Year 11-12 Maths Practice

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Use this page for Year 11-12 Maths learning and practice questions, senior secondary revision, and topic-based exam preparation. Skill Align practice includes student-readable questions, explanations, exercise mode, and test mode for parents comparing Australian senior subject coverage.

This page focuses on Years 11 and 12 maths so the senior secondary pathway, unit, and unit-topic structure can be read without the Year 10 strand matrix in the same table.

Years 11–12 mathematics following the ACARA v9 curriculum is available on the Year 11–12 Maths Practice page. The VCE pathways below are organised by Units 1–4.

Curriculum attribution

Skill Align independently prepares practice pathways aligned to publicly available curriculum and syllabus information.
Skill Align is not affiliated with, endorsed by, or sponsored by ACARA, VCAA, NESA, QCAA, SCSA, SACE, or any state curriculum authority.
Official curriculum, syllabus, study design, and assessment requirements should always be checked on the relevant authority website.
Where Australian Curriculum or QCAA material is referenced or adapted, attribution is provided under the relevant Creative Commons Attribution 4.0 licence.
Skill Align modifies and reorganises referenced material for practice and study-planning purposes.

Maths Topics and Subtopics

Years 11 and 12

Pathway	Year 11 - Unit 1	Year 11 - Unit 2	Year 12 - Unit 1	Year 12 - Unit 2
General Maths	1. Consumer Arithmetic • Use percentages, pricing, wages, and other everyday arithmetic decisions within official General Maths scope. 2. Algebra and Matrices • Keep formula work, algebraic rearrangement, and introductory matrix applications within Unit 1 scope.• Prefer text-first stems and tables where needed; do not generate decorative diagrams for routine algebra or matrix questions. 3. Shape and Measurement text diagram • Use perimeter, area, volume, scale, and practical measurement interpretation with clearly stated dimensions.	1. Univariate Data Analysis and the Statistical Investigation Process text graph • Use summary measures, displays, interpretation, and the logic of a small statistical investigation.• Prefer text-first stems or clearly described tables; do not generate decorative coordinate-plane diagrams for routine univariate data questions. 2. Applications of Trigonometry text diagram • Use right-triangle trigonometry in practical measurement contexts with explicit diagrams or clearly stated geometry.• When a diagram is included, use a single right triangle ABC with A as the observation point, B as the ground/base point, and C vertically above B. Keep direction words in the stem only; do not add coordinate-axis labels such as east-west or north-south to the diagram. 3. Linear Equations and Their Graphs • Use slope, intercept, graph interpretation, and equation solving in official General Maths contexts.• Prefer text-only for routine rule-from-points or intercept-plus-point questions; only use a graph when the plotted line itself supplies mathematical information.• Keep the explanation aligned with the verified gradient, intercept, and final equation.	1. Bivariate Data Analysis text graph diagram • Use scatterplots, association, fitted models, and interpretation of paired data within Unit 3 scope. 2. Growth and Decay in Sequences • Use arithmetic or geometric sequence structure to model growth and decay in senior General Maths contexts. 3. Graphs and Networks text graph diagram • Use vertices, edges, paths, and network interpretation without bringing back legacy internal network buckets.	1. Time Series Analysis text graph • Use trend, seasonality, smoothing, and interpretation from displayed time series data. 2. Loans, Investments and Annuities • Use repayment schedules, compound growth, and annuity decisions in practical financial contexts. 3. Networks and Decision Mathematics text graph • Use network optimisation, decision-making, and matrix-based reasoning only where it belongs to the official Unit 4 topic.
Mathematical Methods	1. Functions and Graphs text graph • Use function notation, domain/range, transformations, and graph features within Year 11 Methods scope. 2. Counting and Probability • Use counting principles, event structure, and introductory probability without Specialist-only techniques.• Prefer text-first arrangement and conditional-probability tasks for the current rollout, and keep the final count or probability aligned exactly across the options, marked answer, and explanation.• Do not generate decorative coordinate-plane diagrams for routine counting or conditional-probability questions. 3. Trigonometric Functions text graph • Use unit-circle reasoning, radians, and sine/cosine/tangent functions in Year 11 Methods scope.• When a diagram is included, prefer standard-position coordinate-plane visuals with a terminal arm or point; do not generate junior right-triangle sketches for this subtopic.• If the stem names a point such as P(3, 4), the coordinate-plane diagram must plot that same labeled point at the exact same coordinates. If the stem gives an unlabeled point such as (3, 4), the single plotted point must still match those coordinates exactly.• Do not emit raw unicode escape text such as \u03b8 in the rendered question or explanation.	1. Exponential Functions text graph • Use exponential rules, graphs, and interpretation of growth or decay in Methods-friendly contexts. 2. Arithmetic and Geometric Sequences and Series • Use nth-term, recursion, sum formulas, and interpretation of arithmetic or geometric growth.• Keep wording plain and readable, and avoid malformed inline fragments such as 'thevalueofx' or 'thevalueofn'.• Prefer exact text-first forms such as a missing arithmetic term, smallest positive n below a threshold, an arithmetic-series sum target for n, or sum of the first n terms of a geometric sequence. 3. Introduction to Differential Calculus • Keep differential calculus introductory: average and instantaneous rate of change, tangent ideas, and simple derivative rules.• Keep this slice text-first until there is a real function-and-tangent renderer; avoid decorative coordinate-plane point diagrams.	1. Further Differentiation and Applications text graph diagram • Use derivative rules, optimisation, tangent behaviour, and other standard Unit 3 differentiation applications. 2. Integrals text graph diagram • Use anti-differentiation, definite integrals, and area or accumulation meaning within Methods Unit 3 scope. 3. Discrete Random Variables text graph • Use expectation, variance, distributions, and interpretation of discrete random variables in official Unit 3 scope.• Text questions must state the probability table or distribution explicitly; graph questions should use a bar chart with exact probabilities and labels.	1. The Logarithmic Function text graph diagram • Use logarithmic rules, graphs, and the inverse relationship with exponentials in official Unit 4 scope. 2. Continuous Random Variables and the Normal Distribution text graph diagram • Use density ideas, normal-distribution interpretation, and probability reasoning without reintroducing old split subtopics. 3. Interval Estimates for Proportions • Use sample proportions, confidence-style interval interpretation, and decision-making within senior-school Methods scope.• Keep endpoint and margin-of-error calculations text-first unless a future interval-specific visual renderer is introduced.
Specialist Maths	1. Combinatorics • Use permutations, combinations, and counting arguments that are clearly within Year 11 Specialist scope.• Keep this rollout slice text-first; do not attach decorative diagrams to arrangement or counting questions.• Prefer exact bounded forms such as repeated-letter strings with one fixed final letter, committee selections with exact subgroup counts, and digit permutations with parity plus simple size constraints. 2. Vectors in the Plane • Use vector notation, magnitude, direction, and geometric interpretation in two dimensions.• Prefer exact rollout forms such as midpoint of two position vectors, translations, simple expressions like 2a - 3b, solving one scalar in w = au + kv, or internal division of AB in a stated ratio.• Keep this rollout slice text-first until a deterministic coordinate-plane vector visual template is available. 3. Geometry • Use Geometry as a parent Unit 1 Specialist grouping only; the selectable rollout lives inside narrower internal slices.• Do not treat this parent node as one broad geometry generator.	1. Trigonometry • Use identities, exact values, and equation solving that belong to Year 11 Specialist rather than Methods.• Keep this rollout slice text-first: exact values, identities, quadrant signs, and equation structure should be stated clearly in the stem rather than supported by decorative diagrams.• Do not expose graph mode until a deterministic trigonometric graph visual template is available. 2. Matrices • Use matrix operations, inverses, and applications within the Year 11 Specialist treatment of matrices.• Keep this rollout slice text-first and prefer exact 2x2 forms such as simple matrix multiplication, determinant-in-x questions with exact integer roots, or the lower-triangular P^2 form that solves one scalar from the (2,1) entry.• Use plain readable wording such as 'what is k?' or 'what are the possible values of x?' and avoid collapsed fragments such as 'whatisk'. 3. Real and Complex Numbers • Use algebraic manipulation and introductory geometric interpretation of complex numbers without later Unit 3 depth.• Keep routine algebra and modulus questions text-first; do not expose diagram or graph mode until an Argand-plane deterministic visual template is available.• Prefer exact rollout forms such as substitution into a simple polynomial in z, multiplication of two complex binomials, or modulus of a + bi with a clean exact value.	1. Complex Numbers • Use algebraic form, the Argand plane, and standard Year 12 Specialist complex-number reasoning without legacy split buckets.• Keep routine complex arithmetic text-first unless a future Argand-specific template makes the visual necessary for solving. 2. Vectors in Three Dimensions • Use vector operations and geometric interpretation in three dimensions within official Unit 3 scope.• Keep component and magnitude calculations text-first until a true three-axis vector renderer is available. 3. Functions and Sketching Graphs text graph • Use rational-style behaviour, transformations, and graph sketching features appropriate to Unit 3 Specialist Maths.• Use graph mode for sketch interpretation; do not use diagram mode for function graphs. Text mode must state the algebraic rule directly.	1. Integration and Applications of Integration text graph diagram • Use integration techniques and applications that sit within official Unit 4 Specialist scope rather than the older advanced-calculus split. 2. Rates of Change and Differential Equations text diagram • Use rate-of-change modelling and differential-equation reasoning at senior-school Specialist depth. 3. Statistical Inference • Use inference, hypothesis-style reasoning, and interpretation within the official Specialist Unit 4 topic.• Keep routine sample-proportion and inference calculations text-first unless a future inference-specific visual is mathematically necessary.