Mathematics Resources Catalogue 2017

Brighter Thinking

MATHEMATICS RESOURCES 2017

cambridge.org/education MATHEMATICS RESOURCES

cambridge.org/education

2

CONTENTS Welcome:

1

GCSE Mathematics GCSE Mathematics Online:

2

WELCOME TO THE 2017 MATHEMATICS CATALOGUE Inside this catalogue you will find our exciting range of resources for secondary level mathematics.

Covering a wide range of UK and international curricula, our resources draw

GCSE Mathematics for AQA: GCSE Mathematics for Edexcel: GCSE Mathematics for OCR:

on the best current practices in mathematics education to support teaching

3-4

and learning worldwide.

Our brand new publishing for A Level Mathematics and Further Mathematics

5-6

addresses the most recent substantial changes to these specifications in England. The new series has been developed for the OCR A and AQA

7-8

specifications and is written by an experienced author team. These resources ensure a strong focus on the development of problem-solving skills, mathematical reasoning and fluency, equipping students and teachers with

A Level Mathematics

exactly what they need to face the challenges of the new A Level curriculum for first teaching in September 2017.

A Level Mathematics for AQA: A Level Further Mathematics for AQA:

11

Also included is our GCSE Mathematics series specifically written for the new AQA, Edexcel and OCR qualifications. This comprehensive suite also includes the innovative GCSE Mathematics Online - our new digital resource that

12

provides an interactive and flexible enhancement to your class. With a strong focus on the development of problem-solving skills, mathematical reasoning

A Level Mathematics for OCR A:

and fluency, our resources support the navigation of the new assessment

13

objectives and exams, and prepare students for the new specifications.

You can also explore our Cambridge IGCSE® Mathematics series, with the

A Level Further Mathematics for OCR A:

14

Teaching Probability:

15

new and fully endorsed digital resource - IGCSE Mathematics Online. Browse our Cambridge Checkpoint Mathematics suite which now feature Skills

Cambridge Advanced Mathematics for OCR:

15

SMP AS/A2 Mathematics for Edexcel and AQA:

16

Builder and Challenge workbooks.

For more information, please contact your local sales consultant, who will be happy to answer your questions or visit Cambridge.org/education.

Best wishes,

The Maths Team

International Examinations Cambridge IGCSE® Mathematics: Cambridge Checkpoint Mathematics:

How to use this catalogue 17 Print book

Digital resource

18

Print book and digital resource bundle

Order your FREE GCSE Mathematics Evaluation Copies Order your free GCSE Mathematics evaluation copies for AQA, Edexcel or OCR. You can also sign up for a free 30 day GCSE Mathematics Online trial - our digital teaching and learning subscription service.

Contact your local Sales Consultant for more details. Please see the back of this catalogue for Sales Consultant contact information.

1

GCSE Mathematics Online The complete online resource for GCSE Mathematics GCSE Mathematics Online is our brand new interactive teaching and learning subscription service available for the AQA, Edexcel and OCR 2015 GCSE Mathematics qualifications. This tablet-friendly resource supports both independent learning and whole class teaching through a suite of flexible resources that includes lesson notes, interactive walkthroughs, explanatory animations, games, worksheets, quick quizzes and levelled assessments.

Sign up for a

30 DAY FREE TRIAL and access to FREE Year 9 Transition Units.

Find out more

www.gcsemaths. cambridge.org

• Allows teachers to set tasks, create tests, auto-mark and compile reports to review student performance.

• A test generator to compile your own assessments.

• Interactive widgets to visually demonstrate concepts.

• Worksheets offering practical activities, discussion points, investigations, games and further practice.

• Walkthroughs that take students through a question step-by-step, with feedback.

• Covers both Foundation and Higher, offering flexibility for moving students betwen tiers.

• Resources organised into chapters corresponding to the Student Books, with explanatory notes for all topics.

• Contains material for all types of classroom set-up, including interactive whiteboards, projectors and tablets.

• Includes a digital PDF version of both the Foundation and Higher Student Books.

• Quick-fire quizzes with leaderboards, providing an opportunity for question practice.

• Levelled questions that assess understanding of each topic.

Whole school site licence NOW AVAILABLE*

*UK Schools only, an unlimited number of teachers and students within the same school.

MATHEMATICS RESOURCES

cambridge.org/education

2

GCSE Mathematics for AQA Launchpad A flow chart of concepts covered in the chapter. Each step tests a different skill, progressing from least to most advanced. Students can assess their most appropriate starting point in the chapter, encouraging them to take ownership of their learning.

What you will learn Short objectives to show the content and mathematical skills covered in the chapter.

Key vocabulary Key terms are highlighted for ease of learning, and gathered in a glossary at the back of Student Book for quick reference.

Using Mathematics Before you start...

Shows how the content of the chapter relates to the world of work, making maths relevant beyond the classroom.

Lists the prerequisite knowledge for the chapter. Includes questions on each concept to assess whether students can recall the necessary knowledge and skills.

Sample pages from AQA Foundation Student Book.

Student Books • Written from scratch and endorsed for the 2015 AQA (8300) GCSE Mathematics qualification.

• A ‘Launchpad’ feature at the beginning of each chapter directs students to their best starting point to optimise progress and allows for both independent and personalised learning.

Problem-solving Books • Questions with worked solutions draw out the reasoning, interpreting, estimating and communication skills required to effectively solve problems.

• Each chapter focuses on a different technique to equip students with a problem-solving toolkit that they can apply to any question, encouraging students to develop problem-solving ‘muscle memory’.

• All questions have star ratings to show the level of difficulty, allowing students to track their progress.

• Questions are colour-coded to show which strands of maths they cover, with questions covering multiple topics to prepare students for the synoptic nature of the exams.

• Topics and problems are introduced through a wide variety of contexts, showing how maths relates to the real world.

• Thousands of questions, including multiple choice questions cover all assessment objectives, offering extensive questions to master key skills.

• A ‘Work it out’ feature encourages students to explore and discuss common errors, helping to draw out misconceptions.

Homework Books • Offer practice questions for students across the full GCSE Mathematics curriculum.

• Contain exercises that correspond to each section of the Student Book, offering hundreds of additional questions for further practice.

• Questions assess a variety of skills, including recall, interpretation, problem-solving and mathematical reasoning.

• Questions increase in difficulty throughout each exercise and chapter to build confidence and allow for progression.

• Ideally sized for school bags.

Teacher’s Resource Our FREE digital Teacher’s Resource for both the Foundation and Higher tiers contains everything necessary to plan and deliver the 2015 AQA (8300) GCSE Mathematics qualification.

3

cambridge.org/education

MATHEMATICS RESOURCES

GCSE Mathematics for AQA GCSE Mathematics for AQA Course Structure

FOUNDATION

HIGHER

Student Books Student Books have a strong focus on the development of problem-solving skills, mathematical reasoning and fluency.

Foundation: 9781107448049 Higher: 9781107448032

GCSE Mathematics Online WHOLE SCHOOL SITE LICENCE NOW AVAILABLE*

GCSE Mathematics Online for AQA is packed with flexible resources that include lesson notes, walkthroughs, animations, games, worksheets, quick quizzes and levelled assessments.

Site Licence (1 Year)* 9781316507841; 1 Year 9781107449800; 2 Years 9781107449770; 3 Years 9781107569317

Student Book and Online Subscription Bundle Contains our print Student Book and GCSE Mathematics Online subscription service for AQA. Foundation: 2 Years 9781107447950; 3 Years 9781107569195 Higher: 2 Years 9781107447943; 3 Years 9781107569140

Problem-solving Books Problem-solving Books contain a variety of questions to develop students’ problem-solving and reasoning skills within the context of the new GCSE curriculum.

Foundation: 9781107450103 Higher: 9781107450073

Homework Books Homework Books are affordable standalone resources and ideal companions to the Student Books.

Foundation: 9781107496910 Higher: 9781107496866

Teacher’s Resource

FREE

Our FREE digital Teacher’s Resource for both the Foundation and Higher tiers is full of teaching ideas and advice. Available from cambridge.org/education.

Editable GCSE Mathematics for AQA 1, 2 and 3 year schemes of work, available at

cambridge.org/ education

9781107468153 *UK Schools only, an unlimited number of teachers and students within the same school.

MATHEMATICS RESOURCES

cambridge.org/education

4

GCSE Mathematics for Edexcel Launchpad A flow chart of concepts covered in the chapter. Each step tests a different skill, progressing from least to most advanced. Students can assess their most appropriate starting point in the chapter, encouraging them to take ownership of their learning.

What you will learn GCSE Mathematics for Edexcel (Higher)

Short objectives to show the content and mathematical skills covered in the chapter.

8 Powers and roots

Tip

Assess your starting point using the Launchpad STEP 1

In this chapter you will learn how to …

• use integers and fractions to represent numbers in index notation.

• calculate with powers and roots.

• apply the rules for multiplying and dividing indices.

1 For more resources relating to this chapter, visit GCSE Mathematics Online.

Write each of these numbers in index notation. a 434343434 b eight cubed GO TO Section 1: Index notation

c five squared d nine to the power of seven e the reciprocal of 3 to the power of 4

Using mathematics: real-life applications

Calculator tip

Financial advisors and investors have to perform calculations involving powers and roots to work out the value of investments. They may use computer technology (apps) to work out different options to help their clients invest their money wisely.

f the reciprocal of 2 to the power of 3

Make sure you know which buttons to use to evaluate different powers and find different roots of numbers.

✓

General hints and reminders to aid students, sometimes including questions to prompt students’ knowledge.

STEP 2

“I have to be able to understand, manipulate and evaluate different formulae to find the best investment. Many of these formulae involve fractional powers and different roots.”

2

(Personal financial adviser)

Using Mathematics Shows how the content of the chapter relates to the world of work, making maths relevant beyond the classroom.

Evaluate these without a calculator. Give the answer in index form and then work out the answer.

64 b 422 3 44 c a 33 3 32 64 65 45 d 3 e 8 f (23)2 4 6

Before you start ...

Ch 1

Ch 4

You should be able to quickly add and subtract pairs of integers mentally.

1

You need to be able to find the squares, cubes, square roots and cube roots of numbers.

2

a 23 1 23

412

b 627

c 4 2 (25)

23 1 26

d 22 1 6

A 6 cm2 3

c

Key vocabulary

3

B 9 cm2

C 12 cm2

B 5.2

C 3

B 90

C 900

index: a power or exponent indicating how many times a base number is used in a multiplication: index 2 means the number is squared (5 3 5); index 3 means it is cubed (5 3 5 3 5).

27 810000

A 9

You need to be able to find the reciprocal of a number or fraction.

925

a The area of a square with sides of 3 cm.

A 9

Ch 6

324

Choose the correct answer.

b

index notation: writing a number as a base and index, for example 23.

Find the reciprocal of each number. Choose from the values in the box. a

3 4

b 12

c

1 25

12 1

GO TO Section 3: Working with powers and roots

GO TO Chapter review

Choose the correct sign: <, 5 or >.

GO TO Section 2: The laws of indices

4 3

1 12

7 5

Find answers at: cambridge.org/ukschools/gcsemaths-studentbookanswers

You can use powers to write repeated multiplications in a shorter form.

For example: 6 3 6 5 62 and 5 3 5 3 5 5 53 53

This is the index.

The index is also called the power or the exponent.

This is the base.

The index tells you how many times the base number is used in a multiplication.

When you write a number using an index you are using index notation.

Tip

5 7

Any number to the power of 1 stays the same number so you don’t usually write powers of 1.

109

Section 1: Index notation

74 is in index notation.

When you write the multiplication out in full you are using expanded form.

7 3 7 3 7 3 7 is in expanded form.

The plural of index is indices.

110

Before you start...

Lists the prerequisite knowledge for the chapter. Includes questions on each concept to assess whether students can recall the necessary knowledge and skills.

Sample pages from Edexel Foundation Student Book.

Book

Student Books • Written from scratch and endorsed for the 2015 Edexcel (1MA1) GCSE Mathematics qualification.

• A ‘Launchpad’ feature at the beginning of each chapter directs students to their best starting point to optimise progress and allows for both independent and personalised learning.

• Topics and problems are introduced through a wide variety of contexts, showing how maths relates to the real world.

• Thousands of questions cover all assessment objectives, offering extensive opportunity to master key skills.

• A ‘Work it out’ feature encourages students to explore and discuss common errors, helping to draw out misconceptions.

Problem-solving Books

Homework Books

• Questions with worked solutions draw out the reasoning, interpreting, estimating and communication skills required to effectively solve problems.

• Endorsed for the 2015 Edexcel GCSE Mathematics qualification.

• Each chapter focuses on a different technique to equip students with a problem-solving toolkit that they can apply to any question, encouraging students to develop problem-solving ‘muscle memory’.

• All questions have star ratings to show the level of difficulty, allowing students to track their progress.

• Questions are colour-coded to show which strands of maths they cover, with questions covering multiple topics to prepare students for the synoptic nature of the exams.

• Offer practice questions for students across the full GCSE Mathematics curriculum.

• Contain exercises that correspond to each section of the Student Book, offering hundreds of additional questions for further practice.

• Questions assess a variety of skills, including recall, interpretation, problem-solving and mathematical reasoning.

• Ideally sized for school bags.

Teacher’s Resource Our FREE digital Teacher’s Resource for both the Foundation and Higher tiers contains everything necessary to plan and deliver the 2015 Edexcel (1MA1) GCSE Mathematics qualification.

5

cambridge.org/education

MATHEMATICS RESOURCES

GCSE Mathematics for Edexcel GCSE Mathematics for Edexcel Course Structure

FOUNDATION

HIGHER

Student Books Student Books have a strong focus on the development of problem-solving skills, mathematical reasoning and fluency.

Foundation: 9781107448025 Higher: 9781107448001

GCSE Mathematics Online WHOLE SCHOOL SITE LICENCE NOW AVAILABLE*

GCSE Mathematics Online for Edexcel is packed with flexible resources that include lesson notes, walkthroughs, animations, games, worksheets, quick quizzes and levelled assessments.

Site Licence (1 Year)* 9781316507834; 1 Year 9781107449718 2 Years 9781107449671; 3 Years 9781107569256

Student Book and Online Subscription Bundle Contains our print Student Book and GCSE Mathematics Online subscription service for Edexcel.

Foundation: 2 Years 9781107447912; 3 Years 9781107569126 Higher: 2 Years 9781107447851; 3 Years 9781107557642

Problem-solving Books Problem-solving Books contain a variety of questions to develop students’ problem-solving and reasoning skills within the context of the new GCSE curriculum.

Foundation: 9781107450066 Higher: 9781107450059

Homework Books Homework Books are affordable standalone resources and ideal companions to the Student Books.

Foundation: 9781107496859 Higher: 9781107496828

Teacher’s Resource

FREE

Our FREE digital Teacher’s Resource for both the Foundation and Higher tiers is full of teaching ideas and advice. Available from cambridge.org/education.

Editable GCSE Mathematics for Edexcel 1, 2 and 3 year schemes of work, available at

cambridge.org/ education

9781107468146 *UK Schools only, an unlimited number of teachers and students within the same school.

MATHEMATICS RESOURCES

cambridge.org/education

6

GCSE Mathematics for OCR Launchpad A flow chart of concepts covered in the chapter. Each step tests a different skill, progressing from least to most advanced. Students can assess their most appropriate starting point in the chapter, encouraging them to take ownership of their learning.

41 Transformations of curves and their equations

What you will learn Short objectives to show the content and mathematical skills covered in the chapter.

Tip

Assess your starting point using the Launchpad

GCSE Mathematics for OCR (Higher)

41 Transformations of curves and their equations

General hints and reminders to aid students, sometimes including questions to prompt students’ knowledge.

STEP 1 1

This is a graph of y 5 x2: y 10 9

In this chapter you will learn how to …

y ⫽ x2

8

For more resources relating to this chapter, visit GCSE Mathematics Online.

s identify translations and reflections of a given graph or equation. s sketch the graphs of these types of transformation.

GO TO Section 1: Quadratic functions and parabolas

7 6 5 4

Using mathematics: real-life applications

3

Tip

Many people study the graphs of curves in the course of their work. Sound engineers are a good example. They mix and balance sounds by looking at curves made by sound waves.

Lower pitch

2

Use ICT when studying this chapter.

This allows you to generate graphs so you can study them quickly and experiment with changing values and comparing results.

1 ⫺9

⫺8

⫺7

⫺6

⫺5

⫺4

⫺3

⫺2

⫺1 0 ⫺1

1

2

3

4

5

6

7

8

9 x

⫺2 ⫺3

Higher pitch

Sketch: a y 5 x2 1 2

“In today’s music industry, we need to be talented in both the arts and the sciences.” (Sound engineer)

b y 5 x2 2 2

c Write the equation of the reflection of this graph about the x-axis.

Before you start...

d What happens to the graph when it is reflected about the y-axis?

Before you start …

Using Mathematics Shows how the content of the chapter relates to the world of work, making maths relevant beyond the classroom.

Ch 18, 19

Ch 33

You need to be able to recognise the graphs of standard functions: y 5 mx 1 c y 5 x2 y 5 ax2 1 bx 1 c 1 y 5 __ x

1

You should be able to sketch the trigonometric functions: y 5 sin x y 5 cos x y 5 tan x

2

Which of these functions would result in a curved graph and which would produce a linear graph?

a y 5 x2 1 9 b 5y 1 x 5 10 2 c y 5 __ d y 5 (x 1 7)2 2 2 x Sketch each function to show its general shape.

STEP 2

Which trigonometric functions are represented by these graphs? a

y

y

b

2

a What are the values of sin 90° and cos 90°?

For what values of u does cos u 5 1? b Sketch graphs of y 5 sin x 1 2 and y 5 cos (x 1 90°).

6 4 2

0

180°

360° x

⫺180°

⫺90°

0

⫺2

90°

180° x

⫺4

GO TO Section 2: Trigonometric functions

⫺6

c Sketch and label the third trigonometric function.

Ch 8

You should be able to complete the square on a quadratic equation.

3

Rewrite y 5 3x2 1 6x 1 7 in the form a(x 2 h)2 1 k.

GO TO Step 3: The Launchpad continues on the next page …

746 Find answers at: cambridge.org/ukschools/gcsemaths-studentbookanswers

747

Lists the prerequisite knowledge for the chapter. Includes questions on each concept to assess whether students can recall the necessary knowledge and skills.

Sample pages from OCR Foundation Student Book.

Student Books • Written from scratch and endorsed for the 2015 OCR (J560) GCSE Mathematics qualification.

• A ‘Launchpad’ feature at the beginning of each chapter directs students to their best starting point to optimise progress and allows for both independent and personalised learning.

• Topics and problems are introduced through a wide variety of contexts, showing how maths relates to the real world.

• Thousands of questions cover all assessment objectives, offering extensive opportunity to master key skills.

• A ‘Work it out’ feature encourages students to explore and discuss common errors, helping to draw out misconceptions.

Problem-solving Books

Homework Books

• Endorsed for the 2015 OCR GCSE Mathematics qualification.

• Endorsed for the 2015 OCR GCSE Mathematics qualification.

• Questions with worked solutions draw out the reasoning, interpreting, estimating and communication skills required to effectively solve problems.

• Offer practice questions for students across the full GCSE Mathematics curriculum.

• Each chapter focuses on a different technique to equip students with a problem-solving toolkit that they can apply to any question, encouraging students to develop problem-solving ‘muscle memory’.

• Contain exercises that correspond to each section of the Student Book, offering hundreds of additional questions for further practice.

• All questions have star ratings to show the level of difficulty, allowing students to track their progress.

• Questions assess a variety of skills, including recall, interpretation, problem-solving and mathematical reasoning.

• Questions are colour-coded to show which strands of maths they cover, with questions covering multiple topics to prepare students for the synoptic nature of the exams.

• Ideally sized for school bags.

Teacher’s Resource Our FREE digital Teacher’s Resource for both the Foundation and Higher tiers contains everything necessary to plan and deliver the 2015 OCR (J560) GCSE Mathematics qualification.

7

cambridge.org/education

MATHEMATICS RESOURCES

GCSE Mathematics for OCR GCSE Mathematics for OCR Course Structure

FOUNDATION

HIGHER

Student Books Student Books have a strong focus on the development of problem-solving skills, mathematical reasoning and fluency.

Foundation: 9781107448094 Higher: 9781107448056

GCSE Mathematics Online WHOLE SCHOOL SITE LICENCE NOW AVAILABLE*

GCSE Mathematics Online for OCR is packed with flexible resources that include lesson notes, walkthroughs, animations, games, worksheets, quick quizzes and levelled assessments.

Site Licence (1 Year)* 9781316507858; 1 Year 9781107449909 2 Years 9781107449855; 3 Years 9781107569386

Student Book and Online Subscription Bundle Contains our print Student Book and GCSE Mathematics Online subscription service for OCR. Foundation: 2 Years 9781107447998; 3 Years 9781107569218 Higher: 2 Years 9781107447967; 3 Years 9781107569201

Problem-solving Books Problem-solving Books contain a variety of questions to develop students’ problem-solving and reasoning skills within the context of the new GCSE curriculum.

Foundation: 9781107450189 Higher: 9781107450165

Homework Books Homework Books are affordable standalone resources and ideal companions to the Student Books.

Foundation: 9781107497009 Higher: 9781107496927

Teacher’s Resource

FREE

Our FREE digital Teacher’s Resource for both the Foundation and Higher tiers is full of teaching ideas and advice. Available from cambridge.org/education.

Editable GCSE Mathematics for OCR 1, 2 and 3 year schemes of work, available at

cambridge.org/ education

9781107468221 *UK Schools only, an unlimited number of teachers and students within the same school.

MATHEMATICS RESOURCES

cambridge.org/education

8

AS/A Level Mathematics & Further Mathematics These resources provide detailed coverage of the new linear specifications, supporting teachers and students every step of the way and providing a firm foundation for study beyond A Level. In particular, the resources: • Follow a structured pedagogical approach, assisting teachers in delivering the new expanded content in a clear effective way.

Learning objectives A short summary of the content that you will learn in each chapter.

• Promote a deeper, more synoptic understanding of mathematics, and help students to develop essential skills in problem-solving, modelling and proof to help meet the new requirements.

• Provide you with Cambridge Elevate editions which encourage adaptations of the student book, alongside other useful resources allowing students and teachers to customise and interact with the material.

The Student Books offer: • A strong pedagogical focus, with an emphasis on the overarching skills integral to the new specifications including problem-solving, modelling and proof, plus active tackling of common misconceptions.

• Frequent assessment opportunities to track your students’ progress, including a wealth of levelled practice and past paper questions, and practice papers to help them prepare.

• Emphasis on developing synoptic links between Pure and Applied areas of maths, helping students to build a coherent mathematical understanding with unique ‘Focus On’ sections as well as cross-topic review exercises.

Before you start A list of things that you should already know from your previous learning and questions to check that you’re ready to start the chapter.

Worked example Questions, followed by fully worked answers, to illustrate the concepts in the chapter.

Please note, we have entered our student books in the approval process with AQA and OCR.* Elevate editions offer:

Key point

• Easy-to-use tools for annotation and customisation, allowing you to add your own resources.

Important points that you will need to learn.

• Gateway to A Level resources to provide bridging from GCSE and support for differentiation, along with worked solutions to all practice questions.

• Availability online and on tablet devices through the Cambridge Elevate app either as part of our digital and print bundle, digital licence or school site licence.

• Free downloadable Schemes of Work are available on our website to assist you with planning the new specification in the time that you have available.

9

cambridge.org/education

MATHEMATICS RESOURCES

Rewind Reminders of where to find useful information that you have covered earlier in your study.

Draft sample pages from AQA Student Book.

A Level Mathematics for OCR

8 Exponential models

If we look at the graphs of exponential functions with different bases we can start to make some generalisations. y=

1 2

x

y y = 5x

y = 2x

Rewind You may observe that the black line is a reflection of the blue line. This is because x ⎛ 1⎞ ⎜ ⎟ = (2−1) 2 x . You know ⎝ 2⎠ from chapter 5 section 3 that replacing x by −x results in the graph being reflected in the y-axis.

In this chapter you will learn: • about graphs of exponential functions • why exponential functions are often used in modelling • how to use logarithms to transform curved graphs into straight lines

y=

3 2

x

x

O

Before you start…

Chapter 7

Chapter 7

You should be able to use the number e and natural logarithms.

1 Simplify: a ln(5e2) b el + ln(5)

You should be able to use the laws of logarithms.

2 If y = 100x3 write log y in the form n + k log x.

Key point 8.1 For all the graphs y = ax: • • •

the y-intercept is always (0,1) because a0 = 1. the graph of the function lies entirely above the x-axis. the x-axis is an asymptote.

If a > 1, then as x increases so does y. This is called exponential growth.

Why use exponential models?

If 0 < a < 1, then as x increases, y decreases. This is called exponential decay.

In many situations in the real world the rate of growth of a quantity is approximately proportional to the amount that is there; for example, the more people there are in a country, the more babies will be born. It turns out that the only functions which have this property are exponential functions, of the form y = ax.

Gradient of an exponential graph For an exponential growth graph the gradient also increases with x. In fact, the gradient is exactly proportional to the y value at every point on the graph. Let us illustrate this on some examples.

Section 1: Graphs of exponential functions This is the graph of y = 2x:

We can find the gradient of a curved graph by drawing a tangent and calculating its gradient. The diagram below shows some tangents to the graph of y = 2x.

y 9 8 7

y = 2x

6 5 4 3 2

y = 2x

1 −3

−2

−1

O

1

2

3

x O

For very large positive values of x, the y value approaches infinity, and for very large negative values of x the y value approaches (but never reaches) 0.

In this case, we would say that the x-axis is an asymptote to the graph.

1

Ch 08.indd 1

29-08-2016 21:52:03

x

−1

0

1

2

y

0.5

1.0

2.0

4.0

Gradient

0.35

0.7

1.4

2.88

OCR’S PUBLISHER PARTNER FOR MATHEMATICS

2

Ch 08.indd 2

29-08-2016 21:52:06

Draft sample pages from OCR Student Book.

MATHEMATICS RESOURCES

cambridge.org/education

10

AS/A Level Mathematics for AQA Student Books Student Book 1 (AS / Year 1) 9781316644225

Student Book 2 (Year 2) 9781316644256

Cambridge Elevate editions Student Book 1 (AS / Year 1) Cambridge Elevate edition (2 Years) 9781316644591

Student Book 2 (Year 2) Cambridge Elevate edition (2 Years) 9781316644621

Student Book 1 (AS / Year 1) Cambridge Elevate edition (1 Year) School Site Licence 9781316644607

Student Book 2 (Year 2) Cambridge Elevate edition (1 Year) School Site Licence 9781316644638

Student Book & Online Subscription Bundles Student Book 1 (AS / Year 1) with Cambridge Elevate edition (2 Years) 9781316644683

Student Book 2 (Year 2) with Cambridge Elevate edition (2 Years) 9781316644690

We have entered an approval process with AQA to publish our student books for their new 2017 AS/A Level Mathematics and Further Mathematics speciďŹ cations.

*AQA only approves the student book. Other AQA resources shown here are not part of the approval process.

11

cambridge.org/education

MATHEMATICS RESOURCES

AS/A Level Further Mathematics for AQA Student Books Student Book 1 (AS / Year 1) 9781316644430 Student Book 2 (Year 2) 9781316644478 Statistics Student Book (AS / A Level) 9781316644508 Mechanics Student Book (AS / A Level) 9781316644539

Elevate editions Student Book 1 (AS / Year 1) Cambridge Elevate edition (2 Years) 9781316644546 Student Book 2 (Year 2) Cambridge Elevate edition (2 Years) 9781316644560 Statistics Student Book (AS / A Level) Cambridge Elevate edition (2 Years) 9781316644584 Mechanics Student Book (AS / A Level) Cambridge Elevate edition (2 Years) 9781316644669 Student Book 1 (AS / Year 1) Cambridge Elevate edition (1 Year) School Site Licence 9781316644553 Student Book 2 (Year 2) Cambridge Elevate edition (1 Year) School Site Licence 9781316644577 Statistics Student Book (AS/A Level) Cambridge Elevate edition (1 Year) School Site Licence 9781316644614 Mechanics Student Book (AS/A Level) Cambridge Elevate edition (1 Year) School Site Licence 9781316644669

Student Book & Online Subscription Bundles Student Book 1 (AS / Year 1) with Cambridge Elevate edition (2 Years) 9781316644294 Student Book 2 (Year 2) with Cambridge Elevate edition (2 Years) 9781316644478 Statistics Student Book (AS/A Level) with Cambridge Elevate edition (2 Years) 9781316644324 Mechanics Student Book (AS / A Level) with Cambridge Elevate edition (2 Years) 9781316644348

MATHEMATICS RESOURCES

cambridge.org/education

12

AS/A Level Mathematics for OCR A Student Books Student Book 1 (AS / Year 1) 9781316644287

Student Book 2 (Year 2) 9781316644300

Cambridge Elevate editions Student Book 1 (AS / Year 1) Cambridge Elevate edition (2 Years) 9781316644331

Student Book 2 (Year 2) Cambridge Elevate edition (2 Years) 9781316644362

Student Book 1 (AS / Year 1) Cambridge Elevate edition (1 Year) School Site Licence 9781316644355

Student Book 2 (Year 2) Cambridge Elevate edition (1 Year) School Site Licence 9781316644379

Student Book & Online Subscription Bundles Student Book 1 (AS / Year 1) with Cambridge Elevate edition (2 Years) 9781316644652

Student Book 2 (Year 2) with Cambridge Elevate edition (2 Years) 9781316644676

We have entered an approval process with OCR to publish our student books for their new 2017 AS/A Level Mathematics and Further Mathematics A specifications. *OCR only approves the student book. Other OCR resources shown here are not part of the approval process.

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OCR’S PUBLISHER PARTNER FOR MATHEMATICS

AS/A Level Further Mathematics for OCR A Student Books Pure Core Student Book 1 (AS / Year 1) 9781316644386 Pure Core Student Book 2 (Year 2) 9781316644393 Statistics Student Book (AS/A Level) 9781316644409 Mechanics Student Book (AS / A Level) 9781316644416

Elevate editions Pure Core Student Book 1 (AS / Year 1) Cambridge Elevate edition (2 years) 9781316644447 Pure Core Student Book 1 (AS / Year 1) Cambridge Elevate edition 9781316644461 Statistics Student Book (AS/A Level) Cambridge Elevate edition (2 Years) 9781316644492 Mechanics Student Book (AS / A Level) Cambridge Elevate edition (2 Years) 9781316644515 Pure Core Student Book 1 (AS / Year 1) Cambridge Elevate edition (1 Year) School Site Licence 9781316644423 Pure Core Student Book 2 (Year 2) Cambridge Elevate edition (1 Year) School Site Licence 9781316644454 Statistics Student Book (AS/A Level) Cambridge Elevate edition (1 Year) School Site Licence 9781316644492 Mechanics Student Book (AS/A Level) Cambridge Elevate edition (1 Year) School Site Licence 9781316644522

Student Book & Online Subscription Bundles Pure Core Student Book 1 (AS / Year 1) with Cambridge Elevate edition (2 Years) 9781316644232 Pure Core Student Book 2 (Year 2) with Cambridge Elevate edition (2 Years) 9781316644249 Statistics Student Book (AS / A Level) with Cambridge Elevate edition (2 Years) 9781316644263 Mechanics Student Book (AS/A Level) with Cambridge Elevate edition (2 Years) 9781316644270

MATHEMATICS RESOURCES

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Teaching Probability David Spiegelhalter and Jenny Gage ISBN: 9781316605899

Understanding probability is a key part in the development of knowledge of risk and chance. Teaching Probability is designed to support teaching concepts in probability by providing a new approach to this difficult subject from a perspective not limited by a syllabus. This gives teachers both theoretical and practical knowledge of an innovative way of teaching probability.

• Written by a renowned and experienced author team specialising in mathematics pedagogy.

• An alternative approach to teaching probability focusing on using experimentation to develop skills as opposed to approaching the subject from a theoretical method.

• Provides lesson materials that can be adapted according to the age and ability of pupils.

IDEAL FOR TEACHING KEY STAGES 4 AND 5

A Level Mathematics Cambridge Advanced Mathematics for OCR Fully endorsed by OCR and matching the current OCR specification, this series has been carefully revised by experienced teachers and provides easy to use texts.

• Clear chapter summaries with learning objectives stated at the beginning of each chapter.

• Stimulating worked examples provide reinforcement throughout.

• Written exercises put new ideas to work.

Core 1 & 2: 9780521548960 Core 3 & 4: 9780521548977 Mechanics 1: 9780521549004 Mechanics 2: 9780521549011 Mechanics 3 & 4: 9780521549028 Statistics 1: 9780521548939 Statistics 2: 9780521548946 Statistics 3 & 4: 9780521548953 Decision 1: 9780521619141 Decision 2: 9780521619158 Further Pure 1: 9780521548984 Further Pure 2 & 3: 9780521548991

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MATHEMATICS RESOURCES

Teaching Probability

SMP AS/A2 Mathematics for Edexcel and AQA Based on extensive feedback from teachers, these popular A Level titles have been written by the experienced team that produced SMP Interact for GCSE. • Clear, user-friendly texts that both teachers and students will enjoy using.

• Chapter objectives are clearly set out and new concepts are carefully developed in a way that involves the student.

• Worked examples are designed to clarify ideas and techniques.

• Plenty of well-graded practice and revision, including past exam questions that show the standard required.

Edexcel

AQA

Core 1 for Edexcel: 9780521605335

Core 1 for AQA: 9780521605250

Core 2 for Edexcel: 9780521605342

Core 2 for AQA: 9780521605267

Core 3 for Edexcel: 9780521605373

Core 3 for AQA: 9780521605298

Core 4 for Edexcel: 9780521605380

Core 4 for AQA: 9780521605304

Mechanics 1 for Edexcel: 9780521605366

Mechanics 1 for AQA: 9780521605281

Mechanics 2 for Edexcel: 9780521605403

Mechanics 2 for AQA: 9780521605328

Statistics 1 for Edexcel: 9780521605359

Statistics 1 for AQA: 9780521605274

Statistics 2 for Edexcel: 9780521605397

Statistics 2 for AQA: 9780521605311

MATHEMATICS RESOURCES

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International Examinations

Cambridge IGCSE® Mathematics This highly illustrated course has been written by experienced authors. The Core and Extended material is combined in one book, offering a comprehensive resource for all students, whatever their capabilities.

Core and Extended Coursebook with CD-ROM and IGCSE Mathematics Online Revised Edition: 9781316629703 Core and Extended Coursebook with CD-ROM: 9781316605639 Core Practice Book:

9781107609884

Extended Practice Book:

9781107672727

Teacher’s Resource CD-ROM: Revision Guide:

® IGCSE is a registered trademark of Cambridge International Examinations.

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MATHEMATICS RESOURCES

9781316609309

9781107611955

Cambridge Checkpoint Mathematics Written by well-respected authors, Cambridge Checkpoint Mathematics provides a comprehensive, structured resource that covers the full Cambridge Secondary 1 Mathematics curriculum framework, for three years of study from Stages 7 to 9 (typically 11–14 years old).

Coursebook 7: Practice Book 7:

9781107641112 9781107695405

Teacher’s Resource 7:

9781107693807

Skills Builder Workbook 7:

9781316637418

Challenge Workbook 7: Coursebook 8: Practice Book 8:

9781107697874 9781107665996

Teacher’s Resource 8:

9781107622456

Skills Builder Workbook 8:

Practice Book 9:

9781316637395 9781316637425

Challenge Workbook 8: Coursebook 9:

9781316637371

9781107668010 9781107698994

Teacher’s Resource 9:

9781107693975

Skills Builder Workbook 9: Challenge Workbook 9:

9781316637401 9781316637432

= Endorsed by Cambridge International Examinations = Working towards endorsement by Cambridge International Examinations

MATHEMATICS RESOURCES

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