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Year 11 ACT Maths - Specialist Methods sample questions

Year 11 ACT Maths - Specialist Methods practice preview

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Year 11 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 11 Specialist Methods questions

These sample questions are visible on the page before login. They show ACT BSSS Year 11 Specialist Methods advanced functions, calculus, probability, regression, and inference explanations before opening the demo.

ACT BSSS Year 11 Specialist Methods Composite functions hard tangent graph

1. For y = (2x2 - 1)5, what is dy/dx at x = 1?

Tangent to a composite-function curve P x = 1 T
Choices
  • 20
  • 10
  • 40
  • 5
Explanation:

By the chain rule, dy/dx = 5(2x2 - 1)4 x 4x. At x = 1, this is 5 x 14 x 4 = 20.

ACT BSSS Year 11 Specialist Methods Product rule hard tangent graph

2. For f(x) = x2ex, what is f'(1)?

Product-rule tangent P x = 1 T
Choices
  • 3e
  • 2e
  • e
  • 4e
Explanation:

Using the product rule, f'(x) = 2xex + x2ex. At x = 1, f'(1) = 2e + e = 3e.

ACT BSSS Year 11 Specialist Methods Trigonometric equations hard unit circle

3. For 0 ≤ x < 2π, how many solutions does 2sin2 x - sin x - 1 = 0 have?

Unit-circle solutions for sine 1 -1/2 θ
Choices
  • 3
  • 2
  • 4
  • 1
Explanation:

Factor as (2sin x + 1)(sin x - 1) = 0. Thus sin x = 1 or sin x = -1/2. On 0 ≤ x < 2π, this gives π/2, 7π/6, and 11π/6, so there are 3 solutions.

ACT BSSS Year 11 Specialist Methods Counting methods hard weighted score chart

4. From 6 senior students and 5 junior students, a committee of 4 must contain exactly 2 senior students. How many committees are possible?

Counting by grouped choices S J 150
Choices
  • 150
  • 300
  • 50
  • 30
Explanation:

Choose 2 of the 6 seniors and 2 of the 5 juniors: C(6, 2) x C(5, 2) = 15 x 10 = 150.

ACT BSSS Year 11 Specialist Methods Exponential modelling hard model graph

5. A quantity is modelled by N = 80e0.18t. How long does it take to quadruple, to the nearest 0.1 years?

Exponential growth threshold N 4N T
Choices
  • 7.7 years
  • 4.0 years
  • 9.9 years
  • 22.2 years
Explanation:

Set 320 = 80e0.18t, so 4 = e0.18t. Hence t = ln 4 / 0.18 = 7.70..., so 7.7 years.

ACT BSSS Year 11 Specialist Methods Normal distribution hard normal curve

6. For X ~ N(52, 72), and Φ(1) = 0.8413, what is P(X < 59)?

Normal curve with z = 1 A B μ
Choices
  • 0.8413
  • 0.1587
  • 0.5000
  • 0.6826
Explanation:

The z-score is (59 - 52)/7 = 1. Therefore P(X < 59) = Φ(1) = 0.8413.

For parents comparing ACT BSSS Year 11 Specialist Methods support

ACT BSSS Year 11 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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Specialist Methods practice questions FAQ

Does this page include Year 11 Specialist Methods practice questions?

Not yet. The Year 11 Specialist 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.