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WACE Mathematics Specialist past exams 2021–2025, by year and topic
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ATARMAxxing indexes 22 official SCSA Mathematics Specialist papers from 2021 to 2025, with 56 questions mapped to 6 topics. Every paper opens on the SCSA website.
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Preview the worked question →WACE Mathematics Specialist exams by year: official papers & marking guidance
Past exams indexed: 2025, 2024, 2023, 2022, 2021. Open the official SCSA papers, with marking guidance where available.
22 official papers across 5 years (2021–2025), 5 with marking guidance, published by SCSA. These span more than one study design; the most recent is Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15). Earlier papers may cover material that has since changed.
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Unit 3 — Topic 3.1: Complex numbers · 13 mapped questions
Modulus, argument, polar form and de Moivre's theorem for integral powers
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q197 marksSuccessive multiplication by w shown on an Argand diagram: w in polar form, values of n placing zw^n in the second quadrant, and a tan identity derived from the geometry.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q13 marksExact modulus/argument facts for z = 3 + bi given tan(theta) = 2.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q84 marksUses the expansion of (a + bi)^3 to find a^2 + b^2 from two real simultaneous equations.Official paper ↗Marking guidance ↗Check tutors for this question →
Addition as vector addition, multiplication as rotation and dilation, and complex-number geometry
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q79 marksRegular hexagon of complex numbers on a circle: exact polar form of a vertex, Arg of a difference, a product of vertices in terms of r, and the real part of the intersection of two tangents.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q107 marksSuccessive multiplication by z on an Argand diagram: polar forms, describing the transformation, z itself and the inverse transformation.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q126 marksArgand-diagram geometry with |z| = 3 and Arg(w) = 2 theta: represents the information and finds k in terms of theta.Official paper ↗Marking guidance ↗Check tutors for this question →
Loci and regions in the complex plane: circles, rays, perpendicular bisectors and |z - a| = k|z - b|
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q106 marksWrites modulus/argument conditions for a shaded locus without x and y, then sketches the intersection of an argument condition and a second relation.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q108 marksCircle in the Argand plane: its equation, exact bounds on |z - i|, and sketching the intersection of an Im-type condition with an argument sector.Official paper ↗Marking guidance ↗Check tutors for this question →
nth roots of unity and of complex numbers; factor and remainder theorems, conjugate roots and polynomial equations
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q14 marksFinds the real constant in z^3 = ki from one root shown on an Argand diagram, then plots the other two cube roots.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q75 marksShows a complex linear factor of a quadratic, then solves a quartic with real coefficients.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q96 marksShows a complex number is a 24th root of unity, finds every n for which it solves z^n = 1, and explains how to locate all roots for the smallest n.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q25 marksFifth-degree real polynomial with two given non-real roots: the quartic factor and the coefficients.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q65 marksFourth roots of a complex number in r cis(theta) form.Official paper ↗Marking guidance ↗Check tutors for this question →
Unit 3 — Topic 3.2: Functions and sketching graphs · 9 mapped questions
Composition of functions: when f(g(x)) is defined, its domain and range
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q25 marksFrom a graph of f: domain of a function built from f^-1 with justification, and the range of a reciprocal-type function.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q411 marksFrom two graphs: an inverse sketch, a composite value, where f(g(x)) is defined, a sketch of f(-|x|), and an absolute-value equation with an interval of solutions.Official paper ↗Marking guidance ↗Check tutors for this question →
One-to-one functions, inverse functions and the reflection property
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q813 marksFunction built from inverse cosine: why the inverse exists, its rule and graph, an implicit-differentiation derivative, and an exact area bounded by a related curve.Official paper ↗Marking guidance ↗Check tutors for this question →
Absolute value, y = 1/f(x), y = |f(x)|, y = f(|x|) and rational functions with vertical, horizontal and oblique asymptotes
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q28 marksFrom a printed graph of f: states the domain of a composite involving f^-1, sketches an inverse and a reciprocal-type transformation, and solves an equation built from f.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q99 marksDetermines, with justification, the rule of a rational function from its graph and states the range of a related function.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q55 marksIdentifies constants of a rational function from its graph (with justification) and finds its inclined asymptote.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q157 marksFamily of absolute-value 'W-graphs': sketches a member, counts solutions of W_k(x) = k, and develops an integral in terms of k.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q14 marksDetermines the constants of a rational function from its graph.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q186 marksRational function with given asymptotes: shows the constants, then an exact area.Official paper ↗Marking guidance ↗Check tutors for this question →
Unit 3 — Topic 3.3: Vectors in three dimensions · 11 mapped questions
3D vector algebra, scalar product and vector proofs of geometric results
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q188 marksSquare pyramid with origin at a diagonal midpoint: vector expressions for edges and midpoints, a dot product in a given form, and the condition for a right angle.Official paper ↗Marking guidance ↗Check tutors for this question →
Lines, line segments, spheres and parametric curves; do the paths cross or do the particles meet?
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q169 marksTwo thrill-seekers on straight wires: speed, angle of descent to the horizontal, and the minimum possible separation if timing and speed can change.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q96 marksSphere in vector form and its intersection points with a line.Official paper ↗Marking guidance ↗Check tutors for this question →
Cross product, planes and systems of three linear equations with their geometric interpretation
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q47 marksSystem of three linear equations with parameters k and c: solves one case, then states the k and c values for a unique point and for no intersection.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q116 marksIntersection point of two lines in space and the Cartesian equation of the plane containing both.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q66 marksSolves a system of three equations, finds k for no unique solution after one coefficient changes, and interprets the result geometrically.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q55 marksTwo planes: why they are not parallel, the geometric interpretation, and the vector equation of their line of intersection.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q1411 marksPlane and line: normal vector, vector form of the plane, line-plane angle, and the plane containing the line perpendicular to the first.Official paper ↗Marking guidance ↗Check tutors for this question →
Vector functions of time: velocity, acceleration, distance travelled, projectile and circular motion
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q1210 marksRacing-car position vector: Cartesian path, distance travelled to 0.01 m, interpreting the integral of r'(t) as a displacement, and locating minimum speed.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q1812 marksDrone with exponential position vector: exact position, velocity, path length, direction of travel, and Cartesian equation (a hyperbola).Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q165 marksFly on a 3D path: initial acceleration vector and path length to 0.001 m.Official paper ↗Marking guidance ↗Check tutors for this question →
Unit 4 — Topic 4.1: Integration and applications of integration · 10 mapped questions
Integration with trigonometric identities and the substitution u = g(x), including exact definite integrals
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q66 marksExact definite integral using a given trigonometric substitution x - 1 = 2 sin u.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q34 marksExact definite integral using the substitution u = 1 - x.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q35 marksExact definite integral with the substitution x = 119u + 1.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q79 marksArea of a circular segment: sets up the integral, then evaluates it exactly with x - 3 = 2 sin(theta).Official paper ↗Marking guidance ↗Check tutors for this question →
Integral of 1/x, f'(x)/f(x) and partial fractions
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q36 marksUnprompted indefinite integral of a rational function requiring partial fractions.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section One: Calculator-free Q46 marksFinds partial-fraction constants and hence integrates a rational function.Official paper ↗Marking guidance ↗Check tutors for this question →
Areas between curves in x and in y, volumes of solids of revolution about either axis, and numerical integration
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q83 marksArea of an ellipse to three decimal places by integration with technology.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q1410 marksMilkshake glass from rotating 16y = x^4 about the y-axis: volume to depth h, related rate of depth, and maximum fill depth allowing for melted ice.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q116 marksDonut (torus) volume by rotating a circle about the y-axis: shows the integral, states its limits, and applies a density and daily limit.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q177 marksVase by revolution about the y-axis: volume integral to depth h, filling time, and the increments formula for a small extra volume.Official paper ↗Marking guidance ↗Check tutors for this question →
Unit 4 — Topic 4.2: Rates of change and differential equations · 9 mapped questions
Implicit differentiation, related rates and the increments formula
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section One: Calculator-free Q55 marksImplicit differentiation of an equation already containing dy/dx, then the exact second derivative at a point using a given tangent line.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q1916 marksBall and its shadow from a light: implicit differentiation of s(10 - h) = 30, h(t) from h'' = -9.8, shadow speed, an integral of ds/dt interpreted, and the fastest shadow speed.Official paper ↗Marking guidance ↗Check tutors for this question →
Separable differential equations and slope fields
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q164 marksValue of a slope field at a point and drawing the solution curve through it.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q115 marksSlope field dy/dx = kxy: finds k, solves for the curve through a point, and draws it.Official paper ↗Marking guidance ↗Check tutors for this question →
Formulating differential equations: exponential, logistic and other growth-rate models
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q1711 marksNon-logistic fish growth-rate equation: sketch P(t), increments-formula estimate, separation of variables to a given form, and why the model fails for a larger initial population.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q138 marksBrumby population given as a logistic function: time to triple, long-run size, the constants r and k in dP/dt = rP(k - P), and maximum growth rate.Official paper ↗Marking guidance ↗Check tutors for this question →
Rectilinear motion with variable acceleration, v dv/dx, and simple harmonic motion
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q156 marksMass on a spring satisfying an SHM relation: amplitude, period and distance travelled over 10 pi seconds.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q125 marksMerry-go-round horse obeying an SHM equation: displacement function and maximum vertical speed.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q179 marksSinking device with dv/dt = -9.8 - 2v: acceleration at a given speed, features of the acceleration graph, separation of variables for v(t), and depth of the seabed.Official paper ↗Marking guidance ↗Check tutors for this question →
Unit 4 — Topic 4.3: Statistical inference · 4 mapped questions
Confidence intervals for a population mean: construction, sample size, width and interpretation
- 2025Year 12 syllabus for teaching from 2025 (current, 2013/28123 v15)Section Two: Calculator-assumed Q1313 marksDart distances: approximate distribution of the sample mean, a probability, recovering n from a reported 95% interval, and judging conclusions drawn from intervals and from 500 simulated intervals.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2024Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q1415 marksAnaesthetic recovery times: distribution of X-bar, probabilities and a 50% interval width, a 99% interval, evaluating two doctors' claims about intervals, and minimum sample size for a given width.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q1311 marksCereal-box weights: distribution of X-bar, a probability, a 95% interval, maximum standard deviation for a width, and judging a claim from 50 intervals.Official paper ↗Marking guidance ↗Check tutors for this question →
- 2023Previous Year 12 syllabus version (before the 2025 minor changes)Section Two: Calculator-assumed Q159 marksBank loans: recovers the sample mean and its standard deviation from a 99% interval, explains a misinterpretation, and recalculates after n and the mean change.Official paper ↗Marking guidance ↗Check tutors for this question →
Also in this topic: The sample mean as a random variable: distribution of X-bar and the central limit theorem — question-level mapping in progress; the year table above links every official paper.
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