Year 11 ACT Maths - Specialist Mathematics sample questions
Year 11 ACT Maths - Specialist Mathematics sample questions
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Year 11 Specialist Mathematics practice questions
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Try a short public sample of Year 11 Specialist Mathematics questions selected from the reviewed Skill Align demo set.
Skills covered
Practice proof, vectors, complex numbers, advanced calculus, mechanics, differential equations, and probability.
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Sample ACT BSSS Year 11 Specialist Mathematics questions
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ACT BSSS Year 11Specialist MathematicsComplex numbershardArgand diagram
1. On the Argand diagram, z = 2 + 3i and w = (1 + i)z. Which Cartesian form gives w?
ACT BSSS Year 11Specialist MathematicsVectorshardvector diagram
2. In the vector diagram, a = (4, 2), b = (1, 5), and p denotes the component of b perpendicular to a. What is |p|?
Choices
9√5/5
14/20
√(20)
9/5
Explanation:
Since b . a = 14 and a . a = 20, proj_a b = (14/20)a. Hence p = b - proj_a b = (-9/5, 18/5), with magnitude √(405)/5 = 9√5/5.
ACT BSSS Year 11Specialist MathematicsMatriceshardtransition diagram
3. A row state vector [A, B] = [120, 80] is multiplied by transition matrix [0.70, 0.30; 0.40, 0.60]. What is the expected value in state A after one step?
Choices
116
120
84
200
Explanation:
Use the A column: 120 x 0.70 + 80 x 0.40 = 84 + 32 = 116.
ACT BSSS Year 11Specialist MathematicsTrigonometric equationshardunit circle
4. For 0 ≤ x < 2π, how many solutions does 2cos2 x + cos 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 π/3, 5π/3, and π, giving three solutions.
ACT BSSS Year 11Specialist MathematicsKinematicshardgraph
5. The velocity-time graph is linear with v(t) = 12 - 2t for 0 ≤ t ≤ 6. What distance is travelled over this interval?
Choices
36 m
24 m
12 m
72 m
Explanation:
Velocity remains non-negative on 0 ≤ t ≤ 6. The distance is the triangular area under the graph: 1/2 x 6 x 12 = 36 m.
ACT BSSS Year 11Specialist MathematicsProof and sequenceshardsequence graph
6. Assume S_k = [k(k + 1)/2]2 for the sum of the first k cubes. Which expression starts the (k + 1)-case correctly?
Choices
[k(k + 1)/2]2 + (k + 1)3
[k(k + 1)/2]2 + k3
(k + 1)3
[k(k + 1)/2]2
Explanation:
The next sum adds the next cube to the assumed k-case. Therefore Sₖ₊₁ starts as [k(k + 1)/2]2 + (k + 1)3 before simplification.
For parents comparing ACT BSSS Year 11 Specialist Mathematics support
ACT BSSS Year 11 Specialist Mathematics practice should make complex numbers, vectors, proof, mechanics, and further calculus feel structured rather than guessable. These examples preview that style before the no-login Specialist Mathematics demo.
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Practice Summary
Year 11 · ACT Maths - Specialist Mathematics · Test mode · 2 questions · 10 min
Questions attempted0 / 2
Correct answersPending
Score-
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