1

3472/2

Additional

Mathematics

Paper 2

2 ½ Hours

September 2010

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PERFECT SCORE 2010

FORM 4

ADDITIONAL MATHEMATICS

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3472/2 2010 Hak Cipta SBP

SULIT

SECTION A

[40 marks]

Answer all questions in this section

1. Solve the simultaneous equations

52 yx

72 xyx

[5 marks]

2. Express 34)( 2 xxxf in the form f (x) = m(x + n)2 + k , where m, n and k are

constants.

(a) State the values of m, n and k.

[3 marks]

(b) Find the maximum or minimum point.

[1 marks]

(c) Sketch the graph of 34)( 2 xxxf

[2 marks]

3. (a) The straight line xy 3 does not intercept to the curve 024 22 xpy

Find the range of p.

[3 marks]

(b) Given p and q are the roots of the quadratic equations 2x2 + 7x = x – 5,

Find the equation that has the roots p + 2 and q + 2.

[4 marks]

4 (a) Solve the equation 32 233 xx

[3 marks]

(b) Solve the equation 34349.7 1 x

[2 marks]

(c) Solve the equation 2)23(log2log 22 xx

[2 marks]

3

5

(a) A set of 6 numbers has a standard deviation of 2.5. Given that the sum of the

numbers, x , is 54. Find

(i) the value of mean

[2 marks]

(ii) the sum of the squares of the numbers.

[3 marks]

(b) If each of the numbers is divided by h and is added by k uniformly , the new

mean and standard deviation of the set are 5 and 1.25 respectively.

Find the value of h and k.

[4 marks]

6. The gradient of the tangent to the curve 2mxxy at the point (2 , n) is 3, where m

and n are constants

Find

(a) the value of m and n.

[4 marks]

(b) the equation of normal to the curve at the point ( 3, 4)

[3 marks]

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3472/2 2010 Hak Cipta SBP

SULIT

SECTION B

Answer four questions in this section

7 Diagram 1 shows function g maps x to y and function h maps z to y.

Given g (x) = mxx

,12

1 and h (z) = 1 + 4z.

(a) State the value of m and n.

[3 marks]

(b) Find )(1 xhg

[3 marks]

(c) Given that function pkxxf 2: and function xxg 21: , where k and

p are constants .If the composite function fg is given by ,522: 2 xxxfg

find the value of k and of p.

[ 4marks]

Diagram 1

x y

z

g

h

4

n

m

5

8. Diagram 2 shows a quadrilateral ABCD with vertices )1.1(A and )6,3(D .The

straight line AB parallel to the x-axis.

Given the equation of BC is 052 xy . Find ,

(a) the equation of AB

[1 marks]

(b) the coordinates of B

[2 marks]

(c) the coordinates of C

[4 marks]

(d) the area of quadrilateral ABCD

[3 marks]

D(3, 6)

A(1, 1)

x B

O

Diagram 2

C

y

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3472/2 2010 Hak Cipta SBP

SULIT

9 Table 1 shows the masses of 50 watermelons collected from Pak Busu”s farm.

Calculate

(a) the mean,

[3 marks]

(b) the standard deviation,

[4 marks]

(c) the third quartile,

[3 marks]

of the distribution

Mass (kg) Number of

watermelons

20-24 4

25-29 7

30-34 16

35-39 13

40-44 10

Table 1

7

C

A

B

D

A Q F

E

10. In diagram 3 , AEF is a semicircle with centre O and has a radius of 8 m.

BOD is a sector of a circle with centre O and A is mid point of OB. OBC is a right

angle triangle

Diagram 3

.

It is given that CB = 20 m . [Use π = 3.142]

Calculate

(a) the angle of COB in radian.

[2 marks]

(b) the area, in m2, of the shaded region,

[4 marks]

(c) the perimeter, in m, of the whole diagram,

[4 marks]

.

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3472/2 2010 Hak Cipta SBP

SULIT

11

(a)

Given that the equation of the curve is xxy 123 2 .Find the coordinate of the

turning point of the curve and determine whether each of the turning points is

maximum or a minimum.

[4 marks]

(b)

Given that the rate of change of x is -10.1 cms , find the rate of change of y ,

in -1cms , when x is 3 cm.

[3 marks]

(c)

It is given that 73uy , where 52 xu . Find dx

dy in terms of x. Hence ,find the

approximate of y if x decrease from 1.95 to 2

[3 marks]

9

SECTION C

Answer two questions in this section

12. Diagram 4 shows two triangles ABC and ACD . BCD is a straight line.

Find ,

(a) ACB

[3 marks]

(b) the length of CD

[3 marks]

(c) the area of triangle ABD

[4 marks]

A

D C

B

40o

9 cm 9 cm

11 cm

Diagram 4

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3472/2 2010 Hak Cipta SBP

SULIT

13

Diagram 5 shows a pyramid ABCV with vertex V and base ABC. BV is a vertical

line.Given that AC = 8 cm, BV = 15 cm. 060ABC and 050ACB . Find

(a) the length of BC

[2 marks]

(b) AVC

[5 marks]

(c) the area of triangle AVC

[3 marks]

Diagram 5

C B

V

A

11

14 Table 2 shows the price indices and percentage of usage of four items, A,B,C and D

,which are the main ingredients in the productions of a brand of cake.

Item

Price index for the year 2010

based on the year 2009

Percentage of Usage(%)

A 125 22

B 110 12

C 140 31

D n 35

(a)

Calculate

(i) The price of item C in the year 2009 if its price in the year 2010 was RM

3.50.

[2 marks]

(ii) The price index of item B for the year 2010 based on the year 2008 if its

price index for the year 2009 based on the year 2008 is 110.

[2 marks]

(b) The composite index of the cost of cake production for the year 2010 based on the

year 2009 is 126.1,Calculate

(i) the value of n.

(ii) the price of a cake in the year 2009 if its corresponding price in the year

2010 was RM 35.

[6 marks]

Table 2

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3472/2 2010 Hak Cipta SBP

SULIT

15 Table 3 shows the price indices and the weightages of four types of Pn Kang yearly

personal items in the year 2009 based on the year 2008.

(a) Calculate the value of m if the price of a trouser in the year 2009 is RM 42 and

RM 32.00 in the year 2008

(b) Find the composite index number for the personal neccesseties in the year 2009

based on the year 2008 .

[5 marks]

(c) calculate the total expenditure in the year 2008 for Pn Kang personal items if the

corresponding expenditure in the year 2009 is RM 1295.

(d) The cost of the items increases by 25% from the year 2009 to the year 2010.Find

the composite index number in the year 2010 based on the year 2008.

END OF THE QUESTIONS

Personal

Item

Price Index for the year 2009

based on the year 2008 Weightage

Shoe 120 1

Bag 125 3

Shirt 118 4

Trouser m 2

Table 3