Cambridge International Catalogue 2024 - Final - Flipbook - Page 31
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MATHEMATICS
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How to use this book
How to use this book
Exercise 15.2
SECTION 3
1 Work out the answer to the following calculations. Show your working clearly
and simplify your answers where possible.
a 2+1
d 3− 3
5
6
b
7
12
+ 15
e
c
9
14
− 72
f
13 26
5
1
+ 5−
8 16 24
+
8
5
KEY
INFORMATION
This is known as a
position-to-term
rule. The position
number is the same
as the number of
white tiles.
To make your study of Cambridge Checkpoint Maths as rewarding as
possible, look out for the following features when you are using the book:
13 8 1
− +
18 9 6
2 Sadiq spends 15 of his earnings on his mortgage. He saves
What fraction of his earnings is left?
3 The numerators of two fractions are hidden as shown.
2
7
of his earnings.
The Greeks
23
40 .
This section gives some historical background to the material in the section.
There are two types of rules which describe the sequence of blue
tiles:
– The number of blue tiles increases by 1 each time.
– The number of blue tiles is always 2 more than the number
of white tiles.
The second rule is useful if we know the number of white tiles and
want to work out the number of blue tiles. For example, if there are
100 white tiles, how many blue tiles are there?
Describe the pattern linking the number of white tiles and the
number of green tiles.
d Use your rule in part (c) to predict the number of green tiles in a
pattern with 100 white tiles.
c
3
Number of blue tiles = number of white tiles + 2
Number of blue tiles = 100 + 2 = 102
Number of white tiles
This green star icon shows the thinking and working mathematically
(TWM) questions. This is an important approach to mathematical thinking
and learning that has been incorporated throughout this book.
Questions involving TWM differ from the more straightforward traditional
question and answer style of mathematical learning. Their aim is to
encourage you to think more deeply about the problem involved, make
connections between different areas of mathematics and articulate your
thinking.
This indicates where you will see how to use a calculator to solve a
problem.
These questions should be answered without a calculator.
There is a link to digital content at the end of each chapter if you are
using the Boost eBook.
3
4
5
4
Worked example
a Draw the next two diagrams in the sequence.
b Copy and complete this table.
These show you how you would approach answering a question.
Number of white tiles
1
2
3
4
5
Number of red tiles
KEY INFORMATION
These give you hints or pointers to solving a problem or understanding a concept.
This highlights ideas and things to think about
2
vi
Return to the contents page
Number of white tiles
1
2
3
1
2
3
4
5
Number of blue tiles
c Describe the pattern linking the number of white tiles and the number of blue tiles.
d Use your rule in part (c) to predict the number of blue tiles in a pattern with 100 white tiles.
Term-to-term rules
a Draw the next two diagrams in the sequence.
b Copy and complete this table.
This book contains lots of activities to help you learn. The questions are
divided into levels by difficulty. Green are the introductory questions, amber
are more challenging and red are questions to challenge yourself. Some
of the questions will also have symbols beside them to help you answer
the questions.
a Draw the next two diagrams in the sequence.
b Copy and complete this table.
Number of white tiles
c Describe the pattern linking the number of white tiles and the number of red tiles.
d Use your rule in part (c) to predict the number of red tiles in a pattern with 100 white
tiles.
This tells you that content is related to another subject.
This tells you that content is available as audio. All audio is available to
download for free from www.hoddereducation.com/cambridgeextras
2
c Describe the pattern linking the number of white tiles and the number of orange tiles.
d Use your rule in part (c) to predict the number of orange tiles in a pattern with 100 white tiles.
1 These diagrams show the first three patterns in a sequence of growing tile patterns.
LET’S TALK
Talk with a partner or a small group to decide your answer when you see this box.
1
Number of orange tiles
Exercise 21.1
Calculate the value of both numerators.
Look out for these symbols:
Look at the
diagrams to
understand the
relationship
between the
white and green
tiles, rather than
just looking for
a pattern in the
table of numbers.
a Draw the next two diagrams in the sequence.
b Copy and complete this table.
= 23
40
These aims show you what you will be covering in the unit.
The sum of the two fractions is
21 Sequences
KEY
INFORMATION
This is known as a
term-to-term rule.
How to use this book
4
5
A rule which describes how to get from one term to the next is called
a term-to-term rule.
Number of green tiles
v
2
3
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