HSC Year 12 Mathematics Advanced practice questions
HSC Year 12 Mathematics Advanced practice questions
Use Skill Align for HSC Year 12 Mathematics Advanced 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.
21 practice skills
HSC Year 12 Mathematics Advanced includes 21 practice skills across Functions and graphs, Calculus and applications, Statistics and probability, and Sequences and modelling.
Australian Years 7-12Exercise and test modeParent-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 12 Mathematics Advanced questions
These sample questions are visible on the page before login. They show HSC Year 12 Mathematics Advanced calculus, functions, modelling, probability, and statistics explanations before opening the demo.
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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Mathematics Advanced practice sits inside NSW Year 12 HSC Mathematics course structures, with Year 11 Preliminary context available through the full curriculum coverage, 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
Functions and graphs: Students practise functions and graphs 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.
Statistics and probability: Students practise statistics and probability 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.
These examples are not the full topic list. Use the curriculum coverage page for the complete mapped pathway.
Functions and graphs
Calculus and applications
Statistics and probability
Sequences and modelling
Who it is for
NSW students studying Mathematics Advanced.
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