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PEARSON EDEXCEL INTERNATIONAL GCSE (9 –1) P E 2 A R S MATHEMATICS A O N E D E X C Student Book 2 E L I N T David Turner, Ian Potts E R N A T I O N A Pearson Edexcel International GCSE (9–1) Mathematics A prepares students for L the International GCSE (9–1) Mathematics A specifi cation. G C S Together, Student Books 1 and 2 provide comprehensive coverage of the E Higher Tier specifi cation. This book is designed to provide students with the best (9 – preparation possible for the examination: 1 ) M • Written by highly experienced International GCSE Mathematics teachers A and authors David Turner and Ian Potts TH • Integrated exam practice throughout, with differentiated revision exercises EM and chapter summaries A T • Signposted transferable skills IC S • Integrated Pearson Progression Scale A • Reviewed by a language specialist to ensure the book is written in a clear PEARSON EDEXCEL INTERNATIONAL GCSE (9 –1) S t and accessible style for students whose fi rst language may not be English u d • Glossary of key Mathematics terminology inecBluodoekd e PEARSON EDEXCEL INTERNATIONAL GCSE (9 –1) n • Full answers included in the back of the book t B 2 • eBook included o o MATHEMATICS A k MATHEMATICS A 2 Interactive practice activities and teacher support provided online as part Student Book 1 of ActiveLearn. ISBN: 9780435181444 For Edexcel International GCSE (9–1) Mathematics specifi cation A (4MA1) Higher Tier for fi rst teaching 2016. Student Book 2 eBook David Turner, Ian Potts included www.pearsonglobalschools.com CVR_IGM2_SB_3059_CVR_V2.indd 1 13/04/2018 14:04 EDEXCEL INTERNATIONAL GCSE (9 –1) MATHEMATICS A Student Book 2 David Turner Ian Potts A01_IGMA_SB_3059_Prelims.indd 1 10/04/2017 14:49 Published by Pearson Education Limited, 80 Strand, London, WC2R 0RL. Endorsement Statement In order to ensure that this resource offers high-quality support for the www.pearsonglobalschools.com associated Pearson qualification, it has been through a review process by the awarding body. This process confirms that this resource fully covers the Copies of official specifications for all Pearson Edexcel qualifications may be found teaching and learning content of the specification or part of a specification at on the website: https://qualifications.pearson.com which it is aimed. It also confirms that it demonstrates an appropriate balance between the development of subject skills, knowledge and understanding, in Text © Pearson Education Limited 2017 addition to preparation for assessment. Edited by Lyn Imeson Answers checked by Laurice Suess Endorsement does not cover any guidance on assessment activities or Designed by Cobalt id processes (e.g. practice questions or advice on how to answer assessment Typeset by Cobalt id questions), included in the resource nor does it prescribe any particular Original illustrations © Pearson Education Limited 2017 approach to the teaching or delivery of a related course. Illustrated by © Cobalt id Cover design by Pearson Education Limited While the publishers have made every attempt to ensure that advice on the Picture research by Andreas Schindler qualification and its assessment is accurate, the official specification and Cover photo/illustration © Shutterstock.com: Grey Carnation associated assessment guidance materials are the only authoritative source of information and should always be referred to for definitive guidance. The rights of David Turner and Ian Potts to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Pearson examiners have not contributed to any sections in this resource Patents Act 1988. relevant to examination papers for which they have responsibility. First published 2017 Examiners will not use endorsed resources as a source of material for any assessment set by Pearson. Endorsement of a resource does not mean that 20 19 18 17 the resource is required to achieve this Pearson qualification, nor does it mean 10 9 8 7 6 5 4 3 that it is the only suitable material available to support the qualification, and any resource lists produced by the awarding body shall include this and other British Library Cataloguing in Publication Data appropriate resources. A catalogue record for this book is available from the British Library ISBN 978 0 435 18305 9 Copyright notice All rights reserved. No part of this publication may be reproduced in any form or by any means (including photocopying or storing it in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright owner, except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, Barnard's Inn, 86 Fetter Lane, London EC4A 1EN (www.cla.co.uk). Applications for the copyright owner’s close space written permission should be addressed to the publisher. Printed by Neografia in Slovakia Dedicated to Viv Hony who started the whole project. Grateful for contributions from Jack Barraclough, Chris Baston, Ian Bettison, Sharon Bolger, Phil Boor, Ian Boote, Linnet Bruce, Andrew Edmondson, Keith Gallick, Rachel Hamar, Kath Hipkiss, Sean McCann, Diane Oliver, Harry Smith, Robert Ward-Penny and our Development Editor: Gwen Burns. F01 Mathematics A SB2 Global 83059.indd 2 11/05/18 1:24 PM CONTENTS iii COURSE STRUCTURE IV ABOUT THIS BOOK VI ASSESSMENT OBJECTIVES VIII UNIT 6 2 UNIT 7 102 UNIT 8 180 UNIT 9 264 UNIT 10 348 FACT FINDERS 436 CHALLENGES 446 EXAMINATION PRACTICE PAPERS 450 GLOSSARY 466 ANSWERS 471 EXAMINATION PRACTICE PAPER ANSWERS 537 INDEX 547 ACKNOWLEDGEMENTS 552 A01_IGMA_SB_3059_Prelims.indd 3 10/04/2017 14:49 iv COURSE STRUCTURE UNIT 6 UNIT 7 UNIT 8 NUMBER 6 2 NUMBER 7 102 NUMBER 8 180 ◼ DIRECT PROPORTION ◼ RECURRING DECIMALS ◼ C ONVERTING BETWEEN ◼ INVERSE PROPORTION ◼ ADVANCED CALCULATOR UNITS OF LENGTH ◼ FRACTIONAL INDICES PROBLEMS ◼ CONVERTING BETWEEN UNITS ◼ NEGATIVE INDICES ◼ EXAM PRACTICE 110 OF AREA ◼ EXAM PRACTICE 19 ◼ SUMMARY 111 ◼ CONVERTING BETWEEN UNITS ◼ SUMMARY 20 OF VOLUME ◼ COMPOUND MEASURES ALGEBRA 7 112 ◼ EXAM PRACTICE 193 ALGEBRA 6 21 ◼ S OLVING QUADRATIC ◼ SUMMARY 194 ◼ PROPORTION EQUATIONS BY FACTORISING ◼ INDICES ◼ S OLVING QUADRATIC ALGEBRA 8 195 ◼ EXAM PRACTICE 41 EQUATIONS BY COMPLETING ◼ SUMMARY 42 THE SQUARE ◼ FUNCTIONS ◼ S OLVING QUADRATIC ◼ DOMAIN AND RANGE EQUATIONS USING THE ◼ COMPOSITE FUNCTIONS SEQUENCES 43 QUADRATIC FORMULA ◼ INVERSE FUNCTION ◼ CONTINUING SEQUENCES ◼ PROBLEMS LEADING TO ◼ EXAM PRACTICE 214 ◼ FORMULAE FOR SEQUENCES QUADRATIC EQUATIONS ◼ SUMMARY 215 ◼ THE DIFFERENCE METHOD ◼ SOLVING QUADRATIC ◼ FINDING A FORMULA FOR A INEQUALITIES GRAPHS 7 216 SEQUENCE ◼ EXAM PRACTICE 125 ◼ ARITHMETIC SEQUENCES ◼ SUMMARY 126 ◼ USING GRAPHS TO SOLVE ◼ SUM OF AN ARITHMETIC QUADRATIC EQUATIONS SEQUENCE ◼ USING GRAPHS TO SOLVE GRAPHS 6 127 ◼ EXAM PRACTICE 64 OTHER EQUATIONS ◼ SUMMARY 65 ◼ CUBIC GRAPHS ◼ USING GRAPHS TO SOLVE ◼ RECIPROCAL GRAPHS NON-LINEAR SIMULTANEOUS ◼ EXAM PRACTICE 138 EQUATIONS SHAPE AND SPACE 6 66 ◼ SUMMARY 139 ◼ EXAM PRACTICE 226 ◼ CIRCLE THEOREMS 2 ◼ SUMMARY 227 ◼ ALTERNATE SEGMENT SHAPE AND SPACE 7 140 THEOREM SHAPE AND SPACE 8 228 ◼ INTERSECTING CHORDS ◼ CIRCLES THEOREMS ◼ SOLIDS ◼ VECTORS AND VECTOR ◼ EXAM PRACTICE 84 ◼ SIMILAR SHAPES NOTATION ◼ SUMMARY 85 ◼ EXAM PRACTICE 164 ◼ MULTIPLICATION OF A ◼ SUMMARY 165 VECTOR BY A SCALAR ◼ VECTOR GEOMETRY SETS 2 86 ◼ EXAM PRACTICE 245 SETS 3 166 ◼ THREE-SET PROBLEMS ◼ SUMMARY 246 ◼ PRACTICAL PROBLEMS ◼ PROBABILITY ◼ SHADING SETS ◼ CONDITIONAL PROBABILITY HANDLING DATA 5 247 ◼ SET-BUILDER NOTATION USING VENN DIAGRAMS ◼ EXAM PRACTICE 100 ◼ EXAM PRACTICE 178 ◼ LAWS OF PROBABILITY ◼ SUMMARY 101 ◼ SUMMARY 179 ◼ COMBINED EVENTS ◼ INDEPENDENT EVENTS AND TREE DIAGRAMS ◼ CONDITIONAL PROBABILITY ◼ EXAM PRACTICE 262 ◼ SUMMARY 263 A01_IGMA_SB_3059_Prelims.indd 4 10/04/2017 14:49 COURSE STRUCTURE v UNIT 9 UNIT 10 NUMBER 9 264 NUMBER 10 348 FACT FINDERS 436 ◼ COMPARATIVE COSTS ◼ RATIONAL AND IRRATIONAL ◼ GOTTHARD BASE TUNNEL ◼ TAXATION NUMBERS ◼ MOUNT VESUVIUS ◼ SALARIES AND INCOME TAX ◼ SURDS ◼ THE SOLAR SYSTEM ◼ FOREIGN CURRENCY ◼ EXAM PRACTICE 360 ◼ THE WORLD’S POPULATION ◼ EXAM PRACTICE 274 ◼ SUMMARY 361 ◼ THE TOUR DE FRANCE 2015 ◼ SUMMARY 275 ALGEBRA 10 362 CHALLENGES 446 ALGEBRA 9 276 ◼ SIMPLIFYING ALGEBRAIC ◼ S OLVING TWO FRACTIONS EXAMINATION SIMULTANEOUS EQUATIONS ◼ ADDING AND SUBTRACTING PRACTICE PAPERS 450 − ONE LINEAR AND ONE ALGEBRAIC FRACTIONS NON-LINEAR ◼ MULTIPLYING AND DIVIDING ◼ PROOF ALGEBRAIC FRACTIONS ◼ EXAM PRACTICE 290 ◼ SOLVING EQUATIONS WITH ◼ SUMMARY 291 ALGEBRAIC FRACTIONS ◼ EXAM PRACTICE 372 ◼ SUMMARY 373 GRAPHS 8 293 ◼ GRADIENT OF A CURVE AT GRAPHS 9 374 A POINT ◼ TRANSLATING GRAPHS ◼ THE GRADIENT OF A ◼ REFLECTING GRAPHS FUNCTION ◼ STRETCHING GRAPHS ◼ DIFFERENTIATION ◼ EXAM PRACTICE 321 ◼ STATIONARY POINTS ◼ SUMMARY 322 ◼ MOTION OF A PARTICLE IN A STRAIGHT LINE ◼ EXAM PRACTICE 393 SHAPE AND SPACE 9 323 ◼ SUMMARY 394 ◼ 3D TRIGONOMETRY ◼ EXAM PRACTICE 331 SHAPE AND SPACE 10 396 ◼ SUMMARY 332 ◼ GRAPHS OF SINE, COSINE AND TANGENT HANDLING DATA 6 333 ◼ SINE RULE ◼ DRAWING HISTOGRAMS ◼ COSINE RULE ◼ INTERPRETING HISTOGRAMS ◼ AREA OF A TRIANGLE ◼ EXAM PRACTICE 346 ◼ EXAM PRACTICE 419 ◼ SUMMARY 347 ◼ SUMMARY 420 HANDLING DATA 7 421 ◼ MORE COMPOUND PROBABILITY ◼ MORE TREE DIAGRAMS ◼ MORE CONDITIONAL PROBABILITY ◼ EXAM PRACTICE 434 ◼ SUMMARY 435 A01_IGMA_SB_3059_Prelims.indd 5 10/04/2017 14:49 vi ABOUT THIS BOOK ABOUT THIS BOOK This two-book series is written for students following the Edexcel International GCSE (9–1) Maths A Higher Tier specification. There is a Student Book for each year of the course. The course has been structured so that these two books can be used in order, both in the classroom and for independent learning. Each book contains five units of work. Each unit contains five sections in the topic areas: Number, Algebra, Sequences, Graphs, Shape and Space, Sets and Handling Data. Each unit contains concise explanations and worked examples, plus numerous exercises that will help you build up confidence. Non-starred and starred parallel exercises are provided, to bring together basic principles before being challenged with more difficult questions. These are supported by parallel revision exercises at the end of each chapter. Challenges, which provide questions applying the basic principles in unusual situations, feature at the back of the book along with Fact Finders which allow you to practise comprehension of real data. 276 ALGEBRA 9 UNIT 9 Points of Interest put the maths you are about ALGEBRA 9 to learn in a real-world context. One of the most famous theorems in mathematics is Fermat’s Last Theorem which states that xn + yn = zn has no non-zero integer solutions when n > 2. Fermat wrote in the margin of his notebook in 1637 ‘I have discovered a truly remarkable proof which this margin is too small to contain.’ Encouraged by this statement, mathematicians struggled for 358 years to prove this theorem before a proof was published in 1995 by Andrew Wiles. The proof itself is over 150 pages long and took seven years to complete. Learning Objectives Pierre de Fermat 1601–65 ▲ Andrew Wiles 1953– ▲ show what you will learn LEARNING OBJECTIVES in each lesson. ◼ Solve simultaneous equations with one equation being quadratic ◼ Prove a result using algebra ◼ Solve simultaneous equations with one equation being a circle BASIC PRINCIPLES ◼ Solve quadratic equations (using factorisation or the quadratic formula). ◼ Solve simultaneous equations (by substitution, elimination or graphically). ◼ Expand brackets. Basic Principles outline ◼ Expand the product of two linear expressions. assumed knowledge ◼ Form and simplify expressions. and key concepts from ◼ Factorise expressions. the beginning. ◼ Complete the square for a quadratic expression. Activities are a gentle way of introducing a SOLVING TWO SIMULTANEOUS EQUATIONS − ONE LINEAR AND ONE NON-LINEAR topic. ACTIVITY 1 ANSAKLYILSLISS Uexq s+ue a2 ttyhio e=n gs1r0a pahn dto x s2o +lv ye2 t=h e2 5simultaneous x2 + y2 = 25 64y 3y = 18 – x 2 Transferable Skills are W3yh =a t4 isx t−h e2 5c oannnde tchteio cni rbcelet wxe2 e+n y t2h =e 2lin5e? –10 –5 0 5 10 x highlighted to show Are there any real solutions to the –2 x + 2y = 10 what skill you are using simultaneous equations –4 3y = 18 − x and x2 + y2 = 25? 3y = 4x – 25 and where. –6 A01_IGMA_SB_3059_Prelims.indd 6 10/04/2017 14:49 ABOUT THIS BOOK vii Key Points boxes 278 ALGEBRA 9 UNIT 9 Language is graded for summarise the speakers of English as essentials. KEY POINTS ◼ If the two equations are of the form y = f(x) and y = g(x): an additional language ◼ Solve the equation f(x) = g(x) to find x. (EAL), with advanced ◼ When x has been found, fi nd y using the easier of the original equations. ◼ Write out your solutions in the correct pairs. Maths-specific terminology highlighted and defined in the Questions have been EXERCISE 1 S1o ▶lv e thye s=i mx u+l t6a,n ye o=u sx 2e quation s. 5 ▶ y = x + 1, y = x2 − 2x + 3 glossary at the back given a Pearson step 10th 2 ▶ y = 2x + 3, y = x2 6 ▶ y = x − 1, y = x2 + 2x − 7 of the book. from 1 to 12. This tells 11th 3 ▶ y = 3x + 4, y = x2 7 ▶ y = x + 1, y = _2x_ you how difficult the 4 ▶ y = 2x + 8, y = x2 8 ▶ y = 1 + _2x_ , y = x question is. The higher tchhea lsletenpg,i nthge t hmeo qreu estion. EXERCISE 11*0th S21o ▶▶lv e thyye s==i m23xxu l−+ta 11n,,e yyo u==s xxe22q +−u a4xtx i+o − n2 s6 , giving your an56s w▶▶e rs cyyo r==r ex1c ++t 2 _2xt_o, , yy3 ==s . _8x _f x3_._ 2 w here appropriate. Nwoonrk- sttoawrraerdd se xgerracdiseess 12th 3 ▶ y = 4x + 2, y = x2 + x − 5 7 ▶ y = 3 √ _x_ , y = x + 1 1–6 on the 9–1 scale. 4 ▶ y = 1 − 3x, y = x2 − 7x + 3 8 ▶ y = 1 + _1 x_5 4_ , y = _ x8_ 2 Example 2 shows how to solve algebraically the pair of simultaneous equations from Activity 1. EXAMPLE 2 Solve the simultaneous equations x + 2y = 10 and x2 + y2 = 25 Starred exercises work SKILLS x + 2y = 10 (1) towards grades 6–9 on ANALYSIS x2 + y2 = 25 (2) the 9–1 scale. Examples provide a Make x the subject of equation (1) (the linear equation): clear, instructional x = 10 − 2y (3) framework. Substitute (3) into (2) (the non-linear equation): (10 − 2y)2 + y2 = 25 (Expand brackets) 100 − 40y + 4y2 + y2 = 25 (Simplify) 5y2 − 40y + 75 = 0 (Divide both sides by 5) More difficult questions y2 − 8y + 15 = 0 (Solve by factorising) appear at the end of (y − 3)(y − 5) = 0 some exercises and are identified by green question numbers. Exam Practice tests 290 EXAM PRACTICE UNIT 9 UNIT 9 CHAPTER SUMMARY 291 cover the whole chapter EXAM PRACTICE: ALGEBRA 9 CHAPTER SaUnMd pMroAvRidYe: AquLiGckE,B RA 9 effective feedback on your progress. 8th 1 Solve these simultaneous equations, giving your answers to 3 s.f. SOLVING TWO SIMULTANEOUS EQUATIONS − ONE LINEAR AND ONE NON-LINEAR y = x2 − 4x + 3 and y = 2x − 3 [4] Graphically this corresponds to the intersection of a line and a curve. 11th Always substitute the linear equation into the non-linear equation. 2 Solve these simultaneous equations: 2x − y = 4 and x2 + y2 = 16 [4] Solve the simultaneous equations yy == xx22 ++ 22, y = 3x (1) y = 3x (2) 3 Give a counter-example to show that (x + 4)2 = x2 + 16 is false. [2] S ubstitu ting (2) i nto (1): Cha p x2 +t e2 =r 3 xS u mm(Raearrriaengse) 290 EXAM PRACTICE UNIT 9 UNIT 9 CHAPTER SUMMARY 291 x2 − 3x + 2 = 0 (Factorise) EXAM PRACTICE: ALGEBRA 9 4 Prove that if tChe dHiff eArenPce Tof tEwoR nu mSberUs isM 4, thMe diffA ereRnceY o:f thAeir LsquGareEs isB a RmulAtiple 9of 8. [2] Substituting into (2) gives sptheto saoiltnutei(xoxt n = s−s t 1 1 ah )oso(x re( 12−f, 32me)) o=ar 0o(2c, s6h).t cimhappotretar.nt 5 Prove that the product of two consecutive odd numbers is odd. [4] y = x 2 + 2 6y y = 3x 8th 1 Solve these simultaneous equations, giving your answers to 3 s.f. 6 a Prove that SxO2 L−V 1IN0xG +T W25O ≥ S 0IM foUrL aTlAl vNaEluOeUsS o Ef QxU. ATIONS − ONE LINEAR AND ONE NON-LINEAR [4] 45 11th 2 yS o=lv xe2 t−h e4sxe + s i3m aunltda nye =o u2sx e−q u3a ti ons: 2x − y = 4 and x2 + y2 = 16 [[44]] c b SFiknedt cthh et hmeGAS inglorwiramlavpapeuyhh msitc h y saep ul= losyb iix nsmt2htt i uti−osul ft t1 acet0noh txeerhr o e+egus rl2spain 5poee hnqa dury sa e =tqtio oux nat2h st−i eo yy 1ni n==0 ti xnexx tr22+os ++ e2t ch522te , i o ynn o= on f3- lxain leinaer ea(1qn)uda ati ocnu.rve. [Total 25 mark[[32s]]] –2 –1 1230 1 2 x 34 GPrioveve a t choaut nift tehr-ee dxiaff merpelne cteo osfh otwwo t hnautm (xb e+r s4 )is2 =4 ,x t2h +e 1d6iff iesr efanlcsee .o f their squares is a multiple of 8. [[22]] S Suubbssttiittuu ttiinngg i(n2t)o i n(2to) g(1iv):es the solu t i xx(xyox22 n = =−+−s 1 3123a x)o xs(= x r (+ 123− ,x2 32 =)) o=0 r 0(2, 6).(((2RFa)ecatrorarinsgee)) STMySh uo=aeblkv xseeli tn +iyttehu 1ateth er ⇒ se e(i 3qm sy)uu u2iab nl=ttjtaeio o(ncx n(et 1 +oio)s: uf1 eseEI)2q q en⇒uuqaau tyttiaXio2ot enin=o (n(x22rs2))T. : xxx+a22 − 2++ xcy Ryy ++22 t 1==1 i 11=v33A 0, xe (( 12−)) yp +R 1r (=3a )0EctSicOe aUctRiviCtieEs San d teacher support are 56 Pac b r oPSFvirkneoe dvtth cetah htt eht t hamhtee ixng p2ir mra−op ud1hmu0 ycx p t =+ oo ixf2n 25tt w −o≥o f 1 0tc0h ofxeon +rgs are2alcl5p uv hta ivylu e e= os x do2d f− xn 1.u 0mxb +e r2s5 i s odd. [Total 25 mark[[[[4324s]]]]] y = x 2 + 2–2 –1 123456y0 1 2y = 3xx Subsxt i2t u+ tyin 2 g= i1n3to (23y) givpSTes etreheoa srovvcl u t x(xx2iixioh22 xd = cn+2++ s −+ 3e xxa3 ee) 22(s − xox+ r ( r6 .d−−− 2 2’3 = x21s, )T2 0+ −= 2o=1 0) h 0R=o n r1 i(32sel, 3i((FD )sn.aiivcinotdeoer icsbu eya) l2r)uscd epe aPsra tdc ookfw fPonerlo aSartsduoadnbe’lsne t A mBcatoitvoeekrLisae l1sa rainnn Ddth i2ge:i tal Solve the simultaneous equations xx22 ++ yy22 == 1133 , x( 1−) y + 1 = 0 21x –• y + 11 = 050 lesson plans The linear equation is equation (2).x − y + 1 = 0 (2) –4 –2 –1O • 210x0 prior knowledge presentations and worksheets Make y the subject of equation (2): –2 yS u=b xs t+itu 1 t e⇒ (3 y) 2i n=t o(x ( 1+): 1)2 ⇒ y2 = x 2 x+2 2+x x +2 +1 2x + 1 = 13(3) ––34 • 90 starter activities, presentations and worksheets 2x2 + 2x − 12 = 0 (Divide by 2) • 200 videos and animations x2 + x − 6 = 0 (Factorise) (x + 3)(x − 2) = 0 x = −3 or 2 • Pearson progression self-assessment charts. Substituting into (2) gives the solutions as (−3, −2) or (2, 3). x 2 + y 2 = 13 3y 2 1x – y + 1 = 0 –4 –2 –1O 2 x –2 –3 –4 F01 Mathematics A SB2 Global 83059.indd 7 11/05/18 1:24 PM viii ASSESSMENT OBJECTIVES ASSESSMENT OBJECTIVES The following tables give an overview of the assessment for this course. We recommend that you study this information closely to help ensure that you are fully prepared for this course and know exactly what to expect in the assessment. PAPER 1 PERCENTAGE MARK TIME AVAILABILITY HIGHER TIER MATHS A 50% 100 2 hours January and June examination series Written examination paper First assessment June 2018 Paper code 4MA1/3H Externally set and assessed by Edexcel PAPER 2 PERCENTAGE MARK TIME AVAILABILITY HIGHER TIER MATHS A 50% 100 2 hours January and June examination series Written examination paper First assessment June 2018 Paper code 4MA1/4H Externally set and assessed by Edexcel ASSESSMENT OBJECTIVES AND WEIGHTINGS ASSESSMENT OBJECTIVE DESCRIPTION % IN INTERNATIONAL GCSE AO1 Demonstrate knowledge, understanding and skills in number 57–63% and algebra: • numbers and the numbering system • calculations • solving numerical problems • equations, formulae and identities • sequences, functions and graphs AO2 Demonstrate knowledge, understanding and skills in shape, 22–28% space and measures: • geometry and trigonometry • vectors and transformation geometry AO3 Demonstrate knowledge, understanding and skills in handling 12–18% data: • statistics • probability A01_IGMA_SB_3059_Prelims.indd 8 10/04/2017 14:49 ASSESSMENT OBJECTIVES ix ASSESSMENT SUMMARY The Edexcel International GCSE (9–1) in Mathematics (Specification A) Higher Tier requires students to demonstrate application and understanding of the following topics. NUMBER STATISTICS • Use numerical skills in a purely mathematical way and • Understand basic ideas of statistical averages. in real-life situations. • Use a range of statistical techniques. • Use basic ideas of probability. ALGEBRA • Use letters as equivalent to numbers and as variables. Students should also be able to demonstrate problem- • Understand the distinction between expressions, solving skills by translating problems in mathematical or equations and formulae. non-mathematical contexts into a process or a series of • Use algebra to set up and solve problems. mathematical processes. • Demonstrate manipulative skills. • Construct and use graphs. Students should be able to demonstrate reasoning skills by GEOMETRY • making deductions and drawing conclusions from • Use the properties of angles. mathematical information • Understand a range of transformations. • constructing chains of reasoning • Work within the metric system. • presenting arguments and proofs • Understand ideas of space and shape. • interpreting and communicating information accurately. • Use ruler, compasses and protractor appropriately. CALCULATORS Students will be expected to have access to a suitable electronic calculator for both examination papers. The electronic calculator to be used by students attempting Higher Tier examination papers (3H and 4H) should have these functions as a minimum: +,−,×,÷,x2, x, memory, brackets, x y, x y1, x, ∑x, ∑fx, standard form, sine, cosine, tangent and their inverses. PROHIBITIONS Calculators with any of the following facilities are prohibited in all examinations: • databanks • retrieval of text or formulae • QWERTY keyboards • built-in symbolic algebra manipulations • symbolic differentiation or integration. A01_IGMA_SB_3059_Prelims.indd 9 10/04/2017 14:49