QCE Year 11-12 Mathematics Practice

Home

Use this page for QCE 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 QCE Maths practice questions Year 12 QCE Maths practice questions

Queensland senior mathematics is organised by Units 1-4, with Units 1-2 usually completed in Year 11 and Units 3-4 in Year 12.

Specialist Mathematics is typically studied alongside Mathematical Methods.

This page focuses on QCE Mathematics pathways so Essential Mathematics, General Mathematics, Mathematical Methods, and Specialist Mathematics can be compared without using ACARA strand naming.

For the ACARA v9 Years 11-12 mathematics curriculum, see the Year 11-12 Maths Practice page. The QCE pathways below are structured 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

Year 11 = Units 1-2 · Year 12 = Units 3-4

Pathway	Year 11 - Unit 1	Year 11 - Unit 2	Year 12 - Unit 3	Year 12 - Unit 4
Essential Mathematics	1. Calculations text calculation graph diagram analysis • Use practical number operations, order of operations, estimation, rounding, calculator use, and checking reasonableness. 2. Number text calculation graph diagram analysis • Use ratios, fractions, percentages, rates, and practical number relationships. 3. Representing Data text calculation graph diagram analysis • Use tables, charts, graphs, and simple interpretation of displayed data. 4. Managing Money text calculation graph diagram analysis • Use budgets, bills, income, expenses, discounts, and personal finance decisions.	1. Calculations text calculation graph diagram analysis • Use practical multi-step calculations, estimation, rounding, and reasonableness checks in data and travel contexts. 2. Data Collection text calculation graph diagram analysis • Use census, surveys, sampling, questionnaire design, sources of bias, and data collection decisions. 3. Graphs text calculation graph diagram analysis • Use graphs to represent and interpret data, including travel and real-world contexts. 4. Time and Motion text calculation graph diagram analysis • Use time, speed, distance, duration, travel graphs, and motion interpretation.	1. Calculations text calculation graph diagram analysis • Use practical number operations, estimation, rounding, unit conversion, and reasonableness checks. 2. Measurement text calculation graph diagram analysis • Use units, length, perimeter, area, volume, capacity, mass, time, geometry, and composite measurement problems. 3. Scales, Plans and Models text calculation graph diagram analysis • Use scale drawings, actual measurements, plans, models, and practical spatial interpretation. 4. Probability and Relative Frequencies text calculation graph diagram analysis • Use chance, relative frequency, simple probability, and interpretation of probability in context.	1. Calculations text calculation graph diagram analysis • Use practical multi-step arithmetic, rounding, estimation, and checking results. 2. Bivariate Graphs text calculation graph diagram analysis • Use Cartesian coordinates, scatterplots, line of best fit, correlation, interpolation, extrapolation, and association. 3. Summarising and Comparing Data text calculation graph diagram analysis • Use measures of centre and spread, histograms, distribution shape, and data comparison. 4. Loans and Compound Interest text calculation graph diagram analysis • Use simple interest, compound interest, loans, repayments, balances, and financial interpretation.
General Mathematics	1. Consumer Arithmetic text calculation graph diagram analysis • Use rates, percentages, earning, spending, managing money, and spreadsheet-style practical contexts. 2. Shape and Measurement text calculation graph diagram analysis • Use perimeter, area, volume, surface area, circles, solids, and practical measurement. 3. Similarity and Scale text calculation graph diagram analysis • Use similar figures, scale factors, scale drawings, and scaling of length, area, surface area, volume, and capacity. 4. Algebra text calculation graph diagram analysis • Use algebraic expressions, formulas, substitution, linear and non-linear relationships, and rearrangement. 5. Linear Equations and Their Graphs text calculation graph diagram analysis • Use linear equations, gradients, intercepts, graph interpretation, simultaneous equations, and practical linear modelling.	1. Applications of Linear Equations and Graphs text calculation graph diagram analysis • Use simultaneous linear equations, piecewise linear graphs, step graphs, and practical modelling. 2. Applications of Trigonometry text calculation graph diagram analysis • Use right-angled and non-right-angled trigonometry, sine rule, cosine rule, bearings, elevation, and depression. 3. Matrices text calculation graph diagram analysis • Use matrix notation, matrix operations, applications, and interpretation. 4. Univariate Data Analysis 1 text calculation graph diagram analysis • Use one-variable data, categorical and numerical variables, data displays, and summary interpretation. 5. Univariate Data Analysis 2 text calculation graph diagram analysis • Use measures of centre and spread, distribution shape, comparison of datasets, and statistical interpretation.	1. Bivariate Data Analysis 1 text calculation graph diagram analysis • Use two-way tables, categorical association, scatterplots, correlation, and coefficient of determination. 2. Bivariate Data Analysis 2 text calculation graph diagram analysis • Use least-squares lines, residual plots, interpolation, extrapolation, association, causation, and prediction. 3. Time Series Analysis text calculation graph diagram analysis • Use time series plots, trend, seasonality, smoothing, moving averages, seasonal indices, and long-term trend modelling. 4. Growth and Decay in Sequences text calculation graph diagram analysis • Use arithmetic sequences, geometric sequences, recurrence, growth, decay, depreciation, interest, and discrete modelling. 5. Earth Geometry and Time Zones text calculation graph diagram analysis • Use latitude, longitude, great circles, time zones, travel, broadcasting, and itinerary contexts.	1. Loans, Investments and Annuities 1 text calculation graph diagram analysis • Use reducing-balance loans, compound interest, present value annuities, repayments, and total interest. 2. Loans, Investments and Annuities 2 text calculation graph diagram analysis • Use future value annuities, recurrence relations, perpetuities, periodic payments, and investment modelling. 3. Graphs and Networks text calculation graph diagram analysis • Use graph terminology, adjacency matrices, paths, trails, circuits, Hamiltonian ideas, and network representation. 4. Networks and Decision Mathematics 1 text calculation graph diagram analysis • Use trees, spanning trees, minimum spanning trees, weighted graphs, and connector problems. 5. Networks and Decision Mathematics 2 text calculation graph diagram analysis • Use network optimisation, shortest paths, scheduling, flow, matching, and decision reasoning.
Mathematical Methods	1. Surds and Quadratic Functions text calculation graph diagram analysis • Use surds, exact values, quadratic functions, graphs, roots, factorisation, and transformations. 2. Binomial Expansion and Cubic Functions text calculation graph diagram analysis • Use binomial expansion, cubic functions, roots, factorisation, graph features, and algebraic reasoning. 3. Functions and Relations text calculation graph diagram analysis • Use function notation, domain, range, relations, inverse ideas, composite functions, and graph interpretation. 4. Trigonometric Functions text calculation graph diagram analysis • Use sine, cosine, tangent, radians, exact values, periodicity, and trigonometric graphs. 5. Probability text calculation graph diagram analysis • Use probability rules, complements, conditional probability, independence, counting, and interpretation.	1. Exponential Functions text calculation graph diagram analysis • Use indices, exponential functions, exponential equations, graphs, growth, decay, and modelling. 2. Logarithms and Logarithmic Functions text calculation graph diagram analysis • Use logarithm laws, logarithmic functions, equations, graphs, and inverse relationships. 3. Introduction to Differential Calculus text calculation graph diagram analysis • Use limits, gradients, derivatives, tangent lines, rates of change, and introductory differentiation rules. 4. Applications of Differential Calculus text calculation graph diagram analysis • Use derivatives for stationary points, rates, curve behaviour, optimisation, and practical modelling.	1. Differentiation of Exponential and Logarithmic Functions text calculation graph diagram analysis • Use derivatives of exponential and logarithmic functions, qualitative graph features, equations, and modelling. 2. Differentiation of Trigonometric Functions and Differentiation Rules text calculation graph diagram analysis • Use derivatives of sine and cosine, chain rule, product rule, quotient rule, composite functions, and mixed differentiation. 3. Further Applications of Differentiation text calculation graph diagram analysis • Use second derivative, concavity, optimisation, motion, displacement, velocity, acceleration, and modelling. 4. Introduction to Integration text calculation graph diagram analysis • Use anti-differentiation, indefinite integrals, motion from velocity or acceleration, and accumulation. 5. Discrete Random Variables text calculation graph diagram analysis • Use discrete probability distributions, expected value, variance, standard deviation, and random-process modelling.	1. Further Integration text calculation graph diagram analysis • Use definite integrals, fundamental theorem of calculus, area under curves, area between curves, trapezoidal rule, and total change. 2. Trigonometry text calculation graph diagram analysis • Use sine rule, cosine rule, ambiguous case, three-dimensional contexts, bearings, elevation, and depression. 3. Continuous Random Variables and the Normal Distribution text calculation graph diagram analysis • Use continuous random variables, density functions, normal distribution, probability, quantiles, and distribution interpretation. 4. Sampling and Proportions text calculation graph diagram analysis • Use random sampling, sampling distributions, sample proportions, and inference-style interpretation. 5. Interval Estimates for Proportions text calculation analysis • Use confidence intervals for proportions, margin of error, interval interpretation, and inference-style reasoning.
Specialist Mathematics	1. Combinatorics text calculation graph diagram analysis • Use arrangements, selections, counting principles, permutations, combinations, and structured cases. 2. Introduction to Proof text calculation graph diagram analysis • Use proof structure, implication, contradiction-style reasoning, direct proof, and justification of mathematical claims. 3. Vectors in the Plane text calculation graph diagram analysis • Use two-dimensional vectors, magnitude, direction, vector addition, scalar multiplication, and geometric interpretation. 4. Algebra of Vectors in Two Dimensions text calculation graph diagram analysis • Use scalar products, projections, vector equations, angle relationships, and vector proofs in two dimensions. 5. Matrices text calculation graph diagram analysis • Use matrix operations, transformations, systems, determinants, and matrix interpretation.	1. Complex Numbers text calculation graph diagram analysis • Use imaginary number definition, complex arithmetic, Cartesian form, Argand-plane basics, modulus, and conjugates. 2. Complex Arithmetic and Algebra text calculation graph diagram analysis • Use algebraic manipulation of complex numbers, equations, factors, roots, and exact complex-number reasoning. 3. Circle and Geometric Proofs text calculation graph diagram analysis • Use circle geometry, geometric relationships, and proof-style reasoning. 4. Trigonometry and Functions text calculation graph diagram analysis • Use trigonometric identities, exact values, equations, function transformations, and graph interpretation. 5. Matrices and Transformations text calculation graph diagram analysis • Use matrices for transformations, composition, geometric effects, and systems.	1. Further Complex Numbers text calculation graph diagram analysis • Use polar form, modulus, argument, De Moivre's theorem, roots of unity, roots of complex numbers, polynomial factorisation, factor theorem, remainder theorem, and conjugate root theorem. 2. Mathematical Induction and Trigonometric Proofs text calculation graph diagram analysis • Use induction structure, sums, divisibility, De Moivre proof, trigonometric proofs, and exact symbolic reasoning. 3. Vectors in Two and Three Dimensions text calculation graph diagram analysis • Use 2D and 3D vectors, scalar product, vector equations, lines, planes, angles, distances, and geometric interpretation. 4. Vector Calculus text calculation graph diagram analysis • Use vector functions, position, velocity, acceleration, motion in two and three dimensions, and calculus-based vector reasoning. 5. Further Matrices text calculation graph diagram analysis • Use matrices beyond 2 by 2, systems of linear equations, Gaussian elimination, geometric interpretation of systems, dominance matrices, and Leslie matrices.	1. Integration Techniques text calculation graph diagram analysis • Use advanced integration methods, inverse trigonometric forms, logarithmic integrals, partial fractions, integration by parts, and exact antiderivatives. 2. Applications of Integral Calculus text calculation graph diagram analysis • Use area between curves, volumes of revolution, Simpson's rule, exponential random variables, and applied integral modelling. 3. Rates of Change and Differential Equations text calculation graph diagram analysis • Use implicit differentiation, related rates, simple differential equations, solutions, long-term behaviour, and interpretation of change. 4. Modelling Motion text calculation graph diagram analysis • Use position, velocity, acceleration, force, motion, differential equations, and kinematics contexts. 5. Statistical Inference text calculation graph diagram analysis • Use sampling distributions, sample means, confidence intervals, normal approximation, statistical reasoning, and interpretation.