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

Trial SPM MRSM 2012 1

Trial SPM Perlis 2012

Diagram 1 shows part of the curve y line x k, where k is a constant.

x(x

k) and the straight

2

Diagram 2 shows the straight line y x 4 intersecting the 2 curve y (x 2) 2x at point A (0, 4) and B.

y

x

y

k A (0, 4) y

x(x

k)

x

O

B

x

O

Diagram 2 Diagram 1

Find

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 [3 marks] 360º about the x-axis.

(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 [3 marks] 360º about the x-axis.

1

Collection of Trial SPM 2012 Questions Paper 2

Form 5 Chapter 3 Integration

Trial SPM Wilayah Persekutuan 2012 3

Trial SPM Penang 2012

Diagram 3 shows part of the curve y

(x

2) 2 .

4

y

Diagram 4 shows the straight line y curve 3y x 2 at point A and point B.

x

6 intersecting the

y y

(x

2)

2

3y

x2 y

x

6

B y O

4 x

3

P

A

Q O

Diagram 3 (a) The gradient of normal to the curve at the point x

x

Diagram 4

a is Find

1 . Find the value of a. 2

[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]

(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]

2

Collection of Trial SPM 2012 Questions Paper 2

Form 5 Chapter 3 Integration

Trial SPM Pahang 2012 5

Trial SPM Zon A Kuching 2012

Diagram 5 shows the straight line y y 3x x 2 at points P and Q.

x

3 intercept the curve

6

y

y y

y

3x

x2

x 3 and the normal to the curve

Diagram 6 shows the curve y at point A(1, 1).

x

y

3

x3

P A(1, 1) O

Q O

x

x

Diagram 6

Diagram 5 Calculate

Find (a) the points P and Q,

[3 marks]

(a) the equation of the normal to the curve at A,

(b) the area of the shaded region,

[4 marks]

(b) the area of the region enclosed by the curve, the normal and the x-axis, [3 marks]

(c) the volume in terms of π under the curve and the x-axis is [3 marks] rotated 360º about the x-axis.

[3 marks]

(c) the volume of the revolution, in terms of π, if the region in [4 marks] 6(b) is rotated through 360º about the x-axis.

3

Collection of Trial SPM 2012 Questions Paper 2

Form 5 Chapter 3 Integration

Trial SPM Selangor 2012 7

Trial SPM Melaka 2012

In Diagram 7, the straight line PQ is a tangent to the curve y 9 x 2 at the point A(2, 5).

8

Diagram 8 shows part of the curve y 4 function . (2x 3) 2

f (x) which has gradient

y y P

y y

f (x)

x

Q

A(2, 5) P(1, 1) y

9

x

3

x2 x

O

Q

x

Diagram 7

Diagram 8

Find The curve intersects the straight line y (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 [3 marks] through 360º about the y-axis.

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] 4

Collection of Trial SPM 2012 Questions Paper 2

Form 5 Chapter 3 Integration

Trial SPM Terengganu 2012 9

Trial SPM Perak 2012

Diagram 9 shows part of the curve y line y 2x 9.

3(x 2

4) and a straight

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.

y

y

C y

2x

9 x

k y

C

3(x

2

4)

y

y

10

f (x) P

Q

x

O

C

C

A (3, 0)

Diagram 9

x C

Diagram 10 (a) Calculate the area of the shaded region.

[6 marks] The curve has a gradient function of

(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 yaxis. Find the volume of revolution, in terms of π. [4 marks]

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 [3 marks] region Q is revolved 360º about the y-axis. 5

Collection of Trial SPM 2012 Questions Paper 2

Form 5 Chapter 3 Integration

Trial SPM Kedah 2012 11

Trial SPM SBP 2012

Diagram 11 shows a shaded region bounded by a curve y 5 x 2 and the straight line y 2x 5.

12

Diagram 8 shows part of the curve y through point ( 1, 4).

f (x) which passes y

y

y y

5

x

f (x)

2

( 1, 4) A

x y

2x

5 Diagram 12

x

The curve has a gradient function of

Diagram 11 Find

4 . x3

(a) Find the equation of the curve.

(a) the coordinates of A,

[3 marks]

(b) the area of shaded region,

[4 marks]

(b) A region bounded by the curve, the x - axis, the line x 5 and the line x 2. (i)

(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 [3 marks] through 360º about the y-axis.

[3 marks]

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] 6