add math form 5 integration collection of trial spm questions 2012 paper 2
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Collection of Trial SPM 2012 Questions Paper 2 Form 5 Chapter 3 Integration
1
Trial SPM MRSM 2012
1 Diagram 1 shows part of the curve y x(x k) and the straight
line x k, where k is a constant.
Diagram 1
The area of the shaded region is 8 unit 2 .
(a) Show that k 2. [3 marks]
(b) Hence, find the volume generated, in terms of π, when the
region bounded by the curve and the x-axis, is revolved
360º about the x-axis. [3 marks]
Trial SPM Perlis 2012
2 Diagram 2 shows the straight line y x 4 intersecting the
curve y (x 2) 2 2x at point A (0, 4) and B.
Diagram 2
Find
(a) the coordinates of point B, [3 marks]
(b) the area of shaded region, [3 marks]
(c) the volume of revolution, in terms of π, when the region
bounded by the curve, x-axis and y-axis is rotate through
360º about the x-axis. [3 marks]
y x(x k)
x k
y
x O
x
y
A (0, 4)
B O
Collection of Trial SPM 2012 Questions Paper 2 Form 5 Chapter 3 Integration
2
Trial SPM Wilayah Persekutuan 2012
3 Diagram 3 shows part of the curve y (x 2) 2 .
Diagram 3
(a) The gradient of normal to the curve at the point x a is
2
1. Find the value of a. [3 marks]
(b) Find the area of the shaded region [4 marks]
(c) The region bounded by the curve, both axes and the line
x 1 is rotated through 360º about the x-axis. Find the
volume of revolution, in terms of π. [3 marks]
Trial SPM Penang 2012
4 Diagram 4 shows the straight line y x 6 intersecting the
curve 3y x 2 at point A and point B.
Diagram 4
Find
(a) the coordinates of A and B, [3 marks]
(b) the area of the shaded region P, [4 marks]
(c) the volume of revolution, in terms of π, when the shaded
region Q is revolved through 360º about the x-axis.
[3 marks]
y
x O 3
y (x 2) 2
y 4
P
Q A
B
O x
y
y x 6 3y x 2
Collection of Trial SPM 2012 Questions Paper 2 Form 5 Chapter 3 Integration
3
Trial SPM Pahang 2012
5 Diagram 5 shows the straight line y x 3 intercept the curve
y 3x x 2 at points P and Q.
Diagram 5
Find
(a) the points P and Q, [3 marks]
(b) the area of the shaded region, [4 marks]
(c) the volume in terms of π under the curve and the x-axis is
rotated 360º about the x-axis.
[3 marks]
Trial SPM Zon A Kuching 2012
6 Diagram 6 shows the curve y x 3 and the normal to the curve
at point A(1, 1).
Diagram 6
Calculate
(a) the equation of the normal to the curve at A, [3 marks]
(b) the area of the region enclosed by the curve, the normal
and the x-axis,
[3 marks]
(c) the volume of the revolution, in terms of π, if the region in
6(b) is rotated through 360º about the x-axis. [4 marks]
x
y
P
Q
O
y 3x x 2
y x 3 y x 3
A(1, 1) x
y
O
Collection of Trial SPM 2012 Questions Paper 2 Form 5 Chapter 3 Integration
4
Trial SPM Selangor 2012
7 In Diagram 7, the straight line PQ is a tangent to the curve
y 9 x 2 at the point A(2, 5).
Diagram 7
Find
(a) the equation of the tangent at A, [3 marks]
(b) the area of the shaded region,
[4 marks]
(c) the volume of revolution, in terms of π, when the region
bounded by the curve, the x-axis and the y-axis, is rotated
through 360º about the y-axis. [3 marks]
Trial SPM Melaka 2012
8 Diagram 8 shows part of the curve y f (x) which has gradient
function .
Diagram 8
The curve intersects the straight line y x at point P(1, 1). Find
(a) the equation of the curve, [3 marks]
(b) the area of the shaded region,
[4 marks]
(c) the volume generated, in terms of π, when the region
which is bounded by the curve, the x-axis and the straight
lines x 1 and x 3, is revolved through 360º about the
x-axis. [3 marks]
y
x
y 9 x 2
A(2, 5)
P
Q O
4
(2x 3) 2
P(1, 1)
Q y f (x)
y x
x 3
x
y
Collection of Trial SPM 2012 Questions Paper 2 Form 5 Chapter 3 Integration
5
Trial SPM Terengganu 2012
9 Diagram 9 shows part of the curve y 3(x 2 4) and a straight
line y 2x 9.
Diagram 9
(a) Calculate the area of the shaded region. [6 marks]
(b) The region enclosed by the curve, the x-axis, the y-axis and
the straight line y k is resolved through 360 about the y-
axis. Find the volume of revolution, in terms of π.
[4 marks]
Trial SPM Perak 2012
10 Diagram 10 shows part of the curve y f (x) which passes
through point A (3, 0) and the straight line x y 10.
Diagram 10
The curve has a gradient function of 2x. Find
(a) the equation of the curve, [3 marks]
(b) the area of shaded region P, [4 marks]
(c) the volume of revolution, in terms of π, when the shaded
region Q is revolved 360º about the y-axis. [3 marks]
y 2x 9
y 3(x 2 4)
x
C
y
C
k
C
O
C x
C
y
y f (x)
P Q
x y 10
A (3, 0)
Collection of Trial SPM 2012 Questions Paper 2 Form 5 Chapter 3 Integration
6
Trial SPM Kedah 2012
11 Diagram 11 shows a shaded region bounded by a curve y
5 x 2 and the straight line y 2x 5.
Diagram 11
Find
(a) the coordinates of A, [3 marks]
(b) the area of shaded region, [4 marks]
(b) the volume of revolution, in terms of π, when the region
bounded by the curve, the x-axis and the y-axis, is revolved
through 360º about the y-axis. [3 marks]
Trial SPM SBP 2012
12 Diagram 8 shows part of the curve y f (x) which passes
through point ( 1, 4).
Diagram 12
The curve has a gradient function of 3
4
x.
(a) Find the equation of the curve. [3 marks]
(b) A region bounded by the curve, the x - axis, the line x
5 and the line x 2.
(i) Find the area of the region.
(ii) The region revolved through 360 about the x - axis.
Find the volume generated, in term of .
[7 marks]
y 5 x 2
y 2x 5
y
x
A
y f (x)
( 1, 4)
x
y
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