What we cover
What Grade 12 mathematics covers in each track
Calculus runs through the one book used by both the Scientific and the Technological track, while Arts and Humanities students work from a separate book. Units match the ministry's 2025 edition.
The Scientific and Technological second-semester book also has a unit on probability distributions; each year's ministry semester plan sets which units are taught.
Limits and continuity
Scientific and Technological · Semester 1Students meet the idea of a limit, calculate limits, work with trigonometric limits and test for continuity. Marks slip when a 0/0 form is left unsimplified or a one-sided limit ignored.
- Concept of a limit
- Trigonometric limits
- Continuity
Differentiation and its rules
Scientific and Technological · Semester 1From rate of change to the formal derivative, then product, quotient and chain rules, exponential, logarithmic and trigonometric derivatives, implicit differentiation and higher derivatives. The chain rule causes most slips.
- Chain rule
- Implicit differentiation
- Higher-order derivatives
Using derivatives: graphs and optimisation
Scientific and Technological · Semester 1Increasing and decreasing functions, extreme values, concavity and inflection lead to curve sketching, optimisation and related rates. Word problems test whether a student can build the function first.
- Extreme values
- Concavity and inflection
- Related rates
Integration techniques
Scientific and Technological · Semester 2Indefinite integrals and their rules, then substitution, integration by parts and partial fractions. Marks go on the wrong technique, a dropped constant of integration or a substitution never reversed.
- Substitution
- Integration by parts
- Partial fractions
Definite integrals and their uses
Scientific and Technological · Semester 2Area under a curve and between two curves, volumes of revolution and applied problems, closing with differential equations. Wrong limits of integration and a missing sketch cost most.
- Area between curves
- Volumes of revolution
- Differential equations
Vectors in the plane and in space
Scientific and Technological · Semester 2Vectors as quantities with size and direction, their operations, the scalar product and vectors in three dimensions. Sign errors in components and in the angle formula are the usual weak spots.
- Vector operations
- Scalar product
- Vectors in 3D
Complex numbers
Scientific and Technological · Semester 2Operations on complex numbers, the complex plane, polar form, and powers and roots. An argument placed in the wrong quadrant carries its error through every later step.
- Complex plane
- Polar form
- Powers and roots
Exponentials, logarithms and sequences
Arts and Humanities · Semester 1Exponential functions and models, logarithms and their properties, exponential and logarithmic equations, then arithmetic and geometric sequences and series. Misapplied laws of logarithms are the most frequent error.
- Laws of logarithms
- Exponential models
- Geometric series
Statistics and probability
Arts and Humanities · Semester 2Sampling methods, data distributions, the normal distribution and margin of error, then conditional probability, permutations and combinations, expected value and decision-making. Whether order matters trips many students.
- Sampling methods
- Normal distribution
- Conditional probability
- Expected value