Year 12 HSC Maths - Mathematics Advanced sample questions
Year 12 HSC Maths - Mathematics Advanced sample questions
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Year 12 HSC Mathematics Advanced practice questions
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Skills covered
Practice functions, calculus, trigonometry, exponential and logarithmic relationships, probability, statistics, and modelling.
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Sample HSC Year 12 Mathematics Advanced questions
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HSC Year 12Mathematics AdvancedIntegral calculushardtangent and area graph
1. The graph shows y = x(5 - x) on 0 ≤ x ≤ 5. What is the exact area enclosed by the curve and the x-axis?
Choices
125/6
25/6
125/3
25
Explanation:
The area is the integral from 0 to 5 of x(5 - x). This is [5x2/2 - x3/3] from 0 to 5 = 125/2 - 125/3 = 125/6.
HSC Year 12Mathematics AdvancedFunctions and transformationshardtransformation graph
2. The graph of y = f(x) has stationary point A(2, -1). For g(x) = 5 - 2f(x - 3), which point is the corresponding stationary point on y = g(x)?
Choices
(5, 7)
(-1, 7)
(5, 3)
(2, 7)
Explanation:
The input x - 3 must equal 2, so x = 5. The output becomes 5 - 2(-1) = 7, so the corresponding stationary point is (5, 7).
HSC Year 12Mathematics AdvancedExponential and logarithmic modellinghardmodel graph
3. A logistic model is N(t) = 100/(1 + 9e-0.3t), where t is measured in hours. At what time is N'(t) greatest?
Choices
(10 ln 9)/3 hours
3 ln 9 / 10 hours
0.3 ln 9 hours
9/0.3 hours
Explanation:
For a logistic model, growth is greatest at half the limiting value, so N = 50. Solve 100/(1 + 9e-0.3t) = 50 to get 9e-0.3t = 1, hence t = (10 ln 9)/3 hours.
HSC Year 12Mathematics AdvancedContinuous probabilityharddensity graph
4. For the continuous random variable X with density f(x) = c(4x - x2), 0 ≤ x ≤ 4, what is P(X > 2)?
Choices
1/2
1/4
2/3
3/4
Explanation:
The total unscaled area is the integral from 0 to 4 of 4x - x2, which is 32/3. The unscaled area from 2 to 4 is 16/3, so P(X > 2) = (16/3)/(32/3) = 1/2.
HSC Year 12Mathematics AdvancedNormal distributionhardnormal curve
5. For X ~ N(μ, σ2), P(X < 52) = 0.1587 and P(X < 68) = 0.8413. Using Φ(-1) = 0.1587 and Φ(1) = 0.8413, what are μ and σ?
Choices
μ = 60, σ = 8
μ = 60, σ = 16
μ = 52, σ = 8
μ = 68, σ = 8
Explanation:
The probabilities place 52 one standard deviation below the mean and 68 one standard deviation above it. The mean is the midpoint (52 + 68)/2 = 60, and the standard deviation is 68 - 60 = 8.
HSC Year 12Mathematics AdvancedDifferential calculushardtangent graph
6. For f(x) = x3 - 4x2 + x, the tangent T is drawn at P where x = 3. What is the gradient of T?
Choices
4
-4
12
0
Explanation:
Differentiate to get f'(x) = 3x2 - 8x + 1. At x = 3, f'(3) = 27 - 24 + 1 = 4.
For parents comparing HSC Year 12 Mathematics Advanced support
HSC Year 12 Mathematics Advanced practice should make calculus, functions, modelling, probability, and statistics testable without losing the worked method. These examples preview that graph-backed style before the no-login Mathematics Advanced demo.
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Practice Summary
Year 12 · HSC Maths - Mathematics Advanced · Test mode · 1 questions · 10 min
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