graph.

Answers Check your own work – the answers are provided online at www.collins.co.uk/ gcsemaths4eanswers.

Homework 23B 1

200

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23 Algebra: Graphs

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Draw a graph of the depth of water in each of these containers as it is filled steadily.

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How to use this book

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1 Number: Basic number 1.1 Solving real-life problems Homework 1A 1

Andy needs enough tiles to cover an area of 12 m2. 25 tiles cover 1 m2. The tile store recommends buying 20 percent more tiles to allow for cutting. Tiles are sold in boxes of 16. Andy buys 24 boxes. Does he have enough tiles?

The organiser of a church fête needs 1000 balloons. Each packet contains 25 balloons and costs 85p. She has a budget of £30. Can she buy enough balloons?

A TV rental shop buys TVs for £110 each. The shop needs to make a profit of at least 10% on each TV to cover its costs. On average, each TV is rented for £3.50 per week for 40 weeks. Does the shop cover its costs?

The annual membership fee for a fishing club is £42. The treasurer of the club has collected £1134 in fees. How many people have paid their membership fees?

Mrs Woodhead saves £14 per week towards her bills. How much does she save each year?

Mark saves £15 each week for a dining set that costs £860. Will he have saved enough money after one year? Show how you worked out your answer.

Sylvia has a part-time job and is paid £18 for every day she works. Last year she worked for 148 days. How much was she paid for the year?

Mutya has a part-time job, working three days each week. She is paid £7 per hour and works for 4 hours each day. Neil has a full-time job, working five days each week. He is paid £8 per hour and works for 7 hours each day. For how many weeks does Mutya have to work to earn at least as much as Neil earns in one week? Show your working.

A coach firm charges £504 for 36 people to go on a day trip to Calais. The cost of the coach is shared equally between the passengers. Mary has £150 to pay for her trip and her shopping. When she gets to Calais, she wants to buy each of her four grandchildren a game that costs €50. The exchange rate is £1 = €1.25. Does she have enough money?

A concert hall has 48 rows of seats with 32 seats in each row. What is the maximum capacity of the hall? 1.1 Solving real-life problems

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Allan is a market gardener. He plants 420 bulbs in rows of 18. How many complete rows will there be?

Sandeep wants a new carpet for her bedroom which is 6 m by 8 m. The carpet she has chosen costs £19 per square metre. a Estimate the cost of the carpet.

b Calculate the exact cost of the carpet.

Paul wants to carpet a room that measures 7 m by 3 m. The carpet warehouse only stocks rolls that are 4 m wide and will only sell pieces that are the full width of the roll. a What is the smallest area of carpet that Paul can buy for his room? b Paul has £300 to spend on the carpet. What is the most he can spend per square metre?

240 students and teachers are going on a school trip. The school has already booked four coaches that can each take 53 passengers. They need to book one more coach. What is the smallest number of seats needed on this coach?

On average, a toy shop sells 38 computer games each week. The manager has a delivery of 150 games each month. Will her stock of games increase or decrease? Show clearly how you decide.

1.2 Multiplication and division with decimals Homework 1B 1

Round each number to the number of decimal places (dp) indicated. a 3.268 (1 dp)

b 0.0936 (2 dp)

c 64.815 93 (3 dp)

d 81.951 (2 dp)

e 512.088 (1 dp)

f 954.672 (2 dp)

g 9.4364 (1 dp)

h 7.91373 (3 dp)

Work these out. a 0.5 × 0.5

b 12.6 × 0.6

c 7.2 × 0.7

d 1.4 × 1.2

e 2.6 × 1.5

For each part of this question: i estimate the answer by first rounding each number to the nearest whole number ii calculate the exact answer iii calculate the difference between your answers to parts i and ii. a 3.7 × 2.4

b 4.8 × 3.1

c 5.1 × 4.2

d 6.5 × 2.5

a Use any method to work out 15 × 16. b Use your answer to part a to work out each of these. i 1.5 × 1.6

ii 0.75 × 3.2

iii 4.5 × 1.6

a Work out 7.2 × 3.4. b Explain how you can use your answer to part a to write down the answer to 6.2 × 3.4.

1 Number: Basic number

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a Work out 2.3 × 7.5. b Use your answer to part a and the fact that 4.1 × 7.5 = 30.75, to work out 6.4 × 7.5.

Evaluate each of these. a 3.12 × 14

b 5.24 × 15

c 1.36 × 22

d 7.53 × 25

e 27.1 × 32

Work out the total cost of each purchase. a Twenty-four litres of petrol at £0.92 per litre b Eighteen pints of milk at £0.32 per pint c Fourteen magazines at £2.25 per copy

A CD case is 0.8 cm thick. How many cases are in a pile of CDs that is 16 cm high?

a Use any method to work out 64 ÷ 4. b Use your answer to part a to work out each of these. i 6.4 ÷ 0.04

ii 0.64 ÷ 4

iii 0.064 ÷ 0.4

Here are three calculations. 43.68 ÷ 5.6

21.7 ÷ 6.2

19.74 ÷ 2.1

Which has the largest answer? Show how you know.

1.3 Approximation of calculations Homework 1C 1

Round each number to 1 significant figure. a 51 203

b 56 189

c 33 261

d 89 998

e 94 999

f 53.71

g 87.24

h 31.06

i 97.835

j 184.23

k 0.5124

l 0.2765

m 0.006 12

n 0.049 21

o 0.000 888

p 9.7

q 85.1

r 91.86

s 196

t 987.65

What are the least and the greatest numbers of people that live in these towns? a Hellaby

population 900 (to 1 significant figure)

b Hook

population 650 (to 2 significant figure)

c Hundleton

population 1050 (to 3 significant figures)

Round each number to 2 significant figures. a 6725

b 35 724

c 68 522

d 41 689

e 27 308

f 6973

g 2174

h 958

i 439

j 327.6

Round each number to the number of significant figures (sf) indicated. a 46 302 (1 sf)

b 6177 (2 sf)

c 89.67 (3 sf)

d 216.7 (2 sf)

e 7.78 (1 sf)

f 1.087 (2 sf)

g 729.9 (3 sf)

h 5821 (1 sf)

i 66.51 (2 sf)

j 5.986 (1 sf)

k 7.552 (1 sf)

l 9.7454 (3 sf)

m 25.76 (2 sf)

n 28.53 (1 sf)

o 869.89 (3 sf)

p 35.88 (1 sf)

q 0.084 71 (2 sf)

r 0.0099 (2 sf)

s 0.0809 (1 sf)

t 0.061 97 (3 sf)

1.3 Approximation of calculations

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A baker estimates that she has baked 100 loaves, to 1 significant figure. She sells two loaves and now has 90 loaves, to 1 significant figure. How many loaves did she start with? Work out all possible answers.

There are 500 cars in a car park, to 1 significant figure. What is the least possible number of cars that could enter the car park so that there are 700 cars in the car park, to 1 significant figure?

Five minutes before closing time, a supermarket manager estimates that there are still 200 people shopping, to 1 significant figure. No more shoppers can enter the supermarket. On average, a checkout serves four customers in five minutes. How many checkouts should be open so that all the customers can be served by closing time?

Homework 1D 1

Write down the answers, without using a calculator. a 50 × 600

b 0.6 × 40

c 0.02 × 400

d (30)2

e 0.5 × 250

f 0.6 × 0.7

g 30 × 40 × 50

h 200 × 0.7 × 40

Write down the answers, without using a calculator. a 4000 ÷ 20

b 8000 ÷ 200

c 400 ÷ 0.5

d 2000 ÷ 0.05

e 1800 ÷ 0.12

f 600 ÷ 0.3

g 200 × 30 ÷ 40

h 300 × 70 ÷ 0.4

You are given that 18 × 21 = 378. Use this information to write down the value of these calculations. a 180 × 210

b 3780 ÷ 21

Match each calculation with its answer and then write out the calculations in order, starting with the smallest answer. 6000 × 300

500 × 7000

10 000 × 900

20 × 80 000

3 500 000

1 800 000

1 600 000

9 000 000

The Moon is approximately 400 000 km from Earth. If a spaceship takes 8 days to travel to the Moon and return to Earth, how far does it travel each day?

Homework 1E 1

Work out approximate answers to each of these. a 4324 × 6.71

b 6170 × 7.311

c 72.35 × 3.142

d 4709 × 3.81

e 63.1 × 4.18 × 8.32

f 320 × 6.95 × 0.98

g 454 ÷ 89.3

h 26.8 ÷ 2.97

i 4964 ÷ 7.23

j 316 ÷ 3.87

k 2489 ÷ 48.58

l 63.94 ÷ 8.302

By rounding each value in the calculation, find approximate answers to each of these. 561 × 99 9.1 × 56 b 491 − 210 c 691 + 320 d 59.1 × 1.8 e a 101 18 25 2.56 989

1 Number: Basic number

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Work out the approximate monthly pay of each person. a Joy: £47 200 per year

b Amy: £24 200 per year

c Tom: £19 135 per year

Work out the approximate annual pay of each person. a Trevor: £570 per week

b Brian: £2728 per month

A groundsman bought 350 kg of seed at a cost of £3.84 per kilogram. Find the approximate total cost of this seed.

By rounding each value in the calculation, find approximate answers to each of these. a 361 × 89 0.48

491 – 110 0.18

211 + 420 0.59

591 × 18 0.49

91 + 880 0.67 – 0.58

A greengrocer sells a box of 250 apples for £47. If he sells them for 20p each, or more, he will make a profit. Does he make a profit? Use approximations to explain why.

Keith runs about 15 km every day. Approximately how far does he run in: a a week

9 10

b a month

c a year?

A litre of paint will cover an area of about 6.8 m2. Approximately how many one-litre cans will I need to paint a fence with a total surface area of 43 m2? A tour of London sets off at 10.13 am and costs £21. It returns at 12.08 pm. What is the approximate cost per hour of the tour?

Round each of the numbers in these statements to a suitable degree of accuracy. a Kris is 1.6248 m tall. b It took me 17 minutes 48.78 seconds to cook the dinner. c My rabbit weighs 2.867 kg. d The temperature at the bottom of the ocean is 1.239 °C. e There were 23 736 people at the baseball game yesterday.

How many jars, each holding 119 cm3 of water, can be filled from a three-litre flask?

If I walk at an average speed of 62 m per minute, how long will it take me to walk a distance of 4 km?

Helen earns £31 500 a year. She works 5 days a week for 45 weeks of the year. How much does she earn per day?

If 10 g of gold costs £2.17, how much will 1 kg of gold cost?

Rewrite this paragraph using sensible numbers. I left home at eleven and a half minutes past two and walked for 49 minutes. The temperature was 12.7623 °C. I could see an aeroplane overhead at 2937.1 feet. Altogether I walked 3.126 miles.

David travelled 350 miles in 5 hours 10 minutes. Trevor travelled half the distance in half the time. Approximately how fast was Trevor travelling?

1.3 Approximation of calculations

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1.4 Multiples, factors, prime numbers, powers and roots Homework 1F 1

From the list of numbers below, write down the: a multiples of 4

b multiples of 5

c prime numbers

d factors of 2700.

During the peak travel time at a railway station, there are north-bound trains setting off every 8 minutes and south-bound trains setting off every 12 minutes. At 5 pm, one train sets off to the north and one train sets off to the south. How many more times will two trains set off at the same time before 6.30 pm?

Write down the negative square root of each number.

a 36

b 81

c 100

d 900

e 361

f 169

g 225

h 1 000 000

i 441

j 1225

Write down the cube root of each number. a 8

b 64

c 125

d 1000

e 27 000

f −27

g −1

h −216

i − 8000

j −343

Square number

Factor of 40

Here are four numbers:

8, 20, 25, 64

Copy and complete this table by putting each number in the correct box.

Cube number Multiple of 5

Use these four number cards to make a cube number.

A number is a factor of 18 and a multiple of 18.

What is the number?

Write down the value of each expression. a

0.36

0.81

1.69

0.09

0.01

1.44

2.25

1.96

4.41

12.25

1.5 Prime factors, LCM and HCF Homework 1G 1

Draw prime factor trees for these numbers. a 144

c 98

d 420

e 560

Write these numbers as products of their prime factors using index notation. a 48

b 75

b 54

c 216

d 1000

e 675

1 Number: Basic number

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a Express 36 as a product of its prime factors. b Write your answer to part a using index notation. c Use you answer to part b to write 18 and 72 as a product of their prime factors using index notation.

119 = 7 × 17 1192 = 14 161 1193 = 1 685 159 a Write 14 161 as a product of prime factors using index notation. b Write 1 685 159 as a product of prime factors using index notation. c Write 11910 as a product of prime factors using index notation.

A mathematician wants to donate a total of £18 to three charities so that they each receive a whole number of pounds and the amount given to each charity is a factor of 18. How much does he give to each charity?

The first three odd prime numbers are all factors of 105. Explain why this means that seven people can share £105 equally so that each receives an exact number of pounds.

Homework 1H 1

Find the LCM of each pair of numbers. a 5 and 7

b 3 and 8

c 6 and 9

d 10 and 12

e 10 and 15

f 12 and 16

g 16 and 24

h 15 and 35

Find the HCF of each pair of numbers. a 21 and 49

b 27 and 45

c 15 and 25

d 25 and 45

e 48 and 60

f 72 and 108

g 54 and 126

h 99 and 132

Write each of these as a single power of x. a x2 × x3

b x4 × x5

Find the HCF of 55 555 and 67 750.

Find the LCM of 144 and 162.

Nuts are sold in packs of 12.

c x6 × x

d x5 × x5

e x3 × x2 × x4

Bolts are sold in packs of 18. What is the least number of each pack that needs to be bought in order to have the same numbers of nuts and bolts?

The HCF of two numbers is 5. The LCM of the same two numbers is 150. What are the numbers?

1.5 Prime factors, LCM and HCF

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1.6 Negative numbers Homework 1I 1

a Work out 17 × (− 4). b The average temperature drops by 4 °C each day for 17 days. By how much has the temperature dropped altogether? c The temperature drops by 6 °C for each of the next four days. Write down the calculation to work out the total change in temperature over these four days.

Write down the answer to each calculation. a −2 × 4 b −3 × 6 c −5 × 7 f −14 ÷ (−2) g −16 ÷ (− 4) h 25 ÷ (−5) k 3 × (−7) l 6 × (−3) m 7 × (− 4) p 28 ÷ (− 4) q 12 ÷ (−3) r − 40 ÷ 8 u −3 × (− 8) v 42 ÷ (− 6) w 7 × (−9)

d i n s x

−3 × (− 4) −16 ÷ (− 8) −3 × (−9) −15 ÷ (−3) −24 ÷ (− 4)

e j o t y

− 8 × (−2) − 8 ÷ (− 4) −7 × (−2) 50 ÷ (−2) −7 × 8

Write down the answer to each calculation. a −2 + 4 b −3 + 6 c −5 + 7 f −14 − (−2) g −16 − (− 4) h 25 − (−5) k 3 + (−7) l 6 + (−3) m 7 + (− 4) p 28 − (− 4) q 12 − (−3) r − 40 − 8 u −3 + (− 8) v 42 − (− 6) w 7 + (− 8)

d i n s x

−3 + (− 4) −16 − (− 8) −3 + (−9) −15 − (−3) −24 − (− 4)

e j o t y

− 8 + (−2) − 8 − (− 4) −7 + (−2) 50 − (−2) −7 + 8

4 5

By what number do you multiply −5 by to get each of these numbers? a 25 b −30 c 50 d −100

e 75

Put these calculations in order from lowest result to highest. −18 ÷ 12 −0.5 × (− 4) −21 ÷ (−14) 0.3 × (−2)

Homework 1J

Work out each of these. Remember to work out the brackets first. a −3 × (−2 + 6) b 8 ÷ (−3 + 2) c (6 − 8) × (−3) d − 4 × (− 6 − 3) e −5 × (− 6 ÷ 2) f (−5 + 3) × (−3) g (6 − 9) × (− 4) h (2 − 5) × (5 − 2)

Work these out. a −5 × (− 4) + 3 e −3 × 4 − 5

b −8 ÷ 8 − 3 f −1 + 42 −5

c 16 ÷ (− 4) + 3 g 5 − 32 + 2

d 2 × (−5) + 6 h −1 + 2 × (−3)

Copy each of these and put in brackets where necessary to make each one true. a 4 × (−3) + 2 = − 4 b − 6 ÷ (−3) + 2 = 4 c − 6 ÷ (−3) + 2 = 6

Work out the value of each expression when a = −3, b = 5 and c = − 4. a (a + b)2 b −(a + c)2 c (a + b)c d a2 + b2 + c2

Work out the value of each expression. a (72 + 22) × 3 b 18 ÷ (2 − 5)2 c 3 × (62 − (1 − 8)2)

d ((7 + 1)2 − (2 − 3)2) ÷ 7

Use each of the numbers 4, 6 and 8 and each of the symbols −, × and ÷ to make a calculation with an answer −3.

Use any four different numbers to make a calculation with an answer of −9.

Use the numbers 1, 2, 3, 4 and 5 in order, from smallest to largest, together with one of each of the symbols +, −, ×, ÷ and two pairs of brackets to make a calculation with an answer of −2.75. For example, to make a calculation with an answer of − 4: (1 + 2) − (3 × 4) + 5 = − 4.

1 Number: Basic number

13834_P005_012.indd 12

02/01/15 9:40 AM