WACE Mathematics Specialist: complex numbers, vectors and differential equations

How the Specialist exam is set out

Specialist uses the same two-part pattern as the other WACE mathematics courses, but its questions lean more on proof, generalisation and unfamiliar settings. The brief says candidates can be asked to make and test conjectures and to prove mathematical relationships, and to adapt a model to a situation they have not met.

A changeover of up to 15 minutes sits between the two, with no writing. Section Two allows drawing instruments, templates, notes on two unfolded A4 sheets and up to three calculators, which can be scientific, graphic or CAS. A formula sheet is supplied. For any part worth more than two marks, your working or justification is part of the answer.

What the two units cover

Complex numbers move from Cartesian to polar form, and the calculus from Methods is extended to sketch graphs and to integrate. Vectors, first met in two dimensions in Year 11, become three-dimensional, with vector equations of lines and planes and vector calculus for motion in space. Unit 4 uses first-order differential equations in biology and kinematics, and ends with the distribution of sample means.

Specialist does not include Newtonian mechanics with forces. Kinematics appears only through vector calculus and differential equations. If you want a guide to Year 12 mechanics anyway, see our Specialist Maths Mechanics guide, and for the wider course shape see Maths Extension 2 and Specialist Maths.

Two worked examples

A power of a complex number in polar form

Find (1 + i)⁶. The modulus of 1 + i is √2 and its argument is π/4, so by de Moivre's theorem:

In Section One you would check by squaring: (1 + i)² = 2i, so (1 + i)⁶ = (2i)³ = 8i³ = −8i.

Are two vectors perpendicular?

For a = (1, 2, 2) and b = (2, 1, −2), the scalar product is 1 × 2 + 2 × 1 + 2 × (−2) = 0. The vectors are perpendicular, and both have magnitude 3. That sort of exact check is typical of a calculator-free question, and proving a relationship is a command word the brief names.

For work on complex numbers there is also our Complex Number Calculator. Our Calculus course covers the integration and differential equations ideas that Unit 4 builds on.

School marks and the ATAR

SCSA sets the weightings of the school-based assessment: response tasks 40%, investigation 20% and examination 40%. The investigation is an extended piece in which you plan, work through and report on a problem. Your school gives an A to E grade and a mark out of 100; that mark is moderated against exam marks at your school and averaged with your exam mark, and TISC calculates the ATAR from the results of your ATAR courses.

Dates

Use the daily papers as a trial

SCSA does not publish trial exams, so your school sets its own. Uni-Sine's free daily papers can act as quick timed trials, each with 8 questions worth 25 to 35 marks, marked as you go. They are not full WACE papers.

• Maths Extension 2 and Specialist Maths fits when it rotates to complex numbers, polar coordinates and differential equations. It also covers proof by induction, hyperbolic functions, matrices, Maclaurin series and volumes of revolution, which are not named in the WACE Year 12 Specialist content, so treat those days as stretch.
• Specialist Maths: Mechanics covers forces, moments, pulleys and friction. WACE Specialist has no forces content, so only the variable-acceleration days connect, through calculus.
• Time yourself on a 30-minute slice of each paper without a calculator first, since half the WACE paper is calculator-free.

Exam answers

The answers and worked mark scheme for each daily paper come with it once it is marked. They are Uni-Sine's own and are not official SCSA answers or past paper solutions.

Mistakes to avoid in Specialist

• Giving a polar form with the wrong quadrant for the argument. Sketch the point before you read off the angle.
• Using a CAS result to claim a proof. Proof questions need the steps written out.
• Forgetting the constant of integration or the initial condition when solving a differential equation.
• Treating the mechanics paper as exam content rather than extension reading.

Read next

Australia · WACEWACE Maths Specialist formula sheet: the SCSA sheetThe SCSA Mathematics Specialist ATAR formula sheet: calculus, vectors, complex numbers and trigonometry, what it leaves out, and worked examples.