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Integration – Trapezium Rule
Question Paper 1
Level
International A Level
Subject
Maths
Exam Board
CIE
Topic
Integration
Sub Topic
Integration – Trapezium Rule
Booklet
Question Paper 1
Time Allowed:
57 minutes
Score:
/47
Percentage:
/100
Grade Boundaries:
A*
>85%
A
777.5%
B
C
D
E
U
70%
62.5%
57.5%
45%
<45%
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1
Use the trapezium rule with four intervals to find an approximation to
5
Ó 2x − 8 dx.
1
2
(a) Show that Ô
16
6
6
dx = ln 125.
2x − 7
3
[5]
(b) Use the trapezium rule with four intervals to find an approximation to
Ó
17
1
log10 x dx,
giving your answer correct to 3 significant figures.
3
(a) Find Ó 4 cos
1
3x
+ 2 dx.
[3]
[2]
(b) Use the trapezium rule with three intervals to find an approximation to
Ó
12
0
4 + x2 dx,
giving your answer correct to 3 significant figures.
4
[3]
(a) Find
e2x + 6
dx,
e2x
[3]
(ii) Ó 3 cos2 x dx.
[3]
(i) Ô
(b) Use the trapezium rule with 2 intervals to estimate the value of
Ô
2
1
6
dx,
ln x + 2
giving your answer correct to 2 decimal places.
[3]
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5
(a) Find Ó sin x − cos x2 dx.
(b)
[4]
(i) Use the trapezium rule with 2 intervals to estimate the value of
Ó
10
2
10
4
cosec x dx,
giving your answer correct to 3 decimal places.
[3]
(ii) Using a sketch of the graph of y = cosec x for 0 < x ≤ 21 0, explain whether the trapezium
rule gives an under-estimate or an over-estimate of the true value of the integral in part (i).
[2]
6
(a) Use the trapezium rule with two intervals to estimate the value of
ä
1
0
1
dx,
6 + 2ex
giving your answer correct to 2 decimal places.
(b) Find ä
(ex − 2)2
dx.
e2x
[3]
[4]
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7
y
M
x
O
The diagram shows the curve y = x − 2 ln x and its minimum point M .
(i) Find the x-coordinate of M .
[2]
(ii) Use the trapezium rule with three intervals to estimate the value of
ã (x − 2 ln x) dx,
5
2
giving your answer correct to 2 decimal places.
[3]
(iii) State, with a reason, whether the trapezium rule gives an under-estimate or an over-estimate of
the true value of the integral in part (ii).
[1]