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HSC Year 11 Mathematics Extension 1 practice questions

HSC Year 11 Mathematics Extension 1 practice questions

Use Skill Align for HSC Year 11 Mathematics Extension 1 practice 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

What is a practice skill?

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)?

Extension transformation of a stationary point A A' g
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?

Unit-circle solutions for sine 1 -1/2 θ
Choices
  • 3
  • 2
  • 4
  • 5
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?

Tangent to x squared log x P x = e T
Choices
  • 3e
  • 2e
  • e
  • 3
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?

Highlighted binomial coefficient x² x³ 160
Choices
  • 160
  • 120
  • 80
  • 20
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|?

Perpendicular component of a vector a b p
Choices
  • 3√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 = 3√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?

Induction step for a square-sum proof Pₖ₊₁ n S
Choices
  • (k + 1)2
  • k2
  • 2k + 1
  • (k + 1)(k + 2)
Explanation:

The k-case sums from 12 to k2. 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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Ready to continue? Use the normal Skill Align pages below to preview questions, check full curriculum coverage, or compare pricing before deciding whether to sign up.

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What this practice 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.

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 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.

Common search wording
HSC Year 11 Mathematics Extension 1 practice questionsHSC Mathematics Extension 1 practice questionsMathematics Extension 1 online practiceHSC Maths - Mathematics Extension 1 practice questions
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Yes. Public sample pages let visitors preview curated Skill Align questions without creating a saved student test record.

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