Year 12 ACT Maths - Specialist Mathematics sample questions
Year 12 ACT Maths - Specialist Mathematics sample questions
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Year 12 Specialist Mathematics practice questions
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Skills covered
Practice proof, vectors, complex numbers, advanced calculus, mechanics, differential equations, and probability.
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Sample ACT BSSS Year 12 Specialist Mathematics questions
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ACT BSSS Year 12Specialist MathematicsComplex rootshardroot diagram
1. The diagram marks point P, the root of z4 = 16 with argument 3π/4. Which exact Cartesian form is P?
Choices
-√2 + √2i
√2 + √2i
-√2 - √2i
2 + √2i
Explanation:
Each root has modulus 161/4 = 2. At argument 3π/4, P = 2(cos 3π/4 + i sin 3π/4) = -√2 + √2i.
ACT BSSS Year 12Specialist MathematicsVectorshardvector diagram
2. Points A(1, 2, 0) and B(4, -1, 2) define a line. Which vector equation represents the line AB?
Choices
r = (1, 2, 0) + λ(3, -3, 2)
r = (1, 2, 0) + λ(5, 1, 2)
r = (4, -1, 2) + λ(3, 3, -2)
r = (3, -3, 2) + λ(1, 2, 0)
Explanation:
The direction vector is AB = (4 - 1, -1 - 2, 2 - 0) = (3, -3, 2). A valid line equation is r = (1, 2, 0) + λ(3, -3, 2).
ACT BSSS Year 12Specialist MathematicsMechanicshardgraph
3. A particle has velocity v(t) = 3t2 - 12t + 5. What is the acceleration at t = 3?
Choices
6 m/s2
-6 m/s2
20 m/s2
0 m/s2
Explanation:
Acceleration is the derivative of velocity. Since v'(t) = 6t - 12, a(3) = 18 - 12 = 6 m/s2.
ACT BSSS Year 12Specialist MathematicsDifferential equationshardslope field
4. A model satisfies dy/dt = 0.4(10 - y), and the drawn solution starts below 10. Which long-term behaviour is consistent with the solution?
Choices
y increases towards 10
y decreases towards 0
y becomes negative
y grows without bound
Explanation:
The equilibrium is y = 10. When y < 10, dy/dt is positive, so the solution increases and approaches the stable equilibrium y = 10.
ACT BSSS Year 12Specialist MathematicsFurther integrationhardtangent and area graph
5. What is the exact value of the integral from 0 to π/2 of sin x cos x dx?
Choices
1/2
1
0
π/4
Explanation:
Use u = sin x, so du = cos x dx. The integral becomes ∫ from 0 to 1 of u du = 1/2.
ACT BSSS Year 12Specialist MathematicsProof and counterexamplehardtransformation graph
6. Which counterexample disproves the claim: if f'(0) = 0, then f has a local maximum at x = 0?
Choices
f(x) = x3
f(x) = -x2
f(x) = 1 - x2
f(x) = 4
Explanation:
For f(x) = x3, f'(x) = 3x2, so f'(0) = 0. But x = 0 is a stationary point of inflection, not a local maximum, so the claim is false.
For parents comparing ACT BSSS Year 12 Specialist Mathematics support
ACT BSSS Year 12 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 12 · ACT Maths - Specialist Mathematics · Test mode · 2 questions · 10 min
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Correct answersPending
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