Year 11 VCE Maths - Specialist Mathematics sample questions
Year 11 VCE Maths - Specialist Mathematics practice preview
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Year 11 VCE Specialist Mathematics practice questions
This public preview page identifies the planned Year 11 VCE Specialist Mathematics 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 Specialist Mathematics practice and will open after the demo questions are reviewed.
Skills covered
Practice proof, vectors, complex numbers, advanced calculus, mechanics, differential equations, and probability.
Exercise and test mode
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Curriculum link
Compare this demo with the VCE Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.
Sample VCE Year 11 Specialist Mathematics questions
These sample questions are visible on the page before login. They show the style of VCE Year 11 Specialist Mathematics complex numbers, vectors, matrices, trigonometry, kinematics, and sequence explanations before opening the demo.
VCE Year 11Specialist MathematicsComplex numbershardcomplex plane
1. On the Argand diagram, point z is 2 + i. Which Cartesian form gives the image iz after multiplying z by i?
Choices
-1 + 2i
1 + 2i
2 - i
-2 + i
Explanation:
Multiplying by i gives iz = i(2 + i) = 2i + i2 = -1 + 2i. Geometrically, multiplication by i rotates the point 90° anticlockwise about the origin.
VCE Year 11Specialist MathematicsVectorshardvector diagram
2. In the vector diagram, a = (4, 3), b = (7, 1), and p denotes the component of b perpendicular to a. What is |p|?
Choices
17/5
5
31/5
√(85)/5
Explanation:
Since b . a = 31 and a . a = 25, proj_a b = (31/25)a. Hence p = b - proj_a b = (51/25, -68/25), with magnitude √(512 + 682)/25 = 85/25 = 17/5.
VCE Year 11Specialist MathematicsMatrices and transformationshardtransformation graph
3. The matrix M = [0, -1; 1, 0] acts on point P(3, -2). What is the image point P'?
Choices
(2, 3)
(-2, 3)
(3, 2)
(-3, -2)
Explanation:
Multiplying gives x' = 0 x 3 + (-1)(-2) = 2 and y' = 1 x 3 + 0 x (-2) = 3. Therefore P' = (2, 3).
VCE Year 11Specialist MathematicsTrigonometric equationshardunit circle
4. For 0 ≤ x < 2π, how many solutions does 2cos2 x - 3cos x + 1 = 0 have?
Choices
3
2
4
5
Explanation:
Factor the equation as (2cos x - 1)(cos x - 1) = 0. Thus cos x = 1/2 or cos x = 1. On 0 ≤ x < 2π, these occur at x = π/3, 5π/3 and 0, giving three solutions.
VCE Year 11Specialist MathematicsKinematicshardgraph
5. The velocity-time graph is linear from v = 6 m/s at t = 0 to v = -4 m/s at t = 5, crossing v = 0 at t = 3. What distance does the particle travel over 0 ≤ t ≤ 5?
Choices
13 m
5 m
9 m
17 m
Explanation:
Distance is the area above the axis plus the magnitude of the area below it: 1/2 x 3 x 6 + 1/2 x 2 x 4 = 9 + 4 = 13 m.
VCE Year 11Specialist MathematicsSequences and proofhardsequence graph
6. A sequence is defined by u₁ = 3 and uₙ₊₁ = 2uₙ + 1. If vₙ = uₙ + 1, then vₙ is geometric. What is u₅?
For parents comparing VCE Year 11 Specialist Mathematics support
VCE Year 11 Specialist Mathematics practice should stretch capable students with complex numbers, vectors, matrices, trigonometry, kinematics, and proof-like sequence reasoning without hiding the method. These examples preview that style before the no-login Specialist Mathematics demo.
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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.
