add math form 5 integration collection of trial spm questions 2012 paper 2

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


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


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


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


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)


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

add math form 5 integration collection of trial spm questions 2012 paper 2

Documents