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VCE Year 12 Mathematical Methods practice questions

VCE Year 12 Mathematical Methods practice questions

Use Skill Align for VCE Year 12 Mathematical Methods practice questions after the relevant topic has been taught. Students can start with the pathway demo, then practise by topic and mode.

37 practice skills

VCE Year 12 Mathematical Methods includes 37 practice skills across Functions and relations, Calculus and rates of change, Probability and statistics, and Graphs and transformations.

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A practice skill is a focused topic or question type designed to help students practise one curriculum-aligned concept with instant feedback and explanations. Skill Align uses practice skills to organise questions by year level, subject, strand, and curriculum focus.

Sample VCE Mathematical Methods questions

These sample questions are visible on the page before login. They show the style of Mathematical Methods answers, graphs, and explanations before opening the VCE Mathematical Methods demo.

VCE Year 12 Mathematical Methods Differentiation and integration hard tangent and area graph

1. The graph shows y = x(4 - x). Tangent T is drawn at P where x = 1, and R is the region between T and the curve from x = 1 to x = 3. What is the exact area of R?

Tangent and enclosed area for y = x(4 - x) P T R
Choices
  • 8/3
  • 4/3
  • 2
  • 10/3
Explanation:

f'(x) = 4 - 2x, so at x = 1 the tangent is y = 2x + 1. On 1 ≤ x ≤ 3, T - f(x) = 2x + 1 - x(4 - x) = (x - 1)2. The area is the integral from 1 to 3 of (x - 1)2, which is 8/3.

VCE Year 12 Mathematical Methods Functions and transformations hard transformation graph

2. The graph of y = f(x) has stationary point A(-2, 5). For g(x) = 3 - 2f(x + 1), which point is the corresponding stationary point on y = g(x)?

Stationary point under a transformation A A' g
Choices
  • (-3, -7)
  • (-1, -7)
  • (-3, 13)
  • (1, -7)
Explanation:

The input x + 1 must equal -2, so x = -3. The output becomes 3 - 2(5) = -7, so the corresponding stationary point is (-3, -7).

VCE Year 12 Mathematical Methods Continuous probability hard density graph

3. For the continuous random variable X with density f(x) = cx(4 - x), 0 ≤ x ≤ 4, what is P(X > 3 | X > 2)?

Conditional probability from a density curve A B R
Choices
  • 5/16
  • 5/32
  • 11/16
  • 3/8
Explanation:

The constant c cancels in the conditional probability. The integral of x(4 - x) from 3 to 4 is 5/3, and from 2 to 4 is 16/3. Hence P(X > 3 | X > 2) = (5/3)/(16/3) = 5/16.

VCE Year 12 Mathematical Methods Optimisation hard optimisation diagram

4. A rectangle has top corners on y = 12 - x2 and base on the x-axis, symmetric about the y-axis. If the right top corner is P(x, 12 - x2), x > 0, which value of x gives the maximum rectangle area?

Maximum rectangle under a parabola P x A
Choices
  • 2
  • √2
  • √(6)
  • 3
Explanation:

The rectangle has width 2x and height 12 - x2, so A(x) = 2x(12 - x2). Then A'(x) = 24 - 6x2, giving x = 2. Also A''(x) = -12x is negative at x = 2, so the area is maximal.

VCE Year 12 Mathematical Methods Exponential and logarithmic modelling hard model graph

5. A revision model is N(t) = 80/(1 + 7e-0.4t), where t is measured in weeks. At what time is N'(t) greatest?

Logistic model and maximum growth rate P L/2 S
Choices
  • 2.5 ln 7 weeks
  • ln 7 / 2.5 weeks
  • 0.4 ln 7 weeks
  • 7 / 2.5 weeks
Explanation:

For a logistic model, growth is greatest at half the limiting value, so N = 40. Solve 80/(1 + 7e-0.4t) = 40 to get 7e-0.4t = 1, so t = ln 7 / 0.4 = 2.5 ln 7 weeks.

VCE Year 12 Mathematical Methods Normal distribution hard normal curve

6. For X ~ N(μ, σ2), P(X < 62) = 0.1587 and P(X < 74) = 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 = 68, σ = 6
  • μ = 68, σ = 12
  • μ = 62, σ = 6
  • μ = 74, σ = 6
Explanation:

The probabilities place 62 one standard deviation below the mean and 74 one standard deviation above it. The mean is the midpoint (62 + 74)/2 = 68, and the standard deviation is 74 - 68 = 6.

For parents comparing VCE Mathematical Methods support

VCE Mathematical Methods practice should make functions, calculus, probability, and modelling feel testable without hiding the method. These examples preview graph-backed, single-best-answer questions before the no-login Mathematical Methods demo.

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What this practice page covers

Mathematical Methods practice sits inside VCE Mathematics Units 3 and 4 practice pathways, with Units 1 and 2 context available through the full curriculum coverage, with Skill Align keeping the route focused on the selected maths pathway.

Senior practice is organised by pathway, unit, topic, and mode so students can revise targeted areas rather than sitting a full-paper workflow every time.

Start with the public sample questions to check the question style, then use the curriculum coverage page to choose a topic that matches the student's current classwork.

Preview question styles
  • Functions and relations: Students practise functions and relations through short targeted questions, explanations, and mode-specific feedback.
  • Calculus and rates of change: Students practise calculus and rates of change through short targeted questions, explanations, and mode-specific feedback.
  • Probability and statistics: Students practise probability and statistics through short targeted questions, explanations, and mode-specific feedback.
Suggested first practice steps
  • Preview the public sample questions before creating a saved student session.
  • Choose one focus area that has already been introduced at school.
  • Use exercise mode for immediate explanations, then test mode when the student is ready for delayed feedback.
Example focus areas
View full curriculum coverage

These examples are not the full topic list. Use the curriculum coverage page for the complete mapped pathway.

  • Functions and relations
  • Calculus and rates of change
  • Probability and statistics
  • Graphs and transformations
Who it is for

Victorian students studying Mathematical Methods.

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