CAPE® Applied Mathematics Syllabus, Specimen Papers, Mark Schemes and Subject Reports

353 Pages·2014·5.83 MB·English

by  Caribbean Examinations Council

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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

www.macmillan-caribbean.com

ISBN 978-0-230-48281-4
© Caribbean Examinations Council (CXC®) 2015
www.cxc.org
www.cxc-store.com

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 edition published 2015

Permission to copy
The material in this book is copyright. However, the publisher grants permission for copies to be
made without fee. Individuals may make copies for their own use or for use by classes of which they
are in charge; institutions may make copies for use within and by the staff and students of that
institution. For copying in any other circumstances, prior permission in writing must be obtained
from Macmillan Publishers Limited. Under no circumstances may the material in this book be used,
in part or in its entirety, for commercial gain. It must not be sold in any format.

Designed by Macmillan Publishers Limited
Cover design by Macmillan Publishers Limited and Red Giraffe
CAPE® APPLIED MATHEMATICS FREE RESOURCES
LIST OF CONTENTS
CAPE® Applied Mathematics Syllabus Extract 3

CAPE® Applied Mathematics Syllabus 4

CAPE® Applied Mathematics Specimen Papers:
Unit 1 Paper 03/2 79
Unit 2 Paper 01 83

CAPE® Applied Mathematics Mark Schemes:
Unit 1 Paper 01 93
Unit 1 Paper 02 95
Unit 1 Paper 03/2 109
Unit 2 Paper 01 115
Unit 2 Paper 02 116
Unit 2 Paper 03/2 130

CAPE® Applied Mathematics Subject Reports:
2005 Subject Report 136
2006 Subject Report 146
2007 Subject Report 167
2008 Subject Report: Trinidad and Tobago 184
2008 Subject Report: Rest of Caribbean 196
2009 Subject Report 212
2010 Subject Report 228
2011 Subject Report 242
2012 Subject Report 261
2013 Subject Report 287
2014 Subject Report 305
2015 Subject Report 330
Applied Mathematics
The main emphasis of the applied course is on developing the ability of the students
to start with a problem in non-mathematical form and transform it into mathematical
language. This will enable them to bring mathematical insights and skills in devising a
solution, and then interpreting this solution in real-world terms.
Students accomplish this by exploring problems using symbolic, graphical, numerical,
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Furthermore, students engage in mathematical thinking and modelling to examine and
solve problems arising from a wide variety of disciplines including, but not limited to,
economics, medicine, agriculture, marine science, law, transportation, engineering,
banking, natural sciences, social sciences and computing.
The syllabus is divided into two (2) Units. Each Unit comprises three (3) Modules.
Unit 1: Statistical Analysis
• Module 1 Collecting and Describing Data
• Module 2 Managing Uncertainty
• Module 3 Analysing and Interpreting Data
Unit 2: Mathematical Applications

• Module 1 Discrete Mathematics
• Module 2 Probability and Distributions
• Module 3 Particle Mechanics
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(cid:3)(cid:2)(cid:5)(cid:4)(cid:35)
APPLIED MATHEMATICS
SYLLABUS
Effective for examinations from May/June 2008
Including amendments up to 2008
(cid:51)(cid:88)(cid:69)(cid:79)(cid:76)(cid:86)(cid:75)(cid:72)(cid:71)(cid:3)(cid:69)(cid:92)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:38)(cid:68)(cid:85)(cid:76)(cid:69)(cid:69)(cid:72)(cid:68)(cid:81)(cid:3)(cid:40)(cid:91)(cid:68)(cid:80)(cid:76)(cid:81)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:86)(cid:3)(cid:38)(cid:82)(cid:88)(cid:81)(cid:70)(cid:76)(cid:79)
© 2010, 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, W.I.
Telephone: [phone]
Facsimile Number: [phone]
E-mail address: [email protected]
Website: www.cxc.org
Copyright © 2007, by Caribbean Examinations Council
The Garrison, St Michael BB14038, Barbados
CXC A9/U2/07
Content
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RATIONALE.........................................................................................................................................1
AIMS......................................................................................................................................................1
SKILLS AND ABILITIES TO BE ASSESSED.........................................................................................2
PRE-REQUISITES OF THE SYLLABUS ...............................................................................................4
STRUCTURE OF THE SYLLABUS.......................................................................................................4
RECOMMENDED 2-UNIT OPTIONS..................................................................................................4
UNIT 1: STATISTICAL ANALYSIS
MODULE 1: Collecting and Describing Data.............................................................................5
MODULE 2: Managing Uncertainty..........................................................................................9
MODULE 3: Analyzing and Interpreting Data...........................................................................17
UNIT 2: MATHEMATICAL APPLICATIONS
MODULE 1: Discrete Mathematics............................................................................................25
MODULE 2: Probability and Distributions................................................................................31
MODULE 3: Particle Mechanics................................................................................................36
OUTLINE OF ASSESSMENT................................................................................................................53
REGULATIONS FOR PRIVATE CANDIDATES..................................................................................68
REGULATIONS FOR RE-SIT CANDIDATES………………………………………………………….....................68
ASSESSMENT GRID .............................................................................................................................68
APPLIED MATHEMATICAL NOTATION...........................................................................................69
MISCELLANEOUS SYMBOLS..............................................................................................................70
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CXC A7/U1/07
The Statistical Analysis and Applied Mathematics Syllabuses were merged to
create a new 2-Unit syllabus for Applied Mathematics.
This document CXC A9/U2/07, therefore, replaces CXC A7/U1/04 and CXC
A9/U1/04 issued in 2004.
Please note that the syllabuses have been revised and amendments are indicated
by italics.
First Issued 1999
Revised 2004, 2007
Please check the website, www.cxc.org for updates on CXC’s syllabuses
CXC A9/U2/07
Introduction

T
he Caribbean Advanced Proficiency Examination (CAPE) is designed to provide certification of the
academic, vocational and technical achievement of students in the Caribbean who, having completed
a minimum of five years of secondary education, wish to further their studies. The examinations address
the skills and knowledge acquired by students under a flexible and articulated system where subjects are
organised in 1-Unit or 2-Unit courses with each Unit containing three Modules. Subjects examined under
CAPE may be studied concurrently or singly.
The Caribbean Examinations Council offers three types of certification. The first is the award of a certificate
showing each CAPE Unit completed. The second is the CAPE diploma, awarded to candidates who have
satisfactorily completed at least six Units, including Caribbean Studies. The third is the CAPE Associate Degree,
awarded for the satisfactory completion of a prescribed cluster of seven CAPE Units including Caribbean Studies
and Communication Studies. For the CAPE diploma and the CAPE Associate Degree, candidates must complete
the cluster of required Units within a maximum period of five years.
Recognized educational institutions presenting candidates for CAPE Associate Degree in one of the nine categories
must, on registering these candidates at the start of the qualifying year, have them confirm in the required form, the
Associate Degree they wish to be awarded. Candidates will not be awarded any possible alternatives for which they
did not apply.
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CXC A7/U1/07
CXC A9/U2/07