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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
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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: .............
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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
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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
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4
10
3
11
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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
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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
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3
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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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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:
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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
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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)
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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
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