Add Maths Perfect Score Module Form 4 Set 2 p1

8/8/2019 Add Maths Perfect Score Module Form 4 Set 2 p1

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PERFECT SCORE 2010

FORM 4

ADDITIONAL MATHEMATICS

3472/1

Additional

Mathematics

Paper 12 Hours

September 2010


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Answer all questions.

1. x y z

4 4 4

2 2 2

0 0 0

1

2

2

2Diagram 2

Diagram 2 shows the mapping ofy tox by the function g : y ay + b and mapping

toz by the function h : y 6

2y b,y

b

2. Find the,

(a) value ofa and value ofb,

(b) the function which mapsx toy,

(c) the function which mapsx toz.

[ 4 marks]Answer: (a) ..

(b) ......

(c)..................................

2.

The following information above refers to the functions f and g .

(a) State the value of h.

(b) Find the value of 1 1gf .[ 4 marks ]

Answer: (a) .

(b) ..............................4

2

4

1

Forexaminers

use only

hxx

xxf

,

3

4:

xxg 21:


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3. Given the inverse function2

32)(

1

xxf , find

(a) the value off(4),

(b) the value of k iff1 (2k) =k3 .

[ 4 marks ]

Answer: (a).........

(b).....................................

4. A functionf is defined as f : x p x

x

3 2, for all values ofx except x = h andp

are constants.

(a) Determine the value h.

(b) Given value 2 is mapped to itself by the function f. Find the value ofp.

[3 marks]

Answer: (a) h=.........

(b)............................

5. Find the values of such that the equation (3 )x2 2( + 1)x + + 1 = 0

has equal roots.

[3 marks]

Answer: .............

For

examiners

use only

4

3

4

4

2

5


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6. y

( 2, 3)

0 x

Diagram 4

In Diagram 4 above point ( 2, 3 ) is the turning point on the graph which has equation

of the formy =p(x + h)2

+ k.

Find the,

a) values ofp, h and k,b) equation of the curve formed when the graph as shown is reflected at the xaxis.

[ 4 marks ]

Answer: (a) ................................

(b) .................................

___________________________________________________________________________

7. Function

2 28 20 1 f x x kx k has a minimum value of

24

r k

, where rand kare constants. Find the values ofkand rif the graph of the function is symmetrical about

213x r .

[ 4 marks ]

Answer: ..................................

8. Solve the equation1

2

25.5

1625

xx

x. [3 marks]

Answer: ..

2

6

For

examiners

use only

3

7

3

8

( 0, 23)


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9. Solve the equation log2x 4 logx16 = 0 [3 marks]

Answer: ..................................

10. Solve the equation 2 1 22 16 2x x .

[3 marks]

Answer: ...................................

11. The triangle with verticesA(4,3), B(-1,1) and C(t , -3) has an area 11 unit2. Find the

possible values of t.

[3 marks]

Answer: t= ..............................

3

9

For

examiners

use only

4

10

3

11


6/12

12. In Diagram 1, the straight line PR cutsy-axis at Q such that PQ : QR = 1 : 3. The

equation ofPS is 2y =x + 3.

(a) Find the coordinates ofR,

(b) Find the equation of the straight lineRS.

[4 marks]

Answer: (a) .........

(b) .........................................

13. A pointR moves along the arc of a circle with centreA(2, 3). The arc passes

through Q(-2, 0). Find the equation of the locus ofR.

[4 marks]

Answer:............

3

12

Forexaminers

use only

4

13

P(3, 0 )

Q( 0, 4 ) S

Ry

xO

Diagram 1


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14. The coordinates of point P and Q are )1,3( and )10,6( respectively. The point Xmoves

such that XP :XQ = 2 : 3 . Find the equation of the locus ofX.

[3 marks]

Answer:...........................

_________________________________________________________________________

15 The scores,x , obtained by 32 students of Class 5 Wira in a test are summarized as2

2496 and 195488.x x The mean and the standard deviation of thescores,y , obtained by 40 students and Class 5 Waja in the test are 66 and 6

respectively.

(a) Find (i) y (ii)2

y

(b) Calculate the mean and the standard deviation of the scores obtained by all the

72 students.[4 marks]

Answer: (a) .

(b) ......4

15

For

examiners

use only

3

14


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16.

Diagram

B

A

O

Given that the area of a sector OAB in Diagram with centre O and radius 20 cm is 240 cm2.

Calculate(a) the length of arcAB

(b) area of shaded region

[4 marks]

Answer:(a).

(b)

17.

B

O

T

Diagram 1

Diagram 1 shows a circle with centre O and OA = 10 cm. Straight lineATis a tangent to the

circle at pointA, andAOTis a triangle. Given that the area of triangle OAT= 60 cm2, find the

area of sector OAB.

[3 marks]

Answer: ......

___________________________________________________________________________

2

16

3

17

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examiners

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18. Diagram 5 shows an arc PQ and an arc RS with centre O.

Find the value ofp if the area of shaded region is 60 cm2

.

[4 marks ]

Answer: ...

___________________________________________________________________________

19. Diagram 6 shows a sector of a circle OPQ with centre O and OPR is a right angle

triangle.

Find the area, in cm2, of the shaded region.

[4 marks]

Answer:

For

xaminers

use only

3

18

O R Q1 cm

5 cm

P

4

19

Diagram 6

P

S

R

O

Q

4p

2p

23

rad


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SULIT 3472/1

3472/1 SULIT

20. Differentiate 52

4 3 7x x with respect tox.

[ 3 marks ]

Answer: .............

___________________________________________________________________________

21. The height of a cylinder is 12 cm. Its radius increases at a rate of 0.3cms-1

. Find therate of increase of its volume at the instant when its radius is 4 cm. Express the

answer in terms .

. [ 3 marks]

Answer: ..

22. The point Q lies on the curve 3

3y x . If the gradient of the normal at P is1

8 ,

find the coordinates ofP..

[3 marks]

Answer: ..

2

21

3

22

Forexaminers

use only

3

20


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SULIT 3472/1

3472/1 SULIT

23. Given the curve2

18

2y x

x .

(a) Find the coordinates of the turning point.

(b) Hence, determine nature of this point.

[4 marks]

Answer: (a)............

(b)....................................

___________________________________________________________________________

24. Given that1

yx

(a) find dydx

,

(b) approximate the value of1

24 95..

[4 marks]

Answer: (a)

(b)

Forexaminers

use only

4

24

4

23


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SULIT 3472/1

3472/1 SULIT

25. Given that 2 and 2 1 y t t x t . Find

(a) in terms ofdy

xdx

(b) the corresponding increase in t, ifx decrease from 4 to 3.98. [4 marks]

Answer:............

END OF QUESTION PAPER

4

25

For

examiners

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Add Maths Perfect Score Module Form 4 Set 2 p1

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