Year 12 ACT Maths - Mathematical Methods sample questions
Year 12 ACT Maths - Mathematical Methods sample questions
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Year 12 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 12 Mathematical Methods questions
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ACT BSSS Year 12Mathematical MethodsIntegral calculushardtangent and area graph
1. What is the exact value of the integral from 0 to 2 of (3x2 - 2x) dx?
Choices
4
8
2
12
Explanation:
An antiderivative is x3 - x2. Evaluating from 0 to 2 gives 8 - 4 = 4.
ACT BSSS Year 12Mathematical MethodsDifferential calculushardtangent graph
2. For f(x) = ln(x2 + 1), the tangent T is drawn at P where x = 2. What is the gradient of T?
Choices
4/5
2/5
5/4
1/5
Explanation:
Using the chain rule, f'(x) = 2x/(x2 + 1). At x = 2, f'(2) = 4/5.
ACT BSSS Year 12Mathematical MethodsExponential and logarithmic modellinghardmodel graph
3. A population is modelled by P(t) = 1200/(1 + 5e-0.4t). What is the exact time when P(t) = 800?
Choices
(5 ln 10)/2 hours
(ln 10)/5 hours
5 ln 2 hours
10 ln 5 hours
Explanation:
Set 800 = 1200/(1 + 5e-0.4t), so 1 + 5e-0.4t = 3/2. Hence e-0.4t = 0.1 and t = ln(10)/0.4 = (5 ln 10)/2.
ACT BSSS Year 12Mathematical MethodsContinuous probabilityharddensity graph
4. For the continuous random variable X with density f(x) = c(2x + 1), 0 ≤ x ≤ 3, what is P(X > 2)?
Choices
1/2
1/3
2/3
3/4
Explanation:
The unscaled total area is the integral from 0 to 3 of 2x + 1, which is 12. The unscaled area from 2 to 3 is 6, so P(X > 2) = 6/12 = 1/2.
ACT BSSS Year 12Mathematical MethodsNormal distributionhardnormal curve
5. For X ~ N(μ, σ2), P(X < 58) = 0.1587 and P(X < 74) = 0.8413. Using Φ(-1) = 0.1587 and Φ(1) = 0.8413, what are μ and σ?
Choices
μ = 66, σ = 8
μ = 66, σ = 16
μ = 58, σ = 8
μ = 74, σ = 8
Explanation:
The two values are one standard deviation below and above the mean. The mean is (58 + 74)/2 = 66, and the standard deviation is 74 - 66 = 8.
ACT BSSS Year 12Mathematical MethodsFunctions and logarithmshardmodel graph
6. For f(x) = 3e0.5x - 2, what exact value of x satisfies f(x) = 10?
Choices
4 ln 2
2 ln 2
ln 4
4
Explanation:
Set 3e0.5x - 2 = 10, so e0.5x = 4. Taking logarithms gives 0.5x = ln 4, hence x = 2 ln 4 = 4 ln 2.
For parents comparing ACT BSSS Year 12 Mathematical Methods support
ACT BSSS Year 12 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 12 · ACT Maths - Mathematical Methods · Test mode · 2 questions · 10 min
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Correct answersPending
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