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Other SSCE HSC Mathematics Advanced topics to explore

Mathematics Advanced HSC

Absolute value functions

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Adding and subtracting algebraic fractions

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Adding and subtracting surds

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Algebraic fractions

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Angle properties of triangles

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Angle review

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Angles of any magnitude

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Angles of elevation and depression

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Applications of the exponential function

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Applications of trigonometric functions

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Approximate methods of integration – Simpson’s rule

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Approximate methods of integration – trapezoidal rule

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Approximations

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Approximations when x is small

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Arc length and sector area of a circle

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Area between two curves

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Area bounded by the y-axis

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Area formulae

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Area of a triangle

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Area under a curve

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Arithmetic series

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Average value of a function

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Basic polynomials

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Circles

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Completing the square

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Completing the square for non-monic equations

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Compound interest applications

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Conditions for differentiability

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Congruent triangles

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Continuity and gradients of tangents

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Coordinate methods in geometry

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Dependent events

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Derivatives of trigonometric functions

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Direction and bearing

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Equation of a straight line

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Equations reducible to quadratics

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Exact values of trigonometric ratios

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Exponential functions

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Exponential growth and decay

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Factorising by grouping in pairs

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Factorising non-monic trinomials

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Factorising quadratic trinomials

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Factorising using the difference of two squares

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Finding the derivative from first principles

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Finite geometric series

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Finite sample spaces

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Functions and relations

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Further applications of series

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Further examples involving discriminants

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Further locus

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General quadratic equations

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Gradient as a rate of change

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Gradient of a curve at a point

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Gradient of a straight line

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Graphical solution of equations

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Graphs of trigonometric functions

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Harder algebraic fractions

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Harder intercept properties of parallel lines

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Identity of two quadratic expressions

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Indefinite integrals

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Independent events

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Index laws with fractional indices

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Index laws with integers as indices

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Infinite geometric series

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Integrating the exponential function

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Intercept properties of parallel lines

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Intersection of two lines

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Introduction to probability

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Limit and continuity

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Linear equations in one variable

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Linear equations involving fractions

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Locus

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Logarithms

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Midpoint of an interval and distance between two points

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Mixed factorisations

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More areas

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More derivatives from first principles

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Motion of a particle in a straight line

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Non-linear inequalities

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Other examples of motion

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Parabolas and discriminants

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Parallel lines

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Perpendicular distance of a point from a line

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Primitive functions

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Primitives of trigonometric functions

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Problem solving with derivatives

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Pythagoras’ theorem

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Quadratic equations

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Quadratic equations with non-rational solutions

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Quadratic equations without a constant term

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Quadratic equations without a linear term

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Quadratic functions

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Quadrilaterals and polygons

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Radian measure of an angle

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Rationalising denominators

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Real numbers and surds

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Regions and inequalities

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Relationship between roots and coefficients

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Repeating decimals

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Review of basics

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Scientific notation (standard form)

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Series and sigma notation

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Sign of a quadratic function

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Significant figures and decimal places

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Similar triangles

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Simple linear inequalities

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Simplifying algebraic expressions

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Simultaneous linear inequalities

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Sketching basic functions

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Sketching rational algebraic functions

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Solution of trigonometric equations

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Solution set of simultaneous equations

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Solving equations with exponents

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Solving equations with logarithms

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Solving quadratic equations by completing the square

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Substitution in formulae

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Successive outcomes

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Sum and difference of two cubes

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Tangents and normals to a curve

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The chain rule

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The cosine rule

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The definite integral and the area under a curve

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The definite integral and the primitive function

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The distributive law

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The first derivative and turning points

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The parabola as a locus

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The product rule

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The quadratic formula

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The quotient rule

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The second derivative and concavity

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The second derivative and turning points

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The sign of the derivative

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The sine rule

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Trigonometric graphs and equations

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Trigonometric identities

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Venn diagrams

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Volume of solids of revolution

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