Year 12 HSC Maths - Mathematics Extension 1 sample questions
Year 12 HSC Maths - Mathematics Extension 1 sample questions
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Year 12 HSC Mathematics Extension 1 practice questions
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Try a short public sample of Year 12 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 12 Mathematics Extension 1 questions
These sample questions are visible on the page before login. They show HSC Year 12 Mathematics Extension 1 induction, vectors, binomial, trigonometry, calculus, and probability explanations before opening the demo.
HSC Year 12Mathematics Extension 1Mathematical inductionhardsequence graph
1. To prove 1 + 3 + 5 + ... + (2n - 1) = n2 by induction, which line correctly uses the k-case to prove the (k + 1)-case?
Choices
k2 + (2k + 1) = (k + 1)2
k2 + 2k = (k + 1)2
k2 + (k + 1) = (k + 1)2
2k + 1 = (k + 1)2
Explanation:
Assume the sum of the first k odd numbers is k2. The next odd number is 2k + 1, so the next sum is k2 + 2k + 1 = (k + 1)2.
HSC Year 12Mathematics Extension 1Vectorshardvector diagram
2. In the vector diagram, a = (3, 1), b = (2, 5), and p denotes the component of b perpendicular to a. What is |p|?
Choices
13√10/10
11/10
√10
13/10
Explanation:
Since b . a = 11 and a . a = 10, proj_a b = (11/10)a. Hence p = b - proj_a b = (-13/10, 39/10), with magnitude √(1690)/10 = 13√10/10.
HSC Year 12Mathematics Extension 1Binomial theoremhardweighted score chart
3. In the expansion of (1 - 2x)7, what is the coefficient of x4?
Choices
560
-560
280
35
Explanation:
The x4 term is C(7, 4)(-2x)4 = 35 x 16x4 = 560x4, so the coefficient is 560.
HSC Year 12Mathematics Extension 1Trigonometric equationshardunit circle
4. For 0 ≤ x < 2π, how many solutions does 2cos2 x + cos x - 1 = 0 have?
Choices
3
2
4
5
Explanation:
Factor the equation as (2cos x - 1)(cos x + 1) = 0. Thus cos x = 1/2 or cos x = -1. On 0 ≤ x < 2π, these occur at π/3, 5π/3 and π, giving three solutions.
HSC Year 12Mathematics Extension 1Integral calculushardtangent and area graph
5. The graph shows y = x and y = x2 between x = 0 and x = 1. What is the exact area between the curves?
Choices
1/6
1/3
1/2
2/3
Explanation:
On 0 ≤ x ≤ 1, x is above x2. The area is the integral from 0 to 1 of x - x2, which is 1/2 - 1/3 = 1/6.
HSC Year 12Mathematics Extension 1Probabilityhardnormal curve
6. Let X be binomial with n = 8 and p = 0.35. What is E(X), and which interpretation is correct?
Choices
2.8 expected successes
0.35 expected successes
8 expected successes
5.2 expected failures
Explanation:
For a binomial random variable, E(X) = np. Here E(X) = 8 x 0.35 = 2.8, meaning the long-run average number of successes is 2.8 per eight trials.
For parents comparing HSC Year 12 Mathematics Extension 1 support
HSC Year 12 Mathematics Extension 1 practice should give strong students enough structure to revise induction, vectors, binomial theorem, trigonometry, calculus, and probability. These examples preview that style before the no-login Extension 1 demo.
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Practice Summary
Year 12 · HSC Maths - Mathematics Extension 1 · Test mode · 2 questions · 10 min
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HSC Mathematics Extension 1 practice questions FAQ
Does this page include Year 12 HSC Mathematics Extension 1 practice questions?
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