Fundamentals of Algebra

Subtopics:

• Arithmetic with pronumerals
• Expanding brackets
• Factoring
• Algebraic fractions
• Solving linear equations
• Solving quadratic equations
• Solving simultaneous equations
• Completing the square

Indices and Surds

Subtopics:

• Whole numbers, integers and rationals
• Real numbers and approximations
• Surds and their arithmetic
• Further simplification of surds
• Rationalising the denominator

Functions and Graphs

• Functions and function notation
• Functions, relations and graphs
• Review of linear graphs
• Quadratics functions — factoring and the graph
• Completing the square and the graph
• The quadratic formulae and the graph
• Powers, polynomials and circles
• Two graphs that have asymptotes
• Four types of relations

Transformations

Subtopicss:

• Translations of known graphs
• Reflections in the x-axis and y-axis
• Even and odd symmetry
• The absolute value function
• Composite functions

Trigonometry

Subtopics:

• Trigonometry with right-angled triangles
• Problems involving right-angled triangles
• Three-dimensional trigonometry
• Trigonometric functions of a general angle
• Quadrant, sign, and related acute angle
• Given one trigonometric function, find another
• Trigonometric identities
• Trigonometric equations
• The sine rule and the area formula
• The cosine rule
• Problems involving general triangles

The Coordinate Plane

Subtopics:

• Lengths and midpoints of intervals
• Gradients of intervals and lines
• Equations of lines
• Further equations of lines
• Using pronumerals in place of numbers

Exponential and Logarithmic Functions

• Indices
• Fractional indices
• Logarithms
• The laws for logarithms
• Equations involving logarithms and indices
• Exponential and logarithmic graphs
• Applications of these functions

Differentiation

• Tangents and the derivative
• The derivative as a limit x
• rule for differentiating powers of x
• Tangents and normals — dy dx notation
• Differentiating powers with negative indices
• Differentiating powers with fractional indices
• The chain rule
• The product rule
• The quotient rule
• Rates of change
• Continuity
• Differentiability

Advanced Calculus

• The exponential function base
• Transformations of exponential functions
• Differentiation of exponential functions
• Differentiation and the graph
• The logarithmic function base e
• Exponential rates using the base e
• Radian measure of angle size
• Solving trigonometric equations
• Arcs and sectors of circles
• Trigonometric graphs in radians

Probability

• Probability and sample spaces
• Sample space graphs and tree diagrams
• Sets and Venn diagrams
• Venn diagrams and the addition theorem
• Multi-stage experiments and the product rule
• Probability tree diagrams
• Conditional probability