Grade 12 Maths · Calculus · Paper 1

Differentiation Grade 12

Real Differentiation past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 14 past paper questions
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videos: 3 videos

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Question 8.1 · May/June 2025 · Paper 1 · National (DBE) · 5 marks

8.1 Determine

f^{'} (x)

from first principles if it is given that

f (x) = x^{2} - 2

.(5)

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Differentiation skills

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More Differentiation Grade 12 questions and answers

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4. Question 8.1 · May/June 2024 · Paper 1 · National (DBE) · 5 marks
8.1 Determine $f^{'} (x)$ from first principles if $f (x) = \frac{1}{x}$ .(5)
Show the memo (5 ticks)Memo
1. ✓
  Writing f(x + h) $f (x + h) = \frac{1}{x + h}$
  1 mark · Differentiate from first principles
2. ✓
  Substitution into the limit formula $f^{'} (x) = lim_{h \to 0} \frac{\frac{1}{x + h} - \frac{1}{x}}{h}$
  1 mark · Differentiate from first principles
3. ✓
  Simplifying the numerator $lim_{h \to 0} \frac{- h}{x ( x + h )} \times \frac{1}{h}$
  1 mark · Differentiate from first principles
4. ✓
  Cancelling h $lim_{h \to 0} \frac{- 1}{x ( x + h )}$
  1 mark · Differentiate from first principles
5. ✓
  Answer $f^{'} (x) = - \frac{1}{x ^{2}}$
  1 mark · Differentiate from first principles
5. Question 8.2 · September 2024 · Paper 1 · Provincial · 5 marks
8.2 Given: $f (x) = \frac{3 x ^{2}}{2} - 24 x$ . Calculate $f^{'} (9)$ .(5)
Show the memo (5 ticks)Memo
1. ✓
  Simplification $\frac{3}{2} x^{2} - 24 x^{\frac{1}{2}}$
  1 mark · Write a root as a power
2. ✓
  Derivative of the first term $3 x$
  1 mark · Differentiate using the power rule
3. ✓
  Derivative of the second term $- 12 x^{- \frac{1}{2}}$
  1 mark · Differentiate using the power rule
4. ✓
  Substitution $3 (9) - \frac{12}{3}$
  1 mark · Substitute into a formula
5. ✓
  Answer $23$
  1 mark · Substitute into a formula
6. Question b · Siyavula Grade 12 Mathematics, 6.7 Applications of differential calculus, Worked example 23 · 2 marks
The height (in metres) of a golf ball $t$ seconds after it has been hit into the air, is given by $H (t) = 20 t - 5 t^{2}$ . Determine the following:
b The vertical velocity of the ball after $1, 5 s$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Derivative $v (t) = H^{'} (t) = \frac{d H}{d t} = 20 - 10 t$
  1 mark · Differentiate using the power rule
2. ✓
  Velocity at 1,5 s $v (1, 5) = 20 - 10 (1, 5) = 5 m.s^{- 1}$
  1 mark · Find a rate of change

Differentiation Grade 12 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Grade 11 Exponents: Rational exponents | Writing roots as powers with rational exponentsMiss Martins Maths and Science

First Principles Calculus Grade 12Kevinmathscience

First Derivative Calculus Grade 12 | PolynomialsKevinmathscience

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