Contents

1. Introduction

2. I. Complex Numbers: Working with complex numbers

   1. Unit 1: Revise the basic operations with complex numbers in standard form

   2. Unit 2: Revise the polar form of complex numbers

   3. Unit 3: Revise the multiplication and division of complex numbers in polar form

   4. Unit 4: Raise complex numbers to exponents using De Moivre’s Theorem

3. II. Complex Numbers: Solve problems with complex numbers

   1. Unit 1: Solve complex number problems

4. III. Functions and algebra: Work with algebraic expressions using the remainder and the factor theorems

   1. Unit 1: Use the remainder and factor theorem to factorise third degree polynomials

5. IV. Functions and algebra: Use a variety of techniques to sketch and interpret information for graphs of the inverse of a function

   1. Unit 1: Determine and sketch the inverse of a linear function

   2. Unit 2: Determine and sketch the inverse of a quadratic function

   3. Unit 3: Determine and sketch the inverse of the exponential function

6. V. Functions and algebra: Use mathematical models to investigate linear programming problems

   1. Unit 1: Solve linear programming problems by optimising a function

7. VI. Functions and algebra: Investigate and use instantaneous rate of change of a variable when interpreting models both in mathematical and real life situations

   1. Unit 1: Use first principles to find the derivative

   2. Unit 2: Work with rules for differentiation

   3. Unit 3: Find the equation of a tangent to a curve

   4. Unit 4: Derivatives as rates of change

   5. Unit 5: Sketch cubic functions

8. VII. Functions and algebra: Analyse and represent mathematical and contextual situations using integrals and find areas under curves by using integration rules

   1. Unit 1: Introduction to integration

   2. Unit 2: Rules for integration

   3. Unit 3: Determine the area under a curve

9. VIII. Space, shape and measurement: Use the Cartesian co-ordinate system to derive and apply equations

   1. Unit 1: Determine the equation of a circle with any centre

   2. Unit 2: Find the equation of a tangent to a circle

10. IX. Space, shape and measurement: Explore, interpret and justify geometric relationships

    1. Unit 1: Finding angles of straight lines and triangles

    2. Unit 2: Circle geometry theorems

    3. Unit 3: Properties of cyclic quadrilaterals

    4. Unit 4: Tangent to circle theorems

11. X. Space, shape and measurement: Solve problems by constructing and interpreting trigonometric models

    1. Unit 1: Work with compound angles

    2. Unit 2: Solve trigonometric equations

    3. Unit 3: Solve 2-D and 3-D trigonometry problems using sine and cosine rules

    4. Unit 4: An introduction to radians

12. XI. Data handling: Represent, analyse and interpret data using various techniques

    1. Unit 1: Use various techniques for data collection, representation and interpretation

13. XII. Data handling: Use variance and regression analysis to interpolate and extrapolate bivariate data

    1. Unit 1: Calculate variance and standard deviation

    2. Unit 2: Represent data using a scatter plot

    3. Unit 3: Linear regression analysis

14. XIII. Data handling: Use experiments, simulation and probability distribution to set and explore probability models

    1. Unit 1: Understand probability and make predictions

    2. Unit 2: Draw Venn diagrams to solve probability problems

    3. Unit 3: Draw tree diagrams to solve probability problems

    4. Unit 4: Complete contingency tables to solve probability problems

15. XIV. Financial mathematics: Use mathematics to plan and control financial instruments

    1. Unit 1: Work with simple and compound growth formulae

    2. Unit 2: Interpret tax tables

    3. Unit 3: Work with simple and compound depreciation

16. Appendix