Year 12 VCE Maths - Specialist Mathematics sample questions
Year 12 VCE Maths - Specialist Mathematics sample questions
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Year 12 VCE 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 VCE Specialist Mathematics questions
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VCE Year 12Specialist MathematicsComplex numbershardcomplex plane
1. On the Argand diagram, point z is 3 + 4i. Which Cartesian equation describes the locus L of points w = x + yi such that |w - z| = |w|?
Choices
6x + 8y = 25
3x + 4y = 5
x2 + y2 = 25
8x - 6y = 25
Explanation:
Points on the locus are equally distant from z and the origin. Squaring distances gives (x - 3)2 + (y - 4)2 = x2 + y2, so 6x + 8y = 25.
VCE Year 12Specialist MathematicsVectorshardvector diagram
2. In the vector diagram, a = (3, 4), b = (7, 1), and p denotes the component of b perpendicular to a. What is |p|?
Choices
5
1
√10
25
Explanation:
Since b . a = 25 and a . a = 25, proj_a b = a = (3, 4). Hence p = b - a = (4, -3), with magnitude √(42 + (-3)2) = 5.
VCE Year 12Specialist MathematicsDifferential equationshardslope field
3. The slope field represents dy/dx = 2y(3 - y), and the drawn solution curve S starts from y(0) = 1. Which long-term behaviour is consistent with S?
Choices
y increases towards 3
y decreases towards 0
y becomes negative
y grows without bound
Explanation:
The equilibrium solutions are y = 0 and y = 3. For 0 < y < 3, 2y(3 - y) is positive, so the solution rises and approaches the stable equilibrium y = 3.
VCE Year 12Specialist MathematicsMechanicshardgraph
4. The velocity-time graph is linear from v = 8 m/s at t = 0 to v = -4 m/s at t = 6, crossing v = 0 at t = 4. What distance does the particle travel over 0 ≤ t ≤ 6?
Choices
20 m
12 m
16 m
24 m
Explanation:
The velocity is zero at t = 4. Distance is the area above the axis plus the magnitude of the area below it: 1/2 x 4 x 8 + 1/2 x 2 x 4 = 16 + 4 = 20 m.
VCE Year 12Specialist MathematicsComplex rootshardroot diagram
5. The diagram marks point P, the root of z6 = 64 with argument 2π/3. Which exact Cartesian form is P?
Choices
-1 + (√3)i
1 + (√3)i
-√3 + i
2 + (√3)i
Explanation:
The modulus of each root is 641/6 = 2. At argument 2π/3, point P is 2(cos 2π/3 + i sin 2π/3) = -1 + (√3)i.
VCE Year 12Specialist MathematicsParametric calculushardtangent graph
6. For x = t2 - 1 and y = t3 - t, the graph marks point P where t = 2 and shows the tangent T. What is dy/dx at P?
Choices
11/4
4/11
5/4
11/2
Explanation:
Use dy/dx = (dy/dt)/(dx/dt). Here dy/dt = 3t2 - 1 and dx/dt = 2t, so at point P where t = 2 the gradient is 11/4.
For parents comparing VCE Specialist Mathematics support
VCE Specialist Mathematics practice should give students enough structure to revise complex numbers, vectors, differential equations, and mechanics without guessing missing information. These examples preview that style before the no-login Specialist Mathematics demo.
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Practice Summary
Year 12 · VCE Maths - Specialist Mathematics · Test mode · 2 questions · 10 min
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Correct answersPending
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