1. The diagram marks point P, the root of z4 = 16 with argument 3π/4. Which exact Cartesian form is P?
Each root has modulus 161/4 = 2. At argument 3π/4, P = 2(cos 3π/4 + i sin 3π/4) = -√2 + √2i.
Use Skill Align for WACE Year 12 Specialist Mathematics practice questions after the relevant topic has been taught. Students can start with the pathway demo, then practise by topic and mode.
WACE Year 12 Specialist Mathematics includes 20 practice skills across Complex numbers and vectors, Proof, algebra and functions, Calculus and differential equations, and Mechanics and modelling.
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.
These sample questions are visible on the page before login. They show WACE Year 12 Specialist Mathematics complex numbers, vectors, proof, mechanics, and further calculus explanations before opening the demo.
Each root has modulus 161/4 = 2. At argument 3π/4, P = 2(cos 3π/4 + i sin 3π/4) = -√2 + √2i.
The direction vector is AB = (4 - 1, -1 - 2, 2 - 0) = (3, -3, 2). A valid line equation is r = (1, 2, 0) + λ(3, -3, 2).
Acceleration is the derivative of velocity. Since v'(t) = 6t - 12, a(3) = 18 - 12 = 6 m/s2.
The equilibrium is y = 10. When y < 10, dy/dt is positive, so the solution increases and approaches the stable equilibrium y = 10.
Use u = sin x, so du = cos x dx. The integral becomes ∫ from 0 to 1 of u du = 1/2.
For f(x) = x3, f'(x) = 3x2, so f'(0) = 0. But x = 0 is a stationary point of inflection, not a local maximum, so the claim is false.
WACE Year 12 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.
Specialist Mathematics practice sits inside WACE Mathematics Year 12 coverage for number, algebra, calculus, statistics, probability, networks, finance, trigonometry, and modelling, 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.
These examples are not the full topic list. Use the curriculum coverage page for the complete mapped pathway.
Western Australian students studying Specialist Mathematics.
Yes. Public sample pages let visitors preview curated Skill Align questions without creating a saved student test record.
No. Skill Align is designed for structured practice after students have learned topics at school or with a teacher.
Yes. Skill Align uses subject-based access, so families can start with the year level and subject the student needs now.