Maths Paper 1, November 2024, question 6.3

Maths P1 · Calculus optimisation and rates

6.34 marks

The diagram below shows the parabola

f (x) = - x^{2} + 6 x + 7

and the straight line

g (x) = 2 x + 2

. The two graphs cross at A on the x-axis and at C

(5; 12)

. A vertical segment EH joins a point E on

f

to a point H on

g

, somewhere between A and C where the parabola lies above the line. Determine the greatest possible length of EH.

NSCBased on Nov 2024 · Paper 1 · Q6.3

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What examiners found

Many candidates built no expression for the vertical length. They solved $f (x) - g (x) = 0$ as if it gave the maximum, which only finds where the graphs meet.

In our words. Source: Department of Basic Education, NSC 2024 Diagnostic Report, Part 1 (Book 1), Q6.3.

Updated 12 November 2026