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LOGO 2

CAPE
PURE MATHEMATICS Unit 1
Study Guide

An easy and convenient way to prepare for your CAPE Pure Mathematics Unit 1 examinations.

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The syllabus aims to:

  1. provide understanding of mathematical concepts and structures, their development and the relationships between them;

  2. enable the development of skills in the use of mathematical tools; make Mathematics fun, interesting, and recognizable;

  3. develop an appreciation of the idea of mathematical proof, the internal logical coherence of Mathematics, and its consequent universal applicability;

  4. develop the ability to make connections between distinct concepts in Mathematics, and between mathematical ideas and those pertaining to other disciplines;

  5. develop skills such as, critical and creative thinking, problem solving, logical reasoning, modelling, collaboration, decision making, research, information communication and technological competences which are integral to everyday life and for life-long learning;

  6. develop positive intrinsic mathematical values, such as, accuracy and rigour;

  7. develop the skills of recognising essential aspects of concrete, real-world problems, formulating these problems into relevant and solvable mathematical problems and mathematical modelling;

  8. integrate Information and Communications Technology (ICT) tools and skills in the teaching and learning processes; and,

  9. prepare students for advanced courses in Mathematics and related areas.

This book seeks to provide valuable resources to all students who are preparing for the CAPE Pure Mathematics Unit 1 examination or for students looking to brush up on their higher level Math skills. This book represents the culmination of years of notes and worksheets which I wrote and compiled from various sources (mainly Cambridge and CXC) over the years. 

All of my students have benefited from these resources, which include several video lessons prepared by me. Some have even informed me that this book has been a tremendous asset in their early years at university. I personally thank all of the students who have assisted me with the preparation of this book by recommending changes and highlighting errors.

I pray that you too find this book and all associated resources helpful as you LEARN, PRACTISE and MASTER the content.

Table of Contents

  • Inequalities

    Surds

    Indices

    Disguised Quadratics

    Introduction to Functions

    Injections

    Surjections

    Bijections

    Inverse Functions

    Piece-Wise Functions

    Polynomial Division

    Factor and Remainder Theorem

    Special Factoring Results

    Cubic Polynomials

    Introduction to Logarithms

    Properties of Logarithms

    Logarithmic Equations

    Exponential Functions

    Equations Involving the Exponential Function

    Mathematical Modelling

    Determining an Unknown Index

    Modulus Equations

    Modulus Inequalities

    Modulus Graphs

    Sequences

    Introduction to Series

    Mathematical Induction

    Cayley Tables

    Closure

    Commutavity

    Associativity

    Identity and Inverse

    Direct Proofs

    Proofs by Contradiction

    Implications

    Truth Tables

    Converse, Inverse and Contrapositive

    Logical Equivalence

    Laws of Boolean Algebra

  • Introduction to Vectors

    Dot Product and Angle Between Vectors

    Vector Equation of a Line

    Vector Equation of a Plane

    Introduction to Equation of a Circle

    Tangents and Normals

    Points of Intersection

    Circles Given 3 Points

    Locus of a Point

    Trigonometric Identities

    Graphs of Trigonometric Functions

    General Solutions

    Trigonometric Equations

    Harmonic Form

    Compound Angle Formulae

    Double Angle Formulae

    Factor Formulae

    Parametric Equations

  • Introduction to Limits

    Limits by Direct Substitution

    Limits as x Tends to Infinity

    Limits as x Tends to Zero (1)

    Limits as x Tends to Zero (2)

    Limits and PieceWise Functions

    Limits and Continuity

    First Principles

    Introduction to Differentiation

    Chain Rule

    Product Rule

    Quotient Rule

    Second Derivatives

    Parametric Differentiation

    Gradients and Differentiation

    Stationary Points

    Optimisation

    Curve Sketching

    Rate of Change

    Introduction to Integration

    Trigonometric Integration

    Differential Equations

    Integration By Substitution

    Definite Integrals

    Equation of a Curve

    Area Under a Curve

    Sum of Rectangles

    Area Below the x-Axis

    Area Bounded by the y-axis

    Volumes of Revolution

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