# Maths: Differential calculus

> 12 questions based on past NSC papers, on differential calculus, 39 marks in our Paper 1 questions. Answer one and see it marked mark by mark.

Canonical: https://sharpkop.co.za/maths/differential-calculus/
Last updated: 2026-11-12

## Questions

- [Nov 2024 · Paper 1 · Q6.3 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-3/): The diagram below shows the parabola f(x) = -x^2 + 6x + 7 and the straight line g(x) = 2x + 2.
- [Nov 2024 · Paper 1 · Q6.4 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-4/): The diagram below shows the parabola f(x) = -x^2 + 6x + 7 and a straight line g.
- [Nov 2024 · Paper 1 · Q8.1.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-1-1/): Find d/dx[7x^2 - 4x].
- [Nov 2024 · Paper 1 · Q8.1.2 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-1-2/): Determine f’(x) if f(x) = 3/(x^4) - 3√(x^5).
- [Nov 2024 · Paper 1 · Q8.2 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-2/): Find the equation of the tangent to the curve g(x) = x^3 - 3x^2 + 4x + 1 at the point where x = 2.
- [Nov 2024 · Paper 1 · Q8.3.1 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-3-1/): Given: g(x) = -4x^2. Use first principles to determine g’(x).
- [Nov 2024 · Paper 1 · Q9.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-1/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3).
- [Nov 2024 · Paper 1 · Q9.2 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-2/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3).
- [Nov 2024 · Paper 1 · Q9.3 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-3/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3).
- [Nov 2024 · Paper 1 · Q9.4 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-4/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3).
- [Nov 2024 · Paper 1 · Q10.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q10-1/): A delivery drone flies from a depot and lands at a warehouse. Its speed, in km/h, after t hours of flight is given by v(t) = -2t^2 + 12t.
- [Nov 2024 · Paper 1 · Q10.2 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q10-2/): A runner travels from checkpoint A and stops at checkpoint B. Her speed (in km/h) after t hours is given by s’(t) = -6t^2 + 24t, where...

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Questions are based on National Senior Certificate papers set by the Department of Basic Education. Sharpkop is not affiliated with or endorsed by the Department.