Cambridge IGCSE Core Mathematics Workbook

97 Pages·2018·1.913 MB·English

by  Alan Whitcomb

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IGCSE®
Cambridge
Core
Mathematics
Ric Pimentel
Terry Wall
9781510421677.indb 1 01/06/18 8:03 PM
®IGCSE is a registered trademark
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© Ric Pimentel and Terry Wall 2018
First published 2018 by
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Typeset in India
Printed in the UK
A catalogue record for this title is available from the British Library.
ISBN: 978 1 5104 2167 7
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Contents
TOPIC 1 Number 4
Chapter 1 Number and language 4
Chapter 2 Accuracy 7
Chapter 3 Calculations and order 9
Chapter 4 Integers, fractions, decimals and percentages 10
Chapter 5 Further percentages 12
Chapter 6 Ratio and proportion 15
Chapter 7 Indices and standard form 19
Chapter 8 Money and finance 23
Chapter 9 Time 27
Chapter 10 Set notation and Venn diagrams 28
TOPIC 2 Algebra and graphs 31
Chapter 11 Algebraic representation and manipulation 31
Chapter 12 Algebraic indices 33
Chapter 13 Equations 34
Chapter 14 Sequences 42
Chapter 15 Graphs in practical situations 44
Chapter 16 Graphs of functions 47
TOPIC 3 Coordinate geometry 53
Chapter 17 Coordinates and straight line graphs 53
TOPIC 4 Geometry 58
Chapter 18 Geometrical vocabulary 58
Chapter 19 Geometrical constructions and scale drawings 61
Chapter 20 Symmetry 62
Chapter 21 Angle properties 63
TOPIC 5 Mensuration 67
Chapter 22 Measures 67
Chapter 23 Perimeter, area and volume 68
TOPIC 6 Trigonometry 77
Chapter 24 Bearings 77
Chapter 25 Right-angled triangles 78
TOPIC 7 Vectors and transformations 81
Chapter 26 Vectors 81
Chapter 27 Transformations 82
TOPIC 8 Probability 85
Chapter 28 Probability 85
TOPIC 9 Statistics 90
Chapter 29 Mean, median, mode and range 90
Chapter 30 Collecting, displaying and interpreting data 91
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1
Number and language
Exercises 1.1–1.8
1 List all the prime numbers between 80 and 100.
............................................................................................................................................................... [2]
2 List all the factors of the following numbers:
a 48 .................................................................................................................................................... [2]
b 200 .................................................................................................................................................. [2]
3 List the prime factors of these numbers and express them as a product of prime numbers:
a 25 .................................................................................................................................................... [2]
b 48 .................................................................................................................................................... [2]
4 Find the highest common factor of the following numbers:
a 51, 68, 85 ......................................................................................................................................... [2]
b 36, 72, 108 ....................................................................................................................................... [2]
5 Find the lowest common multiple of the following numbers:
a 8, 12, 16 ........................................................................................................................................... [2]
b 23, 42, 6 ............................................................................................................................................ [2]
6 Write the reciprocal of these:
a 4 ...............................................................[1] b 5 .............................................................. [1]
5 2

Exercises 1.9–1.12
1 State whether each of the following numbers is rational or irrational:
· ·
a 2.5 .......................................................[1] b 0.14 ........................................................ [1]
c 17 .............................................................[1] d –0.03 ...................................................... [1]
e 144 ................................................................[1] f 5 × 2 ................................................. [1]
16
g .................................................................. [1]
4
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Exercises 1.9–1.12
2 a Draw and name three different 2D shapes where the area is likely to be a rational

number. [3]
b On each of your shapes, write the dimensions that make the area a rational number. Do not
work out the area. [3]
3 a Draw two different compound 2D shapes where the total area is likely to be an irrational
number. [2]
A compound shape is made up of more than one shape.
b On each of your shapes, write the dimensions that make the total area an irrational number.
Do not work out the area. [2]
4 Complete the diagram and find the area of a square of side 2.3 units. [3]
2
0.3
Area = …………….
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1 Number aNd laNguage
Exercises 1.13–1.18
Without using your calculator, work out:
a 0.04 ...............................................................................................................................................

......................................................................................................................................................[1]
b 1 9 ................................................................................................................................................
16

......................................................................................................................................................[2]
c 3 −216 ..............................................................................................................................................
......................................................................................................................................................[2]
d 3155 ...............................................................................................................................................
8

......................................................................................................................................................[2]
Exercise 1.19
1 A hang-glider is launched from a mountainside. It climbs 850 m and then descends 1730 m
before landing.
a How far below the launch point was the hang-glider when it landed?
......................................................................................................................................................[1]
b If the launch point was at 1850 m above sea level, at what height above sea level did the
hang-glider land?
..........................................................................................................................................................[1]

2 A plane flying at 9200 m drops a sonar device onto the ocean floor. If the device falls a total of
11 500 m, how deep is the ocean at this point?
................................................................................................................................................................[2]
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2
Accuracy
Exercises 2.1–2.3
1 Round the following numbers to the degree of accuracy shown in brackets:
a 47 (10) ...................................................... [1] b 1250 (100) ................................................ [1]
c 524 700 (1000) ......................................... [1]
2 Write the following to the number of decimal places shown in brackets:
a 4.98 (1 d.p.) .............................................. [1] b 18.04 (1 d.p.) ............................................ [1]
c 0.0048 (2 d.p.) .......................................... [1]
3 Write the following to the number of significant figures shown in brackets:
a 15.01 (1 s.f.) .............................................. [1] b 0.042 99 (2 s.f.) ......................................... [1]
c 3.049 01 (3 s.f.) ......................................... [1]
Exercise 2.4
1 Without using your calculator, estimate the answers to the following calculations:
a Multiply 22 by 4877 b Divide 7890 by 19
..................................................................... [1] ..................................................................... [1]
c 47×3.8 d 140
18.8 2.22
..................................................................... [1] ..................................................................... [2]
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2 accuracy
2 Estimate the shaded area of the shape. Do not work out an exact answer.
1
Area of a triangle = base × height
2
3.2 cm
14.2 cm
6.8 cm
18.8 cm
Estimated area = ……………. [3]
Exercise 2.5
1 Calculate the upper and lower bounds for each of the following:
a 15 (2 s.f.) ......................................................................................................................................... [2]
b 12.8 (1 d.p.) .................................................................................................................................... [2]
c 100.0 (1 d.p.) .................................................................................................................................. [2]
d 0.75 (2 d.p.) ............................................................................................................................... [2]
e 2.25 (2 d.p.) .................................................................................................................................... [2]
2 A town is built on a rectangular plot of land measuring 3.7 km by 5.2 km, correct to 1 d.p.
What are the upper and lower limits for the length and width?
................................................................................................................................................... [3]
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3
Calculations and order
Exercises 3.1–3.4
1 Represent the inequality –1  x < 4 on the number line.
−2 −1 0 1 2 3 4 5 [2]
2 Write the following sentence using inequality signs:
The finishing time (t seconds) of runners in a 100 m race ranged from 12.1 seconds to
15.8 seconds.
................................................................................................................................................................[1]
3 Write these decimals in order of magnitude, starting with the smallest:

0.5 0.055 5.005 5.500 0.505 0.550
................................................................................................................................................................[1]
Exercises 3.5–3.8
1 Without using your calculator, use the order of operations to work out the following:
a (25 – 2) × 10 + 4 ............................................................................................... ...............................[1]
b 25 – 2 × 10 + 4 ...................................................................................................... ...........................[1]
c 25 – 2 × (10 + 4) ...................................................................................................... ........................[1]
2 Insert any brackets that are needed to make each of these calculations correct:
a 15 ÷ 3 + 2 ÷ 2 = 6 ............................................................................................. ................................[1]
b 15 ÷ 3 + 2 ÷ 2 = 3.75 ............................................................................................ ...........................[1]
c 15 ÷ 3 + 2 ÷ 2 = 1.5 ............................................................................................. .............................[1]
3 Work out the following calculations without using your calculator:
a 8+2×4−3 .......................................................................................................................................[1]
4

b –3 × (–4 + 6) ÷ 4 .............................................................................................................................[1]
−4+7×(−2)
c ........................................................................................................................................[1]
−9

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