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TASC Year 11 Mathematics Specialised practice questions

TASC Year 11 Mathematics Specialised practice questions

Use Skill Align for TASC Year 11 Mathematics Specialised practice questions after the relevant topic has been taught. Students can start with the pathway demo, then practise by topic and mode.

16 practice skills

TASC Year 11 Mathematics Specialised includes 16 practice skills across Complex numbers and vectors, Proof, algebra and functions, Calculus and differential equations, and Mechanics and modelling.

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Australian Years 7-12 Exercise and test mode Parent-managed access

What is a practice skill?

A practice skill is a focused topic or question type designed to help students practise one curriculum-aligned concept with instant feedback and explanations. Skill Align uses practice skills to organise questions by year level, subject, strand, and curriculum focus.

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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Ready to continue? Use the normal Skill Align pages below to preview questions, check full curriculum coverage, or compare pricing before deciding whether to sign up.

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What this practice page covers

Mathematics Specialised practice sits inside TASC Year 11 mathematics planning coverage across essential, general, methods, specialist, algebra, calculus, statistics, probability, finance, and modelling topics, with Skill Align keeping the route focused on the selected maths pathway.

Senior practice is organised by pathway, unit, topic, and mode so students can revise targeted areas rather than sitting a full-paper workflow every time.

Start with the public sample questions to check the question style, then use the curriculum coverage page to choose a topic that matches the student's current classwork.

Preview question styles
  • Complex numbers and vectors: Students practise complex numbers and vectors through short targeted questions, explanations, and mode-specific feedback.
  • Proof, algebra and functions: Students practise proof, algebra and functions through short targeted questions, explanations, and mode-specific feedback.
  • Calculus and differential equations: Students practise calculus and differential equations through short targeted questions, explanations, and mode-specific feedback.
Suggested first practice steps
  • Preview the public sample questions before creating a saved student session.
  • Choose one focus area that has already been introduced at school.
  • Use exercise mode for immediate explanations, then test mode when the student is ready for delayed feedback.
Example focus areas
View full curriculum coverage

These examples are not the full topic list. Use the curriculum coverage page for the complete mapped pathway.

  • Complex numbers and vectors
  • Proof, algebra and functions
  • Calculus and differential equations
  • Mechanics and modelling
Who it is for

Tasmanian students studying Mathematics Specialised.

Common search wording
TASC Year 11 Mathematics Specialised practice questionsTASC Mathematics Specialised practice questionsMathematics Specialised online practiceTAS Maths - Mathematics Specialised practice questions
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Yes. Public sample pages let visitors preview curated Skill Align questions without creating a saved student test record.

Does Skill Align replace school lessons or tutoring?

No. Skill Align is designed for structured practice after students have learned topics at school or with a teacher.

Can parents choose only one subject?

Yes. Skill Align uses subject-based access, so families can start with the year level and subject the student needs now.

Skill Align independently prepares practice pathways aligned to publicly available curriculum and syllabus information. Official requirements should always be checked with the relevant authority.