Complete Mathematics for Cambridge Secondary 1 Book 1

322 Pages·2019·49.27 MB·English

AND BEYOND

‘ASPIRE
JA\2 SOCCEED
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Illustrations by Q2A Media, Phil Burrows and Ian West.
(Contents)

About this book
1. Number and calculation 1
1.1 Number facts
1.2 Adding and subtracting numbers
1.3. Multiplication and associated division facts
1.4 Decimals
1.5 Decimals and place value
1.6 Decimals and your calculator
1.7 Multiplying and dividing decimals by powers
often
1.8 Rounding
1.9 Negative numbers
1.10 Negative numbers and addition
1.11 Subtracting negative numbers
1.12 Some ways we use negative numbers
1.13 Laws of arithmetic and inverse operations
1.14 Order of operations
Consolidation
Summary
2. Expressions
2.1 Expressions
2.2 Simplifying
2.3. Expanding brackets
Consolidation
Summary
3. Shapes and constructions

Lines and angles
Measuring angles
Drawing angles
Looking at triangles
Looking at quadrilaterals
Polygons
Solid shapes
Constructions

Consolidation
Summary

4. Number and calculation 2
4.1 Multiples and factors
4.2 Divisibility tests
4.3. Squares and square roots
4.4 Multiplying and dividing with two digit
numbers
Consolidation
Summary
5. Length, mass and capacity
5.1 Length
5.2 Mass
5.3 Capacity
5.4 Reading scales
Consolidation
Summary
6. Representing information
6.1 Collecting data
6.2 Averages and range
Summary
Review A
7. Fractions
7.1 Calculating fractions
7.2 Equivalent fractions
7.3 Fractions greater than 1
7.4 Adding fractions
75
16
7.7 Applying order of operations rules to
fractions questions
7.8 Problem solving
Consolidation
Summary
8. Equations and formulae
8.1 Substitution into expressions
8.2 Formulae
8.3. Solving equations

Consolidation

Summary

81
82
86
87

90
95
96

99
100
104
107
109
111
112

114
115
119
124
126

128

132
133
136
141
143
145
147

148
149
151
152

154
155
155
157
160
161
9. Geometry
9.1 Relationships between angles
9.2 Coordinates

Consolidation

Summary

10. Fractions and decimals
10.1 Equivalence of fractions and decimals
10.2. Adding and subtracting decimals
10.3. Multiplying and dividing decimals
Consolidation
Summary

11. Time and rates of change
11.1 Time
11.2. Real-life graphs
11.3. Travel graphs
Consolidation
Summary

12. Presenting data and interpreting
results

1 Pictograms

2 Bar charts

3. Pie charts

4 Frequency diagrams for grouped discrete data
5 Using statistics

Consolidation

Summary

Review B

13. Fractions, decimals and
percentages

13.1 Understanding percentages

13.2. Fractions, decimals and percentages

13.3. Finding percentages of amounts
Consolidation

Summary

14. Sequences, functions and graphs
14.1 Looking for patterns.
14.2. Number sequences
14.3, Functions
14.4 Graphs of linear functions
Consolidation
Summary

18.1
18.2
18.3

Symmetry and transformations
Symmetry

2 Reflection

Translation
Rotation
Consolidation
Summary

Ratio and proportion
Making comparisons
Simplifying ratios
Proportion

Consolidation

Summary

Area, perimeter and volume
What is area?

Some of units of area
Areas of rectangles
Perimeters of rectangles
Compound shapes
What is volume?
Volume of cuboids
Surface area
Consolidation
Summary

Probability
Language of probability
Experimental probability
Theoretical probability
Consolidation

Summary

Review C

19.

19.1
19.2
19.3
19.4
195

Index

Sets and Venn diagrams

Sets and their members

How to describe a set

Venn diagrams

Intersection of sets

Common factors, common multiples
Consolidation

Summary

278
280
282

285
286
289

295
295

299

306

307
309
311
313
316
317

319
About this book

This book follows the Cambridge Secondary 1
Mathematics curriculum framework for Cambridge
International Examinations in preparation for the
Checkpoint assessments. It has been written by a
highly experienced teacher, examiner and author .

This book is part of a series of nine books. There are
three student textbooks each covering stages 7, 8 and
9 and three homework books written to closely match
the textbooks, as well as a teacher book for each stage.

The books are carefully balanced between all the
content areas in the framework: number, algebra,
geometry, measure and handling data, Some of the

n the exercises and the investigations within
the book are underpinned by the final framework

area: problem solving, providing a structure for the
application of mathematical skills.

Features of the book:

© Objectives — from the Cambridge Secondary 1
framework.

© What's the point? — providing rationale for
inclusion of topics in a real-world setting.

© Chapter Check in — to asses whether the student
has the required prior knowledge.

© Notes and worked examples — in a clear style

sible English and culturally appropriate

using ac
material.

© Exercises — carefully designed to gradually
increase in difficulty providing plenty of practice of
techniques.

© Considerable variation in question style —
encouraging deeper thinking and learning,
including open questions.

© Comprehensive practice — plenty of initial
questions practice followed by varied questions for
stretch, challenge, cross-over between topics and
links to the real world with questions set in context.

© Extension questions — providing stretch and
challenge for students

@ questions with a box e.g. [1] provide challenge
for the average student

© questions with a filled box e.g. [EJ provide
extra challenge for more able students.

© Technology boxes — direct to websites for review
material, fun games and challenges to enhance

learning.

© Investigation and puzzle boxes — providing extra
fun, challenge and interest.

© Full colour with modern artwork — pleasing to
the eye, more interesting to look at, drawing the
attention of the reader.

© Consolidation examples and exercises — providing
review material on the chapter.

© Summary and Check out — providing a quick
review of chapter's key points aiding revision,
enabling you to to assess progress.

© Review exercises — provided every six chapters
with mixed questions covering all topics.

© Bonus chapter — the work from Chapter 19 is
not in the Cambridge Secondary 1 Mathematics
curriculum. It is in the Cambridge IGCSE®
curriculum and is included to stretch and challenge
more able students.

A note from the author:

If you don’t already love maths as much as I do, I hope
that after working through this book you will enjoy

it more. Maths is more than just learning concepts

and applying them. It isn’t just about right and wrong
answers. It is a wonderful subject full of challenges,
puzzles and beautiful proofs. Studying maths develops
your analysis and problem-solving skills and improves
your logical thinking - all important skills in the
workplace.

Be a responsible learner — if you don’t understand
something, ask or look it up. Be determined and
courageous. Keep trying without giving up when
things go wrong. No one needs to be ‘bad at maths’.
Anyone can improve with hard work and practice in
just the same way sports men and women improve
their skills through training. If you are finding work
too easy, say. Look for challenges, then maths will
never be boring.

Most of all, enjoy the book. Do the ‘training’, enjoy
the challenges and have fun!

Deborah Barton

Number and calculation 1

© Consolidate the rapid recall of number including measurements, to the nearest
facts, including positive integer whole number or one decimal place.
complements to 100, multiplication © Recognise negative numbers as
facts to 10 x 10 and associated positions on a number line and
division facts. order, add and subtract positive and
© Interpret decimal notation and place negative integers in context.
value; multiply and divide whole numbers — @ Use the laws of arithmetic and inverse
and decimals by 10, 100 or 1000. operations to simplify calculations with
© Order decimals including measurements, whole numbers.
changing these to the same units. © Use the order of operations, including
© Round whole numbers to the nearest brackets, to work out simple

10, 100 or 1000 and decimals, calculations.

How many? Who has more? How much?
Questions such as these led early man
to develop number systems. Today,
numbers are everywhere, from banks,
to supermarkets, to airports.

You should know ... Check in

4. A fraction can be shown by a picture: 4 a What fraction of each shape is shaded?

‘s

b Draw shapes to represent

2 16

' 0 M00

jp is shaded
1.1 Number facts

An important skill in mathematics is to be able to do
calculations with numbers without a calculator. We can
use complements to help us. Addition and subtraction
are inverse operations. Sometimes a subtraction
problem can be turned into an addition problem to
make it easier and faster to do.

A common wrong
answer to this

. caloulation is 34.
If we change it to

76 +O = 100
We can then use

100 — 76 =O

4 is the complement to 10 of 6,
76 + 4 = 80.

20 is the complement to
100 of 80, 80 + 20 = 100

Work out units
column first to
avoid. the wrong
answer of 34.

Adding 4, then adding
20 is the same as adding 24.

76 + 24 = 100

2 Write down the answers to:
a 2X7 b 3X6
e¢ 8X4 d 5x4

e 9X7 f 9X8

3 Write down the value of the 4 in:
a 24 b 42

402 d 645

4132 f 49 206

c
e
ge 14873

Exercise 1A

Work out all of the following without a calculator.
You could race a friend to see who is faster and
more accurate.

1 a 39+0=100 b 62+0=100
e 41+0=100 d 100-28
e 100-34 f 100-16
g 100-82

2a 5+14 b 17+5 c¢ 30-16
d 27-19 e 68+23 f 58+34
g 93-48 h 76-28

3 a $22+0=$100 b 43m+O)= 100m
c $14+0=$100 d $100 — $55
e 100em—9lem f 100kg — 4kg

4 Match the complements to 100 to each other.

The first is done for you.

‘You can use the same method to do
complements to 1000.

5 a 240+()= 1000 b 76+[)= 1000
ce 318+()= 1000 d 1000-180
e 1000 — 840 f 1000 — 293
g 1000-96 h 1000 — 544
1.2 Adding and subtracting
numbers

Sometimes you may want to use column addition and
subtraction if calculations are harder.

To add numbers you must line up their place values.

Exercise 1B
1 Add these numbers:
a 13+ 27+ 46
b 162+ 39
© 615 + 34+ 143
d 1068 + 39 +7 + 214

2 = Work out:
a 12529) b 269 — 158
c 463 — 258 d 452 — 168
e227 132, f 1101 — 990

3 At Market School there are 93 students in
Form 1, 105 in Form 2, 87 in Form 3, 79 in
Form 4 and 81 in Form 5. How many students
are there altogether?

4 Orji wants to buy a new bicycle for $1000.
He has saved $824. How much more does
he need?

5 In 3 test cricket tournaments in 2010 Sachin

Tendulkar scored 214 runs, 203 runs and 146
runs. How many runs did he score altogether?

[6] 18 years ago Chris was 5 years old. How old
will he be in 16 years’ time?

1.3 Multiplication and
associated division facts

Itis very important to know the multiplication tables

up to 10 X
calculations.

10. This will help you with many harder

The multiplication grid below looks like a lot of facts
to remember. It can be made easier.

x{1}2)3)4/15)6)]7)] 8/9 | 10
1{ij}2/}/3/4/{[5/6}7]8]9]10
2/2/4 | 6] 8 | 10] 12] 14] 16| 18 | 20
313] 6 | 9 | 12] 15] 18 | 21 | 24 | 27 | 30
4| 41] 8 | 12{ 16 | 20 | 24 | 28 | 32 | 36 | 40
51/5/10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50
6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60
7|7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70
8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80
9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90
10| 10} 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100

The following facts will help you:

* The order you multiply doesn’t matter.
7 X 8 is the same as 8 X 7. This halves the
number of facts to learn.

* Multiplying a number by | doesn’t change the

number.
eg. 4X

4

* Multiplying a number by 10 means you can just
write a zero after the number.
eg. 7X 10=70

* Multiplying by 2 is the same as doubling the

number.
Now there are fewer multiplication facts to learn: x 3 6 7 8
x[1[273 74/75] 6[7][ 8] 9110 3 9
4 6 18 36
3 9 7 21 2 49
4 12 | 16 8 24 48 56 64
5 15 | 20 [25
6 18 | 24 | 30 | 36 Once you have learned your multiplication facts you
7 21 | 28 | 35 [42 | 49 need to remember that multiplication and division are
8 24 | 32 | 40 | 48 | 56 | 64 inverse operations. Sometimes a division problem can
9 27 | 36 | 45 | 54 | 63 | 72 | 81 be turned into a multiplication problem to make it
10 easier and faster to do.

‘There are some other hints that can help if you find
your multiplication tables difficult.

4’s made easy:
* Double a number and then double it again.
5’s made easy:

+ Multiply a number by 10 then halve it.
For example, for 8 X 5, do 8 X 10 = 80,
so8 X 5 = 40 (half of 80).

9°s made easy:

* Hold your hands in front of you with your fingers
spread out.

* For 9 X 4 bend your fourth finger from the left
down. (9 X 7 would be the seventh finger etc.)

* You have 3 fingers in front of the bent finger
(the tens) and 6 after the bent finger (the units).

S09 X 4 = 36.
4th finger 6 units

bent

ne

9x 4=36

Now there are very few to learn. Usually 3 X 3 = 9 is
done well. The red numbers in the table are the ones
that many students find harder. There are only nine
red numbers!

56 + 8 =( can be changed to: (] x 8 = 56.
Then you can use the multiplication tables in reverse.
7X8=56

Exercise 1C

1 Copy and complete this mixed-up tables grid
as fast as you can,

| 4 SOE ZZ AIES OES ans:
7

2

6

8

a

o

S

4

2 Work out:

a 4x8 b 63+9 c¢ 4X7
d 36+4 e 3X6 f 2023
g 8x3 h 48+6 i 6X6
bed k 42+7 I 64+8

3 Jane earns $9 an hour. If she works for 9 hours
how much will she earn?

4 If Wayan shares $45 between his 5 children,
how much do they each get?

5 Learning more multiplication facts can speed
up your working. Try these (they go up to
12 X 12.) Work out:

a 11X9 b 96+12 c¢ 88+8
d 12X7 e 11X11 f 132+11
g 12X12 h 120+12