Matric past papers · DBE (CAPS) · Paper 1
DBE Grade 12 Differential calculus
Every differential calculus question from the DBE NSC Paper 1 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 22 questions, 283 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.
Download
- Questions (English) 23 pages, 0.8 MB
- Solutions (English) 32 pages, 2.1 MB
- Vrae (Afrikaans) 23 pages, 0.8 MB
- Oplossings (Afrikaans) 32 pages, 2.1 MB
Each question is a clip of the original DBE page: the wording, the mark allocations and the diagrams are exactly as they were printed. Only the blank answer space has been removed, so work in a separate book. The solutions booklet is the board’s own marking guideline, not a rewritten one.
What is in it
22 questions in 3 chapters, ordered so you can work through one skill at a time.
| # | Question | Skills | Marks | From |
|---|---|---|---|---|
| 1 | First principles on minus x squared, then two by the rules | Differentiating from first principles, The rules of differentiation | 11 | May/June 2022 Q8 |
| 2 | First principles, then differentiating a product of surds | Differentiating from first principles, The rules of differentiation | 12 | May/June 2021 Q8 |
| 3 | First principles, then dy/dx of a quartic and of a surd | Differentiating from first principles, The rules of differentiation | 12 | November 2021 Q9 |
| 4 | First principles, then the tangent with the least gradient | Differentiating from first principles, The rules of differentiation, Tangents to a curve | 12 | November 2022 Q7 |
| 5 | First principles, then where a tangent's gradient stays positive | Differentiating from first principles, The rules of differentiation, Tangents to a curve | 13 | November 2023 Q7 |
| 6 | First principles, then b and c recovered from a given tangent | Differentiating from first principles, The rules of differentiation, Tangents to a curve | 15 | May/June 2024 Q8 |
| 7 | First principles, then a tangent common to two curves | Differentiating from first principles, The rules of differentiation, Tangents to a curve | 17 | May/June 2025 Q8 |
| 8 | The rules, a tangent at x = 2, then first principles | The rules of differentiation, Tangents to a curve, Differentiating from first principles | 18 | November 2024 Q8 |
| 9 | Reading f' off the turning points of f | The graph of f', Turning points | 8 | November 2024 Q9 |
| 10 | Turning points, then where the cubic is concave up | The cubic graph, Turning points, Concavity and the point of inflection | 11 | May/June 2021 Q9 |
| 11 | Sketch a cubic from four facts, without ever finding its equation | The cubic graph, Sketching the graph, Turning points | 13 | May/June 2021 Q10 |
| 12 | a, b and c from two intercepts, then the local minimum | The cubic graph, Turning points, Sketching the graph | 13 | May/June 2024 Q9 |
| 13 | a and b from two turning points, then the x-intercept | The cubic graph, Turning points, Concavity and the point of inflection | 15 | November 2021 Q10 |
| 14 | Given the graph of f', work back to f | The graph of f', The cubic graph, Concavity and the point of inflection | 17 | November 2022 Q8 |
| 15 | Turning points, a sketch, then reading answers off it | The cubic graph, Turning points, Sketching the graph | 18 | November 2023 Q8 |
| 16 | Show k = 1, then the turning points, the concavity and the sketch | The cubic graph, Turning points, Concavity and the point of inflection, Sketching the graph | 18 | May/June 2025 Q9 |
| 17 | A cubic from its intercepts, and everything that then follows | The cubic graph, Turning points, Sketching the graph, Concavity and the point of inflection | 23 | May/June 2022 Q9 |
| 18 | A printed poster, and the size that wastes the least page | Optimisation: maximum and minimum | 6 | November 2023 Q9 |
| 19 | The speed that keeps a journey's cost as low as possible | Optimisation: maximum and minimum | 7 | November 2021 Q11 |
| 20 | The shortest distance from a point to a parabola | Optimisation: maximum and minimum | 8 | November 2022 Q9 |
| 21 | Show the area is 6x squared minus 3x to the fourth, then maximise it | Optimisation: maximum and minimum | 8 | May/June 2024 Q10 |
| 22 | A cyclist's speed, given as a rate of change | Rates of change, Optimisation: maximum and minimum | 8 | November 2024 Q10 |