3472/1/2 4SECTION 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 f : x→3 x+10 and fg : x→1−9 x3, find g.

[2 marks]Answer:

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3472/1/2 53. It is given that m is a root of the equation x

2+kx+2=0 .

(a) If m2=3m−c , find the numerical values of k and c.

(b) Hence, solve the equation x2+kx+2=0 .

[4 marks]Answer:(a)

(b)

4. Solve the inequality

1x >

1x−3 .

[3 marks]Answer:

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3472/1/2 65. Diagram 5 shows a front view of a tunnel.

Diagram 5

The curve of the tunnel is represented by the equation of y=−x2+5 .The width of the road is 6 metres.Find the maximum height, in m, of the tunnel.

[4 marks]Answer:

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3472/1/2 7

6. Solve the equation 4x+1+3(2x )=1 .

[4 marks]Answer:

7. It is given that log a3=x , log b2= y and log c 4=z .

Find the value of the expression (ax )(b2 y )−c z.

[3 marks]Answer:

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3472/1/2 8

8. Evaluate ( log a b )( log3a )( log√b9 ).[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 y=4 x−5 .Find the coordinates of Q.

[4 marks]Answer:

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S

QP(0,5 )

T x0

R

3472/1/2 910. 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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3472/1/2 1012. Table 12 shows the distribution of age of a group of workers in a factory.

Age (years old) Number of workers23 – 27 628 – 32 x33 – 37 1538 – 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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3472/1/2 1114. 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 y=px2−qx+3 has a stationary point (l, 4).Find the value of p and of q.

[3 marks]Answer:

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3472/1/2 12SECTION B

[30 marks]Answer all questions.

16. Given the function f ( x )=px2+4 x+q , where p and q are constants.

(a) Show that

f ( x )=p(x+ 2p )

2+ pq−4

p[2 marks]

(b) If the minimum point of f ( x ) is (−4 ,2 ), find the value of p and of q.[4 marks]

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3472/1/2 1317. 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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3472/1/2 1418. 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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3472/1/2 1519. 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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3472/1/2 1620. 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

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