Additional Mathematics

Contents

Form 4

Functions - Rational Numbers

  • Relations
  • Function
  • Composite Functions
  • Inverse Functions

Functions - Quadratic Equations

  • 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

Functions - Quadratic Functions

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

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
  • Addition of 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