Last updated Aug 31, 2025
HSC SSCE Mathematics Advanced
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Explore HSC SSCE Mathematics Advanced by Topics
Absolute value functions
Adding and subtracting algebraic fractions
Adding and subtracting surds
Algebraic fractions
Angle properties of triangles
Angle review
Angles of any magnitude
Angles of elevation and depression
Applications of the exponential function
Applications of trigonometric functions
Approximate methods of integration – Simpson’s rule
Approximate methods of integration – trapezoidal rule
Approximations
Approximations when x is small
Arc length and sector area of a circle
Area between two curves
Area bounded by the y-axis
Area formulae
Area of a triangle
Area under a curve
Arithmetic series
Average value of a function
Basic polynomials
Circles
Completing the square
Completing the square for non-monic equations
Compound interest applications
Conditions for differentiability
Congruent triangles
Continuity and gradients of tangents
Coordinate methods in geometry
Dependent events
Derivatives of trigonometric functions
Direction and bearing
Equation of a straight line
Equations reducible to quadratics
Exact values of trigonometric ratios
Exponential functions
Exponential growth and decay
Factorising by grouping in pairs
Factorising non-monic trinomials
Factorising quadratic trinomials
Factorising using the difference of two squares
Finding the derivative from first principles
Finite geometric series
Finite sample spaces
Functions and relations
Further applications of series
Further examples involving discriminants
Further locus
General quadratic equations
Gradient as a rate of change
Gradient of a curve at a point
Gradient of a straight line
Graphical solution of equations
Graphs of trigonometric functions
Harder algebraic fractions
Harder intercept properties of parallel lines
Identity of two quadratic expressions
Indefinite integrals
Independent events
Index laws with fractional indices
Index laws with integers as indices
Infinite geometric series
Integrating the exponential function
Intercept properties of parallel lines
Intersection of two lines
Introduction to probability
Limit and continuity
Linear equations in one variable
Linear equations involving fractions
Locus
Logarithms
Midpoint of an interval and distance between two points
Mixed factorisations
More areas
More derivatives from first principles
More trigonometric exact values
Motion of a particle in a straight line
Non-linear inequalities
Other examples of motion
Parabolas and discriminants
Parallel lines
Perpendicular distance of a point from a line
Primitive functions
Primitives of trigonometric functions
Problem solving with derivatives
Pythagoras’ theorem
Quadratic equations
Quadratic equations with non-rational solutions
Quadratic equations without a constant term
Quadratic equations without a linear term
Quadratic functions
Quadrilaterals and polygons
Radian measure of an angle
Rationalising denominators
Real numbers and surds
Regions and inequalities
Relationship between roots and coefficients
Repeating decimals
Review of basics
Scientific notation (standard form)
Series and sigma notation
Sign of a quadratic function
Significant figures and decimal places
Similar triangles
Simple linear inequalities
Simplifying algebraic expressions
Simultaneous linear inequalities
Sketching basic functions
Sketching rational algebraic functions
Solution of trigonometric equations
Solution set of simultaneous equations
Solving equations with exponents
Solving equations with logarithms
Solving quadratic equations by completing the square
Substitution in formulae
Successive outcomes
Sum and difference of two cubes
Tangents and normals to a curve
The chain rule
The cosine rule
The definite integral and the area under a curve
The definite integral and the primitive function
The distributive law
The first derivative and turning points
The parabola as a locus
The product rule
The quadratic formula
The quotient rule
The second derivative and concavity
The second derivative and turning points
The sign of the derivative
The sine rule
Trigonometric graphs and equations
Trigonometric identities
Venn diagrams
Volume of solids of revolution
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