Pre-Calculus

Course Content

1. Functions

Functions and Relations
Domain and Range
Even and odd functions
Transformation of functions
Trigonometric equations

2. Trigonometry

3 . Polynomials

4. Exponential and Logarithms

5. Conic sections

6. Vectors

7. Complex numbers

8. Matrices

Introduction
Representing linear systems of equations with augmented matrices
Matrix row operations
Row-echelon form and Gaussian elimination
Addition, Subtraction, Multiplication of Matrices
Multiplying matrices by scalars
Properties of matrix addition & scalar multiplication
Properties of matrix multiplication
Matrices as transformations
The determinant of a 2×2 matrix
Finding the inverse of a matrix using its determinant
Solving equations with inverse matrices
Model real-world situations with matrices

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IGCSE

Primary Year

Secondary Year

Junior College

Poly Technique

Course Content

1. Functions

Functions and Relations

Domain and Range

Even and odd functions

Transformation of functions

Trigonometric equations

2. Trigonometry

Graphs of Sine and cosine

Transformations of sine and cosine

Inverse trigonometric functions

Sinusoidal equations and models

Angle addition

Using trigonometric identities

3 . Polynomials

Addition and subtraction of polynomials

Division of polynomials

Binomial theorem

Graphs of polynomial functions and solving equations

Graphing rational functions and reciprocal functions

4. Exponential and Logarithms

Applications of exponential functions

Logarithms

Solving exponential and logarithmic equations

Graphing logarithmic functions

5. Conic sections

Feature of a circle

Equations of a circle

Center, radii, focii of an ellipse

Focus and directrix of a parabola

Hyperbola

6. Vectors

Introduction to vectors

Operations with vectors

Applications of vectors

7. Complex numbers

Complex numbers and imaginary numbers

The complex plane: Complex numbers

Addition, Subtraction and Multiplication of complex numbers

Distance and midpoint of complex numbers

Complex conjugates and dividing complex numbers

Identities with complex numbers

Absolute value and angle of complex numbers

Polar form of complex numbers, multiplication and division

8. Matrices

Introduction

Representing linear systems of equations with augmented matrices

Matrix row operations

Row-echelon form and Gaussian elimination

Addition, Subtraction, Multiplication of Matrices

Multiplying matrices by scalars

Properties of matrix addition & scalar multiplication

Properties of matrix multiplication

Matrices as transformations

The determinant of a 2×2 matrix

Finding the inverse of a matrix using its determinant

Solving equations with inverse matrices

Model real-world situations with matrices

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