Grade 12 Mathematics Paper 1 is the algebra and calculus paper. It carries 150 marks, runs for 3 hours, and follows the same skeleton every year. Knowing the skeleton lets you allocate time before you ever see the questions.
Paper 1 mark allocation (NSC/CAPS)
- Algebra and Equations — ~25 marks
- Number Patterns, Sequences and Series — ~25 marks
- Functions and Graphs — ~35 marks
- Finance, Growth and Decay — ~15 marks
- Differential Calculus — ~35 marks
- Probability — ~15 marks
Question 1 is always quadratics
Every November Paper 1 opens with a quadratic equation, a quadratic inequality, simultaneous equations, and the nature-of-roots discriminant. That's 10–12 marks before any calculus appears. Bank them.
Sequences and series
Sequences questions usually combine a quadratic pattern with arithmetic or geometric sequences and series, often including sigma notation or a sum to infinity. Check the first and second differences before you choose a formula.
Functions and calculus: the two big sections
Together they carry about 70 marks. Functions questions start from a sketch with labelled points; calculus questions build from differentiation to stationary points, a cubic sketch and an optimisation or rate-of-change problem. Practise these as complete questions, because each part depends on the one before.
Finance and probability
Each carries about 15 marks. Finance rewards a clear setup: write i and n before you substitute. Probability rewards organising the information first, with a Venn diagram, a tree diagram or a contingency table.
Where most Paper 1 marks are lost
- Skipping the 'let' or 'where x ≠ ...' setup line in algebra.
- Forgetting to test endpoints when solving quadratic inequalities.
- Misreading f(x) as f'(x) in calculus tangent questions.
- Rounding finance answers too early — always keep 4+ decimals until the final step.
How to use past Paper 1s
Write the paper under timed conditions, mark with the official memo, then rework every wrong question the next day. When a question stops you, snap it into Snap&Learn — you'll get a CAPS-aligned step-by-step explanation in seconds, and your first three AI solutions are free.