Year 12 ACT Maths - Specialist Methods sample questions
Year 12 ACT Maths - Specialist Methods sample questions
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Year 12 Specialist Methods practice questions
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Skills covered
Practice advanced functions, calculus, probability, statistics, and extended mathematical modelling.
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Sample ACT BSSS Year 12 Specialist Methods questions
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ACT BSSS Year 12Specialist MethodsProduct and chain rulehardtangent graph
1. For f(x) = (x2 + 1)ex, what is f'(1)?
Choices
4e
2e
3e
e
Explanation:
Using the product rule, f'(x) = 2xex + (x2 + 1)ex. At x = 1, f'(1) = 2e + 2e = 4e.
ACT BSSS Year 12Specialist MethodsIntegral calculushardtangent and area graph
2. What is the exact value of the integral from 0 to 1 of x/(x2 + 1) dx?
Choices
(ln 2)/2
ln 2
1/2
2 ln 2
Explanation:
Let u = x2 + 1, so du = 2x dx. The integral is (1/2)ln(x2 + 1) from 0 to 1, which is (ln 2)/2.
ACT BSSS Year 12Specialist MethodsDiscrete random variableshardweighted score chart
3. A discrete random variable has P(X = 0) = 0.20, P(X = 1) = 0.35, P(X = 2) = 0.30, and P(X = 3) = 0.15. What is E(X)?
Choices
1.4
1.5
2.0
0.35
Explanation:
E(X) = 0 x 0.20 + 1 x 0.35 + 2 x 0.30 + 3 x 0.15 = 0.35 + 0.60 + 0.45 = 1.4.
ACT BSSS Year 12Specialist MethodsNormal distributionhardnormal curve
4. For X ~ N(72, 82), use z = 1.04 for the 85th percentile. What is the approximate 85th percentile?
Choices
80.3
63.7
73.0
88.6
Explanation:
The percentile value is μ + zσ = 72 + 1.04 x 8 = 80.32, which rounds to 80.3.
ACT BSSS Year 12Specialist MethodsRegressionhardregression graph
5. A regression line is y = 5.2 + 0.74x. For x = 18, the observed value is 20.1. What is the residual, using observed - predicted?
Choices
1.58
-1.58
18.52
20.1
Explanation:
The predicted value is 5.2 + 0.74 x 18 = 18.52. The residual is 20.1 - 18.52 = 1.58.
ACT BSSS Year 12Specialist MethodsStatistical inferencehardnormal curve
6. A sample has 84 successes in 120 trials. Using p̂ = 0.70 and z = 1.96, which interval is the approximate 95% confidence interval for the true proportion?
Choices
0.618 to 0.782
0.658 to 0.742
0.600 to 0.800
0.700 to 0.782
Explanation:
The standard error is √(0.70 x 0.30 / 120) = 0.0418. The margin is 1.96 x 0.0418 = 0.082, so the interval is 0.70 ± 0.082, or 0.618 to 0.782.
For parents comparing ACT BSSS Year 12 Specialist Methods support
ACT BSSS Year 12 Specialist Methods practice should make advanced functions, calculus, probability, regression, and inference feel structured rather than guessable. These examples preview that style before the no-login Specialist Methods demo.
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Practice Summary
Year 12 · ACT Maths - Specialist Methods · Test mode · 2 questions · 10 min
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