HSC Year 11 Mathematics Extension 1 Practice Questions

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HSC Year 11 Mathematics Extension 1 practice questions

Use Skill Align for HSC Year 11 Mathematics Extension 1 practice questions and exercise questions after the relevant topic has been taught. Students can start with the pathway demo, then practise by topic and mode.

16 practice skills

HSC Year 11 Mathematics Extension 1 includes 16 practice skills across Advanced functions and proof, Calculus and applications, Vectors and complex numbers, and Extension problem solving.

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Australian Years 7-12 Exercise and test mode Parent-managed access

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A practice skill is a focused topic or question type designed to help students practise one curriculum-aligned concept with instant feedback and explanations. Skill Align uses practice skills to organise questions by year level, subject, strand, and curriculum focus.

Sample HSC Year 11 Mathematics Extension 1 questions

These sample questions are visible on the page before login. They show HSC Year 11 Mathematics Extension 1 functions, trigonometry, calculus, binomial, vectors, and proof explanations before opening the demo.

HSC Year 11 Mathematics Extension 1 Functions and transformations hard transformation graph

1. The graph of y = f(x) has stationary point A(1, -2). For g(x) = -3f(x + 2) + 4, which point is the corresponding stationary point on y = g(x)?

Choices

(-1, 10)
(3, 10)
(-1, -2)
(1, 10)

Explanation:

The input x + 2 must equal 1, so x = -1. The output becomes -3(-2) + 4 = 10, so the corresponding stationary point is (-1, 10).

HSC Year 11 Mathematics Extension 1 Trigonometric equations hard unit circle

2. For 0 <= x < 2π, how many solutions does 2sin² x - sin x - 1 = 0 have?

Choices

Explanation:

Factor the equation as (2sin x + 1)(sin x - 1) = 0. Thus sin x = -1 / 2 or sin x = 1. On 0 <= x < 2π, these occur at 7π / 6, 11π / 6 and π / 2, giving three solutions.

HSC Year 11 Mathematics Extension 1 Calculus hard tangent graph

3. For f(x) = x² ln x, x > 0, the tangent T is drawn at P where x = e. What is the gradient of T?

Choices

Explanation:

Differentiate using the product rule: f'(x) = 2x ln x + x. At x = e, ln e = 1, so f'(e) = 2e + e = 3e.

HSC Year 11 Mathematics Extension 1 Binomial theorem hard weighted score chart

4. In the expansion of (1 + 2x)⁶, what is the coefficient of x³?

Choices

Explanation:

The x³ term is C(6, 3)(2x)³ = 20 x 8x³ = 160x³, so the coefficient is 160.

HSC Year 11 Mathematics Extension 1 Vectors hard vector diagram

5. In the vector diagram, a = (2, 1), b = (5, 4), and p denotes the component of b perpendicular to a. What is |p|?

Choices

3sqrt(5) / 5
14 / 5
√5
3 / 5

Explanation:

Since b . a = 14 and a . a = 5, proj_a b = (14 / 5)a. Hence p = b - proj_a b = (-3 / 5, 6 / 5), with magnitude √45 / 5 = 3sqrt(5) / 5.

HSC Year 11 Mathematics Extension 1 Proof and sequences hard sequence graph

6. In an induction proof for 1² + 2² + ... + n² = n(n + 1)(2n + 1) / 6, what term is added to the k-case to begin the (k + 1)-case?

Choices

(k + 1)²
k²
2k + 1
(k + 1)(k + 2)

Explanation:

The k-case sums from 1² to k^2. The next case sums from 1² to k² plus the next square, so the added term is (k + 1)^2.

For parents comparing HSC Year 11 Mathematics Extension 1 support

HSC Year 11 Mathematics Extension 1 practice should stretch capable students with proof, vectors, trigonometry, binomial reasoning, and calculus without hiding the method. These examples preview that style before the no-login Extension 1 demo.

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Public samples are free to review before sign-in. Regular full subject access is subscription-based through a parent-managed student account, with included access to start and optional monthly subject access explained on the Pricing page. Exam packs, where available, are separate one-off PDF purchases and are not included in a practice subscription.

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What this practice and exercise page covers

Mathematics Extension 1 practice sits inside NSW Year 11 Preliminary Mathematics coverage across Standard, Advanced, Extension 1, functions, algebra, statistics, probability, finance, networks, and proof, with Skill Align keeping the route focused on the selected maths pathway.

Senior practice is organised by pathway, unit, topic, and mode so students can revise targeted areas rather than sitting a full-paper workflow every time. Skill Align treats practice questions and exercise questions as the same learning workflow: students answer curriculum-aligned questions, review explanations, and move between exercise mode and test mode.

Start with the public sample questions to check the question style, then use the curriculum coverage page to choose a topic that matches the student's current classwork.

Preview question styles

Advanced functions and proof: Students practise advanced functions and proof through short targeted questions, explanations, and mode-specific feedback.
Calculus and applications: Students practise calculus and applications through short targeted questions, explanations, and mode-specific feedback.
Vectors and complex numbers: Students practise vectors and complex numbers through short targeted questions, explanations, and mode-specific feedback.

Suggested first practice steps

Preview the public sample practice and exercise questions before creating a saved student session.
Choose one focus area that has already been introduced at school.
Use exercise mode for immediate explanations, then test mode when the student is ready for delayed feedback.

Example focus areas

View full curriculum coverage

These examples are not the full topic list. Use the curriculum coverage page for the complete mapped pathway.

Advanced functions and proof
Calculus and applications
Vectors and complex numbers
Extension problem solving

Who it is for

NSW students studying Mathematics Extension 1.

How access works

Review public sample questions without signing in.
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Use included access first, then add an optional monthly subject subscription when more practice is needed.

Questions parents ask

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No. Skill Align is designed for structured practice after students have learned topics at school or with a teacher.

Are practice questions and exercise questions the same on Skill Align?

Yes. Families may search for either wording; Skill Align uses one curriculum-aligned practice page for both practice questions and exercise questions.

How does regular hsc year 11 mathematics extension 1 practice questions access work?

Public samples are free before sign-in. Regular full subject access uses a parent-managed account with included access to start and an optional monthly subject subscription when more practice is needed. Exam packs are separate one-off PDF purchases.

Skill Align independently prepares practice pathways aligned to publicly available curriculum and syllabus information. Official requirements should always be checked with the relevant authority.