100+ Free HSC Maths Ext 1 Practice Questions

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Key Facts: HSC Maths Ext 1 Exam

70 marks

Total marks for the HSC Mathematics Extension 1 written examination

NESA - HSC examination specifications / school course advice

10 MCQs

Section I has 10 multiple-choice questions worth 1 mark each

NESA - Mathematics Extension 1 examination structure

2 hours

Working time plus 10 minutes reading time for the exam

NESA - HSC examination advice / 2026 timetable

1.50–4.00 pm

Approximate 2026 written examination session for Mathematics Extension 1

NESA - 2026 HSC written exam timetable

1 unit

Mathematics Extension 1 is a 1-unit course studied with Mathematics Advanced

NESA - Mathematics Extension 1 Stage 6 syllabus

Bands E1–E4

Extension results are reported as performance bands E1 to E4

NESA - Mathematics Extension 1 performance band descriptions

$1,443 AUD

2026 Full Fee Paying Overseas Students HSC fee (no separate Ext 1 subject fee)

NESA overseas students fee schedule 2026

100

Free original MCQ practice questions in this study adaptation

OpenExamPrep

HSC Mathematics Extension 1 is the 1-unit NSW HSC maths extension course examined by NESA. The official written exam is 70 marks in 2 hours plus 10 minutes reading (Section I: 10 MCQs; Section II: 60 marks extended response), scheduled around 1.50–4.00 pm in 2026. Topics span further functions, trigonometry, calculus, combinatorics, mathematical induction, vectors and further probability. Domestic entry is included in HSC enrolment; FFPOS candidates pay AUD $1,443 (2026). This 100-question bank is a free English-language MCQ study adaptation, not an official-format simulation.

Sample HSC Maths Ext 1 Practice Questions

Try these sample questions to test your HSC Maths Ext 1 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1The function f(x) = (x - 2)/(x + 1) is undefined at which value of x?

A.x = 2

B.x = -1

C.x = 1

D.x = 0

Explanation: The denominator is zero when x + 1 = 0, so x = -1.

2If f(x) = 2x + 3 and g(x) = x^2 - 1, what is (f ∘ g)(2)?

A.9

B.7

C.11

D.5

Explanation: g(2) = 3, then f(3) = 2(3) + 3 = 9.

3The inverse of f(x) = 3x - 5 is which function?

A.f^{-1}(x) = 3x + 5

B.f^{-1}(x) = (x - 5)/3

C.f^{-1}(x) = 5 - 3x

D.f^{-1}(x) = (x + 5)/3

Explanation: Set y = 3x - 5, swap: x = 3y - 5 ⇒ y = (x + 5)/3.

4For which values of x is 2x - 1 > 5?

A.x > 2

B.x < 3

C.x > 3

D.x >= 3

Explanation: 2x - 1 > 5 ⇒ 2x > 6 ⇒ x > 3.

5The parametric equations x = 2t, y = t^2 give which Cartesian relation?

A.y = 4x^2

B.y = x^2/4

C.y = x^2/2

D.y = 2x^2

Explanation: t = x/2 ⇒ y = (x/2)^2 = x^2/4.

6If f(x) = √(x - 1), what is the domain of f?

A.x >= 1

B.x > 1

C.x >= 0

D.all real x

Explanation: Require x - 1 >= 0 ⇒ x >= 1.

7The graphs of y = f(x) and y = f^{-1}(x) are reflections of each other in which line?

A.y = -x

B.x = 0

C.y = 0

D.y = x

Explanation: Inverse functions swap coordinates, which is reflection in y = x.

8Solve |2x - 4| = 6.

A.x = 5 only

B.x = 1 or x = -5

C.x = 5 or x = -1

D.x = 3 or x = -3

Explanation: 2x-4=6 ⇒ x=5; 2x-4=-6 ⇒ x=-1.

9If f(x) = x^3 - 3x, which statement is true because f is odd?

A.f(-x) = f(x) for all x

B.f(-x) = -f(x) for all x in the domain

C.f(x) > 0 for all x > 0

D.f has no real roots

Explanation: Odd means f(-x)=-f(x). Here f(-x)=-x^3+3x=-(x^3-3x)=-f(x).

10The range of f(x) = 1/(x^2 + 1) for real x is:

A.0 < y <= 1

B.y >= 1

C.0 <= y <= 1

D.all real y

Explanation: x^2+1>=1 ⇒ 0 < 1/(x^2+1) <= 1.

About the HSC Maths Ext 1 Exam

HSC Mathematics Extension 1 is the 1-unit calculus-based extension mathematics course of the NSW Higher School Certificate, studied with Mathematics Advanced and examined by the NSW Education Standards Authority (NESA). Year 11 topics include Functions, Trigonometric Functions, Calculus and Combinatorics; Year 12 continues Trigonometric Functions and Calculus and adds Proof, Vectors and Statistical Analysis. The written HSC examination runs for 2 hours plus 10 minutes reading time and is worth 70 marks: Section I has 10 one-mark multiple-choice questions and Section II has short-answer and extended-response questions. A NESA reference sheet is supplied and approved calculators are permitted. For the 2026 HSC, the written paper is scheduled in an afternoon session approximately 1.50 pm–4.00 pm. Results are reported in Extension bands E1–E4 rather than a simple pass or fail. This practice bank is an original English-language multiple-choice study adaptation of syllabus concepts; it does not reproduce official NESA questions and does not fully simulate Section II extended-response writing.

Assessment

The written HSC examination has two sections totalling 70 marks. Section I contains 10 multiple-choice questions worth 1 mark each (10 marks). Section II contains short-answer and extended-response questions (60 marks). School-based assessment and the external examination each contribute 50% of the HSC mark for the course.

Time Limit

2 hours of working time plus 10 minutes reading time (2026 written exam approximately 1.50 pm–4.00 pm).

Passing Score

There is no fixed pass mark. NESA reports Extension achievement in bands E1 to E4 (E4 highest). Raw marks out of 70 are moderated and aligned; ATAR is calculated separately by UAC.

Exam Fee

Included in NSW HSC enrolment for domestic students. Full Fee Paying Overseas Students (FFPOS) pay the 2026 NESA HSC fee of $1,443 AUD; there is no separate per-subject Mathematics Extension 1 fee. (NSW Education Standards Authority (NESA))

HSC Maths Ext 1 Exam Content Outline

12%

Functions

Inequalities, inverse functions, graphical relationships between functions, and parametric equations that extend Mathematics Advanced function skills.

15%

Trigonometric Functions

Further trigonometric identities, compound-angle formulae, inverse trigonometric functions, and solving extension-level trigonometric equations.

25%

Calculus

Further differentiation and integration, rates of change, areas and volumes of solids of revolution, and first-order differential equation applications at Ext 1 level.

15%

Combinatorics

Permutations and combinations for counting and probability, and the binomial theorem for expansions and coefficient problems.

10%

Proof

Mathematical induction proofs for summation formulae, divisibility statements and related recursive identities.

13%

Vectors

Two-dimensional vector algebra, geometric applications, and modelling motion in a plane with vector methods.

10%

Statistical Analysis

Further probability focusing on the binomial distribution and related Extension 1 statistical reasoning.

How to Pass the HSC Maths Ext 1 Exam

What You Need to Know

Passing score: There is no fixed pass mark. NESA reports Extension achievement in bands E1 to E4 (E4 highest). Raw marks out of 70 are moderated and aligned; ATAR is calculated separately by UAC.
Assessment: The written HSC examination has two sections totalling 70 marks. Section I contains 10 multiple-choice questions worth 1 mark each (10 marks). Section II contains short-answer and extended-response questions (60 marks). School-based assessment and the external examination each contribute 50% of the HSC mark for the course.
Time limit: 2 hours of working time plus 10 minutes reading time (2026 written exam approximately 1.50 pm–4.00 pm).
Exam fee: Included in NSW HSC enrolment for domestic students. Full Fee Paying Overseas Students (FFPOS) pay the 2026 NESA HSC fee of $1,443 AUD; there is no separate per-subject Mathematics Extension 1 fee.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

HSC Maths Ext 1 Study Tips from Top Performers

1Work past HSC Mathematics Extension 1 papers under timed conditions, starting with Section I to build speed on standard MCQ techniques.

2Memorise which formulae appear on the NESA reference sheet and which Ext 1 results (such as induction templates and vector identities) you must recall yourself.

3For Calculus, practise chain/product/quotient work with inverse trig and then apply integration to volumes and simple differential equations.

4For Combinatorics, separate permutation and combination cases carefully and check restrictions such as adjacent people or identical objects.

5For Proof, write induction in three clear steps: base case, inductive hypothesis, and inductive step with algebraic justification.

6For Vectors, convert between component and magnitude-direction forms early, then apply to geometric and projectile-style motion questions.

7Always show full working in Section II, because method marks are awarded even when a final numerical answer is wrong.

Frequently Asked Questions

How is the HSC Mathematics Extension 1 examination structured?

The written exam totals 70 marks. Section I has 10 multiple-choice questions worth 1 mark each, and Section II has short-answer and extended-response questions worth 60 marks.

How long is the HSC Mathematics Extension 1 exam?

Students have 2 hours of working time plus 10 minutes reading time. In the 2026 HSC written timetable, Mathematics Extension 1 is scheduled approximately 1.50 pm–4.00 pm.

Is there a pass mark for HSC Mathematics Extension 1?

No. NESA reports Extension results in performance bands E1 to E4, with E4 the highest. There is no simple pass or fail mark, and the ATAR is calculated separately by UAC.

What topics are examined in HSC Mathematics Extension 1?

Year 12 content covers continued Trigonometric Functions and Calculus plus Proof, Vectors and Statistical Analysis, with Year 11 Functions, Trigonometric Functions, Calculus and Combinatorics as assumed knowledge that may also be examined.

What does the exam cost?

Domestic NSW candidates do not pay a separate per-subject fee; Mathematics Extension 1 is included in HSC enrolment. Full Fee Paying Overseas Students entered for the HSC pay AUD $1,443 per student under the 2026 NESA overseas fee schedule.

Is this practice bank multiple-choice only?

Yes. This bank is an English-language MCQ study adaptation designed to reinforce Extension 1 calculations and reasoning. Official Section II extended-response writing is not fully simulated by MCQs.

Are these official NESA HSC questions?

No. These are original OpenExamPrep practice questions modelled on the Mathematics Extension 1 syllabus. NESA publishes official past HSC papers and a reference sheet separately.

100+ Free HSC Maths Ext 1 Practice Questions

HSC Mathematics Extension 1 (NSW)