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Year 11 TAS Maths - Mathematics Specialised sample questions

Year 11 TAS Maths - Mathematics Specialised practice preview

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Year 11 Mathematics Specialised practice questions

This public preview page identifies the planned Year 11 Mathematics Specialised 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 Mathematics Specialised practice and will open after the demo questions are reviewed.

Skills covered

Practice functions, complex numbers, matrices, calculus, proof, and advanced problem solving.

Exercise and test mode

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Curriculum link

Compare this demo with the Tasmania Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.

Sample TASC Year 11 Mathematics Specialised questions

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

TASC Year 11 Mathematics Specialised 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.

TASC Year 11 Mathematics Specialised 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.

TASC Year 11 Mathematics Specialised 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.

TASC Year 11 Mathematics Specialised 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.

TASC Year 11 Mathematics Specialised 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.

TASC Year 11 Mathematics Specialised 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 TASC Year 11 Mathematics Specialised support

TASC Year 11 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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Year 11 TAS Maths - Mathematics Specialised is available to purchase, and the public demo preview is still being prepared.

Students can use the purchased subject once subscribed; this anonymous preview will be opened after the curated public question set is ready.

Mathematics Specialised practice questions FAQ

Does this page include Year 11 Mathematics Specialised practice questions?

Not yet. The Year 11 Mathematics Specialised 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 Tasmania Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.