What is in VCE Specialist Maths Units 3 and 4

Six areas of study: discrete mathematics, functions, relations and graphs, algebra, number and structure, calculus, space and measurement, and data analysis, probability and statistics. Both examinations can test all of Units 3 and 4.

Weeks before your first examination

Hours a week for Specialist Maths

Discrete mathematics

Functions, relations and graphs

Algebra, number and structure

Calculus

Space and measurement

Data analysis, probability and statistics

26 weeks, 104 hours in all

Start with Calculus

30 of your hours. It is 5 of the 16 units in the course, 31%.

Hours per area of study
Area of study	Your hours	Share of the course
Calculus	30	31%
Space and measurement	18	19%
Data analysis, probability and statistics	18	19%
Discrete mathematics	12	13%
Algebra, number and structure	12	13%
Functions, relations and graphs	6	6%

Week by week

Week 1Calculus
Week 2Calculus
Week 3Calculus
Week 4Calculus
Week 5Calculus
Week 6Calculus
Week 7Calculus
Week 8Calculus, Space and measurement
Week 9Space and measurement
Week 10Space and measurement
Week 11Space and measurement
Week 12Space and measurement
Week 13Data analysis, probability and statistics
Week 14Data analysis, probability and statistics
Week 15Data analysis, probability and statistics
Week 16Data analysis, probability and statistics
Week 17Data analysis, probability and statistics, Discrete mathematics
Week 18Discrete mathematics
Week 19Discrete mathematics
Week 20Discrete mathematics, Algebra, number and structure
Week 21Algebra, number and structure
Week 22Algebra, number and structure
Week 23Algebra, number and structure, Functions, relations and graphs
Week 24Functions, relations and graphs
Week 25Timed paper 1 (Examination 1 style, no technology), then review every lost mark
Week 26Timed paper 2 (Examination 2 style), then review every lost mark

Check your units with the free test

Examination 1	40 marks in 1 hour, no technology or notes
Examination 2	20 multiple-choice questions and 60 marks of extended answers, 2 hours
Study score	Examination 1 20%, Examination 2 40%, coursework 40%
Reading time	15 minutes before each examination; a formula sheet with both

The six areas

Discrete mathematics: implications, converses and contrapositives, direct proof, proof by contradiction and by contrapositive, counter-examples, and proof by mathematical induction.
Functions, relations and graphs, and algebra, number and structure: partial fractions and rational functions; complex numbers in polar form, De Moivre's theorem, roots and polynomials over the complex numbers.
Calculus, space and measurement, and statistics: inverse circular functions, integration techniques, volumes and arc lengths, differential equations and kinematics; vectors, lines and planes and vector calculus; linear combinations of random variables, confidence intervals and hypothesis tests for a mean.

School-assessed Coursework

School-assessed Coursework for Unit 3 and for Unit 4 each makes up 20% of the study score. It is set and marked by your school, so this course describes it but does not practise it.

How this course maps the study design

The course splits the six areas into sixteen units and a unit on the two examinations, each with a lesson, Examination 2 multiple-choice questions, Examination 1 questions without technology and Examination 2 extended-answer questions. Set the planner above with the weeks you have and how sure you are of each area, and it splits your hours.

Try 3 questions

Examination 2 · Section A · 1 mark · Complex numbers in polar form
The principal argument of $-\sqrt{3} + i$ is
Answer it, every step marked
Examination 1 · No technology · 5 marks · Complex numbers in polar form
Let $z = 1 - \sqrt{3} i$ and $w = 2 i$ .
Answer it, every step marked
Examination 2 · Section B · 11 marks · Complex numbers in polar form
The tip of a robot arm moves in a horizontal plane, modelled as the complex plane with the pivot of the arm at the origin $O$ and distances in metres. The tip starts at $z_0 = 2 \sqrt{3} + 2 i$ . A turn command rotates the arm anticlockwise about $O$ through $\frac{\pi}{6}$ without changing its length, so after $n$ turn commands the tip is at $z_n = \left(\mathrm{cis}\left(\frac{\pi}{6}\right)\right)^{n} z_0$ .
Answer it, every step marked

Next step

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Questions people ask

What do the examinations count for?

Examination 1 is 20% and Examination 2 is 40% of the study score. School-assessed Coursework for Units 3 and 4 is the other 40%.

Which study design does the course follow?

The VCE Mathematics Study Design accredited from 2023, Units 3 and 4: Specialist Mathematics, for the 2027 examinations.

Does this course cover Mathematical Methods?

No. It is built for Specialist Mathematics only. VCE Maths Methods Prep is a separate course.