§-Mock exam
Maths Extension 1 mock exam
Higher School Certificate Examination - Mathematics Extension 1. Sit it in one block, time yourself with the on-screen clock, then self-mark against the model answers.
Paper structure from the official NESA page.
Want the real thing? Open the 2025 Maths Extension 1 paper walkthrough for the official structure and marking criteria.
Paper at a glance
Reading time
10 min
Working time
120 min
Total marks
70
Sections
2
| Section | Questions | Marks | Recommended time |
|---|---|---|---|
| Section I - Objective response | 10 | 10 | 15 min |
| Section II - Free response | 19 | 60 | 105 min |
Before you start
What this mock covers
- Section I - Objective response: 10 multiple-choice questions, auto-marked when you submit.
- Section II - Free response: 19 short-answer questions (60 marks), self-marked against a model answer.
17 syllabus dot points covered
Syllabus dot points examined in this paper:
- Combinations: counting unordered selections with nCr, the 2^n subset count, the symmetry nCr = nC(n-r), and restriction techniques (at least, complement, conditional, geometry)
- Defining curves parametrically and eliminating the parameter
- General solutions of trigonometric equations: $\sin$, $\cos$ and $\tan$
- Geometric proofs with vectors: parallel, perpendicular, midpoint and ratio properties
- Integrals giving inverse trig functions: $\arcsin$, $\arctan$ and the patterns to recognise
- Inverse trigonometric functions: definitions, principal branches, domains, ranges and graphs
- Mathematical induction for series identities
- Normal approximation of the binomial distribution: continuity, validity and z-scores
- Polynomial and rational inequalities: sign analysis, critical points and excluded values
- Product-to-sum and sum-to-product identities for trigonometric expressions
- Projectile motion: parametric equations, range, maximum height and time of flight
- Related rates of change: linking changing quantities via implicit differentiation
- Roots and coefficients of polynomials: Vieta's formulas for cubics and quartics
- Sketching y = 1/f(x) from the graph of y = f(x)
- The binomial theorem and Pascal's triangle: expansion of $(a + b)^n$ and the general term
- The scalar (dot) product: component formula, geometric formula, angle between vectors and orthogonality
- Vector projection: scalar projection and vector projection of one vector onto another
Multiple-choice questions are drawn from the Binomial Theorem and Combinatorics (HSC Maths Extension 1, 2026), Mathematical Induction (HSC Maths Extension 1, 2026), Vectors (HSC Maths Extension 1, 2026) quizzes.
Your answers, the clock and your self-marks save on this device as you go, so a reload picks up where you left off.