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Year 11 SACE Maths - Specialist Mathematics sample questions

Year 11 SACE Maths - Specialist Mathematics practice preview

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Year 11 SACE Specialist Mathematics practice questions

This public preview page identifies the planned Year 11 SACE 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 SACE 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 SACE Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.

Sample SACE Year 11 Specialist Mathematics questions

These sample questions are visible on the page before login. They show SACE Year 11 Specialist Mathematics complex numbers, vectors, proof, mechanics, and further calculus explanations before opening the demo.

SACE Year 11 Specialist Mathematics Complex numbers hard Argand diagram

1. On the Argand diagram, z = 2 + 3i and w = (1 + i)z. Which Cartesian form gives w?

Argand-plane multiplication by 1 + i z w Re Im
Choices
  • -1 + 5i
  • 5 - i
  • 1 + 5i
  • -5 + i
Explanation:

Expand w = (1 + i)(2 + 3i) = 2 + 3i + 2i + 3i2 = -1 + 5i.

SACE Year 11 Specialist Mathematics Vectors hard vector 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|?

Perpendicular component in a vector diagram a b 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.

SACE Year 11 Specialist Mathematics Matrices hard transition 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?

Two-state transition matrix A B T
Choices
  • 116
  • 120
  • 84
  • 200
Explanation:

Use the A column: 120 x 0.70 + 80 x 0.40 = 84 + 32 = 116.

SACE Year 11 Specialist Mathematics Trigonometric equations hard unit circle

4. For 0 ≤ x < 2π, how many solutions does 2cos2 x + cos x - 1 = 0 have?

Unit-circle cosine solutions 1 1/2 θ
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.

SACE Year 11 Specialist Mathematics Kinematics hard graph

5. The velocity-time graph is linear with v(t) = 12 - 2t for 0 ≤ t ≤ 6. What distance is travelled over this interval?

Area under a velocity-time graph v t 6
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.

SACE Year 11 Specialist Mathematics Proof and sequences hard sequence 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?

Induction step for cube sums Pₖ₊₁ n S
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 SACE Year 11 Specialist Mathematics support

SACE 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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SACE Specialist Mathematics practice questions FAQ

Does this page include Year 11 SACE Specialist Mathematics practice questions?

Not yet. The Year 11 SACE Specialist Mathematics demo route is public, but the interactive sample questions will open after the reviewed public set is ready.

Can students try the demo without signing up?

No sign-up is required to view the preview status. The no-login interactive demo will be available after the sample set is completed.

How does this demo relate to curriculum coverage?

This demo is linked with the SACE Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.