# Book Information

## Series:

Mathematics for the International Student (IB Diploma)

## Title:

Mathematics HL Core EXAM PREPARATION & PRACTICE GUIDE (2nd edition)

## Price:

Australia: AU\$29.15 (inc. GST)
Overseas: AU\$26.50 (ex. GST)

David Martin
Paul Urban
Robert Haese
Sandra Haese
Michael Haese
Mark Humphries

2009

## ISBN-13:

978-1-921500-12-1

136 pages

Available now

## Sample chapters for download

To view the sample chapters you must have Adobe Reader installed.

## About the book

This aim of this Guide is to help students prepare for the Mathematics HL final examinations. The Guide has three distinct sections:

• the first part covers all seven topics in the course. Each topic begins with a succinct summary of important concepts followed by a set of ‘skill builder’ questions. The number of ‘skill builder’ questions has been increased in this second edition.
• the second part comprises fifteen ‘exam practice’ sets, with about 26 questions in each. In this second edition, each exam practice set is categorised as ‘calculator’ or ‘no calculator’ in response to the introduction of a calculator-free examination paper.
• the third part provides the fully worked solutions to all the skill builder questions and examination practice sets, altogether a total of almost 700 questions.

Good examination techniques come from good examination preparation and practice – and we hope this Guide will help you succeed.

## Table of contents

 Mathematics HL CoreExam Preparation & Practice Guide (2nd edition) Page No. of additional questions 1 ALGEBRA 5 Sequences and series 5 Exponentials and logarithms 5 Complex numbers 5 Counting and the binomial theorem 5 Mathematical induction 6 Skill builder questions 6 79 2 FUNCTIONS AND EQUATIONS 8 Functions f : x → f(x) or y = f(x) 8 Graphs of functions 9 Quadratic functions 9 Quadratic equations 9 Inequalities in one variable 9 Real polynomials 9 Exponential and logarithmic functions 10 Skill builder questions 10 54 3 CIRCULAR FUNCTIONS AND TRIGONOMETRY 11 The general sine function 12 Other trigonometric functions 12 Trigonometric identities 12 Trigonometric equations 12 Skill builder questions 12 42 4 MATRICES 13 Skill builder questions 14 26 5 VECTORS 15 Lines 15 Planes 16 Intersection of planes 16 Skill builder questions 16 24 6 STATISTICS AND PROBABILITY 17 Descriptive statistics 17 Probability 18 Discrete random variables 18 Continuous random variables 19 Skill builder questions 19 23 7 CALCULUS 20 Limits 20 Differentiation 21 Implicit differentiation 21 Properties of curves 21 Kinematic problems 21 Optimisation problems 21 Integration 21 Solids of revolution 22 Differential equations 22 Skill builder questions 22 39 EXAMINATION PRACTICE SETS 23 Exam Practice Set 1 No calculators 23 26 Exam Practice Set 2 Calculators 24 26 Exam Practice Set 3 No calculators 26 26 Exam Practice Set 4 Calculators 27 26 Exam Practice Set 5 No calculators 29 26 Exam Practice Set 6 Calculators 30 26 Exam Practice Set 7 No calculators 31 26 Exam Practice Set 8 Calculators 32 26 Exam Practice Set 9 No calculators 33 26 Exam Practice Set 10 Calculators 34 26 Exam Practice Set 11 No calculators 35 26 Exam Practice Set 12 Calculators 36 26 Exam Practice Set 13 No calculators 38 26 Exam Practice Set 14 Calculators 38 26 Exam Practice Set 15 Calculators 40 26 Total: 677 SOLUTIONS 42 Solutions to Topic 1 (Algebra) 42 Solutions to Topic 2 (Functions and equations) 51 Solutions to Topic 3 (Circular functions and trigonometry) 57 Solutions to Topic 4 (Matrices) 61 Solutions to Topic 5 (Vectors) 64 Solutions to Topic 6 (Statistics and probability) 67 Solutions to Topic 7 (Calculus) 71 Solutions to Examination Practice Set 1 76 Solutions to Examination Practice Set 2 80 Solutions to Examination Practice Set 3 83 Solutions to Examination Practice Set 4 87 Solutions to Examination Practice Set 5 92 Solutions to Examination Practice Set 6 97 Solutions to Examination Practice Set 7 100 Solutions to Examination Practice Set 8 104 Solutions to Examination Practice Set 9 109 Solutions to Examination Practice Set 10 113 Solutions to Examination Practice Set 11 117 Solutions to Examination Practice Set 12 121 Solutions to Examination Practice Set 13 125 Solutions to Examination Practice Set 14 129 Solutions to Examination Practice Set 15 133