Year 11 HSC Maths - Mathematics Extension 1 sample questions
Year 11 HSC Maths - Mathematics Extension 1 sample questions
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Year 11 HSC Mathematics Extension 1 practice questions
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Try a short public sample of Year 11 HSC Mathematics Extension 1 questions selected from the reviewed Skill Align demo set.
Skills covered
Practice advanced functions, trigonometry, calculus, proof, vectors, combinatorics, and harder multi-step reasoning.
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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 11Mathematics Extension 1Functions and transformationshardtransformation 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 11Mathematics Extension 1Trigonometric equationshardunit circle
2. For 0 ≤ x < 2π, how many solutions does 2sin2 x - sin x - 1 = 0 have?
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 11Mathematics Extension 1Calculushardtangent 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
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 11Mathematics Extension 1Binomial theoremhardweighted score chart
4. In the expansion of (1 + 2x)6, what is the coefficient of x3?
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 11Mathematics Extension 1Vectorshardvector 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
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 11Mathematics Extension 1Proof and sequenceshardsequence 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 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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Practice Summary
Year 11 · HSC Maths - Mathematics Extension 1 · Test mode · 6 questions · 10 min
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Correct answersPending
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HSC Mathematics Extension 1 practice questions FAQ
Does this page include Year 11 HSC Mathematics Extension 1 practice questions?
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This demo is linked with the HSC Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.
