Year 11 TAS Maths - Mathematics Specialised sample questions
Year 11 TAS Maths - Mathematics Specialised sample questions
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Year 11 Mathematics Specialised practice questions
Use this no-login public demo to preview Skill Align's Year 11 Mathematics Specialised sample questions, explanations, exercise mode, and test mode before regular practice.
Sample-question focus
Try a short public sample of Year 11 Mathematics Specialised questions selected from the reviewed Skill Align demo set.
Skills covered
Practice functions, complex numbers, matrices, calculus, proof, and advanced problem solving.
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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 11Mathematics SpecialisedComplex numbershardArgand diagram
1. On the Argand diagram, z = 2 + 3i and w = (1 + i)z. Which Cartesian form gives w?
TASC Year 11Mathematics SpecialisedVectorshardvector 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|?
Choices
9sqrt(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 = 9sqrt(5) / 5.
TASC Year 11Mathematics SpecialisedMatriceshardtransition 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?
Choices
116
120
84
200
Explanation:
Use the A column: 120 x 0.70 + 80 x 0.40 = 84 + 32 = 116.
TASC Year 11Mathematics SpecialisedTrigonometric equationshardunit circle
4. For 0 <= x < 2π, how many solutions does 2cos² x + cos x - 1 = 0 have?
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 11Mathematics SpecialisedKinematicshardgraph
5. The velocity-time graph is linear with v(t) = 12 - 2t for 0 <= t <= 6. What distance is travelled over this interval?
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 11Mathematics SpecialisedProof and sequenceshardsequence 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?
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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Practice Summary
Year 11 · TAS Maths - Mathematics Specialised · Test mode · 4 questions · 10 min
Questions attempted0 / 4
Correct answersPending
Score-
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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.
