CAPE® Pure Mathematics Syllabus, Specimen Papers, Mark ...

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Mathematics

MtMiacastthPhueemrme SYLLABUS SPECIMEN PAPER MARK SCHEME SUBJECT REPORTS

Macmillan Education 4 Crinan Street, London, N1 9XW A division of Macmillan Publishers Limited Companies and representatives throughout the world

macmillan-

ISBN 978-0-230-48247-0

? Caribbean Examinations Council (CXC?) 2015 cxc-

The author has asserted their right to be identified as the author of this work in accordance with the Copyright, Design and Patents Act 1988.

First published 2014 This revised version published 2015

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Designed by Macmillan Publishers Limited Cover design by Macmillan Publishers Limited and Red Giraffe

CAPE? Pure Mathematics Free Resources

LIST OF CONTENTS

CAPE? Pure Mathematics Syllabus Extract

3

CAPE? Pure Mathematics Syllabus

4

CAPE? Pure Mathematics Specimen Papers:

Unit 1 Paper 01

68

Unit 1 Paper 02

76

Unit 1 Paper 032

82

Unit 2 Paper 01

86

Unit 2 Paper 02

94

Unit 2 Paper 032

99

CAPE? Pure Mathematics Mark Schemes:

Unit 1 Paper 01

103

Unit 1 Paper 02

105

Unit 1 Paper 032

118

Unit 2 Paper 01

123

Unit 2 Paper 02

125

Unit 2 Paper 032

138

CAPE? Pure Mathematics Subject Reports:

2004 Subject Report

143

2005 Subject Report

181

2006 Subject Report

213

2007 Subject Report

243

2008 Subject Report Trinidad and Tobago

275

2008 Subject Report Rest of Caribbean

294

2009 Subject Report

313

2010 Subject Report

332

2011 Subject Report

355

2012 Subject Report

379

2013 Subject Report

402

2014 Subject Report

422

Pure Mathematics

Mathematics is one of the oldest and most universal means of creating, communicating, connecting and applying structural and quantitative ideas. Students doing this syllabus will have already been exposed to Mathematics in some form mainly through courses that emphasise skills in using mathematics as a tool, rather than giving insight into the underlying concepts.

This syllabus will not only provide students with more advanced mathematical ideas, skills and techniques, but encourage them to understand the concepts involved, why and how they "work" and how they are interconnected. It is also to be hoped that, in this way, students will lose the fear associated with having to learn a multiplicity of seemingly unconnected facts, procedures and formulae. In addition, the course should show them that mathematical concepts lend themselves to generalisations, and that there is enormous scope for applications to solving real problems. The course is therefore intended to provide quality in selected areas rather than in a large number of topics.

The syllabus is arranged into two (2) Units, each Unit consists of three Modules.

Unit 1: Algebra, Geometry and Calculus

Module 1 ? Module 2 ? Module 3 ?

Basic Algebra and Functions Trigonometry, Geometry and Vectors Calculus I

Unit 2: Complex Numbers, Analysis and Matrices

Module 1 ? Module 2 ? Module 3 ?

Complex Numbers and Calculus II Sequences, Series and Approximations Counting, Matrices and Differential Equations

CARIBBEAN EXAMINATIONS COUNCIL

Caribbean Advanced Proficiency Examination?

CAPE?

PURE MATHEMATICS

Effective for examinations from May?June 2013

CXC A6/U2/12

Published by the Caribbean Examinations Council ? 2012, Caribbean Examinations Council All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means electronic, photocopying, recording or otherwise without prior permission of the author or publisher.

Correspondence related to the syllabus should be addressed to: The Pro-Registrar Caribbean Examinations Council Caenwood Centre 37 Arnold Road, Kingston 5, Jamaica Telephone Number:+1(876) 630-5200 Facsimile Number: +1(876) 967-4972 E-mail Address: cxcwzo@ Website: Copyright ? 2012 by Caribbean Examinations Council The Garrison, St Michael BB14038, Barbados

CXC A6/U2/12

This document CXC A6/U2/12 replaces CXC A6/U2/07 issued in 2007. Please note that the syllabus has been amended and amendments are indicated by italics.

First issued 1999 Revised 2004 Revised 2007 Amended 2012

Please check the website for updates on CXC's syllabuses.

CXC A6/U2/12

Contents

ContentsIntroduction

INTRODUCTION .................................................................................................................... i RATIONALE ........................................................................................................................... 1 AIMS ...................................................................................................................................... 2 SKILLS AND ABILITIES TO BE ASSESSED ................................................................................. 3 PRE-REQUISITES OF THE SYLLABUS....................................................................................... 3 STRUCTURE OF THE SYLLABUS.............................................................................................. 3 RECOMMENDED 2-UNIT OPTIONS........................................................................................ 4 MATHEMATICAL MODELLING ............................................................................................... 4 UNIT 1: ALGEBRA, GEOMETRY AND CALCULUS

MODULE 1 : BASIC ALGEBRA AND FUNCTIONS ............................................................ 7 MODULE 2 : TRIGONOMETRY, GEOMETRY AND VECTORS........................................... 16 MODULE 3 : CALCULUS I ............................................................................................... 21 UNIT 2: COMPLEX NUMBERS, ANALYSIS AND MATRICES MODULE 1 : COMPLEX NUMBERS AND CALCULUS II.................................................... 27 MODULE 2 : SEQUENCES, SERIES AND APPROXIMATIONS........................................... 33 MODULE 3 : COUNTING, MATRICES AND DIFFERENTIAL EQUATIONS ......................... 40 OUTLINE OF ASSESSMENT .................................................................................................... 46 REGULATIONS FOR PRIVATE CANDIDATES ........................................................................... 54 REGULATIONS FOR RE-SIT CANDIDATES ............................................................................... 54 ASSESSMENT GRID ................................................................................................................ 55 MATHEMATICAL NOTATION ................................................................................................. 56

CXC A6/U2/12

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