Perfect Score Sbp 2007

7/28/2019 Perfect Score Sbp 2007

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PERFECT SCORE SBP

ADDITIONALMATHEMATICS

MODULE 1

( 3472 / 1 )


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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 factor of , state

a) the domainb) 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


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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

2+xandfg:x

5

nmx +,

where m andn 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 are in the ratio of 2 : 3.033102 =+ kxx

(a) find the roots

(b) hence, find the value of k.

[4 marks]

Answer: (a)..

(b)..


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)

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

y

O x

( )25,3

7

DIAGRAM 2

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

[ 3 marks]

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

7 Find the range of values ofp 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:


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9 Find the range of values ofx 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 andym =27log xn =3log , express in terms ofx and y34

9log nm .

[4 marks]

Answer:

13 Given that x = 5k and y = 5h , express2

3

5125

logy

xin terms of k and h.

[ 4 marks ]

Answer:


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

(a) the ninth term,

ext 20 terms after the 9th terms.

[4 marks]

Answer: (a)

_________________________________________

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

.Sn = 1332

nn +

Find

b) the sum of the n(

(b)

________________________________

1

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)

6 Diagram 3 shows a straight line

(b)

63 += xy1 which is perpendicular to theand B(m

Express m in terms of n. [3 marks]

Answer

straight line that joins points A(2, 3) ,n).y

B(m,n)

x

DIAGRAM 3

A(2 , 3)

O

y=3x+6


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eter KLM , with centre L.

iven that the equation of the straight line KLM is

17 Diagram 4 shows a semicircle KLMN, of diam

y

K

M

L

N(x,y)

x

DIAGRAM 4

0

134

=+yx

G and pointN( x , y ) lies on

[ 3 marks ]

Answer

k

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

Answer: k=

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

18 Given that x and y are related by the equation y = Ax4 , where A andkare

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

( 143

, 10)

( 53

, 4)

log 8x

log 8y

0

DIAGRAM 5

A =


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Given that x and y are related by the equation 12

2

2

2

=q

y

p

x19 , wherep and q are

positive constants. When the graph of against is plotted, a straight line with

gradient

2y

2x

4

1and passes through the point )

4

9,0( is obtained.

[ 4 marks]

Jawapan :p = ..

0 Find the equation of the tangent to the curve

Find the values of p and q.

.

q = .

3)5(

5

=

xy2 at the point (3, 4).

[2 marks]

Answer:

___________ ________________________________________

Given that

________________ _____

xdx

yd6

2

2

=21 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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2 Given that and , finddx

dy12 += my .

1m

mx +=2 in terms ofm.

marks]

Answer:

3

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

[4 marks]

Answer:

[3

2

O

AT

B

DIAGRAM 6

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]


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24 Diagram 7 shows a semicircle ABC with center O.

A B

Answer:

5 Given thatA(-1, 4), B(2, -3) andO is origin.

C

O

arc BC is 2, find the value of,

[ 4 marks ]

DIAGRAM 7

The length of 20 cm and the area of sector BOC is 105.68 cm

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

2

(a) express AB

in term of jyix + ,

(b) find AB

.

[3 marks]

Answer:(a)

(b)..

AB , CB and AC26 The information below shows the vectors

Find the value ofh and ofk.

[3 marks]

Answer: h =

k=

constantare,,24

3

32

khjih

jki

ji

AC

CBAB

=

=

=


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

[2 marks]

Answer: a =

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

D C

A

DIAGRAM 8

Find the value of a and of b.

b = .

82

B

GivenAD= 4a + 2b, AC= 6a + 3b andEC= AC3

1. ExpressBE in terms of a andb.

[3 marks]

Answer:

29 Find the value of

E

+ 2

2

3

2lim

n

n

n.

[ 2 marks ]

Answer:


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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,

3 marks]

Answer:

31 Given that

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

[

2

2710

xxy += , calculate

(a) the value ofdx

dywhen x = 3,

(b) the approximate value of y, in terms ofp, when 3 ,x p= + wherep is small.arks ]

Answer: (a)

(b)..

The equation of a curve is

[ 4 m

2

4

xxy +=32 . Find the coordinate of the turning point of the

[ 3 marks ]

Answer: (a)

(b)..

33 Given that y =

curve.

..

3

2 3

x

x +and

dx

dyxh =)(5 , find the value of +

2

1

]4)([ dxxh .

[ 4 marks ]

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


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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

y

O 2 x

B

C

2

2x

ky =

DIAGRAM 9

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

Answer: ....

5 Diagram 10 shows the curve2

2

xy =3 , the straight lines x = 1 andx = k

Find the value of kif the area of shaded region is5

8unit

[4 marks]

Answer:....

36 Solve the equation

2 .

0 0 3sin(60 ) sin(60 )2

x x + = for 0x 360.

[ 3 marks ]

Answer: ..

y

1 k

2

2

xy =

O x

DIAGRAM 10

A


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7 Find all the values of x, between and , which satisfy the equation

[4 marks]

Answer:

8 Solve the equation for 0x 360.[4 marks]

Answer: (a)

(b) .

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

y

Find the value ofa andb.

[ 2 marks ]

Answer: a =

b= .

00

0360

)sin1(cos2sin2 xxx += .3

8tansec6 2 += xx

3

.

3

O 180 0 360 x0

-3

DIAGRAM 11


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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 are formed from the digits 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 B C D E F 2 3 4 5

DIAGRAM 12

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: .


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

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

DIAGRAM 13

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: .


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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 isp .

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


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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.

0.1

0.2

0.3

0.4

f z

-k k z

DIAGRAM 14

DIAGRAM 15

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


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PERFECT SCOREADDITIONAL

MATHEMATICS

MODULE 2

( 3472/2 )

Part A

23


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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 at two points.22 =xyx

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 ).

24

x+ y = 4.

A

B

y

0

x

DIAGRAM 1

Find

a) the value of k , [2 marks]

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

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


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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

25

DIAGRAM 2

A

T

O

C

B

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 ]


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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

Number

ofstudents

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 2 cm.

The height of the first cone is h cm. The height of the second cone is ( h + 1 ) cm

and the height of the third cone is ( h + 2 ) cm. The height of each cone is increaseby 1 cm compared to the previous cone.

DIAGRAM 3

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 ]

26


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

Given that the = 135o

andAOC BOC = 900 .

DIAGRAM 4

O 4 cmO

A

C

B

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 lineAD is perpendicular to thestraight line CD and the equation of the straight lineBC is 2x + 3y +6 =0.y

y

A (1,5)

B (-6,2)

C(0,h)

MD (k,2)

x

DIAGRAM 5

27


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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 quadrilateralABCD. [2 marks ]

b) IfM is the intersection point between AC andBD, find the ratio of

AM: 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

4QR = and

2

1RS= ,

20

h

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

(b) find the value of h ifRSis parallel to PQ ,

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

[7 marks]

12 The minimum value of isnmxxxf 42)( 2 ++= 4 whenx = 6.

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

28


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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 equationy2

= ax + bx2, where a

andb are constants. Table 2 shows the corresponding values ofx andy obtained from

an experiment :

x 2 4 6 8 10

y 2.82 4.91 7.01 9.02 11.2

TABLE 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 andb, [2 marks]

(ii) the values ofx satisfies (a5)x + bx2 = 0. [3 marks]

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

x 3 4 5 6

y 4.5 8.9 18.1 36.0

TABLE 3

It is known that the variablesx andy are related by the equation y =pq wherepandq are constants.

3x

a) Plot a graph of log10y against (x3) and draw a line of best fit. [5 marks]b) Use your graph from (a) to find

i) the value ofy whenx = 2 [2 marks]ii) the values ofp andq [3 marks]

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15 Diagram 6 shows a curve and a straight liney = x 3.92 +=xy

31

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 and the y-axis is revolved through

3600

about the y-axis.

92 +=xy

Calculate the volume generated in term of .

[5 marks]

y

y = x 3

A

0

B

DIAGRAM 6

C

x


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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 cm

3, is given by

( 3272

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

value is a maximum or a minimum.

[ 5 marks ]

y(b)

32

A

O Cx

y =5

y = x2

+ 1

P

Q

B

Q

P

DIAGRAM 7

Diagram 7 shows a rectangle enclosed by the y-axis , thex-axis, the straightline y = 5 and the straight line BC. The curve y = x

2+ 1 divides the rectangle

OABCinto two sections , P and Q . Find the ratio of the area P: area Q.

[ 5 marks ]

17 In Diagram 8, and2OM p

=%

5ON q

=%

.

DIAGRAM 8

A B

M

Lp%

2

O N5 q

%


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(a) Given that 3 MAOM = and ONAB 2= . Express each of the following interms ofp

%

and/or .q%

(i) MN

(ii) OB

[3 marks]

(b) Given that and , show thatLN h MN

= LB k OB

=

and .2 5(1 )OL h p h q

= + % %

(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 lineDB intersectsthe lineEC at F.

BA

FE

D

C

DIAGRAM 9

Given that DADE

5

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 triangleDEF is 4 unit2, evaluate the area

of triangleDAB.

[3 marks ]

33


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19 a) Prove (cos 2x + 1) tanx = 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 and3sin 3 3sin 4sinA A= A

33 4 3kos A kos A kosA=

Prove thatsin 3 sin

tan3

A AA

kosA kos A

=

+[3 marks]

(b) Solve the equation for01)30sin(3)30(sin2 002 =+ xx

.

[3 marks]oo

x 3600

(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 after

the 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 theminimum mark for a candidate to obtain an excellent grade.

[ 5 marks]

34


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22 (a) A study on post graduate students, revealed that 70% out of them obtained jobssix months after graduating.

(i) If 15 post graduates were chosen at random, find the probability of not more

than 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 of58kg and variance of 25kg2. Find

(i) the number of students with the mass of more than 70 kg.

(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

34

3V r=

.

A pump puts air into a spherical balloon at the rate of 250 cm3

s-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 ]

35


32/40

24 Diagram 10 shows the straight lines PQSandQRT. Q is the midpoint ofPS.

y

DIAGRAM 10

R (0 ,1)

0

T

Q

8x + 3y = 12

P

S

x

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 Wmoves in such a way that its distance from point Tis twice its distance frompoint 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 ]

36


33/40

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

centre O.

C OD

AQP

DIAGRAM 11

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 perimeter , in cm, of regions P and Q [3 marks]

37


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MODULE 4

( 3472/2 )Part C

38


35/40

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 for,942 2 += tts 3t , where t is the time in seconds

after passing through a pointB on the line. Find

(a) the distanceAB, [1 marks]

(b) the distance fromA 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

pointA with a speed of 5 , its acceleration , a ms-2

, is given by1ms .28 ta =

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

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

For the journey fromA toB,

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

(b) find the time taken [3 marks]

(c) find the distance traveled [4 marks]

39


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

of preparation time and 45 minutes of machine time. The lady makesx cushions andy

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 theconditions described above.

(b) Using a scale of 2 cm to 2 hours on both axes , construct and shade the regionRin which every point satisfies all the conditions.

(c) Based on the graph obtained in (b) , find the maximum profit made by the lady ifthe profit on each cushion is RM4 and the profit on each table cloth is RM2.

29 Pak Abu plans to plantx papaya trees andy rambutan trees on a plot of land of area

1000 m2

. He has allocated RM2000 to buy some seedlings. A papaya seedling costs

RM2 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 more

than that oframbutan trees by at least 100 trees.

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

conditions described above.

0x 0y

(b) Using a scale of 2 cm to 100 trees on both xaxis , and 2 cm to 50 trees on theyaxis, construct and shade the regionR in which every point satisfies all theconditions.

(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 thatPak Abu can acquire during the period.

40


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

D

B

C

A

4808'

DIAGRAM 12

Calculate(a) the length ofAC [2 marks]

(b) the length ofAB [2 marks]

(c) the area ofABC [4 marks]

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

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

CQ = 7 cm.

42

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. Sis a point on PR such that QS= 6 cm.

P

S

Q

9 cm

6 cm

R

300

Calculate

B

DIAGRAM 13

DIAGRAM 14

(a) the length ofPS, [3 marks]

(b) the length ofSR, [4 mars ]

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


39/40

33 Diagram 15 shows, PQ is parallel to TS . Given that PQ = 12 cm, PT= 7 cm,

RT= 5 cm and PST= 20.

P T

DIAGRAM 15

Given that the area of PQTis 35 cm2, calculate

(a)

QPT, [2 marks]

(b) the length ofRS [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 year

2003 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 totalof 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 price indices of item C and D are not changing from the year2003 to 2005. Find the composite index in the year 2005 based on the year

2003.

[10 marks]

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

MaterialUnit price (RM) I (based on the year

2003)

2005

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

TABLE 5

75

155

N

M

LK

a) Find the value ofp, q andr.[3 marks]

b) i) Calculate the composite index of the cost for producing the weed killer for theyear 2005 based on the year 2003.

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

Perfect Score Sbp 2007

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