Year 11 ACT Maths - Mathematical Methods sample questions
Year 11 ACT Maths - Mathematical Methods sample questions
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Year 11 Mathematical Methods practice questions
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Skills covered
Practice functions, relations, algebra, calculus, probability, transformations, graphs, and mathematical modelling.
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Sample ACT BSSS Year 11 Mathematical Methods questions
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ACT BSSS Year 11Mathematical MethodsFunctions and transformationshardtransformation graph
1. The graph of y = x² is transformed to y = 2(x + 1)² - 5. What is the turning point of the transformed graph?
Choices
(-1, -5)
(1, -5)
(-1, 5)
(2, -5)
Explanation:
The rule is in turning-point form y = a(x - h)² + k. Since x + 1 = x - (-1), the turning point is (-1, -5).
ACT BSSS Year 11Mathematical MethodsDifferential calculushardtangent graph
2. For f(x) = x³ - 3x² + 4x, the tangent T is drawn at P where x = 2. What is the gradient of T?
Choices
4
8
0
-4
Explanation:
Differentiate to get f'(x) = 3x² - 6x + 4. At x = 2, f'(2) = 12 - 12 + 4 = 4.
ACT BSSS Year 11Mathematical MethodsIntegral calculushardtangent and area graph
3. The graph shows y = 6x - x² above the x-axis from x = 0 to x = 3. What is the exact area under the curve on this interval?
Choices
18
9
27
12
Explanation:
Integrate 6x - x² from 0 to 3: [3x² - x³ / 3] from 0 to 3 = 27 - 9 = 18.
ACT BSSS Year 11Mathematical MethodsExponential modellinghardmodel graph
4. A medicine level is modelled by A = 250(0.5)^(t / 12). How long until the level first falls to 100, to the nearest 0.1 years?
Choices
15.9 years
12.0 years
7.6 years
19.9 years
Explanation:
Set 100 = 250(0.5)^(t / 12), so 0.4 = (0.5)^(t / 12). Taking logarithms gives t = 12 log(0.4) / log(0.5) = 15.863..., so 15.9 years.
ACT BSSS Year 11Mathematical MethodsContinuous probabilityharddensity graph
5. For the continuous random variable X with density f(x) = kx(3 - x), 0 <= x <= 3, what is P(X > 1)?
Choices
20 / 27
7 / 27
2 / 3
5 / 9
Explanation:
The unscaled total area is the integral from 0 to 3 of x(3 - x), which is 9 / 2. The unscaled area from 1 to 3 is 10 / 3. Hence P(X > 1) = (10 / 3) / (9 / 2) = 20 / 27.
ACT BSSS Year 11Mathematical MethodsNormal distributionhardnormal curve
6. For X ~ N(μ, σ²), P(X < 64) = 0.1587 and P(X < 76) = 0.8413. Using Φ(-1) = 0.1587 and Φ(1) = 0.8413, what are μ and σ?
Choices
μ = 70, σ = 6
μ = 70, σ = 12
μ = 64, σ = 6
μ = 76, σ = 6
Explanation:
The probabilities place 64 one standard deviation below the mean and 76 one standard deviation above it. The mean is (64 + 76) / 2 = 70, and the standard deviation is 76 - 70 = 6.
For parents comparing ACT BSSS Year 11 Mathematical Methods support
ACT BSSS Year 11 Mathematical Methods practice should make functions, calculus, probability, modelling, and statistics feel structured rather than guessable. These examples preview that style before the no-login Mathematical Methods demo.
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Practice Summary
Year 11 · ACT Maths - Mathematical Methods · Test mode · 6 questions · 10 min
Questions attempted0 / 6
Correct answersPending
Score-
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