SACE Year 11-12 Mathematics Practice

Home

Use this page for SACE Maths 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.

Try practice questions:

Year 11 SACE Maths practice questions Year 12 SACE Maths practice questions

South Australian senior mathematics is organised into Stage 1 and Stage 2 subjects. Stage 1 usually corresponds to Year 11 and Stage 2 usually corresponds to Year 12.

This page presents Skill Align practice pathways across Essential Mathematics, General Mathematics, Mathematical Methods, and Specialist Mathematics so conceptual, calculation, graph, diagram, and analysis requirements can be compared clearly.

Stage 1 Mathematics provides the foundation for Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics.

Note: In SACE, Stage 1 Mathematics is used as the preparation pathway for Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics. Skill Align separates these into Methods and Specialist practice rows so students can practise toward their intended Stage 2 pathway.

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.
Skill Align modifies and reorganises referenced material for practice and study-planning purposes.

Mathematics Topics and Subtopics

Stage 1 = Year 11; Stage 2 = Year 12

Pathway	Stage 1 (Year 11)	Stage 2 (Year 12)
Essential Mathematics	1. Calculations and Number text calculation graph diagram analysis • Use whole numbers, fractions, decimals, percentages, ratios, rates, estimation, rounding, and practical number operations. 2. Money and Finance text calculation graph diagram analysis • Use income, expenses, budgets, bills, discounts, simple interest, and personal finance decisions. 3. Measurement and Geometry text calculation graph diagram analysis • Use length, perimeter, area, volume, capacity, mass, scale, plans, and practical geometry. 4. Data and Graphs text calculation graph diagram analysis • Use tables, charts, graphs, summary values, and interpretation of displayed data.	1. Scales, Plans and Models text calculation graph diagram analysis • Use scale drawings, maps, plans, model dimensions, actual measurements, and practical spatial interpretation. 2. Measurement text calculation graph diagram analysis • Use units, length, perimeter, area, volume, capacity, mass, composite shapes, and practical measurement problems. 3. Business Applications text calculation graph diagram analysis • Use business calculations, costs, revenue, profit, loss, mark-up, discounts, GST, wages, and practical decision-making. 4. Statistics text calculation graph diagram analysis • Use data displays, summary statistics, distribution shape, comparison of datasets, and interpretation in social or workplace contexts. 5. Investments and Loans text calculation graph diagram analysis • Use simple interest, compound interest, repayments, balances, total cost, investments, loans, and financial interpretation.
General Mathematics	1. Algebra and Linear Models text calculation graph diagram analysis • Use formulas, substitution, equations, linear relationships, gradients, intercepts, graph interpretation, and practical modelling. 2. Measurement and Trigonometry text calculation graph diagram analysis • Use perimeter, area, volume, scale, right-triangle trigonometry, bearings, and practical measurement. 3. Statistics and Probability text calculation graph diagram analysis • Use data displays, summary statistics, probability models, simple events, and interpretation. 4. Matrices and Networks text calculation graph diagram analysis • Use matrix notation, matrix operations, simple networks, paths, and applied discrete contexts.	1. Modelling with Linear Relationships text calculation graph diagram analysis • Use linear models, gradients, intercepts, equations, graph interpretation, trend, prediction, and practical problem-solving. 2. Modelling with Matrices text calculation graph diagram analysis • Use matrix operations, transition matrices, networks, applications, and interpretation. 3. Statistical Models text calculation graph diagram analysis • Use statistical investigation, bivariate data, association, correlation, regression-style interpretation, and variability. 4. Financial Models text calculation graph diagram analysis • Use compound interest, loans, repayments, annuities, recurrence, investment decisions, and financial interpretation. 5. Discrete Models text calculation graph diagram analysis • Use sequences, recursion, networks, matrices, graph theory, scheduling, optimisation, and discrete decision models.
Mathematical Methods	1. Functions and Graphs text calculation graph diagram analysis • Use function notation, domain, range, transformations, graph features, polynomial functions, exponential functions, and modelling. 2. Algebra and Equations text calculation graph diagram analysis • Use equations, inequalities, exact algebraic manipulation, factorisation, logarithmic/exponential equations where suitable, and symbolic reasoning. 3. Trigonometry text calculation graph diagram analysis • Use radians, exact values, sine, cosine, tangent, trigonometric equations, identities, and graph interpretation. 4. Introductory Calculus text calculation graph diagram analysis • Use limits, gradients, derivatives, tangent lines, rates of change, and introductory differentiation rules. 5. Probability and Statistics text calculation graph diagram analysis • Use probability rules, data displays, summary statistics, probability models, and interpretation.	1. Further Differentiation and Applications text calculation graph diagram analysis • Use derivative rules, product rule, quotient rule, chain rule, curve sketching, rates of change, optimisation, and applications. 2. Discrete Random Variables text calculation graph diagram analysis • Use discrete probability distributions, expected value, variance, standard deviation, binomial/geometric-style models, and interpretation. 3. Integral Calculus text calculation graph diagram analysis • Use anti-differentiation, definite integrals, area under curves, accumulation, and applications of integration. 4. Logarithmic Functions text calculation graph diagram analysis • Use logarithm laws, logarithmic functions, inverse relationships with exponentials, equations, graphs, and modelling. 5. Continuous Random Variables and the Normal Distribution text calculation graph diagram analysis • Use continuous random variables, density functions, cumulative probability, normal distribution, standardisation, quantiles, and interpretation. 6. Sampling and Confidence Intervals text calculation graph diagram analysis • Use random sampling, sampling distributions, sample proportions or means where appropriate, confidence intervals, margin of error, and inference-style interpretation.
Specialist Mathematics	1. Combinatorics text calculation graph diagram analysis • Use arrangements, selections, counting principles, permutations, combinations, and structured cases. 2. Proof text calculation graph diagram analysis • Use direct proof, contradiction-style reasoning, implication, counterexample, proof structure, and justification. 3. Vectors text calculation graph diagram analysis • Use vector notation, magnitude, direction, vector addition, scalar multiplication, scalar product, projections, and geometric interpretation. 4. Trigonometry and Functions text calculation graph diagram analysis • Use trigonometric identities, exact values, equations, transformations, and graph interpretation. 5. Advanced Algebra and Functions text calculation graph diagram analysis • Use polynomials, transformations, higher-order functions, exact algebra, and Stage 2 Specialist preparation.	1. Mathematical Induction text calculation graph diagram analysis • Use base case, inductive step, summation identities, divisibility, inequalities, recurrence-style statements, and clear proof structure. 2. Complex Numbers text calculation graph diagram analysis • Use Cartesian and polar form, modulus, argument, Argand diagrams, roots, De Moivre's theorem, roots of unity, loci, and complex-number algebra. 3. Functions and Sketching Graphs text calculation graph diagram analysis • Use graph features, asymptotes, transformations, inverse functions, rational functions, calculus-supported sketching, and interpretation. 4. Vectors in Three Dimensions text calculation graph diagram analysis • Use 3D vectors, scalar product, vector equations, lines, planes, angles, distances, vector motion contexts, and geometric interpretation. 5. Integration Techniques and Applications text calculation graph diagram analysis • Use advanced integration methods, substitution, integration by parts, partial fractions, area between curves, volumes, and applied integral modelling. 6. Rates of Change and Differential Equations text calculation graph diagram analysis • Use implicit differentiation, related rates, separable differential equations, growth/decay, slope fields, solutions, long-term behaviour, and modelling.