Collins GCSE Maths course guide 2024

New edition

Unlock GCSE Maths

Secure your students’ mathematical knowledge with fully-updated and revised textbooks

Available for AQA and Edexcel Edexcel and Working endorsed towards Edexcel AQA approved endorsement and AQA approval

Collins GCSE Maths 5th Edition Refreshed and updated for today’s students, drawing on 25 years of knowledge and expertise.

The programme maximises and secures knowledge needed for success in GCSE maths with high-quality practice and carefully refined pacing to support students’ progress.

Student Books l

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Contextualise learning and promote career opportunities with features written and reviewed by the WISE (Women into Science and Engineering) Young Professionals’ Board Enhance exam preparation with new exam practice questions and worked exemplars to reflect the recent GCSE maths exams Help all students reach their potential with content reviewed and adjusted for greater accessibility as well as challenging content for Higher students Strengthen knowledge and deepen understanding with high-quality explanations and hundreds of worked examples Foster independence and self-reflection with answers at the back Practise reasoning, explaining and problem-solving using the facts and methods they have been taught

3

Statistics: Statistical diagrams and averages

3.1 Statistical representation This section will show you how to:

Key terms

• draw and interpret bar charts and pie charts

line graph

• draw and interpret line graphs.

Bar charts and pie charts You are already familiar with bar charts in which the vertical axis represents frequency and the horizontal axis represents categorical data – the data you are considering.

This chapter is going to show you:

The frequency table shows the average monthly rainfall over a six-month period.

• how to draw and interpret pie charts

Month

• how to draw and interpret line graphs

January

February

March

April

May

June

10

25

20

35

15

5

Rainfall (mm)

• how to solve problems that use averages

The diagrams below show three different ways the data can be represented.

• how to calculate averages from frequency tables

As a pictogram:

• how to draw scatter diagrams and lines of best fit.

As a bar chart:

Average monthly rainfall over a six-month period

You should already know:

40

Jan

• how to calculate and use the mode, median and mean

Feb Mar

Context and careers

Average monthly rainfall over a six-month period

30 Rainfall (mm)

• how to extract information from tables and diagrams.

Apr

20 10

A pioneer of presenting information visually was Florence Nightingale (1820–1910), who was very good at mathematics from an early age. In 1859, she was elected the first female member of the Royal Statistical Society. Florence developed a form of the pie chart, now known as the ‘Polar Area Diagram’ or the ‘Nightingale Rose Diagram’, which illustrated monthly patient deaths in military field hospitals. She called these diagrams ‘coxcombs’ and used them to present reports on the conditions of Florence Nightingale was a nurse and hospital medical care in the Crimean War to Parliament and reformer. She used charts to civil servants who may not have fully understood and graphs in her work. traditional statistical reports.

May

Key represents 5 mm

Jun

0

Jan

Feb

Mar

Apr

May

Jun

Month

As a vertical line chart:

40

Average monthly rainfall over a six-month period

Rainfall (mm)

30

Careers that use this maths • Stockbrokers use line graphs to see patterns that help to reveal information about when or where to invest a client’s money.

20 10

• Market researchers use scatter diagrams to see the relationship between advertising methods and sales.

0

Jan

Feb

Mar

Apr

May

Jun

Month

• Epidemiologists use statistical diagrams and averages to determine which groups of people may be at high risk of health issues.

You should also be able to recognise and use multiple or dual bar charts and composite bar charts, which can be used to compare two sets of related data as shown in the next example.

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9780008647308_Edexcel GCSE Math Higher_Chapter 3.indd 58

trend

3.1 Statistical representation

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9780008647308_Edexcel GCSE Math Higher_Chapter 3.indd 59

Updated chapter openers with topic context and related career opportunities in collaboration with WISE Young Professionals’ Board

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Sample from Edexcel GCSE Maths Higher Student Book

25/01/24 10:36 PM

Teacher Packs l

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Carefully structured lessons and thorough explanations of the mathematical facts, concepts, methods and strategies to ensure a smooth transition from KS3 to GCSE Save time and use the detailed, practical schemes of work to prepare and plan your lessons Extra support on more challenging topics Tackle common misconceptions head on and help students to make mathematical connections

Refreshed worked exemplars at the end of each chapter

New exam-style questions at the end of each chapter

Worked exemplars 1

Ready to progress?

This table shows the grades for 2880 candidates in an exam.

Grade

A

B

C

D

E

Candidates

208

888

1032

696

56

a Show the results on a pie chart.

I can draw and interpret pie charts.

I can draw and interpret line graphs.

I can calculate the mode, median, mean and range and decide which average to use.

I can calculate the mean from a frequency table.

I can estimate the mean from a grouped frequency table.

I can draw and interpret a scatter diagram.

I can draw a line of best fit on a scatter diagram.

[4 marks]

This pie chart shows the results of a different exam.

E

A

D

320 candidates were awarded grade A.

C

b How many candidates took the exam?

B

[2 marks]

Review questions 1

Remember that in a pie chart the fraction of the circle shows the fraction of the total. There are 360° in a whole circle.

a

The pie chart gives information about the mathematics examination GCSE grades of some students.

Mathematics examination grades

Work out the angle for each grade.

Grade

Frequency

A B

Calculation

Angle

208

208 2880 × 360°

26°

888

888 × 360° 2880

111°

1032

1032 × 360° 2880

129°

D

696

696 × 360° 2880

87°

56

56 × 360° 2880

7°

Total

2880

Grade 6

Take care to interpret the information you are given accurately.

80°

40°

140°

100° Grade 8

Grade 7

C

E

Grade 9

Remember to check that all the angles add up to 360°.

a What grade was the mode?

[1 mark]

b What fraction of the students obtained a grade 8?

[1 mark]

c 24 of the students got grade 9.

360° [2]

Exam grades

You do not need to show the angles.

A

[1 mark]

ii How many of the students took the examination?

[1 mark]

This accurate pie chart gives information about the English examination grades for a different set of students.

Remember to label the pie chart.

E

i How many of the students got grade 6?

English examination grades Grade 6

D

Grade 9

B C Grade 7

[2]

b The angle for grade A is 72°.

[1]

72 1 = 360 5 320 =

1 of the total 5

Total number of candidates = 320 × 5 = 1600

72 = 360 ÷ 5 [1]

Use the value of 320 given in the question.

3 Worked exemplars

9780008647308_Edexcel GCSE Math Higher_Chapter 3.indd 79

Grade 8

Measure the angle with a protractor.

CM

d Lizzy says: “More students got a grade 8 in English than in mathematics.”

Explain why Lizzy could be wrong.

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82

[2 marks]

3 Statistics: Statistical diagrams and averages

9780008647308_Edexcel GCSE Math Higher_Chapter 3.indd 82

25/01/24 10:36 PM

Sample from Edexcel GCSE Maths Higher Student Book

The new Student Books are Edexcel endorsed and AQA approved The AQA and Edexcel Teacher Packs have not been through the AQA approval or Edexcel endorsement process

Support for GCSE Maths Practice Books for fluency l

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Designed to support students in achieving Assessment Objective AO1 – using and applying standard techniques Build students’ confidence with hundreds of differentiated practice questions Easily identify topics for further practice, intervention, prior knowledge recall and revision and retrieval

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Challenge your most able students with plenty of ambitious questions

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Ideal for use both in the classroom or as a homework resource

Skills Books for reasoning and problem solving l

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Designed to support students in achieving Assessment Objectives AO2 and AO3: reason, interpret and communicate mathematically; and solve problems Improve literacy, thinking skills and investigative strategies by providing opportunities for students to tackle problems within and outside mathematics Build confidence in tackling longer questions in class and provide further practice at home Encourage students to think and analyse their work with questions designed to encourage independence

Workbooks

Write-in workbooks with plenty of additional practice to support students to reach their full potential. l l

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Ideal for both classroom and home learning Targeted practice at exactly the right level to help every student with recovery Designed to build skills and boost confidence with lots of exam-style questions

Digital support available l

Unlimited access for teachers and students to the full Student Book

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Prior knowledge quizzes for each chapter

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Additional retrieval quizzes

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Worked solution videos for exam-style questions

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Easy to use for front-of-class teaching or access at home on computers, tablets and smartphones

Talk to your local rep for a free demo, pricing information or any further questions.

25 years of Collins GCSE Maths Celebrating 25 years in print, the fifth edition of this classic and beloved GCSE Maths textbook has been updated for today’s students.

First published in 1997, the Collins GCSE Maths programme have been tested in classrooms across the UK and carefully refined over time by a highly experienced team of expert authors: Kevin Evans, Keith Gordon, Trevor Senior, Brian Speed and Michael Kent.

Meet the 5th edition author team Kath Hipkiss is currently a Trust Lead for maths with over 22 years’ teaching experience as a Head of Department, AST and Lead Practitioner. She has worked as an ELE with a keen interest in metacognition. In addition to this, she has been a GCSE and A level examiner for 15 years with multiple exam boards and has authored a number of books and teacher guides.

Anne Stothers MBA is a secondary maths consultant with over 30 years’ teaching and leadership experience.

She is an examiner for multiple exam boards and a conference speaker. She has authored books and created video content for several organisations and she specialises in CPD creation and delivery.

Michael Kent has 30 years’ experience teaching secondary maths, 12 of them also leading a successful department.

He co-authored the most recent editions of Collins GCSE Maths Student Books.

Chris Pearce has an MA in maths and over 30 years’ teaching experience at secondary level from KS3 to A level.

Previously an education advisor and examiner, he is now a full-time author and has written many bestselling KS3 and KS4 materials for Collins.

collins.co.uk

Working with WISE WISE (Women into Science and Engineering) are leaders in creating positive cultural change in the STEM industry, driving gender equality and diversity. We have worked with the WISE Young Professionals’ Board to feature a broad range of inspiring and real-life careers in the unit openers. Find out more about WISE wisecampaign.org.uk and try their My Skills My Life quiz with your class.

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NEW Edexcel GCSE Maths Foundation Student 978-0-00-864731-5 £22.99 Book, 5th edition NEW Edexcel GCSE Maths Higher Student 978-0-00-864730-8 £22.99 Book, 5th edition

NEW AQA GCSE Maths Foundation Student Book, 978-0-00-864733-9 £22.99 5th edition NEW AQA GCSE Maths Higher Student Book, 5th edition

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Foundation Teacher Pack

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Higher Teacher Pack

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Foundation Student Book, 1 year Collins Hub subscription

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Foundation Student Book, Homework and Tests, 3 year Collins Hub subscription

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Higher Student Book, 1 year Collins Hub subscription

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£700.00 +VAT

AQA Support Books Foundation Skills Book

978-0-00-811386-5

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Foundation Practice Book

978-0-00-811384-1

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Higher Teacher Pack

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Foundation Student Book, 1 year Collins Hub subscription Foundation Student Book, 3 year Collins Hub subscription Higher Student Book, 1 year Collins Hub subscription Higher Student Book, 3 year Collins Hub subscription

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Foundation Skills Book

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Edexcel Workbooks

AQA Workbooks Grade 1–3 Workbook

978-0-00-832253-3

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Grade 1–3 Workbook

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Grade 4–5 Workbook

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Grade 5–7 Workbook

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