Grade 12 scientific maths builds on itself: integration is differentiation in reverse, and the applications use both. Revise in that order, and end each block with mixed questions. Check the lessons against your own textbook edition, since chapters can be reordered.
Block 1: differentiation (about 3 weeks)
- Rules: power, product, quotient, chain; derivatives of trigonometric, exponential and logarithmic functions.
- L'Hôpital's rule for 0/0 limits, and implicit differentiation.
- Meaning: slope and tangent lines; velocity and acceleration.
Block 2: applications of differentiation (about 2 weeks)
- Increasing and decreasing intervals and the first derivative test.
- Critical numbers, local and absolute extremes.
- Concavity and inflection points (second derivative).
- Optimisation word problems: write the function, find its domain, then differentiate.
Block 3: matrices (about 2 weeks)
- Order, special matrices, addition and multiplication (and why multiplication is not commutative).
- Determinants and the inverse of a 2×2 matrix.
- Solving linear systems: inverse matrix, Cramer's rule and Gaussian elimination.
Block 4: integration (about 3 weeks)
- Antiderivatives, indefinite integral rules and the constant of integration.
- Finding a curve from its derivative; motion problems.
- Substitution, integration by parts and partial fractions.
- Partitions and Riemann sums, the definite integral and the fundamental theorem.
- Area between curves and volumes of revolution.
End every block with a mixed set and one timed past-style paper. A lesson only counts as revised when you can do it among other topics.
How EXAMEV helps
The EXAMEV Scientific Mathematics Test Bank for grade 12 has over 1,000 questions organised by these lessons, with explanations and progress by topic, so you can see which block needs more time. For worked examples, read our guide to solving Tawjihi maths problems step by step.