Grade 12 · Mathematics · Paper 1 · CAPS
Differential Calculus – Grade 12 Mathematics (Paper 1)
What Differential Calculus covers, how it is examined in Mathematics Paper 1, the 8 sections to study and how long it takes – plus live online lessons when you get stuck.
- Study sections
- 8
- Exam-style questions
- 14
- Marks of practice
- 161
- Study time
- ≈ 8 h 20 min
What it covers
Calculus begins with limits and the derivative from first principles, then the shortcut rules of differentiation and the equation of a tangent to a curve. The centre of the topic is the cubic function: locating its turning points and where its concavity changes, deciding where the graph increases or decreases, sketching it, and reading information from the graph of its derivative. It finishes with rates of change and optimisation problems, where you find a maximum or minimum value in a real situation.
How it is examined
- Paper
- Mathematics Paper 1 – Friday 23 October 2026, 09:00 (3 hours, 150 marks)
- Weighting
- Differential calculus ≈ 35/150 in Paper 1
- Questions
- In a typical paper you will find it in Questions 7–9 of Mathematics Paper 1.
Question numbers and mark splits are typical, not fixed – they vary a little from year to year.
Sections to study
- Limits, average gradient and the derivative from first principles35 min
- Rules of differentiation and notation25 min
- Tangents to curves35 min
- Interpreting the derivative: increasing, stationary points, concavity40 min
- Sketching cubic graphs and finding their equations45 min
- Interpreting cubic graphs and the graph of f′45 min
- Rates of change and motion30 min
- Optimisation (maximum and minimum problems)40 min
Study time
| Notes and worked examples8 sections | 4 h 55 min |
|---|---|
| Exam-style questions14 questions · 161 marks × 1,2 min per mark | 3 h 15 min |
| Topic quiz | 10 min |
| Total | ≈ 8 h 20 min |
Mathematics Paper 1 is written on Friday 23 October 2026 at 09:00.
What you get in the portal
- 14 exam-style questions on Differential Calculus (161 marks in total), each with a full marking memo
- Worked examples with diagrams and step-by-step calculations for each of the 8 sections
- Tutor notes added to sections and questions – for the whole class or just for you
- A topic quiz, mock papers and a study plan that counts down to Mathematics Paper 1
Notes, worked examples, questions and memos open once the tutor approves your account – usually with your first confirmed lesson.
Stuck on Differential Calculus? Book a one-on-one lesson.
R250 per hour – 60, 90 or 120 minutes, online from anywhere in South Africa. Pick Differential Calculus as your topic; you pay by EFT only after the tutor confirms.
Related Maths P1 topics
Questions about Differential Calculus
How many marks is Differential Calculus worth in the matric exam?
In Mathematics Paper 1 (3 hours, 150 marks) the usual weighting is: Differential calculus ≈ 35/150 in Paper 1. In a typical paper you will find it in Questions 7–9 of Mathematics Paper 1. The exact marks change a little from year to year.
How long does it take to study Differential Calculus?
About 8 h 20 min: 4 h 55 min for the notes and worked examples in its 8 sections, 3 h 15 min for the 14 exam-style questions (161 marks) at exam pace of 1,2 minutes per mark, and a 10-minute quiz.
When is the Mathematics Paper 1 exam in 2026?
Mathematics Paper 1 is written on Friday 23 October 2026 at 09:00 and lasts 3 hours (150 marks), according to the DBE’s 2026 NSC timetable. Confirm the date with your school, because the DBE can amend the timetable.
Can I get online lessons for Differential Calculus?
Yes. Create a free account in the Adventuity portal, request a one-on-one online lesson of 60, 90 or 120 minutes (or a seat in a group class) and choose Differential Calculus as your topic. You pay by EFT only after the tutor confirms the booking.