Assessment and exam practice.

Try this with Mathematics Extension 1

1. Check the task format, time limit and permitted materials with your school.
2. Start with one timed section or task and record where you spent the most time.
3. Review errors before attempting another section. Separate missing knowledge from timing problems.

View Mathematics Extension 1 resources on ATARMAXXING ↗

Practice paper focus areas

• Exam 1 — Proof by Mathematical Induction (series sum and divisibility — emphasis topic); Vectors (2D projection and 3D magnitude/perpendicularity); Trigonometric Equations (auxiliary-angle R-method and double-angle)
• Exam 2 — Vectors (projection, geometry proof, relative motion/collision, projectile modelling) — emphasised, ~21/60 marks; Proof by Mathematical Induction (series summation); Trigonometric Equations (quadratic-in-sin and double-angle reduction)
• Exam 3 — Trigonometric Equations (emphasis): double-angle reduction, auxiliary-angle R-method, factoring trig equations over a restricted domain; Calculus: inverse-trig differentiation, integration by reduction identity and u-substitution, volumes of revolution; Vectors: projection, angle between vectors, internal division of an interval
• Exam 4 — Further Calculus Skills (integration by substitution, inverse trig differentiation & integration); Vectors (dot product, projection, angle); Trigonometric Equations (double-angle & t-formula)
• Exam 5 — Applications of Calculus (Newton's law of cooling modelling, related rates, areas/volumes, SHM) — the paper's emphasis; Proof by Mathematical Induction (divisibility); Vectors (dot product, angle, scalar/vector projection)
• Exam 6 — The Binomial Distribution (Bin(n,p), exact probabilities, mean/variance, normal approximation to a sample proportion) — the flagged emphasis, ~35/60 marks; Proof by Mathematical Induction (series identity and divisibility); Vectors (dot product, angle between vectors, scalar projection)
• Exam 7 — Proof by Mathematical Induction (series, divisibility and inequality forms); Projectile motion and exponential modelling applications of calculus; The Binomial Distribution including normal approximation and sample proportions
• Exam 8 — Vectors (28/60 marks — emphasis): projection, collision modelling, Varignon proof, perpendicularity/parallelism, extended projectile-by-vectors; Proof by Mathematical Induction; Trigonometric Equations
• Exam 9 — Trigonometric Equations (auxiliary-angle, quadratic-in-sin, modelling); Proof by Mathematical Induction; Vectors (projection and perpendicular component)
• Exam 10 — Further Calculus Skills (substitution, by parts, inverse-trig & double-angle integration) — dominant weighting; Applications of Calculus (Newton's Law of Cooling model, SHM, related rates); Proof by Mathematical Induction (series result)
• Exam 11 — Applications of Calculus (related rates, exponential growth/decay DEs, projectile motion, volumes of revolution); Proof by Mathematical Induction; Vectors (projection, angle, perpendicularity)
• Exam 12 — The Binomial Distribution (emphasis): exact/cumulative probabilities, mean & variance, sample proportions with normal approximation, multi-part modelling; Full Year 12 coverage: Mathematical Induction (series + divisibility), Vectors (dot product, projection, projectile, geometric proof), Trigonometric Equations, Further Calculus Skills, Applications of Calculus; Realistic HSC Ext 1 weighting and graduated difficulty, with every numerical answer recomputed and verified in Python/SymPy
• Exam 13 — Proof by Mathematical Induction (series, divisibility and inequality forms) — the emphasis of this paper; Vectors — projections, perpendicularity and 3D angle/dot product; Trigonometric equations — quadratic-in-sin, t-formula and auxiliary-angle methods
• Exam 14 — Vectors (projection, geometry proofs, projectile motion as vectors) — emphasised per exam flavour; Proof by Mathematical Induction; Trigonometric Equations (quadratic-in-sin, auxiliary-angle method)
• Exam 15 — Trigonometric Equations (emphasis); Proof by Mathematical Induction; Vectors
• Exam 16 — Further Calculus Skills (integration by substitution, inverse-trig derivatives/integrals); Applications of Calculus (related rates, volumes of revolution, exponential models); Proof by Mathematical Induction (divisibility)
• Exam 17 — Applications of Calculus (SHM, projectile modelling, area/volume of revolution); Further Calculus Skills (inverse-trig derivatives, integration by substitution and reverse chain); The Binomial Distribution (probabilities, mean/SD, recurrence and mode)
• Exam 18 — The Binomial Distribution (emphasis - 21/60 marks): Bernoulli trials, P(X=k)=C(n,k)p^k q^(n-k), mean np and sd sqrt(npq), most likely value, normal approximation and sample proportions; Proof by Mathematical Induction: divisibility and series-sum proofs with rigorous inductive step; Vectors: scalar (dot) product, projection, perpendicularity, geometry proofs and projectile motion
• Exam 19 — Proof by Mathematical Induction (series identity and divisibility); Vectors (projection, angle, geometric proof); Trigonometric equations and Further Calculus Skills
• Exam 20 — Vectors (35%): components, projection, angle, geometric proofs, projectile motion in vector form; Proof by Mathematical Induction (series sum and divisibility); Trigonometric Equations (quadratic-in-sin and auxiliary-angle method)