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2.18 Differentiation
Question Paper
Course
CIE IGCSE Maths
Section
2. Algebra & Graphs
Topic
2.18 Differentiation
Difficulty
Hard
Time allowed:
70
Score:
/55
Percentage:
/100
Page 1 of 8
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Question 1a
A curve has the equation y = x 3 + 8x 2 + 5x .
Work out the coordinates of the two turning points.
(.................... , ....................) and (.................... , ....................)
[9 marks]
Question 1b
Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.
[3 marks]
Page 2 of 8
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Question 2
y = x 4 − 4x 3
Find the two stationary points on the graph of y = x 4 − 4x 3 .
( ..................... , ..................... )
( ..................... , ..................... )
[6 marks]
Page 3 of 8
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Question 3
A curve has equation y = 4x 3 − 3x + 3 .
i)
Find the coordinates of the two stationary points.
( .................... , .................... ) and ( .................... , .................... ) [5]
ii)
Determine whether each of the stationary points is a maximum or a minimum.
Give reasons for your answers.
[3]
[8 marks]
Page 4 of 8
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Question 4a
A curve has equation y = x 3 − 3x + 4 .
Work out the coordinates of the two stationary points.
( .................... , ....................)
( .................... , ....................)
[5 marks]
Question 4b
Determine whether each stationary point is a maximum or a minimum.
Give reasons for your answers.
[3 marks]
Page 5 of 8
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Question 5a
A curve has equation y = x 3 – 6x 2 + 16.
Find the coordinates of the two turning points.
(............ , ............) and (............ , ............)
[6 marks]
Question 5b
Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.
[3 marks]
Page 6 of 8
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Question 6a
The curve C has equation y = 5x 3 – x 2 – 6x + 4 .
Find
dy
.
dx
dy
= ..............................................
dx
[2 marks]
Question 6b
There are two points on the curve C at which the gradient of the curve is 2 .
Find the x coordinate of each of these two points.
Show clear algebraic working.
[4 marks]
Question 7a
y = x 3 – 6x 2 – 15x .
Find
dy
.
dx
dy
= ....................................
dx
[2 marks]
Page 7 of 8
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Question 7b
The curve with equation y = x 3 – 6x 2 – 15x has two stationary points.
Work out the coordinates of these two stationary points.
[4 marks]
Page 8 of 8
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