Differentiation | CIE IGCSE Maths: Extended Calculator Questions 2025

1a

9 marks

A curve has the equation $y = x^{3} + 8 x^{2} + 5 x .$

Work out the coordinates of the two turning points.

(.................... , ....................) and (.................... , ....................)

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1b

3 marks

Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.

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1

2 marks

$y = 2 x^{k} + u x^{7} and \frac{d y}{d x} = 18 x^{k - 1} + 21 x^{6}$

Find the value of $k$ and the value of $u$ .

$k$ = ....................................................
$u$ = ....................................................

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1

6 marks

The curve $C$ has equation $y = a x^{3} + b x^{2} - 12 x + 6$ where $a$ and $b$ are constants.

The point $A$ with coordinates (2, –6) lies on $C$ .
The gradient of the curve at $A$ is 16.

Find the $y$ coordinate of the point on the curve whose $x$ coordinate is 3.
Show clear algebraic working.

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Differentiation (CIE IGCSE Maths: Extended)

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