Grade 12 Maths · Calculus · Paper 1

Optimisation (Maxima and Minima) Grade 12

Real Optimisation (Maxima and Minima) 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: 5 past paper questions
skill: 1 skill
videos: 1 videos

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Question 9.5 · May/June 2025 · Paper 1 · National (DBE) · 6 marks

Given:

f (x) = x^{3} - 6 x^{2} + 9 x - 4 = (x - 4) (x - k)^{2}

9.5 Calculate the maximum vertical distance between

f

and

h

for

1 < x < 3

, if

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

.(6)

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Optimisation (Maxima and Minima) skills

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Find stationary pointsFind the turning points of a curve by setting the derivative equal to 0 and solving, then say which are maximums and which are minimums.11 past paper questions · 3 videos

More Optimisation (Maxima and Minima) Grade 12 questions and answers

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4. Question 10 · September 2024 · Paper 1 · Provincial · 8 marks
The diagram below shows the plan for a verandah which is to be built onto the corner of a cottage. A railing ABCDE is to be constructed around the four edges of the verandah. It is given that $A B = D E = x$ and $BC = C D = y$ , and the length of the railing must be 30 metres.
10 Calculate the value of x and y for which the veranda will have a maximum area.(8)
Show the memo (8 ticks)Memo
1. ✓
  Expression for FE and FA $FE = F A = y - x$
  1 mark · Set up an expression or equation
2. ✓
  Expression for y $2 x + 2 y = 30$ $y = 15 - x$
  1 mark · Set up an expression or equation
3. ✓
  Substitute into the area formula $A (x) = y^{2} - (y - x)^{2} = 2 x y - x^{2}$
  1 mark · Calculate area or perimeter
4. ✓
  Substitute for y $A (x) = 2 x (15 - x) - x^{2}$
  1 mark · Substitute into a formula
5. ✓
  Expression for the area $A (x) = 30 x - 3 x^{2}$
  1 mark · Collect like terms
6. ✓
  Derivative = 0For a maximum: $A^{'} (x) = 30 - 6 x = 0$
  1 mark · Find stationary points
7. ✓
  Value of x $x = 5$ m
  1 mark · Find stationary points
8. ✓
  Value of y $y = 15 - 5 = 10$ m
  1 mark · Substitute into a formula

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