Leckie Maths 2021 by Collins

MATHS 2021

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Classroom textbooks and revision resources: the right choice for you and your students From S1 through to Higher, Leckie offers a clear, complete and consistent pathway through the Sciences/Maths Curriculum for Excellence.

Written by highly experienced and knowledgeable Scottish authors including Principal

Teachers and SQA assessors, Leckie books are accessible and authoritative resources to help you teach with confidence.

Our range of S1–National 4 textbooks are eligible for Pupil Equity Funding.

CONTENTS Collins Connect for Leckie

2–3

BGE Pupil Books for Maths

4–5

National 3/4 Applications of Maths Student Book

National 4 to 5 Maths Bridging Skills Book

NationalClassroom 4 Maths Student Book textbooks

and revision resources: 8–9 National 5 Applications of Mathematics Student Book the right choice for you and your students 10–11 National 5 Maths Student Book

12–13

5 Maths Practice 14–15 WeNational are Scotland’s leadingComplete educational Revision publisher – & dedicated to creating resources designed specifically for Scottish teachers and students National 5 Maths Practice Workbook

16–17

We work with highly experienced and knowledgeable Scottish authors, including Principal Teachers Higher Maths 18–19 and SQA markers andStudent assessors Book We offer affordable, accessible and authoritative core resources for classroom teaching from S1 to Higher Maths Complete Revision and Practice 20–21 Advanced Higher

Maths Booster 22–23 WeHigher have updated allGrade our N5 books in line with the new SQA assessments and we will be updating our Higher books early in 2019 Higher Maths Practice Workbook

24–25

Our maths resources are recognised as the best on the market and offer a complete and consistent pathway from S1Higher to Advanced Higher Advanced Maths Student Book 26 Our new range of S1 – National 4 books are eligible for Pupil Equity Funding

Advanced Higher Maths Practice Papers for SQA Exams

Third Level, National 3/4/5, Higher and Advanced Higher Maths Practice Question Books

28–29

N5 and Higher Study Skills

Maths Coverage Grid JOIN OUR COMMUNITY!

Order form

32–33

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telephone: 01484 668148 • fax: 01484 665736 2019 Leckie Maths Catalogue.indd 2

1 18/01/2019 15:53:27

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ISBN

RRP (ex VAT)

CfE Maths Second Level Student Book (ebook 1 year)

9780008440855

£6.49

CfE Maths Second Level Student Book (ebook course)

9780008449032

£9.99

CfE Maths Third Level Student Book: Benchmark Edition (ebook 1 year)

9780008441548

£6.49

CfE Maths Third Level Student Book: Benchmark Edition (ebook course)

9780008448837

£9.99

CfE Third Level Maths Practice Question Book (ebook 1 year)

9780008441296

£3.49

CfE Third Level Maths Practice Question Book (ebook course)

9780008448639

£5.99

CfE Maths Fourth Level Pupil Book (ebook 1 year)

9780008440862

£6.49

CfE Maths Fourth Level Pupil Book (ebook course)

9780008449049

£9.99

CfE Maths Problem-Solving Skills Pupil Book (2nd edition) (ebook 1 year)

9780008441555

£3.99

CfE Maths Problem-Solving Skills Pupil Book (2nd edition) (ebook course)

9780008448844

£6.49

National 3/4 Applications of Maths Student Book (ebook 1 year)

9780008441289

£7.49

National 3/4 Applications of Maths Student Book (ebook course)

9780008448622

£11.49

National 3/4/5 Applications of Maths Student Book (ebook 1 year)

9780008441302

£3.49

National 3/4/5 Applications of Maths Student Book (ebook course)

9780008448646

£5.99

National 4 Mathematics Student Book (ebook 1 year)

9780008440879

£7.49

National 4 Mathematics Student Book (ebook course)

9780008448585

£11.49

National 4 Maths Practice Question Book (ebook 1 year)

9780008423940

£3.49

National 4 Maths Practice Question Book (ebook course)

9780008448288

£5.99

National 4 to 5 Maths Bridging Skills Book (ebook 1 year)

9780008441197

£3.49

National 4 to 5 Maths Bridging Skills Book (ebook course)

9780008449155

£5.99

National 5 Maths Student Book (2nd edition) (ebook 1 year)

9780008423476

£7.49

National 5 Maths Student Book (2nd edition) (ebook course)

9780008448431

£11.49

National 5 Applications of Maths Student Book (2nd edition) (ebook 1 year)

9780008423414

£7.49

National 5 Applications of Maths Student Book (2nd edition) (ebook course)

9780008448455

£11.49

National 5 Maths Practice Question Book (ebook 1 year)

9780008423469

£3.49

National 5 Maths Practice Question Book (ebook course)

9780008448295

£5.99

CfE Higher Maths Student Book (2nd edition) (ebook 1 year)

9780008423797

£8.49

CfE Higher Maths Student Book (2nd edition) (ebook course)

9780008448486

£13.49

CfE Higher Maths Grade Booster (ebook 1 year)

9780008440954

£3.99

CfE Higher Maths Grade Booster (ebook course)

9780008449063

£6.49

CfE Advanced Higher Maths Student Book (2nd edition) (ebook 1 year)

9780008423780

£10.99

CfE Advanced Higher Maths Student Book (2nd edition) (ebook course)

9780008448509

£17.49

Advanced Higher Maths Practice Question Book (ebook 1 year)

9780008441319

£3.49

Advanced Higher Maths Practice Question Book (ebook course)

9780008448653

£5.99

Titles available

telephone: 01484 668148 • fax: 01484 665736

PUPIL BOOKS FOR MATHS Maths Pupil Books CRAIG LOWTHER, JOHN BOATH, ROBIN CHRISTIE, CLAIRE CROSSMAN, KEITH EVANS, KEITH GORDON, IAN MACANDIE, JEANETTE MUMFORD These flexible resources support pupils at Second, Third and Fourth Levels and are specifically designed for the Secondary Maths classroom. THE PUPIL BOOKS WILL ALLOW YOU TO: • T each the curriculum with confidence with fresh content covering all the Experiences and Outcomes for each level and underpinned with the CfE principles for Maths

Third Level

Maths

• E nsure sufficient practice is available for every Experience and Outcome. Each chapter is packed with questions, examples are given to walk through each problem-type, questions that test problemsolving skills are identified throughout, and key questions are highlighted and are linked to chapter summaries

Benchmark edition

Student Book

“A very attractive textbook and one which I’m sure will be popular among mathematics teachers in Scotland.” Scottish Mathematical Council Journal, writing about the CfE Maths Third Level Pupil Book

Third Level

Maths Problem Solving Skills Benchmark edition

Third Level Maths Student Books: Benchmark edition ISBN: 9780008407766 • £16.99 Second Level Pupil Book • ISBN: 9781843729167 • £16.99 Fourth Level Pupil Book • ISBN: 9781843729181 • £16.99

Student Book

ABOUT THE AUTHORS Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. John Boath is Faculty Head at Webster’s High School, Angus. Robin Christie teaches at Webster’s High School. Claire Crossman is a class teacher at Elgin High School, Moray. Ian MacAndie is a Maths teacher at Elgin Academy, Moray.

Maths Problem-solving Skills Pupil Book KEITH GORDON, CHRIS PEARCE, TREVOR SENIOR • C reatively explore maths in the real world with this stand-alone resource for active classroom learning, projects or homework throughout S1–S3 • D evelop and consolidate pupils’ problem-solving skills with graded investigations using real data within engaging contexts • E nsure pupil tasks are relevant, with CfE Experiences and Outcomes identified throughout and cross-curricular links highlighted for each activity Problem-solving Skills Pupil Book ISBN: 9780008406219 • £10.99 • Available June 2020

Jeanette Mumford was formerly a primary school teacher in Glasgow.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

PUPIL BOOKS FOR MATHS ns Expressions and equatio

Flexible structure = easy integration into existing courses

and evaluate ic terms, simplify expressions

I can collect like algebra using substitution.

MTH 3-14a

you how to: This chapter will show

d of numbers s and other symbols instea write expressions using letter s ssion expre raic algeb in • collect like terms raic terms • add and subtract algeb le algebraic terms • multiply and divide simp s. substituting numbers for letter • evaluate expressions by

•

: You should already know

AS how to apply the rules of BODM how to use index form tive numbers • how to work with nega on. • how to simplify a fracti

•

d expressions Algebraic terms an

ing three words: variable, term

In algebra, you will keep meet

29174_P165_176.indd 165

Examples worked through step-by-step = greater confidence for pupils

and expression.

e value can vary. Some of a term or an expression whos Variable. This is the letter in t. and n y, x, bles are the letters most used for varia sion with the variable x, the s simpler, and to avoid confu ssion n in expre make In algebra, to than one letter they are writte lly left out, and if there is more usua is × sign tion plica multi front of the variables. So: go inber ers numb Num the s, ssion , mon expre ler ey and measure alphabetical order. In the simp + t)n you give Whe n × (d + t) = n(d a particular value to the varia d × 4c = 4cd = 7w 7 × w ab = b ble in an expression, the expre × a 3 × m = 3m on a particular value. ssion takes short rule in a by ced repla is usually it ad, Inste out. left just be The division sign ÷ cannot For example, if the variable n takes the value of 4, then the terms and expressions whic the style of a fraction. So: include this variable will have h n particular values, as shown d below: = a ) t + d ( ÷ n w = c 4 d÷ 3 = b t ÷ + a d = 7 ÷ w n c 4 4 3n = 3 × 4 = 12 3÷ m = b 2 = 7 2 = 2 m n = 4 = 16 8−n=8−4=4 2 2 letters) (or combinatio n − 3n=of 4−3=1 2n + 7 = 2 × 4 + 7 = 15 tity which contains only a letter Term. This is an algebraic quan For example: and may contain a number. Rules of algebra The rules (conventions) of algebra are iplied by the variable n the same rules that are used mult 3 s mean 3n For example: in arithmetic. n 2 by ed means n divid 3+4=4+3 a + b = b + a red’) 2 squa (normally said as ‘n means n multiplied by itself 3×4= 4×3 n2 a × b = b × a or ab = ba bers. bles) and signs, often with num (varia n of letters inatio comb a is But This n. remember, for example, that: Expressio For example: 7−5≠5−7 a−b≠b−a means subtract n from 8 8−n a b 6 ÷3≠3÷6 3 from n act ≠ subtr s mean 3 − n b a 7 add then 2 by iplied From one fact, other facts can be means n mult 2n + 7 stated. For example: 165 3+4=7 a + b = 10 gives 7 − 4 = 3 and 7 − 3 = 4 gives 10 − a = b and 10 − b=a 21/02/20 4:48 PM 3 × 4 = 12 ab = 10 gives 12 = 4 and 12 = 3 gives 10 = b and 10 = a 3 4 a b Example 19·1

Show by substitution of suita ble numbers that a + b − c ≠ c + b − a (the symb ol ≠ means ‘is not equal to’) Choosing a = 2, b = 5 and c = 3 we get a+b−c=2+5−3=4 and c+b−a=3+5−2=6 so a + b − c ≠ c + b − a

Example 19·2

Work out the value of these a 5x2 a 5x2 = 5 × (3 × 3) =5×9 = 45

expressions when x = 3. b

(5x)2

(5x)2 = (5 × 3)2 = 152 = 225

166

29174_P165_176.indd 166 21/02/20 4:48 PM

telephone: 01484 668148 • fax: 01484 665736

NATIONAL 3/4 MATHS National 3/4 Applications of Mathematics Student Book CRAIG LOWTHER, JUDITH WALKER, MARY LUCAS AND ALYSOUN WILSON The National 3/4 Applications of Mathematics Student Book helps teachers and students map their route through National 3 and 4, providing comprehensive and authoritative guidance for the courses. It gives a practical supportive approach to help deliver the curriculum and offer a blend of sound teaching and learning with assessment guidance. • F ull coverage of National 3/4 course specifications with lists of learning intentions • Attractive layout with easy to follow text features • Clear definition between National 3 and National 4 material • K ey questions highlight crucial concepts and techniques that need to be grasped by students in order to progress to the next learning intention • Worked examples guide the reader through the topics • Case studies provided at the end of each unit

National 3/4 Applications of Mathematics Student Book ISBN: 9780008242381 • £19.99

ABOUT THE AUTHORS Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. Judith Walker is a Maths teacher at Boroughmuir High School. Mary Lucas was Principal Teacher in the Faculty of Mathematics and Numeracy at Kemnay Academy. Alysoun Wilson is a Maths teacher at Peebles High School.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

NATIONAL 4/5 MATHS National 4 to 5 Maths Bridging Skills Book CRAIG LOWTHER, CLARE FORD AND DOMINIC KENNEDY

Bridge the skills gap between National 4 and National 5

This book is designed to motivate and support the many students who find the transition from National 4 to National 5 a big challenge, and who need extra guidance and practice to ensure they are working successfully towards the standard required at N5. It can be used either alongside the Leckie N5 Maths Student Book or as a flexible standalone resource to build confidence and consolidate learning. Practice exam questions with exemplar answers and preparation for assessments are at the heart of this invaluable resource for those aiming to achieve N5 Maths at any point following a N4 pass. • M ain learning points are summarised clearly in each chapter • Practice questions and examples with worked solutions help with difficult concepts • Key questions assess students’ grasp of each topic • Hints and comments give advice and guide students through problems • Review exercises at the end of each chapter cover the key points National 4 to 5 Maths Bridging Skills Book ISBN: 9780008209063 • £9.99

ABOUT THE AUTHORS Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. Clare Ford teaches maths at Hamilton College. Dominic Kennedy is Depute Head Teacher at St Aidan’s High School, Wishaw.

telephone: 01484 668148 • fax: 01484 665736

NATIONAL 4 MATHS National 4 Maths Student Book CRAIG LOWTHER, JUDITH WALKER, ROBIN CHRISTIE, BRENDA HARDEN, ANDREW THOMPSON, JOHN WARD, STUART WELSH National 4 Maths Student Book is the complete core resource for the N4 qualification, combining all the course content with essential exam and assessment guidance. The book has a clear layout with plenty of tables, diagrams and illustrations that bring the course to life. Answers are available free online. PROGRESS AND ATTAINMENT FOR ALL

The complete core resource for the National 4 qualification

• T his book is structured to map exactly to the course and unit specifications • You should already know sections identify prior learning and skills • Packed with worked examples that introduce new topics, techniques and skills clearly, breaking the process into manageable steps • Exercises are carefully graded in difficulty throughout the book • Key questions ensure that every student can progress securely • B uilds on the approach and quality of the highly successful CfE Maths Pupil Books for Second to Fourth Levels ACTIVE LEARNING

ABOUT THE AUTHORS Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. Judith Walker teaches maths at Boroughmuir High School. Robin Christie teaches at Webster’s High School.

• Summary sections at the end of each chapter encourage regular review of knowledge ASSESSMENT AND PRACTICE YOU CAN RELY ON • Preparation for Assessment sections and an Added Value assessment section features questions and examples that ensure students are fully prepared for each assessment type National 4 Maths Student Book ISBN: 9780007504619 • £19.99

Brenda Harden is Principal Teacher of Maths at Northfield Academy, Aberdeen. Andrew Thompson is Curriculum Area Development Officer–Mathematics, Numeracy and Business Education (Highland). John Ward teaches mathematics at Balerno Community High School, Edinburgh. Stuart Welsh is Principal Teacher of Mathematics at the High School of Glasgow.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

NATIONAL 4 MATHS Structured to map exactly to the course and unit specifications

You should already know sections identify prior learning and skills

Hints are given for extra support

Summary sections at the end of each chapter encourage regular review of knowledge

Key questions ensure that every student can progress securely

telephone: 01484 668148 • fax: 01484 665736

NATIONAL 5 APPLICATIONS OF MATHS National 5 Applications of Mathematics Student Book

CRAIG LOWTHER, JUDITH WALKER, BRENDA HARDEN, JENNIFER SMITH, ALYSOUN WILSON National 5 Applications of Mathematics Student Book is the complete core resource for the N5 qualification, combining full coverage of the course with essential exam and assessment guidance. The book has a clear layout with plenty of tables, diagrams and illustrations bringing the course to life. Answers are available free online.

Successfully map your route through the course

PROGRESS AND ATTAINMENT FOR ALL • T his book is structured to map exactly to the course and unit specifications • C overs all of the course units: Managing Finance and Statistics, Geometry and Measures, and Numeracy • You should already know sections identify prior learning and skills • Key questions ensure that every student can progress securely • P ractice questions are rooted in real-world contexts to ensure students are able to apply maths skills to actual situations ACTIVE LEARNING • C ase studies are included for all skills covered in the course ensuring the vital practice required is provided to develop knowledge and skills • S ummary sections at the end of each chapter encourage regular review of knowledge

ABOUT THE AUTHORS

• L inks to Higher show how the National 5 course articulates with Higher Maths

Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI.

ASSESSMENT AND PRACTICE YOU CAN RELY ON

Judith Walker teaches maths at Boroughmuir High School.

National 5 Applications of Maths ISBN: 9780008282066 • £19.99

Brenda Harden is Principal Teacher of Maths at Northfield Academy, Aberdeen.

• P reparation for Assessment is included in a dedicated section at the end of each unit

Jennifer Smith is Faculty Head of Maths and Numeracy at Aberdeen Grammar School. Alysoun Wilson is a Maths teacher at Peebles High School.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

NATIONAL MATHS NATIONAL 5 APPLICATIONS OF55MATHS NATIONAL MATHS NATIONAL 5 MATHS Activities Activities Activities Activities throughout provide opportunities to opportunities to opportunities to opportunities to apply knowledge apply knowledge apply knowledge applyand knowledge solve and solve and solve and solve problems problems problems problems

Hintboxes boxes Hint Hint boxes Hinthelpful boxes tips give give helpfultips tips give helpful give helpful tips and highlight and highlight highlight andimportant highlight important important important information information information information Worked Worked Worked Workedclearly examples examples clearly examples clearly examples clearly show the process, show process, show the process, show the process, strategy and strategy and strategy and strategy and communications communications communications communications of solutions for all types of question

Key Key Key Key questions questions questions questions ensure that ensure that ensure that ensure that every student every student every student every student can progress can progress canprogress progress can securely securely securely securely

telephone: 01484 668148 • telephone: 01484 668148 telephone:01484 01484668148 668148 ••• telephone:

fax:01484 01484 665736 fax: 665736 fax:01484 01484665736 665736 fax:

9 11 99

NATIONAL 5 MATHS National 5 Maths Student Book CRAIG LOWTHER, JUDITH WALKER, ROBIN CHRISTIE, BRENDA HARDEN, ANDREW THOMPSON, JOHN WARD AND STUART WELSH The National 5 Maths Student Book provides comprehensive and authoritative coverage of the whole course. Updated for 2018 and beyond. • F ull coverage of National 5 course specifications with list of learning intentions • Attractive layout with clear text features • Key questions highlight crucial concepts and techniques that need to be grasped by students in order to progress to the next learning intention • What the examiner/assessor is looking for to help teachers and students feel secure • Exam-style questions with worked answers and examiners commentary, self-assessment • Keep your learning on track/Stretch yourself to encourage self evaluation and provide challenge for higher ability students

• Active learning ideas: ‘You Should Already Know’, lists for student to check they are confident with before proceeding AND ‘Make the link’ highlights links between the topic and other areas of the course and/ or across different subjects • A ssessment questions, exemplar work, model answers, suggested topic work National 5 Maths Student Book ISBN: 9780008282004 • £19.99

Robin Christie teaches at Webster’s High School. Brenda Harden is Principal Teacher of Maths at Northfield Academy, Aberdeen. Andrew Thompson is Curriculum Area Development Officer – Mathematics, Numeracy and Business Education (Highland). John Ward teaches mathematics at Balerno Community High School, Edinburgh. Stuart Welsh is Principal Teacher of Mathematics at the High School of Glasgow.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

NATIONAL 5 MATHS Structured to map exactly to the course and unit specifications

You should already know sections identify prior learning and skills

Key questions ensure that every student can progress securely

telephone: 01484 668148 • fax: 01484 665736

NATIONAL 5 MATHS National 5 Maths Complete Revision & Practice KEN NISBET Two books in one! Combining a revision guide and a full set of practice test paers, this fantastic resource is all you need to revise for your National 5 Maths exam. PROGRESS AND ATTAINMENT FOR ALL The revision guide • Covers all of the topics in the new CfE National 5 Maths curriculum, broken down into manageable chunks for easy revision • Clearly explains key concepts, research evidence and real-life applications • Contains Quick Tests to let students check their knowledge and understanding as they go along The practice test papers • Are in the format and the style of the SQA exam, giving students an opportunity to practice taking the National 5 Maths exam • Marking instructions and sample answers are provided online, so students can check their progress National 5 Maths Complete Revision & Practice ISBN: 9780008435325 • £10.99

ABOUT THE AUTHOR Ken Nisbet is retired Principal Teacher of Maths at Madras College, St Andrews and author of several Leckie maths resources.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

NATIONAL 5 MATHS

‘Traffic light’ revision checklists help students manage and track their progress in the lead up to the exams

Top Tips keep students focused on the exam’s precise demands

Exam questions give students an opportunity to test their understanding and build exam confidence

telephone: 01484 668148 • fax: 01484 665736

NATIONAL 5 MATHS National 5 Maths Practice Workbook CRAIG LOWTHER JUDITH WALKER Practice questions on every topic of the National 5 Maths curriculum to help students learn; and mixed exam question practice to test their understanding • Master even the trickiest of topics by practising tons of questions • C heck understanding by reviewing the example answers which contain workings-out • B uilds confidence with the Mixed Exam Question Practice section, to prepare for the type and level of questions in the SQA National 5 Maths exam • U nderstand how the exam will be marked with detailed answers to all of the questions • Learn how to approach different types of question with hints and tips • A ll answers can be found online at https://collins.co.uk/pages/scottishcurriculum-free-resources Can be used at school or at home – for revision, homework, independent study or exam practice. National 5 Maths Practice Workbook ISBN: 9780008446765 • £6.99

ABOUT THE AUTHOR Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. Judith Walker teaches maths at Boroughmuir High School.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

NATIONAL 5 MATHS

Questions on every topic, with worked answers and hints and tips, help students learn and consolidate their knowledge

Exam papers check understanding, show students where marks are awarded, and build exam confidence

telephone: 01484 668148 • fax: 01484 665736

HIGHER MATHS Higher Maths Student Book CRAIG LOWTHER, ANDREW THOMPSON, STUART WELSH, CLAIRE ANDERSON, ROBIN CHRISTIE The Higher Maths Student Book is now fully updated for the revised Higher assessments. • Full coverage of the new Higher course specifications with list of learning intentions • Attractive layout with clear text features

The complete core resource for the Higher qualification

• Key questions highlight crucial concepts and techniques that need to be grasped by students in order to progress to the next learning intention • What the examiner/assessor is looking for to help teachers & students feel secure • End of unit material – unit assessment, exam-style questions with worked answers and examiners commentary, self-assessment Student Books give a practical, supportive approach to help deliver the new curriculum and offer a blend of sound teaching and learning with assessment guidance.

Higher Maths Student Book ISBN: 9780008383503 • £22.99

ABOUT THE AUTHORS Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. Andrew Thompson is Curriculum Area Development Officer – Mathematics, Numeracy and Business Education (Highland). Stuart Welsh is Principal Teacher of Mathematics at the High School of Glasgow. Claire Anderson teaches Maths at the High School of Glasgow. Robin Christie teaches Maths at Websters High School, Angus.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

HIGHER MATHS

Worked examples clearly show the process, strategy and communications of solutions for all types of question

Key questions ensure that every student can progress securely

telephone: 01484 668148 • fax: 01484 665736

HIGHER MATHS Higher Maths Complete Revision and Practice KEN NISBET Complete Revision and Practice is the newest resource from Leckie. Combining two books in one resulting in a revision guide and a full set of practice test papers, this fantastic resource is all you need to revise for exam. THE REVISION GUIDE:

The ultimate revision resource!

• Covers all of the topics in the new revised assessments for Higher Maths curriculum, broken down into manageable chunks for easy revision • Clearly explains key concepts, research evidence and real-life applications • Contains Quick Tests to let students check their knowledge and understanding as they go along THE PRACTICE TEST PAPERS: • Are presented in the format and style of the exam, for authentic practice Marking instructions and sample answers are provided online, so students can check their progress.

Higher Maths Complete Revision and Practice ISBN: 9780008365233 • £10.99

ABOUT THE AUTHOR Ken Nisbet is retired Principal Teacher of Maths at Madras College, St Andrews and author of several Leckie maths resources.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

HIGHER MATHS hs Functions and grap

Got it ?

’Traffic light’ revision checklists help students manage and track their progress in the lead up to the exams

Combining effects

up this combined effect ined you will need to split When several effects are comb t encounter are explained migh you splits al typic into individual effects. Some aim is to draw a related the graph y = f (x) and your below. Usually you are given y = f (x) and you should be a few points on the graph graph. You will also know s are on the related graph. able to ﬁnd where these point related graph. f (x) and A’ and B’ are on the Note: A and B are on y = y = 3f (x – 5) Aim: B(–4, –1) A(4, 2) y = f (x) Start: (1, –1) (9, 2) 5) – (x f = y 5 units right: B’(1, –3) A’(9, 6) 5) – (x 3f = y y-axis scaling (factor 3): f (x + 1) – 3 y= –1 Aim: 2 B(0, –1) A(3, 6) Top Tip y = f (x) Start: (–1, –1) (2, 6) If you know the y = f (x + 1) 1 unit left: 1 coordinates of a   –1, –  1 1 point on the graph  (2, 3)  = f (x + 1) 2 y = f (x) then a y-axis scaling factor 2: y 2 corresponding 1   –1,  1 point should –3) (2, 1) +  2 y = – f (x appear on your ﬂip in x-axis: 2 sketch of the 5  related graph. 1 –6) B’–1, – 2 y = – f (x + 1) – 3 A’(2,  3 units down: 2

Solution

Example

Split into two steps: Step 1 graph of y = –f (x)

The graph of y = f (x) is shown: y

Step 2 graph of y = 2 – f (x)

(22, 2)

1 O

Worked examples clearly explain the best methods to get right to the answer

Got it ?

(1, 2)

Relate

1 x

Sketch the graph y = 2 – f (x)

O 21

d log g raphs

Example

shift up 2 units

in x-axis

‘flip’ tten as –f (x) + 2 resulting in Note: 2 – f (x) can be rewri up 2 units moving the graph y = –f (x)

This is a sk et of the grap ch of part h of y = lo g3 x

Expon

ential

Solution

Quick Test 4 n. Sketch the indicated The graph of y = f (x) is show s. images of the named point graphs showing clearly the 1.

y = –f (x) + 2

y = f (x + 1) – 1

Exam Practice

A: NQ H

igher M

LAE LIST

FORMU

Sketch the graph y = log

ulae:

etric form

Trigonom

cos (A ±

B) = cos

−f ) and

∓ sin A sin

Table of

standard

ves:

derivati

standard

s: integral

si 2 cos A −

n A

2 A− = 2cos

st 6

y 5 log x 5

A 1 − 2sin O

f ′(x)

f (x)

a cos ax −a sin ax

f (x)

sin ax cos ax

65233_P02

0-031.indd

6.indd

P145-15

On yo ur calc ul calcul ate log ator, to e 23 pres s

Change ‘p ower state ments’ to ‘log state ments’ an d ‘log statements’ to ‘power statements’ a) 92 = 10 x : b) 4 = e y c) 4 = lo g10 t d) log A =B e

Top Tips throughout ensure students know what the examiner will be look for 03/10/19

1 ax + C − a cos 1 sin ax + C a

65233_

(1, 0)

(5, 1)

Sketch th e graphs: a) y = log 5 x + 1 b) y = log 5 (x + 1) c) y = –log 5x d) y = log 5 (x – 2) – 1

∫ f (x) dx

Page 14

Top Ti

sin ax cos ax

Table of

Calculate log Solution as a power e 23 and hence writ e 23 log of e to 2 de cimal plac e 23 = 3·13 5… es. so 23 = e 3·135… e 3·14

5 log x e

ample

sin B

Quick Te

cos 2A =

x On your calculator , the keys The keys 10 x and log give e x and base 10 ca ln give base e ca lculations lculations . . Ex

A in A cos

2s sin 2A =

l base e

± cos A

A cos B

There are two comm on bases us The specia ed for expo l number nential an e = 2·7182 d logarithm the natura 8182… us ic functions l ed as a ba : 10 and e exponent y se gives: ial and its in function y verse function, the natura l logarithm ic functio 1 n y5 x y

+ 2 y2 + 2gx radius r tion x + , b) and The equa 2 2 centre (a −c db f + ts a circle g een a an 2 represen tw 2 be us r e radi e angl − b) =  b1  re θ is th a)2 + (y  he  − w  , (x θ n s  tio  b co   a1  The equa a.b = a  d b =  b2     a2 an uct:  = od b a pr re 3    whe Scalar b a 3 +  3  a3  b + a 2b 2 a.b = a 1 1 or A cos B

(x + 3) +

The sp ecia

ics

athemat

ntre (−g,

) = sin n (A ± B

y (0, 2)

03/10/19 6:02 PM

circle ce

a presents

0 re 2fy + c =

Circle:

Then move graph up 1 unit

(22, 1)

B 21 O 21

(1, 0)

65233_P008_019.indd 17

Here is th e resulting graph... (3, 1) (0, 2) (1, 0) (–2, 1)

y = log (x + 3) + 1 3

Move the giv graph 3 un en its left

(3, 1) O

and lo garithm

ic funct io

Practice papers that look just like the SQA exam format 03/10/19

Quick Test on every topic provides the practice that experts say is essential for effective recall

6:42 PM

5:51 PM

148

telephone: 01484 668148 • fax: 01484 665736

HIGHER MATHS Higher Maths Grade Booster STUART WELSH This Higher Maths Grade Booster is the essential guide to exam skills and has been written by an experienced teacher and exam expert. All the papers reflect the type and level of questions students are likely to meet; the formats of different questions papers and assessment methods; and the type of marking schemes used by the SQA.

Help support your students improve their grade, whatever they’re aiming for

• Detailed advice on how to approach all the different types of question you will find in the exam will develop your skills and help you to avoid common pitfalls • Essential guide to structuring your responses shows you how to formulate and improve your answers • A dedicated chapter on the Assignment ensures that you have a great foundation for your grade before you even enter the exam room Leckie Grade Boosters support aspiring college & university students get the Higher grade they need to secure the place on the course they want. Grade Boosters focus on how the student translates his or her own knowledge into the types of response demanded by the CfE Higher course. This Grade Booster is particularly focused on helping Higher candidates secure at least a C pass grade which many will need for the world of work or further education. • A complete outline of the new CfE Higher course and assessment structure ensures a full understanding of what to expect in the exam • Content ensures students have the tools to do their best, focusing on skills for the final exam, the assignment and unit assessments • Advice on writing the best response will be drawn from comments contained within the annual External assessors reports, published by SQA • Examples of weak, strong and excellent responses are provided to help students understand how to develop and improve their own answers to get the most marks • Plentiful case studies throughout for authentic practice

ABOUT THE AUTHOR Stuart Welsh is Head of Department at the High School of Glasgow

Higher Maths Grade Booster ISBN: 9780007590827 • £10.99

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

HIGHER MATHS Chapters in user-friendly sections help to present topics in bite-sized chunks You should be able to sections at the start of each chapter identify prior learning and skills

Examples for each topic clearly show the steps required in working through calculations to reach a solution

telephone: 01484 668148 • fax: 01484 665736

HIGHER MATHS Higher Maths Practice Workbook CRAIG LOWTHER, KEN NISBET AND LECKIE Practice questions on every topic of the Higher Maths curriculum to help students learn; and mixed exam question practice to test their understanding • Master even the trickiest of topics by practising tons of questions • Check understanding by reviewing the example answers which contain workings-out • Builds confidence with the Mixed Exam Question Practice section, to prepare for the type and level of questions in the SQA Higher Maths exam • Understand how the exam will be marked with detailed answers to all of the questions • Learn how to approach different types of question with hints and tips • All answers can be found online at https://collins.co.uk/pages/scottishcurriculum-free-resources Can be used at school or at home – for revision, homework, independent study or exam practice.

Higher Maths Practice Workbook ISBN: 9780008446727 • £10.99

ABOUT THE AUTHOR Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. Ken Nisbet is retired Principal Teacher of Maths at Madras College, St Andrews and author of several Leckie maths resources.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

HIGHER MATHS

Questions on every topic, with worked answers and hints and tips, help students learn and consolidate their knowledge

Exam papers check understanding, show students where marks are awarded, and build exam confidence

telephone: 01484 668148 • fax: 01484 665736

ADVANCED HIGHER MATHS Advanced Higher Maths Student Book Second edition CRAIG LOWTHER, JOHN BALLANTYNE, CLARE FORD, MONICA KIRSON AND DEIRDRE MURRAY The Advanced Higher Maths Student Book provides comprehensive and authoritative guidance for the course. • Attractive layout with clear text features

The complete core resource for the Advanced Higher qualification

ABOUT THE AUTHOR Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI. John Ballantyne teaches maths at Inverness College, UHI. Clare Ford teaches maths at Hamilton College. Monica Kirson teaches maths at Our Lady’s High School, Cumbernauld. Deirdre Murray teaches maths at Alness Academy.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

ADVANCED HIGHER MATHS Advanced Higher Maths Practice Papers for SQA Exams CRAIG LOWTHER, DOMINIC KENNEDY AND GRAEME NOLAN The Advanced Higher Maths Practice Papers will help you to prepare your students for the look and feel of the Advanced Higher exam– so they can do their best on the big day! All the papers reflect the type and level of questions students are likely to meet; the formats of different questions papers and assessment methods; and the type of marking schemes used by the SQA. EACH BOOK COMPRISES:

Feel confident with the exam experience!

• Several practice papers that look just like the SQA exam format – familiarising your students with the demands of the exam and the expectations of the examiner, boosting confidence • Detailed answers to all of the questions show students exactly how their exam will be marked • Fully worked examples ensure students know how to give the best possible answer and gain most marks • A topic index helps teachers to quickly set classwork and homework, and students can select and practice questions on specific areas of the course when revising • Hints throughout explain how to approach different types of question • Worked answers are fully referenced to the Advanced Higher Maths Student Book, making it easy to check back to the relevant sections to consolidate learning. YOU CAN RELY ON ADVANCED HIGHER PRACTICE PAPERS FOR SQA EXAMS TO: • Help teachers, students and parents to feel confident with the new exam experience • Provide a wealth of practice at the right level • Make sure students won’t lose any marks, and help them learn how to give the best possible answer

ABOUT THE AUTHOR Craig Lowther is our Series Editor for Maths. He was previously Education Officer for Moray and is now at Inverness College, UHI.

Advanced Higher Maths Practice Papers ISBN: 9780008209056 • £9.99

Dominic Kennedy is Depute Head Teacher at St Aidan’s High School, Wishaw. Graeme Nolan is Depute Head Teacher at Airdrie Academy.

telephone: 01484 668148 • fax: 01484 665736

QUESTION PRACTICE – FROM THIRD LEVEL TO ADVANCED HIGHER

Third Level, National 3/4/5, Higher and Advanced Higher Maths Practice Question Books CRAIG LOWTHER, GRAEME NOLAN, MIKE SMITH, IAN MACANDIE, KEN NISBET AND THE LECKIE TEAM Building on the widely trusted approach of our CfE Third Level, National 3/4/5, Higher and Advanced Higher Maths Student Books, these new Practice Question Books offer masses of practice questions grouped by topic, to ensure your students have plentiful opportunities to practise specific areas of their course at the appropriate time. They are ideal for almost any context: for homework activities, for revision and consolidation, for cover lessons, or for individual student support.

National 3/4/5 Applications of Maths Practice Question Book ISBN: 9780008263553 · £9.99 Third Level Maths Practice Question Book ISBN: 9780008263546 · £9.99

National 4 Maths Practice Question Book ISBN: 9780008209070 • £9.99

National 5 Maths Practice Question Book ISBN: 9780008209087 • £9.99

ABOUT THE AUTHORS Craig Lowther is our Series Editor for Maths He was previously Education Officer for Moray and is now at Inverness College, UHI. Graeme Nolan is Depute Head Teacher at Airdrie Academy. Mike Smith was Head of Department at Trinity Academy and is currently teaching at Lasswade High School. Ian MacAndie is a Maths teacher at Elgin Academy, Moray. Ken Nisbet was a Teacher of Maths at Madras College, St Andrews.

Higher Maths Practice Question Book ISBN: 9780008242329 • £9.99

Advanced Higher Maths Practice Question Book ISBN: 9780008263560 • £9.99

Consolidate learning with plenty of practice questions

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

QUESTION PRACTICE – FROM THIRD LEVEL TO ADVANCED HIGHER Examples with worked solutions provide support for particularly tricky concepts.

High

n Questio ractice P s th a er M

Book

Questions which require reasoning skills are marked with a icon.

N5 Maths

Practice Q

Book N4 Maths Practice Question

uestion Bo ok

Use of calculators: Questions to be attempted without a calculator are marked with a icon. Questions where you can use a calculator are marked with a icon.

Reminders: Reminders are included where a handy refresher might be needed

Hints: Where appropriate, hints are provided to help give extra guidance and support.

Answers: Check your own work. The answers are provided online at: www.leckiescotland.co.uk/page/Resources

telephone: 01484 668148 • fax: 01484 665736

N5 & HIGHER STUDY SKILLS N5 & Higher Study Skills DANIELLE BROWN, LEE JACKSON, NICOLA MORGAN, M-C MCINALLY, ERIC SUMMERS This must-have guide provides your students with effective advice and strategies for studying and exam performance based on the latest research. All the papers reflect the type and level of questions students are likely to meet; the formats of different questions papers and assessment methods; and the type of marking schemes used by the SQA.

A must-have for every student taking SQA exams! ABOUT THE AUTHORS Danielle Brown is double Paralympic gold medallist in archery and three times world champion. She is a motivational speaker who gives talks and runs workshops on helping people achieve their best. Nicola Morgan is a bestselling author and speaker who specialises in the teenage brain, stress and wellbeing. Lee Jackson is one of the UK’s most experienced motivational speakers in business and education. M-C McInally is the Head Teacher at Monifeith Higher School, Angus. She was coauthor of the previous edition of Study Skills from Leckie

A fantastic team of experts share how the teenage brain, lifestyle, stress and attitude can all affect learning and performance and provide easy to implement strategies so your students can achieve their best. • Packed full of revision tips and to-the-point advice that students can dip into for support. The guide covers: • Get motivated – find out how positive beliefs can help get the best results • L ook after yourself – simple and effective ways for your students to look after their brains and bodies for their best exam performance • Know your own mind – learn to recognise stress and how to alleviate it • Tackle pressure head on – control nerves and build confidence with expert advice from a Paralympic champion • P lan for success – prioritise commitments and make the most of study time • Take responsibility for your own learning – demonstrates how a positive mindset and effective organisation can help students excel in their exams • Get ready for the exams – invaluable countdown to the exams to ensure your students go into the exam room feeling prepared and confident

N5 & Higher Study Skills ISBN: 9780008113537 • £5.99

Eric Summers is a recently retired headteacher from Kirriemuir, Angus. He was coauthor of the previous edition of Study Skills from Leckie.

www.leckiescotland.co.uk • email: leckiescotland@harpercollins.co.uk

MATHS COVERAGE GRID We cover the entire maths curriculum from Primary through to Secondary. Primary Maths for Scotland is our primary resource for delivering numeracy Problemand mathematics aligned to the Curriculum for Excellence. Primary Maths for Solving Scotland prepares children for a smooth transition between all levels, including coming soon those beyond primary. Leckie provides classroom resources, revision books Primary and teacher guides, from Early Level though to Advanced Higher (including The maths mastery programme Application of Maths) in secondary education. developed by an expert team of Scottish authors to raise attainment in Scotland

Primary

Textbook

Teacher Guide

Assessment Pack

Digital Package

Wipe-clean templates

Primary Practice workbook

To help pupils fully understand mathematical concepts

Planning and teaching support

Tracking and recording children’s progress

Online resource to support teachers

Reusable maths templates

Illustrated workbooks that make learning fun

Early level

First level

Second level

Secondary

Student Book

Comprehensive course coverage

@LeckieScotland

Student Book Practice Workbook

Comprehensive course Complete revision and coverage practice Problem-Solving

Problem-Solving

Second Level

Third Level

pplication

gher

Scotland

We cover the e curriculum, from learni We cover the entire maths We cover the entire maths to revision, curriculum, from learning through at curriculum, from learning through to revision, to revision, at every level at every level

Secondary

ving

of Maths

Secondary Secondary

Student Book

Practice Workbook

Practice Exam Papers

Complete Revision and Practice

Grade Booster

Practice Workbook Practice Exam Papers

Complete Revision Practice Exam Papers and Practice

Complete Revision Grade Booster and Practice

Practice Grade Booster Question Book

Practice Question Book

Comprehensive course coverage

Complete revision and practice

Brand new practice papers, Complete revision and modelled on practice the SQA exams

Brand new practice papers, A revision guide and on a fullmodelled set of practice the SQA exams test papers

Brand new practice papers, A revision guide and modelled on a full set of practice the SQA exams test papers A revision guide and Topoftips on maximising Top tips on maximising Plenty questions for every a full and set of practice markswith andmore minimising marks minimising topic, of the test papers mistakes mistakes tricky ones

www.leckiescotland.co.uk

Top tips on maximising Plent marks and minimising to mistakes Plenty of questions for every topic, with more of the tricky ones

LeckieforScotland

Third Level National 3/4 Applications of Maths National 3/4 Applications of Maths

National 4

National 5 Application of Maths

Bridging Skills

National 5

Higher

New!

New! Advanced Higher

New!

Advanced Higher

www.leckiescotland.co.uk LeckieforScotland www.leckiescotland.co.uk www.leckiescotland.co.uk

@LeckieScotland @LeckieScotland

telephone: 01484 668148 • fax: 01484 665736

LeckieforScotlan

NOTES

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MATHEMATICS ORDER FORM Level

Series

ISBN

RRP

Third Level

Maths Student Book: Benchmark Edition

9780008407766

£16.99

Second Level

Maths Pupil Book

9781843729167

£16.99

Fourth Level

Maths Pupil Book

9781843729181

£16.99

Third Level

Problem Solving Skills

9780008406219

£10.99

National 3/4

Applications of Mathematics Student Book

9780008242381

£19.99

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Maths Bridging Skills Book

9780008209063

£9.99

National 4

Maths Student Book

9780007504619

£19.99

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Applications of Mathematics Student Book

9780008282066

£19.99

National 5

Maths Student Book, 2e

9780008282004

£19.99

National 5

Maths Complete Revision & Practice

9780008435325

£10.99

National 5

Maths Practice Workbook

9780008446765

£6.99

Higher

Maths Student Book, 2e

9780008383503

£22.99

Higher

Maths Complete Revision and Practice

9780008365233

£10.99

Higher

Maths Grade Booster

9780007590827

£10.99

Higher

Maths Practice Workbook

9780008446727

£6.99

Advanced Higher

Maths Student Book, 2e

9780008384456

£29.99

National 3/4/5

Applications of Maths Practice Question Book

9780008263553

£9.99

Third Level

Maths Practice Question Book

9780008263546

£9.99

National 4

Maths Practice Question Book

9780008209070

£9.99

National 5

Maths Practice Question Book

9780008209087

£9.99

Higher

Maths Practice Question Book

9780008242329

£9.99

Advanced Higher

Maths Practice Question Book

9780008263560

£9.99

N5 & Higher

Study Skills

9780008113537

£5.99

Advanced Higher

Maths Practice Papers for SQA Exams

9780008209056

£9.99

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Leckie Maths 2021

Articles inside

National 3/4 Applications of Maths Student Book

Advanced Higher Maths Practice Papers for SQA Exams

N5 and Higher Study Skills