The 150 marks, by topic
Every CAPS National Senior Certificate (NSC) Mathematics Paper 1 is built from the same six topic areas, with the same mark split. This is documented in the DBE Mathematics Examination Guidelines and has not changed for years. Knowing it means you can plan your prep time around where the marks actually sit.
| Topic | Marks | Share |
|---|---|---|
| Algebra, Equations & Inequalities | 25 | 17% |
| Number Patterns | 25 | 17% |
| Functions & Graphs | 35 | 23% |
| Finance, Growth & Decay | 15 | 10% |
| Differential Calculus | 35 | 23% |
| Counting Principle & Probability | 15 | 10% |
| Total | 150 | 100% |
The paper runs for 3 hours. Functions & Graphs and Differential Calculus together make up 70 marks out of 150, close to half the paper. If your prep time is limited, those two are where you bank the highest return per hour of study.
What to expect in each section
Algebra, Equations & Inequalities (25 marks)
This is usually the opening question of the paper. Expect:
- Solving quadratic equations by factorising, by completing the square, or with the quadratic formula
- Solving simultaneous equations (one linear, one quadratic)
- Solving inequalities and expressing solutions in interval or set-builder notation
- Exponential and surd equations (rational exponents, solving with logs if needed)
- Nature of roots: using the discriminant to classify real, equal, unequal, rational or non-real roots
This section rewards speed and accuracy on standard techniques. You should be able to factorise and apply the quadratic formula without hesitation.
Number Patterns (25 marks)
This usually comes early in the paper, often the second or third question.
- Arithmetic sequences: common difference, general term, sum of first n terms
- Geometric sequences: common ratio, general term, sum of first n terms, sum to infinity (when the ratio is between -1 and 1)
- Quadratic sequences: second differences, general term
- Sigma notation and the link between sequences and series
- Applications and proofs, for example compound interest as a geometric series
Learn the four formulas and when each applies. Most of the marks come from identifying the type of sequence correctly.
Functions & Graphs (35 marks)
This is a heavy section and usually a multi-part question. The DBE tests:
- Parabolas: turning point, axis of symmetry, intercepts, minimum/maximum
- Hyperbolas: asymptotes, intercepts, domain and range
- Exponential functions: horizontal asymptote, intercepts, transformations
- Logarithmic functions: relationship to exponential, domain
- Inverses (especially the inverse of the parabola and exponential)
- Transformations: translations, reflections, stretches
- Interpretation of graphs, including finding points of intersection and solving inequalities graphically
This section rewards candidates who can read graphs and switch between the graph and the equation fluently.
Finance, Growth & Decay (15 marks)
Smaller section, often examined in one question with several sub-parts.
- Simple and compound interest (per period and per year)
- Nominal and effective interest rates
- Present and future value annuities
- Sinking funds and loan repayments
- Depreciation (straight-line and reducing balance)
- Timeline problems with deposits and withdrawals on a loan or investment
A common trap is mixing up nominal and effective rates, or misreading the number of compounding periods.
Differential Calculus (35 marks)
The other heavyweight. Typical mark split across first principles, rules and application.
- Differentiation from first principles (definition as a limit)
- Rules: power rule, sum rule, differentiating polynomials, roots (as rational exponents) and constants
- Gradient of a curve at a point, equation of a tangent
- Stationary points (max, min, inflection), concavity
- Sketching cubic graphs
- Rate-of-change and optimisation word problems (volume, cost, distance)
Optimisation questions are where many candidates lose marks. Practise setting up the constraint and the function you're optimising before you try to differentiate.
Counting Principle & Probability (15 marks)
The last section in most papers.
- Fundamental counting principle
- Permutations and combinations (arranging letters, seating problems)
- Tree diagrams, Venn diagrams and contingency tables
- Mutually exclusive and independent events
- Addition and product rules
- Conditional probability (tested increasingly often in recent papers)
This section feels easier than Calculus for many candidates. Don't skip it; the 15 marks here are often the difference between a B and an A.
How to allocate your prep time
If you're starting from scratch, a sensible study split reflects the mark weighting, not your comfort level:
- Functions & Graphs: 23% of prep time
- Differential Calculus: 23%
- Algebra: 17%
- Number Patterns: 17%
- Finance: 10%
- Probability: 10%
Set aside 20% to 30% on top of this for full past-paper sittings under exam conditions. The best predictor of Paper 1 performance is not how many textbook exercises you complete, it's how many full papers you sit with a timer and then mark against the memo.
Where to get past papers
NavyBlue hosts free CAPS Grade 12 Mathematics past papers and memos organised by year, term and province. Start with the most recent official NSC papers (previous year and the year before) and work backwards.
- Grade 12 Mathematics past papers
- Grade 11 Mathematics past papers (for rebuilding fundamentals)
- Free APS calculator (see what a strong Paper 1 unlocks)
Exam-day tactics
- Work through the paper in order for the first 90 minutes. Paper 1 builds in difficulty across each question, so the early marks in every section are the most accessible.
- Leave space next to each answer to come back and check. Most candidates lose marks to silly arithmetic, not to conceptual gaps.
- On Functions, always label your intercepts, turning points and asymptotes on any graph you draw.
- On Calculus optimisation, write down the variable, the constraint and the function to be optimised before you differentiate.
- On Probability, draw the Venn diagram or tree even if the question doesn't ask for it. Marks flow much faster when the structure is visible.