2 hours exam

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SECTION A
[50 marks]
Answer all questions.
1. Diagram 1 shows the relation between x and y.
Diagram 1
State
(a) the value of h,
(b) the range of relation.
[2 marks]
Answer:
(a)
(b)
2. Given 103:  xxf and 3
91: xxfg  , find g.
[2 marks]
Answer:

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3. It is given that m is a root of the equation 022
 kxx .
(a) If cmm  32
, find the numerical values of k and c.
(b) Hence, solve the equation 022
 kxx .
[4 marks]
Answer:
(a)
(b)
4. Solve the inequality
x
1
>
3
1
x
.
[3 marks]
Answer:

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5. Diagram 5 shows a front view of a tunnel.
Diagram 5
The curve of the tunnel is represented by the equation of 52
 xy .
The width of the road is 6 metres.
Find the maximum height, in m, of the tunnel.
[4 marks]
Answer:

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6. Solve the equation 1)2(34 1
 xx
.
[4 marks]
Answer:
7. It is given that xa 3log , yb 2log and zc 4log .
Find the value of the expression zyx
cba ))(( 2
.
[3 marks]
Answer:

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8. Evaluate )9)(log)(log(log 3 ba ab .
[3 marks]
Answer:
9. Diagram 9 shows the straight line PT which is perpendicular to the straight line RS at
point Q.
y
Diagram 9
Given that the equation of the straight line RS is 54  xy .
Find the coordinates of Q.
[4 marks]
Answer:
0 x
)5,0(P Q
S
R
T

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10. Given point M is (1, -3) and point N is (6, 5). Point P moves along the circumference of
the circle with diameter MN. Find the locus of point P.
[3 marks]
Answer:
11. Diagram 11, OPS is an isosceles triangle and OQR is a sector of a circle with centre O.
Diagram 11
Given that OP : PQ = 2 : 3 and the length of the arc QR is 13 cm.
Find the area, in cm2, of the shaded region.
[4 marks]
Answer:

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12. Table 12 shows the distribution of age of a group of workers in a factory.
Age (years old) Number of workers
23 – 27 6
28 – 32 x
33 – 37 15
38 – 42 11
Table 12
Given the median age of the workers is 34.5 years old.
(a) Determine the range of age of the workers.
(b) Calculate the value of x.
[4 marks]
Answer:
(a)
(b)
13. A set of seven numbers has a mean of 15 and a standard deviation 50 . A number 23 is
added to this set and the mean increases by 1. Find the new variance.
[3 marks]
Answer:

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14. A block of metal in the form of a cube is heated. The block expands such that its total
surface area increases at a rate of 2.4 cm2s–1. Find the rate of change of the side of the
block when the total surface area is 54 cm2.
[4 marks]
Answer:
15. Given the curve 32
 qxpxy has a stationary point (l, 4).
Find the value of p and of q.
[3 marks]
Answer:

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SECTION B
[30 marks]
Answer all questions.
16. Given the function qxpxxf  4)( 2
, where p and q are constants.
(a) Show that
p
pq
p
xpxf
42
)(
2








[2 marks]
(b) If the minimum point of )(xf is )2,4( , find the value of p and of q.
[4 marks]

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17. Diagram 2 shows a rectangular plank.
Diagram 2
Pak Ali wants to cut the plank into two triangular planks. The perimeter of each triangular
plank is 24 cm and the measurement of the longest side of the triangle is (x + y) cm.
Calculate the area, in cm2, of the plank.
[7 marks]

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18. Diagram 18 shows a piece of a square tile.
Diagram 18
The tile is divided into 8 sectors with radius 8 cm and centre O.
Find
(a) the length of the side of the tile,
[2 marks]
(b) the area, in cm2, of the shaded region,
[4 marks]
(c) the perimeter, in cm, of the unshaded region.
[3 marks]

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19. Diagram 19 shows the right angled triangle PQR. ABCQ is a rectangle inscribed in the
right angled triangle PQR.
Diagram 19
(a) Express the area of the shaded region, A cm2, in terms of x.
[4 marks]
(b) Find the values of x and y such that the area of the shaded region is a minimum.
[4 marks]

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20. A type of liquid is formed by mixing three types of raw materials P, Q and R in the ratio
5 : 3 : 4. Diagram 20 shows the price indices of the raw materials for the year 2013 based
on the year 2011.
Diagram 20
(a) If the price of 1 litre of raw materials for the year 2013 is RM6.50, calculate the
corresponding price for the year 2011.
[1 mark]
(b) Calculate the composite index for the raw materials in the year 2013 using the year
2011 as the base year. Hence, describe your answer according to the composite
index.
[3 marks]
(c) The composite index number for the raw materials increases by 20% from the year
2013 to the year 2015, calculate
(i) the composite index number for the raw materials in year 2015 based on the
year 2011,
(ii) the cost of the raw materials to produce 1 container of liquid for the year 2015
if the corresponding cost for the year 2011 is RM550.
[4 marks]
(d) If the price index of material Q for the year 2013 based on the year 2012 is 120,
calculate the percentage of increases or decreases of the price of item Q from the
year 2012 to 2013.
[2 marks]
END OF QUESTION PAPER