ATARMAxxing · Mathematics Extension 1
HSC Mathematics Extension 1 Practice Exams with Worked Solutions
20 full-length papers · worked solutions for every question
The 20 practice exams inside the HSC Mathematics Extension 1 Mastery Pack, each set out like the real paper with a separate worked-solution guide. Open any paper to see what it covers.
- 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)
- Calculus (further skills, motion in a line, exponential modelling, projectile)
- The Binomial Distribution (probabilities, mean and variance)
- 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)
- Further Calculus Skills + Applications of Calculus (substitution, inverse-trig integrals, exponential decay)
- The Binomial Distribution (probabilities, mean/SD, mode/most-likely value)
- 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
- Proof by Mathematical Induction and the Binomial Distribution
- Multi-part SHM modelling application worth 5+ marks
- Further Calculus Skills (integration by substitution, inverse trig differentiation & integration)
- Vectors (dot product, projection, angle)
- Trigonometric Equations (double-angle & t-formula)
- Proof by Mathematical Induction (divisibility)
- The Binomial Distribution & sample proportions
- 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)
- Trigonometric Equations (quadratic-in-sin, auxiliary R cos(x-a) form)
- The Binomial Distribution (exact probabilities, mean/variance, normal approximation to a sample proportion)
- 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)
- Trigonometric Equations and Further Calculus Skills (inverse-trig differentiation/integration)
- Applications of Calculus (exponential growth/decay modelling)
- 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
- Vectors: scalar product, projection and geometric proof
- Further calculus skills: integration by substitution and trigonometric integrals
- Vectors (28/60 marks — emphasis): projection, collision modelling, Varignon proof, perpendicularity/parallelism, extended projectile-by-vectors
- Proof by Mathematical Induction
- Trigonometric Equations
- Further Calculus Skills (substitution, double-angle integrals, inverse functions)
- Applications of Calculus (SHM) and The Binomial Distribution
- Trigonometric Equations (auxiliary-angle, quadratic-in-sin, modelling)
- Proof by Mathematical Induction
- Vectors (projection and perpendicular component)
- The Binomial Distribution
- Further Calculus Skills & Applications (SHM, integration by substitution)
- 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)
- Vectors (2D projection + projectile motion)
- Trigonometric Equations & The Binomial Distribution
- Applications of Calculus (related rates, exponential growth/decay DEs, projectile motion, volumes of revolution)
- Proof by Mathematical Induction
- Vectors (projection, angle, perpendicularity)
- The Binomial Distribution
- Trigonometric equations & Further Calculus integration skills
- 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
- 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
- Further calculus and Applications of calculus — differentiation/integration of inverse-trig & exponential functions, Newton's Law of Cooling modelling
- The Binomial distribution and the binomial expansion (independent term)
- Vectors (projection, geometry proofs, projectile motion as vectors) — emphasised per exam flavour
- Proof by Mathematical Induction
- Trigonometric Equations (quadratic-in-sin, auxiliary-angle method)
- Further Calculus Skills & Applications of Calculus (inverse-trig integration)
- The Binomial Distribution (probabilities, mean, variance)
- Trigonometric Equations (emphasis)
- Proof by Mathematical Induction
- Vectors
- Further Calculus Skills & Applications of Calculus
- The Binomial Distribution
- 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)
- Vectors (projection, projectile motion)
- The Binomial Distribution & trigonometric equations (auxiliary angle, double angle)
- 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)
- Vectors (projection, angle, perpendicularity, geometric proof)
- Proof by Mathematical Induction and Trigonometric Equations
- The Binomial Distribution (emphasis - 21/60 marks): Bernoulli trials, P(X=k)=C(n,k)pk q^(n-k), mean np and sd √(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
- Trigonometric Equations: auxiliary-angle method and double-angle factorisation over a given domain
- Further Calculus Skills & Applications of Calculus: integration by substitution, inverse-trig integrals, related rates, volumes of revolution, exponential growth
- Proof by Mathematical Induction (series identity and divisibility)
- Vectors (projection, angle, geometric proof)
- Trigonometric equations and Further Calculus Skills
- Applications of Calculus (projectile motion, related rates, SHM)
- The Binomial Distribution
- 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)
- Calculus (further integration skills, volumes, exponential/Newton-cooling modelling)
- The Binomial Distribution (exact probabilities, mean/sd, sample proportion)
Included in the HSC Mathematics Extension 1 Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
Unlock Mathematics Extension 1 — $20
Preview a sample note and question free on the HSC Mathematics Extension 1 hub →