GCSE Maths for AQA Linear (A) - Foundation Student Book

603 Pages·2006·0.58 MB·English

by  Brian Speed

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BRIAN SPEED
KEITH GORDON
KEVIN EVANS
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William Collins’dream of knowledge for all began with the publication of his first book in
1819. Aself-educated mill worker, he not only enriched millions of lives, but also founded
a flourishing publishing house. Today, staying true to this spirit, Collins books are packed
with inspiration, innovation and a practical expertise. They place you at the centre of a
world of possibility and give you exactly what you need to explore it.
Collins. Do more.
Published by Collins Acknowledgements
An imprint of HarperCollinsPublishers
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London The Publishers gratefully acknowledge the following for permission to
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make the necessary arrangements at the first opportunity.
www.collinseducation.com
AQAmaterial is reproduced by permission of the Assessment and
© HarperCollinsPublishers Limited 2006 Qualifications Alliance. Please note that all questions used dated before
2003 are NOT from the live examinations for the current specification.
ISBN-13 978-0-00-721578-9 New specifications for GCSE were introduced in 2003.
ISBN-10 0-00-721578-9
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Internal design by JPD
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Page make-up by Gray Publishing
Page make-up of Really Useful Maths! spreads by EMC Design
Illustrations by Gray Publishing, EMC Design, Lisa Alderson (Advocate),
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Production by Natasha Buckland
Printed and bound in Italy by Eurografica SpA
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CONTENTS
Chapter 1 Basic number 1
Chapter 2 Fractions 25
Chapter 3 Negative numbers 49
Chapter 4 More about number 67
Chapter 5 Perimeter and area 95
Chapter 6 Statistical representation 119
Chapter 7 Basic algebra 143
Chapter 8 Further number skills 167
Chapter 9 Ratios, fractions, speed and proportion 195
Chapter 10 Symmetry 213
Chapter 11 Averages 225
Chapter 12 Percentages 257
Chapter 13 Equations and inequalities 275
Chapter 14 Graphs 299
Chapter 15 Angles 327
Chapter 16 Circles 355
Chapter 17 Scale and drawing 373
Chapter 18 Probability 397
Chapter 19 Transformations 427
Chapter 20 Constructions 453
Chapter 21 Units 473
Chapter 22 Pie charts, scatter diagrams and surveys 483
Chapter 23 Pattern 505
Chapter 24 Surface area and volume of 3-D shapes 523
Chapter 25 Quadratic graphs 539
Chapter 26 Pythagoras’ theorem 549
Answers 563
Index 599
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Welcome to Collins GCSE Maths, the easiest way to learn and succeed in
Mathematics. This textbook uses a stimulating approach that really appeals to
students. Here are some of the key features of the textbook, to explain why.
Each chapter of the textbook begins with an Overview. The
Overview lists the Sections you will encounter in the chapter,
the key ideas you will learn, and shows how these ideas relate
to, and build upon, each other. The Overview also highlights
what you should already know, and if you’re not sure, there is
a short Quick Check activity to test yourself and recap.
Maths can be useful to us every day of
our lives, so look out for these Really
Useful Maths!pages. These double page
spreads use big, bright illustrations to
depict real-life situations, and present a
short series of real-world problems for
you to practice your latest mathematical
skills on.
EachSectionbegins first by explaining
what mathematical ideas you are
aiming to learn, and then lists the key
words you will meet and use. The ideas
are clearly explained, and this is
followed by several examples showing
how they can be applied to real
problems. Then it’s your turn to work
through the exercises and improve your
skills. Notice the different coloured
panels along the outside of the exercise
pages. These show the equivalent exam
grade of the questions you are working
on, so you can always tell how well
you are doing.
iv
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Every chapter in this textbook contains
lots of Exam Questions.These provide
ideal preparation for your examinations.
Each exam question section also
concludes with a fully worked example.
Compare this with your own work, and
pay special attention to the examiner’s
comments, which will ensure you
understand how to score maximum
marks.
Throughout the textbook you will find
Puzzlesand Activities– highlighted in
the green panels – designed to
challenge your thinking and improve
your understanding.
Review the Grade Yourselfpages at the
very end of the chapter. This will show
what exam grade you are currently
working at. Doublecheck What you
should now know to confirm that you
have the knowledge you need to
progress.
Working through these sections in the right way should mean you achieve your very best
in GCSE Maths. Remember though, if you get stuck, answers to all the questions are at
the back of the book (except the exam question answers which your teacher has).
We do hope you enjoy using Collins GCSE Maths, and wish you every good luck in
your studies!
Brian Speed, Keith Gordon, Kevin Evans
v
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ICONS
You may use your calculator for this question
You should not use your calculator for this question
Indicates a Using and Applying Mathematics question
Indicates a Proof question
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1 Adding with
This chapter will show you …
grids
(cid:2) how to use basic number skills without a calculator
Visual overview
2 Times table
check
Addition In grids
Subtraction
Up to four digits
3 Order of
Place value BODMAS
operations and
Rounding off
Multiplication
BODMAS
Division Single-digit numbers
4 Place value
What you should already know
and ordering
(cid:2) Times tables up to 10 × 10
numbers
(cid:2) Addition and subtraction of numbers less than 20
(cid:2) Simple multiplication and division
5 Rounding
(cid:2) How to multiply numbers by 10 and 100
6 Adding and Quick check
subtracting
How quickly can you complete these?
numbers with
1 4 × 6 2 3 × 7 3 5 × 8 4 9 × 2
up to four digits
5 6 × 7 6 13 + 14 7 15 + 15 8 18 – 12
9 19 – 7 10 11 – 6 11 50 ÷ 5 12 48 ÷ 6
7 Multiplying and
13 35 ÷ 7 14 42 ÷ 6 15 36 ÷ 9 16 8 × 10
dividing by
single-digit 17 9 × 100 18 3 × 10 19 14 × 100 20 17 × 10
numbers
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1.1 Adding with grids
In this section you will learn how to: Key words
(cid:2) add and subtract single-digit numbers in a grid add
(cid:2) use row and column totals to find missing numbers column
in a grid grid
row
Adding with grids
You need a set of cards marked 0 to 9.
0 1 2 3 4 5 6 7 8 9
Shuffle the cards and lay them out in a 3 by 3 grid. 3 5 0
You will have one card left over.
7 6 4
8 2 9
Copy your grid onto a piece of paper. Then add up
3 5 0 8
each row and each column and write down their totals.
7 6 4 17
Finally, find the grand total and write it in the box at the
8 2 9 19
bottom right.
18 13 13 44
Look out for things that help. For example:
• in the first column, 3 + 7 make 10 and 10 + 8 = 18
• in the last column, 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13
Reshuffle the cards, lay them out again and copy the new grid. Copy the new grid
again on a fresh sheet of paper, leaving out some of the numbers.
4 5 8
4 5 8 17 4 8 17
0 2 6 0 2 6 8 2 8
9 1 7 9 1 7 17 9 7
13 8 21 42 8 21 42
Pass this last grid to a friend to work out the missing numbers. You can make it
quite hard because you are using only the numbers from 0 to 9. Remember:
once a number has been used, it cannot be used again in that grid.
Example Find the numbers missing from this grid.
9 17
2 11
8
19 3 17
2 © HarperCollinsPublishers Limited 2007
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CHAPTER 1: BASIC NUMBER
Clues The two numbers missing from the second column must add up to 1, so they
must be 0 and 1. The two numbers missing from the first column add to 11, so they
could be 7 and 4 or 6 and 5. Now, 6 or 5 won’t work with 0 or 1 to give 17 across
the top row. That means it has to be:
7 1 9 17 7 1 9 17
4 2 11 giving 4 2 5 11 as the answer.
8 0 8 0 3 11
19 3 17 19 3 17 39
You can use your cards to try out your ideas.
EXERCISE 1A
Find the row and column totals for each of these grids.
a 1 3 7 b 0 6 7 c 0 8 7
9 2 8 8 1 4 1 6 2
6 5 4 9 5 3 9 3 4
d 2 4 6 e 5 9 3 f 0 8 3
3 5 7 6 1 8 7 2 4
8 9 1 2 7 4 1 6 5
g 9 4 8 h 0 8 6 i 1 8 7
7 0 5 7 1 4 6 2 5
1 6 3 5 9 2 0 9 3
Find the numbers missing from each of these grids. Remember: the numbers missing from each grid
must be chosen from 0 to 9 without any repeats.
a 1 7 16 b 1 3 6 c 9 3 18
3 6 9 5 4 15 4 5 9
5 2 11 7 8 24 2 8 11
6 14 16 36 14 15 16 35 14 5 19 38
d 16 e 2 6 17 f 1 16
2 4 13 1 2 4 12
8 5 0 13 5 8 13 9 3
19 13 10 42 11 17 38 12 15
g 0 2 3 h 3 4 i 4 10
9 7 4 2
4 5 17 9 6 20 8 15
17 13 42 18 12 15 36
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1.2 Times table check
In this section you will:
(cid:2) recall and use your knowledge of times tables
Special table facts
You need a sheet of squared paper.
Start by writing in the easy tables. These are the 1×, 2×, 5×, 10× and 9× tables.
Now draw up a 10 by 10 tables square ×
1 2 3 4 5 6 7 8 9 10
before you go any further. (Time yourself
doing this and see if you can get faster.) 1
2
Once you have filled it in, shade in all
the easy tables. You should be left with 3 9 12 18 21 24
something like the square on the right. 4 12 16 24 28 32
5
6 18 24 36 42 48
7 21 28 42 49 56
8 24 32 48 56 64
9
10
Now cross out one of each pair that ×
1 2 3 4 5 6 7 8 9 10
have the same answer, such as
3 × 4 and 4 × 3. This leaves you with: 1
2
3 9
4 12 16
5
6 18 24 36
7 21 28 42 49
8 24 32 48 56 64
9
10
Now there are just 15 table facts. Do learn them.
The rest are easy tables, so you should know all of them. But keep practising!
4 © HarperCollinsPublishers Limited 2007