CAIE IGCSE Mathematics Extended E2.12 Diffe…ation

[Maximum number: 5]

Figure for Question 1 — CAIE IGCSE Mathematics Extended

The diagram shows a sketch of $y=18+5 x-2 x^{2}$ .

(a)

Differentiate 18+5 x-2 x^2.

[ 2 ]

(b)

Find the coordinates of the point on y=18+5 x-2 x^2 where the gradient is 17 .

[ 3 ]

(-3,-15)
B2FT for x=-3
OR M1 for their (b) = 17
M1dep for correct substitution of their x into $18+5x-2x^2$ shown

[Maximum number: 5]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

\mathrm{f}(x)=x(x+2)(x-3)

A is the point (1,-6).

The tangent to the graph of y=f(x) at A meets the y-axis at B.
Find the coordinates of B.
(

[Maximum number: 8]

(a)

A curve has equation $y=4 x^{3}-3 x+3$ .

[ 8 ]

(i)

Find the coordinates of the two stationary points.

(___, ___) and (___, ___)

[ 5 ]

$\left(-\frac{1}{2},4\right)$ and $\left(\frac{1}{2},2\right)$
B2 for $12x^2-3=0$ , or B1 for $12x^2$ or -3.
M1 for derivative =0 or $\frac{dy}{dx}=0$ .
B1 for $x=-\frac{1}{2}$ and $x=\frac{1}{2}$ , or one coordinate pair correct.

(ii)

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

[ 3 ]

$\begin{aligned} \left(-\frac{1}{2},4\right)&\text{ maximum with reason}\\ \left(\frac{1}{2},2\right)&\text{ minimum with reason} \end{aligned}$
B2 for one correct with reason, or M1 for a correct attempt such as second derivative, gradients, or sketch.

[Maximum number: 3]

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

Table for Question 4 — CAIE IGCSE Mathematics Extended

(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]

Figure for Question 5 — CAIE IGCSE Mathematics Extended

The diagram shows a sketch of $y=18+5 x-2 x^{2}$ .

Differentiate 18+5 x-2 x^2.

[Maximum number: 3]

A curve has equation $y=4 x^{3}-3 x+3$ .

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

$\begin{aligned} \left(-\frac{1}{2},4\right)&\text{ maximum with reason}\\ \left(\frac{1}{2},2\right)&\text{ minimum with reason} \end{aligned}$
B2 for one correct with reason, or M1 for a correct attempt such as second derivative, gradients, or sketch.

CAIE IGCSE Mathematics Extended E2.12 Differentiation Topic Practice

Covered syllabus points

CAIE IGCSE Mathematics Extended E2.12 Differentiation Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question (a)

Question (b)

Question 5

Question 6