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Year 11 ACT Maths - Mathematical Methods sample questions

Year 11 ACT Maths - Mathematical Methods practice preview

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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

These sample questions are visible on the page before login. They show ACT BSSS Year 11 Mathematical Methods functions, calculus, probability, modelling, and statistics explanations before opening the demo.

ACT BSSS Year 11 Mathematical Methods Functions and transformations hard transformation 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?

Parabola transformation P T A
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 11 Mathematical Methods Differential calculus hard tangent graph

2. For f(x) = x3 - 3x2 + 4x, the tangent T is drawn at P where x = 2. What is the gradient of T?

Tangent to a cubic at x = 2 P x = 2 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 11 Mathematical Methods Integral calculus hard tangent 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?

Area under a quadratic curve P T R
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 11 Mathematical Methods Exponential modelling hard model 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?

Exponential decay threshold A T L
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 11 Mathematical Methods Continuous probability hard density graph

5. For the continuous random variable X with density f(x) = kx(3 - x), 0 ≤ x ≤ 3, what is P(X > 1)?

Right-tail probability from a density curve A B R
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 11 Mathematical Methods Normal distribution hard normal 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?

Normal curve with symmetric z-scores A B μ
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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Mathematical Methods practice questions FAQ

Does this page include Year 11 Mathematical Methods practice questions?

Not yet. The Year 11 Mathematical Methods demo route is public, but the interactive sample questions will open after the reviewed public set is ready.

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How does this demo relate to curriculum coverage?

This demo is linked with the ACT Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.