Year 12 TAS Maths - Mathematics Specialised sample questions
Year 12 TAS Maths - Mathematics Specialised sample questions
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Year 12 Mathematics Specialised practice questions
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Skills covered
Practice functions, complex numbers, matrices, calculus, proof, and advanced problem solving.
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Sample TASC Year 12 Mathematics Specialised questions
These sample questions are visible on the page before login. They show TASC Year 12 Mathematics Specialised complex numbers, vectors, proof, mechanics, and further calculus explanations before opening the demo.
TASC Year 12Mathematics SpecialisedComplex 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 16^(1 / 4) = 2. At argument 3π / 4, P = 2(cos 3π / 4 + i sin 3π / 4) = -√2 + √2i.
TASC Year 12Mathematics SpecialisedVectorshardvector 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).
TASC Year 12Mathematics SpecialisedMechanicshardgraph
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 / s^2.
TASC Year 12Mathematics SpecialisedDifferential 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.
TASC Year 12Mathematics SpecialisedFurther 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.
TASC Year 12Mathematics SpecialisedProof 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 TASC Year 12 Mathematics Specialised support
TASC Year 12 Mathematics Specialised 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 Mathematics Specialised demo.
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Practice Summary
Year 12 · TAS Maths - Mathematics Specialised · Test mode · 4 questions · 10 min
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Correct answersPending
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