Description

Number and algebra

• Operations with numbers in standard form
• Complex numbers
• Exponential form of a complex number
• Conversion between forms of a complex number
• Geometric interpretation of complex numbers

Functions

• Points of intersection
• Exponential growth and decay models
• Quadratic models
• The parameters of a model
• Piecewise models

Geometry and trigonometry

• Distance between points in three-dimensional space
• Use of sine, cosine, tangent ratios in right-angled triangles
• The cosine rule
• Area of a triangle
• Applications of trigonometry
• Area of a sector
• Geometric transformations using matrices
• Concept of a vector
• Vector product and geometrical interpretation
• Graph theory
• Directed graphs
• Walks
• Eulerian trails and circuits

Statistics and probability

• Interpretation of outliers
• Cumulative frequency graphs
• Measures of dispersion
• The binomial distribution
• The normal distribution
• Chi-squared test for independence
• Non-linear regression
• Sum of square residuals
• Linear combinations of random variables
• Critical regions, hypothesis testing, type II errors

Calculus

• Derivatives
• Tangents
• Volumes of revolution
• Exact solutions and future paths of coupled systems