QCE Specialist Mathematics: complete 2026 guide to Units 3 and 4 (General subject)
A complete 2026 guide to QCE General Specialist Mathematics Units 3 and 4. Covers the IA1 problem-solving and modelling task, the IA2 and IA3 internal examinations, the External Assessment, what each instrument assesses, how the marks combine, and links to every dot-point answer we have written for Unit 3 (induction, complex numbers, vectors, matrices) and Unit 4 (integration, differential.
QCE General Specialist Mathematics Units 3 and 4 is the Year 12 sequence assessed across three internal assessments and one External Assessment. It is designed to be studied alongside Mathematical Methods, extending its calculus and statistics. Unit 3 is the priority for IA2; Unit 4 is the priority for IA3; the EA tests Units 3 and 4 cumulatively at the end of the year.
This page is the index. Below you will find the structure of the course, what each instrument assesses, and links to every dot-point answer we have written for QCE Specialist Mathematics.
The four instruments in 2026
- IA1: Problem-solving and modelling task
- A school-based response developing and evaluating a mathematical model for a given scenario, submitted as a report with assumptions, solution and justified decisions. It assesses modelling judgement and communication rather than timed technique. Weighting 20 percent.
- IA2: Examination (Unit 3)
- An internal examination drawn from Unit 3 subject matter (induction, vectors, matrices and complex numbers), with short-response and extended items. Weighting 15 percent.
- IA3: Examination (Unit 4)
- An internal examination drawn from Unit 4 subject matter (integration, differential equations and statistical inference). Weighting 15 percent.
- EA: External Assessment
- A centrally set external examination at the end of Unit 4, marked by QCAA, assessing Units 3 and 4 cumulatively. Weighting 50 percent. Three of the four instruments (IA2, IA3 and the EA) are examinations.
Unit 3: Mathematical induction, and further vectors, matrices and complex numbers
Unit 3 develops rigorous proof and the algebra of vectors, matrices and complex numbers. It is the basis of IA2 and contributes to the EA.
- Proof by mathematical induction
- The base step and inductive step structure applied to sums, divisibility and inequalities.
- Vectors in two and three dimensions
- Dot and cross products, angles, scalar and vector projections, and the equations of lines.
- Further matrices
- Determinants, inverses and the interpretation of matrices as linear transformations of the plane.
- Further complex numbers
- Polar and exponential form, de Moivre's theorem, and the roots of a complex number on the Argand plane.
Unit 4: Further calculus, and statistical inference
Unit 4 extends integration and introduces statistical inference. It is the basis of IA3 and contributes to the EA.
- Integration and applications
- Substitution, partial fractions, trigonometric integrals and volumes of solids of revolution.
- Rates of change and differential equations
- First-order equations solved by separation of variables, including growth, decay, cooling and logistic models.
- Statistical inference
- The sampling distribution of the mean, the central limit theorem, and confidence intervals for a population mean.
Our 2026 QCE Specialist Mathematics dot-point answers
Every link below is a focused answer to one QCAA subject-matter dot point. Each page identifies the dot point, gives a rigorous worked answer with correct notation, and flags the mistakes QCAA markers penalise.
Unit 3: Induction, vectors, matrices and complex numbers
- Mathematical induction
- Trigonometric proofs and methods of proof
- Vectors in three dimensions, dot and cross products
- Vector and Cartesian equations of lines
- Vector and Cartesian equations of planes
- Matrices and linear transformations of the plane
- Systems of linear equations and larger matrices
- Complex numbers in polar form and de Moivre's theorem
- Factorising polynomials over the complex field
- Regions and curves in the complex plane
Unit 4: Further calculus and statistical inference
- Integration techniques: substitution and partial fractions
- Integration by parts and trigonometric integrals
- Areas between curves and volumes of revolution
- Simpson's rule for numerical integration
- First-order differential equations and separation of variables
- Slope fields of first-order differential equations
- Implicit differentiation and related rates
- Growth, decay, cooling and logistic models
- Distribution of the sample mean and the central limit theorem
- Confidence intervals for a population mean
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