Contents

### Form 4

#### Functions - Rational Numbers

• Relations
• Function
• Composite Functions
• Inverse Functions

• The Quadratic Equation and Its Roots
• Completing the Square and the Quadratic Formula
• Forming Quadratic Equations from Given Roots
• The Discriminant of a Quadratic Equation

• Quadratic Functions and Their Graphs
• Sketching the Graph of a Quadratic Function

#### Functions - Simultaneous Equations

• Simultaneous Equations

#### Functions - Indices and Logarithms

• Laws of Indices
• Laws of Logarithms
• Logarithms and Its Base
• Applications of Logarithms and Indices

#### Functions - Coordinate Geometry

• Distance and Division
• The Area of Polygons
• Intercept and Gradient of a Straight Line
• Equation of a Straight Line
• Parallel Lines and Perpendicular Lines
• Equation of Locus

#### Functions - Statistics

• Mean, Median and Mode for Ungrouped Data
• Mean, Median and Mode for Grouped Data
• Solving Problems Involving Measures of Central Tendency
• The Range and Interquartile Range
• The Variance and Standard Deviation
• Solving Problems Involving Measures of Dispersion

#### Functions - Circular Measures

• Radian and length of an arc
• Radian and perimeter of segments of circles
• Radian and Area of sector of a circle

#### Functions - Differentiation

• The Derivative of a Function
• Derivative of Polynomial Functions
• Differentiation Techniques
• Tangent and Normal at a Point on a Curve
• Maximum and Minimum Points of a Curve
• Rates of Change and Small Changes
• Second Order Differentiation

#### Functions - Solution of Triangles

• Sine Rule
• Cosine Rule
• Solving Problems Involving the Sine and Cosine Ruless
• Area of Triangles and Three Dimensional Objects

### Form 5

#### Progressions - Rational Numbers

• Arithmetic Progressions
• Sum of Arithmetic Progressions
• Geometric Progressions
• The Sum to the First n Terms of Geometric Progressions

#### Progressions - Linear Law

• Lines of Best Fit
• Reducing Non-linear Relations to Linear Form
• Application of Linear Law to Non-linear Relations

#### Progressions - Integration

• Indefinite Integrals
• Finding the Equations of Curves from Gradient Functions
• Integration by Substitution
• Definite Integrals
• Areas Under a Curve and The x-axis
• Areas Under a Curve and The y-axis or a Straight Line
• Volumes of Revolution

#### Progressions - Vectors

• Vectors
• Equal and Parallel Vectors
• Vectors in the Cartesian Plane
• Operations on Vectors
• Solving Problems Involving Vectors

#### Progressions - Trigonometric Functions

• Positive and Negative Angles
• The 6 Trigonometric Functions
• Trigonometric Functions
• Solving Trigonometric Equations
• Graphs of Sine Cosine and Tangent
• Solving Trigonometric Equations Using Drawn Graphs
• Trigonometric Identities
• Addition Formulae and Double-Angle Formulae

#### Progressions - Permutations and Combinations

• Permutations
• Permutations of n Different Objects Taken r at a Time for Given Conditions
• Combinations

#### Progressions - Probability

• Probability
• Mutually Exclusive and Independent Events

#### Progressions - Probability Distributions

• Binomial Distribution and Its Graph
• Solving Problems Involving Binomial Distributions
• Normal Distribution
• Standard Normal Distribution and The z-score
• Solving Problems Involving Normal Distributions

#### Progressions - Motion Along a Straight Line

• Displacement and Distance
• Velocity and Displacement
• Acceleration and Velocity
• Solving Problems Involving Motion Along a Straight Line

#### Progressions - Linear Programming

• Relations
• Solving Problems Involving Positive and Negative Fractions