Table of Contents

About This Book
The Non-Calculator Paper
Algebra
Sequences and Series
Sequences and Series – Applications
Exponents and Logarithms
Permutations and Combinations
Binomial Expansion
Proof by Induction
Complex Numbers
The Complex Plane
De Moivre's Theorem
Systems of Equations
Functions and Equations
Basics of Functions
Graphs of Functions
Reciprocal Functions
Quadratic Functions
Solving Quadratic Equations
Sum and Product of Roots
Inequalities
Polynomial Functions
Exponential and Logarithmic Functions
Circular Functions and Trigonometry
Definitions and Formulae
Trigonometric Formulae
Solving Trigonometric Equations
The Solution of Triangles
Graphing Periodic Functions
Vectors
Basics of Vectors
Scalar (Dot) Product
Vector (Cross) Product
Equations of Lines
Equations of Planes
Equations of Lines and Planes – Summary
Intersections
Angles in Three Dimensions
Miscellaneous Vector Questions
Statistics and Probability
Statistics
Probability Notation and Formulae
Lists and Tables of Outcomes
Venn Diagrams
Tree Diagrams
Bayes’ Theorem
Discrete Probability Distributions
Binomial Distribution
Poisson Distribution
Continuous Distributions
The Normal Distribution
Calculus
Differentiation – The Basics
Differentiation from First Principles
The Chain Rule
Product and Quotient Rules
Second Derivative
Applications of Differentiation
Implicit Differentiation
Graphical behaviour of functions
Sketching Graphs – Examples
Indefinite Integration
Definite Integration
Integration by Substitution
Integration by Parts
General Methods for Integration
Further Kinematics
Volumes of Revolution
Calculus – Non-Calculator Techniques
Maximising Your Marks
Assessment Details
Practice Questions
Answers to Practice Questions

About the Author

Ian Lucas has been teaching mathematics at all levels for over 40 years, more than half of which were spent at Sevenoaks School, UK. His particular emphasis has been on preparing students for exams. He has taught IB maths since 1981 and has been teaching study and revision courses around the world since 2000. He wrote some of the very first OSC Publishing Study & Revision Guides and was instrumental in the launch of the Guides series.