Year 11 VCE Maths - Mathematical Methods sample questions
Year 11 VCE Maths - Mathematical Methods sample questions
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Year 11 VCE 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 VCE Year 11 Mathematical Methods questions
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VCE Year 11Mathematical MethodsFunctions and transformationshardtransformation 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)?
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 11Mathematical MethodsIntroductory calculushardtangent graph
2. For f(x) = x³ - 6x² + 5x, the tangent T is drawn at P where x = 4. What is the gradient of 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 11Mathematical MethodsContinuous probabilityharddensity graph
3. For the continuous random variable X with density f(x) = kx, 0 <= x <= 4, what is P(X > 3)?
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 11Mathematical MethodsOptimisationhardoptimisation 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?
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 - 6x^2. Setting A'(x) = 0 gives x² = 10 / 3, so x = √(10 / 3).
VCE Year 11Mathematical MethodsExponential modellinghardmodel graph
5. A culture model is P(t) = 80e^(0.25t), where t is measured in hours. At what time does the model first reach 160?
VCE Year 11Mathematical MethodsNormal distributionhardnormal 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?
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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Practice Summary
Year 11 · VCE Maths - Mathematical Methods · Test mode · 6 questions · 10 min
Questions attempted0 / 6
Correct answersPending
Score-
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