THE ASCENT LIBRARY
Specialist MathematicsOne idea at a time.
Explore proof, complex numbers, vectors and deeper calculus, alongside Mathematical Methods.
Years 11–12 · SACE01 / YOUR YEAR LEVEL
Start where you are.
02 / EXPLORE THE TOPICS
73 lessons availableYear 12 starts here.
Build rigorous mathematical reasoning through complex numbers, vectors and advanced calculus.
73 subtopics
01
Mathematical induction
6 subtopics1.1Base case and induction hypothesis1.2Constructing the induction step1.3Proofs of summation formulas1.4Divisibility proofs1.5Identities involving powers and integers1.6Recognising incomplete or invalid induction arguments
Topic review6 practice tests02
Real Polynomials
9 subtopics2.1Polynomial notation and operations2.2Zeros, roots and factors2.3Polynomial identities and coefficient comparison2.4Polynomial division2.5Remainder theorem2.6Factor theorem2.7Finding and factorising real polynomial roots2.8Graphing real polynomials2.9Solving real polynomial equations
Topic review6 practice tests03
Functions and graph sketching
8 subtopics3.1Composition and domain restrictions3.2One-to-one functions3.3Inverse functions and restricted domains3.4Absolute-value graphs3.5Reciprocal/composite transformations3.6Rational functions3.7Intercepts, stationary behaviour and asymptotes3.8Combining graphical/algebraic/calculus information in sketches
Topic review6 practice tests04
Complex Numbers
10 subtopics4.1Cartesian/polar forms4.2Modulus and argument4.3Complex arithmetic in both forms4.4Multiplication as rotation/dilation4.5De Moivre's theorem4.6Powers and roots4.7Roots of unity4.8Complex loci and geometry4.9Factorisation over the complex numbers4.10Conjugate-root results for real polynomials
Topic review6 practice tests05
Vectors in three dimensions
11 subtopics5.1Three-dimensional coordinates, magnitude and unit vectors5.2Vector operations5.3Dot product and projection5.4Cross product and determinant calculations5.5Geometric areas and perpendicular vectors5.6Vector/Cartesian equations of lines5.7Plane equations and normal vectors5.8Line/plane intersections and angles5.9Closest points and distances including skew lines5.10Systems of three linear equations5.11Row operations and geometric interpretation of solution sets
Topic review6 practice tests06
Integration techniques and applications
11 subtopics6.1Further antiderivatives6.2Inverse-trigonometric derivatives and integrals6.3Substitution6.4Trigonometric identities in integration6.5Simple partial fractions6.6Integration by parts6.7Selecting/combining methods6.8Definite integration6.9Areas6.10Volumes of revolution about either coordinate axis6.11Interpreting a result in context
Topic review6 practice tests07
Rates of change and differential equations
8 subtopics7.1Implicit differentiation7.2Related-rate problems7.3Differential equations and initial conditions7.4Slope fields7.5Direct integration7.6Separation of variables7.7Exponential and logistic models7.8Interpreting motion equations and simple harmonic motion
Topic review6 practice tests08
Vector calculus
10 subtopics8.1Parametric descriptions of curves8.2Coordinates varying at constant rates8.3Polynomially varying coordinates8.4Bézier paths8.5Vector-valued position functions8.6Differentiating and integrating components8.7Velocity, acceleration and speed8.8Parametric gradients and tangent directions8.9Sine/cosine parameterisations and circular motion8.10Arc length in two and three dimensions
Topic review6 practice testsSchools may teach these topics in a different order.
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