CAIE IGCSE Mathematics Extended E2.12 Differentiation Question Bank

Practise differentiating algebraic functions, then using dy/dx to find gradients, turning points and tangent equations on graphs.

Exam points

differentiate polynomial terms and substitute an x-value to calculate a curve gradient
set dy/dx=0 to find turning-point coordinates from a quadratic derivative
use a gradient and point on the curve to form a tangent equation y=mx+c

[Maximum number: 3]

The table shows some values for $y=x^{3}+4 x^{2}-4$ .

(a)

Draw the tangent to the graph at the point (1,1).

[ 1 ]

(b)

Use your tangent to estimate the gradient of the curve at the point (1,1).

[ 2 ]

[Maximum number: 2]

Find the derivative, $\frac{dy}{dx}$ , of $y=3x^2+4x-1$ .

[Maximum number: 2]

(a)

$y=3 x^{2}-12 x+7$

[ 2 ]

(i)

Find the coordinates of the point on the graph of $y=3x^2-12x+7$ where the gradient is 0.
$(\qquad,\qquad)$

[ 2 ]

(2,-5)
B1 for each
If 0 scored, M1 for their $6x-12=0$ or states $\frac{dy}{dx}=0$

(b)

When $y=2x^p+qx^2$ , $\frac{dy}{dx}=14x^6+6x$ .
Find the value of p$ and the value of $q.
$\begin{aligned}p&=\\q&=\end{aligned}$

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