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Year 11 VCE Maths - Mathematical Methods sample questions

Year 11 VCE Maths - Mathematical Methods practice preview

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Year 11 VCE Mathematical Methods practice questions

This public preview page identifies the planned Year 11 VCE Mathematical Methods demo route and links it to curriculum coverage while the reviewed sample question set is being completed.

Sample-question focus

The planned public sample is for Year 11 VCE Mathematical Methods practice and will open after the demo questions are reviewed.

Skills covered

Practice functions, relations, algebra, calculus, probability, transformations, graphs, and mathematical modelling.

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Compare this demo with the VCE Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.

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Sample VCE Year 11 Mathematical Methods questions

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

VCE Year 11 Mathematical Methods Functions and transformations hard transformation graph

1. The graph of y = f(x) has stationary point A(2, -3). For g(x) = 4 - f(x - 1), which point is the corresponding stationary point on y = g(x)?

Stationary point under a Year 11 transformation A A' g
Choices
  • (3, 7)
  • (1, 7)
  • (3, 1)
  • (1, -7)
Explanation:

The input x - 1 must equal 2, so x = 3. The output becomes 4 - (-3) = 7, so the corresponding stationary point is (3, 7).

VCE Year 11 Mathematical Methods Introductory calculus hard tangent graph

2. For f(x) = x3 - 6x2 + 5x, the tangent T is drawn at P where x = 4. What is the gradient of T?

Tangent to a cubic at x = 4 P x = 4 T
Choices
  • 5
  • -5
  • 21
  • 0
Explanation:

Differentiate to get f'(x) = 3x2 - 12x + 5. At x = 4, f'(4) = 48 - 48 + 5 = 5, so the tangent gradient is 5.

VCE Year 11 Mathematical Methods Continuous probability hard density graph

3. For the continuous random variable X with density f(x) = kx, 0 ≤ x ≤ 4, what is P(X > 3)?

Right-tail probability from a linear density A B R
Choices
  • 7/16
  • 1/4
  • 9/16
  • 3/4
Explanation:

First 1 = the integral from 0 to 4 of kx, so 1 = 8k and k = 1/8. Then P(X > 3) is the integral from 3 to 4 of x/8, which is (16 - 9)/16 = 7/16.

VCE Year 11 Mathematical Methods Optimisation hard optimisation diagram

4. A rectangle has top corners on y = 10 - x2 and base on the x-axis, symmetric about the y-axis. If the right top corner is P(x, 10 - x2), x > 0, which value of x gives the maximum rectangle area?

Maximum rectangle under a Year 11 parabola P x A
Choices
  • √(10/3)
  • √5
  • √10
  • 10/3
Explanation:

The rectangle has width 2x and height 10 - x2, so A(x) = 2x(10 - x2). Then A'(x) = 20 - 6x2. Setting A'(x) = 0 gives x2 = 10/3, so x = √(10/3).

VCE Year 11 Mathematical Methods Exponential modelling hard model graph

5. A culture model is P(t) = 80e0.25t, where t is measured in hours. At what time does the model first reach 160?

Exponential doubling model P 2P t
Choices
  • 4 ln 2 hours
  • ln 2 / 4 hours
  • 0.25 ln 2 hours
  • 2 ln 4 hours
Explanation:

Solve 80e0.25t = 160, so e0.25t = 2. Taking natural logarithms gives 0.25t = ln 2, hence t = 4 ln 2 hours.

VCE Year 11 Mathematical Methods Normal distribution hard normal curve

6. For X ~ N(μ, σ2), P(X < 54) = 0.1587 and P(X < 66) = 0.8413. Using Φ(-1) = 0.1587 and Φ(1) = 0.8413, what are μ and σ?

Normal curve with Year 11 z-score markers A B μ
Choices
  • μ = 60, σ = 6
  • μ = 60, σ = 12
  • μ = 54, σ = 6
  • μ = 66, σ = 6
Explanation:

The probabilities place 54 one standard deviation below the mean and 66 one standard deviation above it. The mean is the midpoint (54 + 66)/2 = 60, and the standard deviation is 66 - 60 = 6.

For parents comparing VCE Year 11 Mathematical Methods support

VCE Year 11 Mathematical Methods practice should make functions, introductory calculus, probability, and modelling feel exact but learnable. These examples preview graph-backed, single-best-answer questions before the no-login Mathematical Methods demo.

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VCE Mathematical Methods practice questions FAQ

Does this page include Year 11 VCE Mathematical Methods practice questions?

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

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No sign-up is required to view the preview status. The no-login interactive demo will be available after the sample set is completed.

How does this demo relate to curriculum coverage?

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