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IGCSE Math a3.4 CalculusTopic Practice

3.4 Calculus

Edexcel IGCSE Math a 3.4 Calculus question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Math a practice aligned to Edexcel, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

Question 13

[Maximum number: 7]

A curve C has equation y=x3−x2−8x+12y=x^{3}-x^{2}-8 x+12

Question 13(a)

(a)

Find dy dx\frac{\mathrm{d} y}{\mathrm{~d} x}

dy dx=\frac{\mathrm{d} y}{\mathrm{~d} x}=

The curve C has two turning points.

[ 2 ]

Question 13(b)

(b)

Work out the x coordinates of the two turning points.

Show your working clearly.

[ 3 ]

Question 13(c)

(c)

Show that the x-axis is a tangent to the curve C.

[ 2 ]

Question 13

[Maximum number: 6]

The curve C has equation y=5x3−x2−6x+4y=5 x^{3}-x^{2}-6 x+4

Question 13(a)

(a)

Find dy dx\frac{\mathrm{d} y}{\mathrm{~d} x}

dy dx=\frac{\mathrm{d} y}{\mathrm{~d} x}=

There are two points on the curve C at which the gradient of the curve is 2

[ 2 ]

Question 13(b)

(b)

Find the x coordinate of each of these two points.

Show clear algebraic working.

[ 4 ]

Question 18

A particle is moving along a straight line that passes through the fixed point O The displacement, s metres, of the particle from O at time t seconds is given by

s=2t3−5t2+6t−5s=2 t^{3}-5 t^{2}+6 t-5

Find the value of t when the acceleration of the particle is 5 m/s25 \mathrm{~m} / \mathrm{s}^{2}

t=

Question 12

[Maximum number: 5]

The curve C has equation y=13x3−9x+1y=\frac{1}{3} x^{3}-9 x+1

Question 12(a)

(a)

Find dy dx\frac{\mathrm{d} y}{\mathrm{~d} x}

dy dx=\frac{\mathrm{d} y}{\mathrm{~d} x}=
[ 2 ]

Question 12(b)

(b)

Find the range of values of x for which C has a negative gradient.

[ 3 ]

Question 17

[Maximum number: 6]

17y=4x3+5x2+2x17 y=4 x^{3}+5 x^{2}+2 x

Question 17(a)

(a)

Find dy dx\frac{\mathrm{d} y}{\mathrm{~d} x}

dy dx=\frac{\mathrm{d} y}{\mathrm{~d} x}=
[ 2 ]

Question 17(b)

(b)

Find the coordinates of the turning points on the graph with equation y=4x3+5x2+2xy=4 x^{3}+5 x^{2}+2 x
Show clear algebraic working.

[ 4 ]

Question 15(b)

[Maximum number: 5]
Question image

Diagram NOT accurately drawn

The diagram shows a cuboid of volume V cm3V \mathrm{~cm}^{3}

Find this value of x.

Show your working clearly.
Give your answer correct to 3 significant figures.

x=

Question 19

A curve C has equation y=x3−8x2−12x+5y=x^{3}-8 x^{2}-12 x+5

Curve C has exactly two stationary points, one at point A and one at point B such that x coordinate of point A>x coordinate of point B

Find the coordinates of point A
Show clear algebraic working. )

Question 16

A curve has equation y=4x3−8x+5y=4 x^{3}-8 x+5

Find the x coordinates of the two points on the curve where the gradient is 13\frac{1}{3}

Question 20

The radius of a right circular cylinder is x cmx \mathrm{~cm}.
The height of the cylinder is (800πx−x)cm\left(\frac{800}{\pi x}-x\right) \mathrm{cm}.
The volume of the cylinder is V cm3V \mathrm{~cm}^{3}
Find the maximum value of V
Give your answer correct to the nearest whole number.

Turn over for Question 21

Question 18

A curve C has equation y=x3−40x+1y=x^{3}-40 x+1
Find the coordinates of both the points on C at which the gradient is 8 )
(, )

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