Chapter 1, tell me if you need more chaptersFull description
Revision of maths topics for year 5 in the UK.
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Maths Frameworking PB 9.3 Chs 1–9
29/5/08
18:33
Page i
Year Y ear 9, Pupil Book 3
NEW MATHS FRAMEWORKING Matches the revised KS3 Framework
Kevin Evans, Keith Gordon, Trevor Senior, Brian Speed
Maths Frameworking PB 9.3 Chs 1–9
29/5/08
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Page ii
Contents
Introduction
CHAPTER
CHAPTER
CHAPTER
ii
1
2
3
vi
Algebra 1 & 2 Sequences
1
Quadratic sequences
4
Functions
6
Graphs
8
Limits of sequences
11
National Test questions
12
Functional Maths – Mobile phone tariffs
14
Number 1 The four rules governing fractions
16
Percentages and compound interest
19
Reverse percentages and percentage change
22
Direct and inverse proportion
25
Ratio in area and volume
28
Numbers between 0 and 1
32
Reciprocal of a number
34
Rounding and estimation
35
National Test questions
37
Functional Maths – The London Olympics 2012
40
Algebra
3
Equations, formulae and identities
42
Simultaneous equations
45
Solving by substitution
47
Equations involving fractions
48
Inequalities
50
Graphs showing direct proportion
52
Solving simultaneous equations by graphs
55
National Test questions
57
Maths Frameworking PB 9.3 Chs 1–9
29/5/08
18:33
Page ii
Contents
Introduction
CHAPTER
CHAPTER
CHAPTER
ii
1
2
3
vi
Algebra 1 & 2 Sequences
1
Quadratic sequences
4
Functions
6
Graphs
8
Limits of sequences
11
National Test questions
12
Functional Maths – Mobile phone tariffs
14
Number 1 The four rules governing fractions
16
Percentages and compound interest
19
Reverse percentages and percentage change
22
Direct and inverse proportion
25
Ratio in area and volume
28
Numbers between 0 and 1
32
Reciprocal of a number
34
Rounding and estimation
35
National Test questions
37
Functional Maths – The London Olympics 2012
40
Algebra
3
Equations, formulae and identities
42
Simultaneous equations
45
Solving by substitution
47
Equations involving fractions
48
Inequalities
50
Graphs showing direct proportion
52
Solving simultaneous equations by graphs
55
National Test questions
57
Maths Frameworking PB 9.3 Chs 1–9
CHAPTER
CHAPTER
CHAPTER
CHAPTER
4
5
6
7
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Page iii
Geometry and Measures 1 Pythagoras’ theorem
58
Solving problems using Pythagoras’ theorem
62
Loci
64
Congruent triangles
68
Circle theorems
70
Tessellations and regular polygons
73
Practical Pythagoras
75
National Test questions
77
Functional Maths – Garden design
80
Statistics
1
Scatter graphs and correlation
82
Scatter graphs and lines of best fit
85
Time series graphs
88
Two-way tables
91
Cumulative frequency diagrams
93
Estimation of a mean from grouped data
95
Statistical investigations
98
National Test questions
101
Functional Maths – Rainforest deforestation
106
Geometry and Measures 2 Similar triangles
108
Metric units for area and volume
112
Length of an arc and area of a sector
114
Volume of a cylinder
116
Rate of change
118
National Test questions
122
Functional Maths – Athletics stadium
124
Number
2
Standard form
126
Multiplying with numbers in standard form
128
Dividing with numbers in standard form
130
Upper and lower bounds 1
132
Upper and lower bounds 2
134
Recurring decimals
136
Efficient use of calculators
139
National Test questions
141
Functional Maths – Paper
144
iii
Maths Frameworking PB 9.3 Chs 1–9
CHAPTER
8
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Page iv
Algebra 4 Index notation with algebra – negative powers
146
Square roots, cube roots and other fractional powers 148
CHAPTER
CHAPTER
CHAPTER
CHAPTER
iv
9
Quadratic graphs
151
Cubic graphs
153
National Test questions
155
Functional Maths – Packages
156
Statistics 2 Probability statements
158
Mutually exclusive events and exhaustive events
160
Combining probabilities and tree diagrams
163
Estimates of probability
165
National Test questions
169
Functional Maths – Class test
172
10 Geometry and Measures 3 Fractional enlargements
174
Trigonometry – The tangent of an angle
178
Trigonometry – The sine and cosine of an angle
183
Solving problems using trigonometry
187
National Test questions
189
Functional Maths – Map reading
192
11 Algebra 5 Expansion
194
Factorisation
197
Quadratic expansion
199
Quadratic factorisation
201
Change of subject
202
Graphs from equations in the form A y ± B x = C
205
National Test questions
206
Functional Maths – Trip to Rome
208
12 Solving Problems and Revision Number 1 – Fractions, percentages and decimals
210
Number 2 – The first four rules, ratios and standard form
213
Algebra 1 – Rules of algebra and solving equations
215
Algebra 2 – Graphs
216
Geometry and measures
219
Statistics
222
Maths Frameworking PB 9.3 Chs 1–9
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER
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Page v
13 Statistics 3 and Revision Statistical techniques
225
A handling data project
231
14 Geometry and Measures 4 and Revision Geometry and measures revision
234
Geometry and measures investigations
236
Symmetry revision
237
Symmetry investigations
239
15 Statistics 4 and Revision Revision of probability
241
A probability investigation
246
16 GCSE Preparation Solving quadratic equations
249
Quadratic equations of the form a x 2 + b x + c
250
Quadratic equations
251
The quadratic formula
252
Completing the square
253
The difference of two squares
255
GCSE past-paper questions
256
17 Functional Maths Practice The Eden Project
260
Road safety
262
Squirrels
264
Mobile shop
266
Index
268
Garden design activity worksheet
271
v
Maths Frameworking PB 9.3 Chs 1–9
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Page vi
Introduction
Learning objectives
See what you are going to cover and what you should already know at the start of each chapter. The purple and blue boxes set the topic in context and provide a handy checklist.
National Curriculum levels
Know what level you are working at so you can easily track your progress with the colour-coded levels at the side of the page.
Worked examples
Understand the topic before you start the exercises by reading the examples in blue boxes. These take you through how to answer a question step-by-step.
Functional Maths
Practise your Functional Maths skills to see how people use Maths in everyday life. Look out for the Functional Maths icon on the page.
Extension activities
Stretch your thinking and investigative skills by working through the extension activities. By tackling these you are working at a higher level.
vi
Maths Frameworking PB 9.3 Chs 1–9
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Page vii
Level booster
Progress to the next level by checking the Level boosters at the end of each chapter. These clearly show you what you need to know at each level and how to improve. National Test questions
Practise the past paper Test questions to feel confident and prepared for your KS3 National Curriculum Tests. The questions are levelled so you can check what level you are working at. Extra interactive National Test practice
Watch and listen to the audio/visual National Test questions on the separate Interactive Book CD-ROM to help you revise as a class on a whiteboard. Look out for the computer mouse icon on the page and on the screen. Functional Maths activities
Put Maths into context with these colourful pages showing real-world situations involving Maths. You are practising your Functional Maths skills by analysing data to solve problems. Extra interactive Functional Maths questions and video clips
Extend your Functional Maths skills by taking part in the interactive questions on the separate Interactive Book CD-ROM. Your teacher can put these on the whiteboard so the class can answer the questions on the board.
N E W
Hone your Functional Maths skills further by doing the four exciting tasks given in the new chapter – Functional Maths Practice.
See Maths in action by watching the video clips and doing the related Worksheets on the Interactive Book CD-ROM. The videos bring the Functional Maths activities to life and help you see how Maths is used in the real world. Look out for the computer mouse icon on the page and on the screen.
