Perfect Score Sbp Add Mth 2007[1]

8/14/2019 Perfect Score Sbp Add Mth 2007[1]

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3/453472/1 6

Answer all questions

1 It is given that set P = { 4 , 6 , 9 , 25 } and set Q = { 2 , 3 , 5 }. If the relation

between set P and set Q is the multiple of , state

a) the domain

b) the image of 9

[2 marks]

Answer: (a)

(b)

_________________________________________________________________________

2 Diagram 1 shows the relation between set A and set B.

set B

2 4 6 8 set A

State

(a) the objects of 20(b) the range of this relation.

[ 2 marks]

Answer: (a).

(b).

DIAGRAM 1

10

15

5

20


4/453472/1 7

3 Given that ,3

23)(1

xxh find

(a) h(5),

(b) the value ofm if 32)3(1 mmh .[4 marks]

Answer: (a)

(b)

4 Given the function f: x 2x + 5 , g : x 5

2xand fg: x

5

nmx ,

where m and n are constants , find

(a) the value of m and of n,

(b) the value ofgf(2).

[4 marks ]

Answer: (a) m =..n =.

(b)....

5 The roots of the quadratic equation 033102 kxx are in the ratio of 2 : 3.

(a) find the roots

(b) hence, find the value of k.

[4 marks]

Answer: (a)..

(b)..


5/453472/1 8

6 Diagram 2 shows the graph of the function f(x) = ax2+bx + c

y

O x

25,3

DIAGRAM 2

The point 25,3 is a minimum point of a curve. Find the equation of the curve.

[ 3 marks]

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

7 Find the range of values of p if 2)1()( pxxpxxf is always positive. [3 marks]

Answer:

8 If the minimum value of the function

2

5)2(3)(

2 nxxf is 3,

find the value of n.

[2 marks]

Answer:

7


6/453472/1 9

9 Find the range of values of x for which 12)2)(1( xx[3 marks]

Answer:

_________________________________________________________________________

10 Solve the equation 2422 2343 xx .[3 marks]

Answer:

11 Solve the equation 23log2log 93 x .

[ 3 marks ]

Answer:

12 Given that ym 27log and xn 3log , express34

9log nm in terms of x and y.

[4 marks]

Answer:

13 Given that x = 5k

and y = 5h

, express2

3

5125

logy

xin terms of k and h.

[ 4 marks ]

Answer:


7/453472/1 10

14 The sum of the first n terms of an arithmetic progression is given by .1332

nnSn

Find

(a) the ninth term,

(b) the sum of the next 20 terms after the 9th

terms.

[4 marks]

Answer: (a)

(b)

_________________________________________________________________________

15 The first term of a geometric progression is a , and the common ratio, r, is positive.

Given that the sum of the second and the third term is9

10aand the sum of the first

four terms is 65. Find

(a) the common ratio,

(b) the first term.

[ 4 marks ]

Answer: (a)

(b)

16 Diagram 3 shows a straight line 63 xy which is perpendicular to thestraight line that joins points A(2, 3) and B(m,n).

Express m in terms of n. [3 marks]

Answer

y

B(m,n)

A(2 , 3)x

O

y=3x+6

DIAGRAM 3


8/453472/1 11

17 Diagram 4 shows a semicircle KLMN, of diameter KLM , with centre L.

Given that the equation of the straight line KLM is 134

yx

and point N( x , y ) lies on

the circumference of a circle KLMN , find the equation of the locus of the movingpoint N.

[ 3 marks ]

Answer

18 Given that x and y are related by the equation y = Ax4k

, where A and k are

constants. A straight line is obtained by plotting log 8 y against log 8 x, asshown in diagram 5.

Calculate the value of A and ofk. [4 marks]

Answer: k=

A =

( 143

, 10)

( 53

, 4)

log 8 x

log 8 y

0

DIAGRAM 5

K

M

L

N(x,y)

x

DIAGRAM 4

0

y


9/453472/1 12

19 Given that x and y are related by the equation 12

2

2

2

q

y

p

x, where p and q are

positive constants. When the graph of 2y against2

x is plotted, a straight line with

gradient4

1and passes through the point )

4

9,0( is obtained.

Find the values of p and q.

[ 4 marks]

Jawapan : p = ...

q = .

20 Find the equation of the tangent to the curve3

)5(

5

xy at the point (3, 4).

[2 marks]

Answer:

________________________________________________________________________

21 Given that xdx

yd6

2

2

and gradient of the curve is 12 when x = 2. If P (2,4)

lies on the curve, find

(a) the equation of the normal at P,

(b) the equation of the curve. [ 4 marks ]

Answer: (a)

(b)


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22 Given that 12 my and .1

mm

x , finddx

dyin terms ofm.

[3 marks]

Answer:

23

Diagram 6 shows a circle, with center O and radius 10 cm. Tangent to the

circle at A meet the line OB at T. Given the area of the triangle

OAT = 60 cm, find the area of sector OAB.

[ use = 3.142][4 marks]

Answer:

O

AT

B

DIAGRAM 6


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24 Diagram 7 shows a semicircle ABC with center O.

A B

Answer:

25 Given that A(-1, 4), B(2, -3) and O is origin.

(a) express AB

in term of jyix ,

(b) find AB

.

[3 marks]

Answer:(a)

(b)..

26 The information below shows the vectors AB , CB and AC

Find the value of h and ofk.

[3 marks]

Answer: h =

k=

constantare,,24

3

32

khjih

jki

ji

AC

CBAB

DIAGRAM 7

The length of arc BC is 20 cm and the area of sector BOC is 105.68 cm2, find the value of

in radian. Give your answer correct to four significant figures.

[ 4 marks ]

O

C


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27 Given that (4a 44) p = (b + 5) q , where p and q are not parallel.

Find the value of a and of b.

[2 marks]

Answer: a =

b = .

28 Diagram 8 shows a parallelogram ABCD such that AEC is a straight line.

D C

A B

DIAGRAM 8

Given AD = 4a + 2b, AC= 6a + 3b and EC= AC3

1. Express BE in terms of a and b.

[3 marks]

Answer:

29 Find the value of

2

2

3

2lim

n

n

n.

[ 2 marks ]

Answer:

E


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30 The height of a cone is 10 cm. If its radius is increasing at the rate of 0.5 cm s-1

,

find the rate of increase of its volume at the instant its radius is 5 cm.

[ 3 marks]

Answer:

31 Given that2

2710

xxy , calculate

(a) the value ofdx

dywhen x = 3,

(b) the approximate value of y, in terms ofp, when ,3 px where p is small.[ 4 marks ]

Answer: (a)

(b)..

32 The equation of a curve is2

4

xxy . Find the coordinate of the turning point of the

curve.

[ 3 marks ]

Answer: (a)

(b).. ..

33 Given that y =3

2 3

x

x and

dx

dyxh )(5 , find the value of

2

1

]4)([ dxxh .

[ 4 marks ]

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


14/453472/1 17

34 Diagram 9 shows the shaded region bounded by the curve2

2x

ky .

Given that the volume generated when the shaded region OABC is revolved by 360o

about

axisy is 28, find the value ofk.[ 4 marks ]

Answer: ....

35 Diagram 10 shows the curve2

2

xy , the straight lines x = 1 and x = k

Find the value of kif the area of shaded region is5

8unit 2 .

[4 marks]

Answer:....

36 Solve the equation2

3)60(sin)60sin(

00 xx for 0 x 360.

[ 3 marks ]

Answer: ..

y

1 k

2

2

xy

O x

DIAGRAM 10

y

O 2 x

B

C

2

2x

ky

DIAGRAM 9

A


15/453472/1 18

37 Find all the values of x, between0

0 and0

360 , which satisfy the equation

)sin1(cos2sin2 xxx .[4 marks]

Answer:

38 Solve the equation 8tansec62 xx for 0 x 360.

[4 marks]

Answer: (a)

(b) ..

39 Diagram 11 shows graph for the function y = a sin bx

y

Find the value ofa and b.

[ 2 marks ]

Answer: a =

b= ..

3

O 180 0 3600

x

-3

DIAGRAM 11


16/453472/1 19

40 A chess club has 10 members of whom 6 are men and 4 are women. A team of

4 members is selected to play in a match. Find the number of different ways of

selecting the team if

(a) all the players are to be of the same gender,

(b) there must be an equal number of men and women.

[3 marks]

Answer: (a)

(b)...

41 It is given that six digits numbers 1, 2, 3, 4, 5, and 6. Calculate the different

ways of odd numbers which are less than 200 000 can be formed with out

repetitions.

[ 3 marks ]

Answer: .

42 Five letters from the word INTEGRAL are to be arranged . Calculate

the number of possible arrangements if they must begin and end with a vowel.

. [2 marks]

Answer: .

43 Diagram 12 shows 6 letters and 4 digits .

A code is to be formed using the letters and digits. Each code must consist of 4 letters

followed by 2 digits. Find the different codes that can be formed if repetitions are not

allowed.

[ 3 marks ]

Answer: .

A B C D E F 2 3 4 5

DIAGRAM 12


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44 Diagram 13 shows a set of data with a mean of 4.

Given that m + n = 14 and standard deviation3

76.

Find the values of m and n if m n.[4 marks]

Answer: .

45 Table 1 shows the frequency distribution of ages of workers.

Age ( years ) 28-32 33-37 38-42 43-47 48-52

Number of workers 16 38 26 11 9

TABLE 1

Given the third quartile of ages of workers is 575

G

FLK . Find the values of

K, L , G and F.

[ 4 marks ]

Answer: K=.

L = ........................................

G =

F=.......

46 There were 12 girls and 3 boys in a group of children. One child was chosen at

random from the group. Another child was chosen at random from the remaining

children.Calculate the probability that a child of each gender was chosen.

[ 3 marks ]

Answer: .

1 , 1 , 7 , 2 , 1 , 3 , 7, m , n

DIAGRAM 13


18/453472/1 21

47 Hanif , Zaki and Fauzi will be taking a driving test. The probabilities that Hanif ,

Zaki and Fauzi will pass the test are1 1

,2 3

and1

4respectively. Calculate the

probability that

(a) only Hanif will pass the test

(b) at least one of them will pass the test. [ 3 marks ]

Answer: (a)

(b) .......

48 In a lucky draw, the probability to obtain a prize is p .

(a) Find the number of draws required and the value ofp such that

the mean is 15

and the standard deviation is .2

63

(b) If 8 draws are carried out, find the probability that at least one draw

will win the prize.

[ 4 marks ]

Answer: (a)

(b) ..


19/453472/1 22

49 Diagram 14 shows the graph that represents the binomial probability distribution.

P(X=x)

0 1 2 3 x

Calculate

(a) P ( X = 1)

(b) P ( X < 2 )

[ 2 marks ]

Answer: (a).

(b).

50 Diagram 15 shows a standard normal distribution graph.

Given that the area of shaded region in the diagram is 0.7828 , calculate the value of k.

[ 2 marks ]

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

END OF QUESTION PAPER

0.1

0.2

0.3

0.4

f z

-k k z

DIAGRAM 14

DIAGRAM 15


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PERFECT SCORE PROGRAM

ADDITIONAL MATHEMATICS 2007

Module 1(3472/1)

1. (a)

(b)

{4 , 6 , 9 , 25 }

2 and 3

26 h = - , k = 1

2 (a)

(b)

4 dan 6

{5,15,20}

27 k =10/3

3 (a)

(b)

17/3

4/5

28 2a + b

4 (a)

(b)

a = 2, b = 29

11/5

29

3

2

5 k = 7 30 1/8

6 f(x) = 2x 7122

x 31 (a)

(b)

8

33+ 8p

7 0


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PERFECT SCORE SBP 2007

MODULE 2

ADD MTH

( 3472/2 )Part A


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1 Solve the simultaneous equations 72 yx andxyx

y

y

x 71 .

[5 marks]

2 A straight line 0132 yx intersects a curve 22 xyx at two points.

Find the coordinate of the points.

[5 marks]

3. Diagram 1 shows the curve has a gradient function k- 2x , where kis a constant.

The straight line x+ y = 4 is tangent to the curve at ( 1,3 ).

x+ y = 4.

Finda) the value of k , [2 marks]

b) the equation of the curve, [4 marks]

c) the area of the shaded region. [2 marks]

DIAGRAM 1

A

B

y

x0


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25

4 Diagram 2 shows a circle with centre O and a radius of 5 cm. Radius OA is

perpendicular to the radius OB. Tis the mid point ofOB.

D

Find

(a) AOC, [2 marks]

(b) the length of the major arc ofADC, [2 marks]

(c) the area of the shaded region. [4 marks]

5 A study has been carried out in a village to determine the age of a male got married. Asample of 150 males had been studied and the table below shows the results.

Age (years) Number of males

16-20 9

21-25 63

26-30 49

31-35 20

36-40 9

Calculate

(a) the mean [ 3 marks ]

(b) the variance [ 3 marks ]

A

B

C

O

T

DIAGRAM 2


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26

6 Table 1 shows the points in a competition for 40 students.

Point 20-29 30-39 40-49 50-59 60-69 70-79

Numberof

students

3 5 9 12 7 4

TABLE 1

Find(a) the mean, [ 5 marks ]

(b) the standard deviation of frequency of distribution. [ 2 marks ]

7 Diagram 3 shows a series of cones. The base radius of each one is fixed at 4 cm.

The height of the first cone is h cm. The height of the second cone is ( h + 1 ) cmand the height of the third cone is ( h + 2 ) cm. The height of each cone is increase

by 1 cm compared to the previous cone.

a) Determine whether the volumes, in cm3

, of these cones are in an arithmetic orgeometric progression. Hence, state the common difference or common ration.

[ 4 marks ]

b) If h = 3 , find the sum of the volumes of the first 13 cones, in term of .

[ Volume of cone = hr2

3

1 ]

[ 3 marks ]

DIAGRAM 3


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8 Diagram 4 shows a sector OABC , with centre O and a radius of 4 cm.

Given that the AOC = 135o and BOC = 900 .

Find

(a) the perimeter of the shaded region, [4 marks]

(b) the area of the shaded region. [4 marks]

9 Solutions to this question by scale drawing will not accepted.

Diagram 5 shows a quadrilateral ABCD whose vertices A (1,5), B (-6,2),C(0, h) and D( k,2). Given that the straight line AD is perpendicular to the

straight line CD and the equation of the straight line BC is 2x + 3y +6 =0.

DIAGRAM 4

O 4 cmO

A

C

B

A (1,5)

B (-6,2)

C(0,h)

D (k,2)

y

x

DIAGRAM 5

M

y


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a) Find

(i) the value of h and ofk, [2 marks ]

(ii) the equation of the straight line AC, [2 marks ]

(iii) the area of quadrilateral ABCD. [2 marks ]

b) If M is the intersection point between AC and BD, find the ratio ofAM: MC.

[2 marks ]

10 A vessel is filled with water after t second. The depth of the water, x cm in the vessel

increases at the rate of 1.44 cm s-1.Given that the vessel is empty when t = 0. Find

(a) the value of t when x = 18.

(b) small change in x when t increases from 4.0 to 4.1

[ 5 marks ]

11 Given that PQ =

7

4, QR =

2

1and RS =

20

h,

(a) express as a column vector of PQ + 3 QR ,

(b) find the value of h if RS is parallel to PQ ,

(c) the unit vector in the direction of PQ .

[7 marks]

12 The minimum value of nmxxxf 42)( 2 is 4 when x = 6.

(a) Without using differentiation method, find the values of m and

of n.

( b) Hence, sketch the graph of nmxxxf 42)( 2 for the domain

92 x .(c) Find the range of nmxxxf 42)( 2 for the domain 92 x .

[7 marks]


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MODULE 3

( 3472/2 )Part B


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Part B

13 The variables x and y are known to be related by the equation y2

= ax + bx2

, where a

and b are constants. Table 2 shows the corresponding values ofx and y obtained froman experiment :

x 2 4 6 8 10y 2.82 4.91 7.01 9.02 11.2

(a) By using a scale of 2 cm to represent 1 unit on both axes, plotx

y2

against x

Hence, draw the line of best fit. [5 marks]

(b) Use the graph in (a) to find

(i) the values ofa and b, [2 marks](ii) the values ofx satisfies (a5)x + bx2 = 0. [3 marks]

14 The values of two variables, x and y , obtained from an experiment are as shown inthe Table 3.

x 3 4 5 6

y 4.5 8.9 18.1 36.0

It is known that the variables x and y are related by the equation y = pq 3x where p

and q are constants.

a) Plot a graph of log 10y against (x3) and draw a line of best fit. [5 marks]

b) Use your graph from (a) to find

i) the value ofy when x = 2 [2 marks]

ii) the values ofp and q [3 marks]

TABLE 2

TABLE 3


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15 Diagram 6 shows a curve 92 xy and a straight line y = x 3.

92 xy

(a) Find the coordinates ofA , B and C.

Hence, calculate the area of shaded region.

[5 marks]

(b) A region which bounded by the curve 92 xy and the y-axis is revolved through

3600

about the y-axis.

Calculate the volume generated in term of .

[5 marks]

y = x 3

A

C

y

0x

B

DIAGRAM 6


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16 ( a) A circular cylinder, open at one ends, has radius r cm and external surface area

27 cm2

. Given that the volume of the cylinder , V cm3

, is given by

3272

rrV

. Find the stationary value of V, hence, determine whether this

value is a maximum or a minimum.[ 5 marks ]

(b)

Diagram 7 shows a rectangle enclosed by the y-axis , the x-axis, the straight

line y = 5 and the straight line BC. The curve y = x2

+ 1 divides the rectangleOABCinto two sections , P and Q . Find the ratio of the area P : area Q.

[ 5 marks ]

17 In Diagram 8, 2OM p

and 5ON q

.

DIAGRAM 8

A B

N

M

L

5 q

2 p

O

y

DIAGRAM 7

A

O Cx

y =5

y = x2

+ 1

P

Q

B

P

Q


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(a) Given that MAOM and ONAB 2 . Express each of the following in terms ofp

and/or q

.

(i) MN

(ii) OB

[3 marks]

(b) Given that LN h MN

and LB k OB

, show that

2 5(1 )OL h p h q

and (8 8 ) (10 10 )OL k p k q

.

Hence , find the value ofh and ofk.

[5 marks]

18 In Diagram 9, ABCD is a quadrilateral such that the line DB intersects

the line EC at F.

Given that DADE5

2 , ,10,10,

2

1yDCxDAECAB

DF= DBm and .ECnDEDF

a) Find the value of m and of n. [4 marks ]

b) Hence, find DF:FB. [3 marks ]

c) If the area of triangle DEF is 4 unit2, evaluate the area

of triangle DAB.

[3 marks ]

A B

CE F

DDIAGRAM 9


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19 a) Prove (cos 2x + 1) tan x = sin 2x.

[4 marks]

b) i) Sketch the graph of 1 3cosy x for 20 x

ii) Find the equation of a suitable line for solving the equation 3 cos 2x x .

Hence, using the same axes, sketch the straight line and state the number ofsolutions to the equation 3 cos 2x x for 20 x .

[ 7 marks]

20 (a) Given that 3sin 3 3sin 4sin A A A and33 4 3kos A kos A kosA

Prove thatsin 3 sin

tan3

A AA

kosA kos A

[3 marks]

(b) Solve the equation 01)30sin(3)30(sin2 002 xx foroo x 3600 .

[3 marks]

(c) Sketch the graph of y = 3 sin ( 2 ) for 0 x 22

x

.

Hence , find the number of solutions to the equation

2 1x

cos x

for 0 x 2 [4 marks]

21 (a) A study shows that 40 % of the students in a school entered university afterthe SPM. A sample of 10 students was chosen at random.

Calculate

i) the probability of at least 9 students entering university.ii) the number of SPM students to be taken in order that the probability of at

least one student who enters university is more than 0.85

[ 5 marks]b) The marks for 500 candidates in an Additional Mathematics examination in

normally distributed with a mean of 45 and a standard deviation of 5 marks.i) If a candidate is chosen at random, calculate the probability of his

marks between 47 and 52.

ii) Given that 5 % of the students obtained excellent grades, find the

minimum mark for a candidate to obtain an excellent grade.

[ 5 marks]


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22 (a) A study on post graduate students, revealed that 70% out of them obtained jobs

six months after graduating.

(i) If 15 post graduates were chosen at random, find the probability of not morethan 2 students not getting jobs after six months.

(ii) It is expected that 280 students will succeed in obtaining jobs after sixmonths. Find the total number of students involved in the study.

[5 marks]

(b) The mass of 5000 students in a college is normally distributed with a mean of

58kg and variance of 25kg2. Find

(i) the number of students with the mass of more than 90kg.

(ii) the value of w if 10% of the students in the colleges are less than w kg.

[5 marks]

23 (a) The volume , Vcm3

, of the sphere of radius rcm , is given by the formula 4

3V r3

.A pump puts air into a spherical balloon at the rate of 250 cm

3s

-1. Calculate

(i) the rate of surface area of the balloon when the radius is 10 cm,

(ii) approximate change in volume as the radius decreases from 10 cm to 9.95 cm.

( give your answer in terms of )[ 6 marks ]

(b) Given that 2)54(8

1

)(

xxg , evaluate

2

1''

g .

[ 4 marks ]


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24 Diagram 10 shows the straight lines PQS and QRT. Q is the midpoint ofPS.

a) Find

i) the coordinate of point Q,

ii) the area of the quadrilateral OPQR.

[ 3 marks ]b) Given that QR : RT= 1: 3, find the coordinates of point T.

[ 2 marks ]

c) A point W moves in such a way that its distance from point T is twice its distance from

point S.i) Find the equation of the locus of the locus of point W,

ii) Hence, determine whether the locus will intersect the x-axis or not.

[ 5 marks ]

y

x

S

Q

8x + 3y = 12

P

R (0 ,1)

0

T

DIAGRAM 10


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37

25 Diagram 11 shows two arcs, AD and BC , of two concentric circles, with the same

centre O.

BD is perpendicular to OC. It is given that OA = OD = 5 cm, OC = 14 cm and

AOD = 1.2056 radians.Using = 3.142, calculate(a) the area of region P, in cm [4 marks]

(b) the perimeter of region Q , in cm [3 marks]

(c) the total perimeter , in cm, of regions P and Q [3 marks]

CO

D

AQP

DIAGRAM 11

B


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38

MODULE 4

( 3472/2 )Part C


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39

Part C

26 A particle moves in a straight line so that its distance, s metres, from a fixed point A

on the line is given by ,942 2 tts for 3t , where t is the time in seconds

after passing through a point B on the line. Find

(a) the distance AB, [1 mark]

(b) the distance from A of the particle when it is instantaneously at rest,[2 marks]

(c) the total distance traveled by the particle in the period t= 0 to t= 3,[3 marks]

(d) If t =3 , the acceleration of the particle is changed to ( t 8 ) ms-2

,

the instantaneous velocity remaining unchanged. Hence, find the next value of

tat which the particle comes to instantaneous rest.[4 marks]

27 A car moves along a straight horizontal road so that, t seconds after passing a fixed

point A with a speed of 5 1ms , its acceleration , a ms-2, is given by .28 ta

On reaching its greatest speed, the brakes are applied and the car decelarates at a

constant rate of 3 2ms , coming to rest at point B .

For the journey from A to B,

(a) sketch the velocity time graph [3 marks]

(b) find the time taken [3 marks]

(c) find the distance traveled [4 marks]


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28 A summer gala is being held in a village to raise funds for the school and one lady

offers to make cushions and table cloths. One cushion requires 50 minutes of

preparation time and 75 minutes of machine time. One table cloth requires 60 minutes

of preparation time and 45 minutes of machine time. The lady makes x cushions and y

table cloths. Given that at least2

112 hours is spent on preparation and that the machine

is available for a maximum of 15 hours. Given also that the total preparation time isless than or equal to the total machine time.

(a) Write three inequalities , other than 0x and 0y , which satisfy all the

conditions described above.

(b) Using a scale of 2 cm to 2 hours on both axes , construct and shade the region R

in which every point satisfies all the conditions.

(c) Based on the graph obtained in (b) , find the maximum profit made by the lady if

the profit on each cushion is RM4 and the profit on each table cloth is RM2.

[10 marks]

29 Pak Abu plans to plant x papaya trees and y rambutan trees on a plot of land of area

1000 m2

. He has allocated RM2000 to buy some seedlings. A papaya seedling costsRM2 and requires a land area of 1.5 m2. A rambutan seedling costs RM10 and

requires

a land area of 2 m2

. The number of papaya trees Pak Abu intends to plant is morethan that oframbutan trees by at least 100 trees.

(a) Write three inequalities , other than 0x and 0y , which satisfy all the

conditions described above.

(b) Using a scale of 2 cm to 100 trees on both xaxis , and 2 cm to 50 trees on the

yaxis, construct and shade the region R in which every point satisfies all the

conditions.

(c) Based on the graph obtained in (b) , answer each of the following questions.

(i) If the cost for buying the seedlings is a maximum, find the land area

required to plant the most number of both types of trees.

(ii) During a certain period, a papaya tree yields RM120 of profit whereas arambutan tree yields RM 400 of profit, find the maximum total profit that

Pak Abu can acquire during the period.

[10 marks]


39/45

41

30 Diagram 12 shows BDC is a straight line. Given that ADB = 115 10', AD = 7.2 cmand DC= 8.1cm.

D

B

C

A

4808 '

Calculate

(a) the length of AC [2 marks]

(b) the length ofAB [2 marks]

(c) the area of ABC [4 marks]

(d) the length of the perpendiculer line from A to BC. [2 marks]

DIAGRAM 12


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42

31 Digram 13 shows triangle PQR . Given that PB = 20 cm, BR = 6 cm, RC= 8 cm ,

CQ = 7 cm and sin QRP =25

24

Calculate

(a) the length of PQ, [3marks]

(b) sin QPR, [3 marks]

(c) the length of AP if the area of triangle PAD and RBC are equal. [4 marks]

32 Diagram 14 shows PSR is a straight line. Given that PQ = 9 cm, QR = 6 cm, and

QPR = 30. S is a point on PR such that QS = 6 cm.

P

S

Q

9 cm

6 cm

R

3 0 0

Calculate

(a) the length ofPS, [3 marks]

(b) the length ofSR, [4 mars ]

(c) the area of the triangle PQR . [3 marks]

B

DIAGRAM 13

DIAGRAM 14


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43

33 Diagram 15 shows, PQ is parallel to TS . Given that PQ = 12 cm, PT= 7 cm,RT= 5 cm and PST= 20.

Given that the area of PQTis 35 cm2, calculate

(a) QPT, [2 marks]

(b) the length of RS [5 marks]

(c) the area of the triangle PRT, [3 marks]

34 (a) Table 4 shows , prices indices and weightages for four items in the year2003 based on the year 2000.

Item Price index weightage

A 120 7

B 130 4C 145 m

D 110 n

TABLE 4

The composite index in the year 2003 based on the year 2000 is 128 and the total

of weightage is 20(a) Calculate the price of item A in the year 2003 if the price in the year 2000

is RM42.50.

(b) Find the value of m and n(c) The price index of item A increase by 20%, the price index of item B decrease

by 15%,the cost of item C and D are not changing from the year 2003 to

2005. Find the composite index in the year 2005 based on the year 2003.[10 marks]

P T

DIAGRAM 15


42/45

44

35 Table 5 shows the price indices of four raw materials, K, L, M and N, needed to

produce a type of weed killer. The pie chart below the table shows the relative

amount of the materials K, L, M and N used in producing the weed killer.

MaterialUnit price (RM) I 2005 (based on the year

2003)Year 2003 Year 2005

K 1.40 1.75 p

L 4.00 6.00 150

M 2.00 q 140

N r 2.40 80

a) Find the value ofp, q and r.

[3 marks]b) i) Calculate the composite index of the cost for producing the weed killer for the

year 2005 based on the year 2003.

ii) Hence, calculate the corresponding selling price of a bottle of weed killer in the

year 2003 if its selling price in the year 2005 was RM38.00

[5 marks]c) From the year 2005 to the year 2007, the cost of producing the weed killer is

expected to increase by the same margin as from the year 2003 to the year 2005.

Calculate the expected composite index for the year 2007 based on the year 2003.[2 marks]

END OF QUESTION PAPER

75

155

N

M

LK

TABLE 5


43/45

PERFECT SCORE PROGRAM

ADDITIONAL MATHEMATICS 2007

ANSWER PAPER

N0 MODULE 2(3472/2)

PART A

1 1,3;3,2 yxyx

2)

15

7,

5

6(),1,1(

3 a) k = 1 b) y = x x2 + 3c)

6

5

4 a) 2.2134 rad b) 20.3485 cm c) 17.673

5 (a) 26.567 (b) 23.602

6 a) 51.25 b) 13.67

7(a) AP,

3

4 (b) 144

8 a) 16.798 cm b) 14.283 cm2

9 a) i) h = -2 , k = 4 iii) 23unit2

ii) y = 7x - 2

b) 3 : 4

10 a) t=5 b) 576.0x

11a)

13

1, b)

7

80c)

65

74 ji

12 a) m = -6 , n = 8 12)(0 xf

2 4 8

12

0

5

9


44/45

N0 MODULE 3(3472/2)

PART B

13 b) i) a = 1.80, b = 1.075 ii) x = 3.0

14 b) i) 2.239 ii) p = 4.47 , q = 2.01

15 a) A (0,3), B (0,-3),

C(7,4)21.667 b) 583.2

16 (a) 84.4 cm3 , Maximum

valueb) 8 : 7

17 i) 5q 2p ( ii) 8p + 10q b) h = 2/3 , k = 5/6

18 a) m = 2/5 , n =

1/5

b) 5 : 2 c) 25 unit2

19 graph ii) 2xy

,

No. of solutions = 2

20 b) x = 600,

, 1200

,1800

Bil. Peny. = 4

21 a) i) 0.001677 ii) 4 b) i) 0.2638 (ii) 53.225

22 (a) (i) 0.1268 (ii)400 (b) (i) 82or 83 (ii) 38.77 or 38.79

23a) (i) 50 (ii) - 20

(b)27

64

24 a) i)3 , 24

ii)7

18

b)1

2 , 24

c)(i)2 248 48 72 576 879 0 x y x y

ii) No

25

a) 85.46 b) 28.11 c) 40.91

3

2

1


45/45

MODULE 4(3472/2)

PART C

26 (a) 9 (b) 7 (c) 10 (d) 5

27(b) 11 (c)

61136

287565 yx

6035 yx

xy3

5

(c) RM44

29100 xy

10005 yx

200043 yx

(c) (i) 999.5 m2

(ii) RM 101 800

30 a) 8.237 b) 8.751 c) 35.44 d) 6.516

31 a) 26.13 b) 0.5511 c) 8.353 cm

32 a) 3.826 cm b) 7.937 cm c) 26.47 cm2

33 a) 56o

26

b) 8.641 c) 17.48 cm2

34 a) RM 51.00 b) m = 6 c) 132.5

n = 3

35 a) p = 125

q = 2.80

r = 3.00

b) i) 119.65

ii) RM 31.76

c) 143.16

v

21

t4

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Perfect Score Sbp Add Mth 2007[1]

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