THE ASCENT LIBRARY

Specialist MathematicsOne idea at a time.

Explore proof, complex numbers, vectors and deeper calculus, alongside Mathematical Methods.

Years 11–12 · SACE

01 / YOUR YEAR LEVEL

Start where you are.

02 / EXPLORE THE TOPICS

Year 11 starts here.

Extend your Stage 1 Mathematics with the foundations for the Specialist pathway.

64 lessons available

64 subtopics

01

Proof and circle geometry

10 subtopics

1.1Statements, implication, converse and equivalence 1.2Counterexamples 1.3Direct proof and contradiction 1.4Rational/irrational numbers and simple number proofs 1.5Interval notation 1.6Angle properties of circles 1.7Cyclic quadrilaterals 1.8Chords and tangents 1.9Intersecting-chord/secant/tangent length relationships 1.10Congruence and similarity in geometric proofs

Topic review5 practice tests

02

Further trigonometry

9 subtopics

2.1Review of radians and unit-circle values 2.2Transformed sinusoidal models including phase shift 2.3Solving trig equations and describing all solutions 2.4Compound-angle identities 2.5Double-angle identities and derived forms 2.6Expressing a sine/cosine combination as one sinusoid 2.7Reciprocal trig functions and their graphs 2.8Verifying identities 2.9Periodic modelling

Topic review5 practice tests

03

Vectors in two dimensions

11 subtopics

3.1Magnitude and direction 3.2Vector equality and opposite vectors 3.3Addition/subtraction and scalar multiplication 3.4Component and unit-vector notation 3.5Position and displacement vectors 3.6Parallelism and collinearity 3.7Dot product 3.8Angle between vectors 3.9Scalar/vector projections 3.10Perpendicularity 3.11Vector geometry proofs

Topic review5 practice tests

04

Matrices and transformations

14 subtopics

4.1Matrix notation, order and entries 4.2Addition/subtraction/scalar multiplication 4.3Matrix multiplication and non-commutativity 4.4Identity and zero matrices 4.5Determinants and inverses of 2×2 matrices 4.6Singular matrices 4.7Solving matrix equations and systems 4.8Translations as vectors 4.9Matrices acting on position vectors 4.10Rotations, reflections and dilations 4.11Projections onto coordinate axes 4.12Combined transformations and their order 4.13Inverse transformations 4.14Determinant and area scale

Topic review5 practice tests

05

Sequences and series

10 subtopics

5.1Recurrence rules and explicit terms 5.2Arithmetic sequences 5.3Arithmetic sums 5.4Geometric sequences 5.5Finite geometric sums 5.6Infinite geometric sums and convergence 5.7Recurrence models 5.8Financial and other sequence applications 5.9Introduction to proof by induction 5.10Induction proofs of simple sums and arithmetic/geometric-series results

Topic review5 practice tests

06

Complex numbers

10 subtopics

6.1Why the imaginary unit is needed 6.2Real and imaginary parts 6.3Complex-number arithmetic 6.4Conjugates and division 6.5Quadratic equations with non-real roots 6.6Conjugate roots of real quadratics 6.7Argand diagrams 6.8Modulus 6.9Vector interpretation of addition and conjugation 6.10Linear factorisation over the complex numbers

Topic review5 practice tests

Schools may teach these topics in a different order.

Official curriculum outline

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