add mth perfect score 09

8/7/2019 Add Mth Perfect Score 09

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1

Answer all questions.

1.

In Diagram 1, the functionfmaps set A to set B and the functiongmaps set B to set C.Determine

(a) f(3 )

(b)g(-1)

(c)gf(3)

[ 3 marks]

Answer: (a) ..

(b) ...

(c)....................................

2. Given function f :x 3 4x and function g :xx2 1, find

(a)f1,

(b) the value off1g(3).

[ 3 marks]

Answer: (a) ..

2

1

For exa

use

f g

Diagram 1

Set A Set B Set C

3-1 6


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2

(b) ...

3 Given the function f(x) = 4x, 0x and the composite functionf g(x) =x

16. Find

(a)g(x),

(b) the value ofx wheng(x) = 8.

Answer: .........

4 Solve the quadratic equation ( ) ( )( )3252 += xxxx . Give your answer correct tofour significant figures.

[ 3 marks ]

Answer: .........

r examinersuse only

3

4

3

3

[3 marks]


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3

5 (a) Givenx =4

2

y, find the range ofx if y > 10.

(b) Find the range ofx ifx2 2x 3. [4 marks]

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

___________________________________________________________________________

6 Diagram below shows the graph of a quadratic function )(xfy = . The straight line9=y is a tangent to the curve )(xfy = .

a) Write the equation of the axis of symmetry of the curve.

b) Express )(xf in form of qpx ++ 2)( , wherep and q are constants.

[ 3 marks ]

Answer: (a) ........................

(b) ........................

7 Solve the equation 324x = 48x + 6

6

For examuse o

r examiners

use only

)(xfy =

0 1 7

y

y = -9

Diagram 1


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4

[3 marks]

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

8. Given log5 3 = 0.683 and log5 7 = 1.209. Calculate

(i) log5 1.4,

(ii) log7 75.

[ 4 marks]

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

9. Solve the equation log x 16 log x 2 = 3. [3marks]

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

10. The first terms of the series are 2,x , 8. Find the value ofx such that the series is a

3

7

3

9

4

8

For exa

use


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5

(a) an arithmetic progression,

(b) a geometric progression. [2 marks ]

Answer: .........

11. The sum of the first n terms of an arithmetic progression is given by .133 2 nnSn +=

Find

(a) the ninth term,

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

[3 marks]

Answer: a)............

b) ....................................

12. Given that 1 0.166666666.....p

=

3

8

10

11

Forxaminers

use only


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6

0.1 ............a b= + + + [ 3 marks]

Find the values of a and b. Hence, find the value ofp.

Answer: a =.... b =.......

p = ........................

___________________________________________________________________________

13. Diagram 2 shows a linear graph of x

yagainst x2

x

y

Given thatx

y= hx2 + k, where kand h are contants.

Calculate the value of h and k. [3 marks]

Answer: h = ...

k= ........

(4,1)

(1,-5)

x2

3

13

4

12

For exause o

DIAGRAM 2


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7

14. The equation of a straight linePQ is3

x

+2

y= 1. Find the equation of a straight

line that is parallel toPQ and passes through the point (6 , 3). [3

marks]

Answer: .

15 Given u =

9

7dan v =

3

1p, find the possible values ofp for each of the

followingcase:

(a) u and v are parallel, [2 marks](b) vu = . [2

marks]

Answer: a)..

b)

15

14


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8

16 P

The diagram above shows OR = r,

OS = s,

OP and

PQ are drawn in the square

grid.

Express in terms of r and s.

(i)

OP

(ii) PQuuur

.

[ 3 marks ]

Answer: a) OPuuu

= ....

b) PQuuu

=.....

___________________________________________________________________________

17. Solve the equation 3 cos2 + sin 2 = 0 for 00 3600 . [ 4 marks ]

R S

Q

r s

O

16

4

17

r examiners

use only

3

16


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9

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

18.

Diagram above shows a length of wire in the form of sector OPQ, centre O.

The length of the wire is 100 cm. Given the arc length PQ is 20 cm, find

(a) the angle in radian, [2 marks](b) area of the sector OPQ. [2 marks]

Answer: a)

b)

___________________________________________________________________________

19. Find the equation of the tangent to the curve 3)5(

5

=

xy at the point (3, 4).

[2 marks]

Answer:

19

18

For exause P

QO


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10

20. A roll of wire of length 60 cm is bent into the shape of a circle. When above the

wire is heated, its length increases at a rate of 0.1 cms 1. (Use = 3.142)

(i) Calculate the rate of change of radius of the circle. [2 marks](ii) Hence, calculate the radius of the circle after 4 seconds. [2 marks]

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

___________________________________________________________________________

21. Given4

0( )f x dx = 5 and

3

1( )g x dx = 6.

Find the value

(a)4 1

0 32 ( ) ( ) f x dx g x dx+ , [1 marks]

(b) kif3

1 [ ( ) ]g x k x dx =14. [2 marks]

Answer: a) ..

k=...

22. 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]

5

20

3

21

3

22

r examinersuse only


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11

Answer:p = .

.

23. (a) Given that the mean for four positive integer is 9. When a number y is added to thefour positive integer, the mean becomes 10. Find the value of y.

[2 marks](b) Find the standard deviation for the set of numbers 5, 6, 6, 4, 7. [3 marks]

Answer: a)............

b) ...............................

___________________________________________________________________________

24. 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:

For exause

2

2


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12

25. Diagram below 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

2

25

r examinersuse only

-k k z


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13

JAWAPAN

1 (a) 1 (b) 6 (c) 6 13 h = 2 , k= 7

2(a) f1 = 3

4x (b) 5

4

14 3y = 2x 3

3(a) g(x) = 0,

4

x

x

(b)2

1=x

15(a)

3

10(b) 10, 12

4 3.562 , -0.5616 16 (b)(i) 3r + 2s (ii) r 3s

5. (a) x < 3 (b) 1 x 3 17 90, 123 41, 270, 303 41

6 a) 4=x

b) 9)4()( 2 = xxf 18(a)

2

1(b) 400

7 x = 3 19 15x + 16y 109 = 0

8 ( i) 0.209 (ii) 2.219 20 ( i) 0.01591 cms1 (ii) 9.612

9 x = 4 21 (a) 4 (b) k = 210 a) 5 b) 4 22 14 553

11 (a) 64 ( b) 2540 23 (a ) 14 (b) 1.020

12 a = 0.06 , b = 0.006 , p = 6 24 (a) 9/35 ( b) 5/6

25 k = 1.234


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SECTION A

[40 marks][40 markah]

Answerall questions in this section .

1. Solve the equations x2 y + y2 = 2x + 2y = 10.

[5 mark

[ Answer x = 2, y = 3; x =2

5, y =

2

5

2 Given kx2 x is the gradient function for a curve such that kis a constant. y 5x + 7 = 0 is the

equation of tangent at the point (1, 2) to the curve.

Find,

(a) the value of k, [2 marks]

(b) the equation of the curve. [3 marks]

[ Answer k = 6

[ y =2

7

22

2

3

xx

3

Diagram 3

Diagram 3 shows a string of length 125 cm is cut and made into ten circle as shown above .

The diameter of each subsequent circles are difrent by 1 cm from its previous.

Calculate,

(i) the diameter of the smallest circle ,

(ii) the number or a circle if the length of a circle is 400

[6 mark

Answer : (b)(i) 8 (ii) 2

4 Table 2 shows the frequency distribution of the marks of a group of form 4 students in a test.

Mark Number of students

20 29 2

30 39 10

40 49 36

50 59 55


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(a) It is given that the first quartile score it 44.5. Find the value ofk.

[ 3 marks ]

(b) [ Use the graph paper to answer this question]

Using the scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 10 students on the vertical

axis, draw a histogram based on the given data. Hence, estimate the mode mark

[ 3marks ]

(c) Calculate the mean marks.

[2 marks ]

[ Answer k = 12, mode = 52.25 mean = 55.81

5 a) Prove that

sec

1- sec = - tansin

[3 mark

(b) Sketch xy 2sin1= for x0 . Hence using the same axes , draw a suitable straight

line to find the number of solutions of the equation 02sin =xx . State the number of

solutions [ line ]1+

=

xy , 4 number of solution ]

[5 mark

6 5x

A B

4y P

D C

x

In the diagram above, AB

= 5x, AD

= 4y and

DC = x.

(i) Express,

(a)

AC

(b) BD

in terms ofx and y. [2 marks]

(ii) Given AP

= h AC and BP = k

BD.

State AP

(a) in terms of h, x and y,

(b) in terms of k, x and y.

Hence, or otherwise, prove that h = k. [5 marks]

Answer (i)(a) 4y + x, (b) 5x + 4y (ii)(a) h(4y + x) (b)( (5 5k)x + 4ky; k =6

5


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SECTION B

[ 40 Marks ]

Answer four equations from this section.

7 Table 7 shows the values of two variables x and y ,obtained from an experiment. Variablex andy arrelated by the equations y = abx , where a and b are constants. One of the value ofy is wrongly

recorded.

x 1 2 3 4 5

y 41.

7

38.

7

28.

9

27.

5

20.1

(a) Plot log 10y against x.(b) By using your graph find,

(i) the value ofy which is wrongly recorded and determine the correct value

(ii) the value of a and the value ofb(iii) the value of y when x = 2.5 .

8 y

y = a

Q y =x2 + 1

x

3

1

O 3

1

(a) Refer to the diagram above, answer the following question:

(i) Calculate the area of the shaded region.

(ii) Q is a solid obtained when the region bounded by the curvey =x2 + 1 and the liney = a is

revolved through 180 at the y - axis. If the volume of Q is2

1 unit2 Find the value a.

[6 mark

(b) Find the equation of tangent to the curvey = 2x2 + rat point x = k. If the tangentpasses through the point (2, 0), find rin terms ofk.

[4 marks

[Answer 16. (a)(i)81

56(ii) a = 2 (b) y (2k2 + r) = 4k(x k); r = 2k2 8k ]


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

9.

y U(5, 6)

T(0, 4)

x

O V(p, q)

W

Diagram above shows the vertices of a rectangle TUVW in a Cartesian plane.(a) Find the equation which relates p and q by using the gradient of UV.

[3mak

(b) Shows that the area of the TUVcan be expressed as p 5

2q + 10. [2marks

(c) Hence, calculate the coordinates of Vgiven the area of the rectangle TUVW is 5 unit2.[3marks]

(d) Find the equation of the straight line TWin the intercept form. [2mark

10

Diagram above shows a sector MJKL of a circle centre M and two sectors, PJM and

QML, with centre P and Q respectively. Given the angle of the major sector JML is 3.6

radian.

Find,

(a) the radius of the sector MJKL, [2 marks]

(b) perimeter of the shaded region, [2 marks]

(c) the area of sector PJM, [2 marks]

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


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[ Answer 11. (a) 4.795 (b) 27.24 (c)2

25

11 (a) In a centre of chicken eggs incubation, 30% of the eggs hatched are male chickens.

If 10 newly born chickens are chosen at random, find the probability (correct to four

decimal places) that

(i) 4 eggs hatched are male chicken,

(ii) at least 9 eggs hatched are female chickens. [4 marks]

(b) The mass of guava fruits produced in a farm shows a normal distribution with

mean 420 g and standard deviation 12 g. Guava fruits with mass between 406 g

and 441 g are sold in market, whereas those with mass 406 g or less are sent to the

factory to be processed as drinks.

Calculate,

(i) the probability (correct to four decimal places) that a guava fruit chosen

randomly from the farm will be sold in the market,

(ii) the number of guava fruits that has been sent to the factory and also not sold

in the market, if the farm produced 2 500 guava fruits. [6 marks]

[ Answer (a)(i) 0.2001 (ii) 0.1493 (b)(i) 0.8383 (ii) 100

Sections C

Answertwo questions from this section.

12 .

A B

P 8 m Q

In the diagram above, P and Q are two fixed points on a straight line such that

PQ = 8 m. At a certain instant, particle A passes the point P with a velocity

VA = 2t 6, whereas particle B passes the point Q with a velocity VB = 5 t where t

is time in second after the particle A and the particle B have passed the point P and the

point Q.

[Assume direction P to Q is the positive.]

(a) Find the distance between the particle A and particle B at the instant when particle

A stopped momentarily.

[3marks ]

(d) Find the time, t1, when the distance between the particle A and particle B is maximum before thetwo particles meet.. [ 2 marks ]

(c) For how long the two particles A and B are moving in the same direction?

(d)(i) Find the time, t2, when the particles A and B meets.

(ii) Hence, find the distance from the point P when the two particles meet.. [3 marks

[Answer (a) 27

2

1m (b)

3

11s (c) 2 s (d)(i) 8 s (ii) 16 m


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13 A small factory produces a certain goods of A model and B model. In a day, the factory producesx units o

A model and y units of B model where x 0 and y 0. Time taken to produce one unit A model and one uni

B model is 5 minutes and minutes respectively. The production of these goods in a certain day is

restricted by the following conditions:

I. The number of units of A model is not more than 60,

II. The number of units of B model is more than two times the number of units of A model by

10 units or less.

III. The total time for the production of A model and B model is not more than 400 minutes.

Write an inequality for each of the above condition.. Hence draw the graphs for the three inequalities. Mark

and shades the region R which satisfy the above conditions.

Use your graph to answer the following questions:

(a) Find the range of the number of units of A model which can be produced if 40

units of B model are produced.

(b) Find the total maximum profits which can be obtained if the profit gained fromone unit of A model and one unit of B model is RM 6 and RM 3 respectively.

(c) If the factory intends to produce the same number of units of A model and

B model, find the maximum number of units which can be produced for each o A model and B

model.

Answer x 60, y 2x 10, 5x + 4y 400 (a) 15 x 48 (b) RM435 (c) 4

14 . Diagram 6 shows a quadrilateral ABCD such that ABC is acute.

D

9.8 cm 5.2 cm

C

A 40.5 12.3 cm9.5 cm

DIAGRAM 6

B

(a) Calculate,

(i) ABC,

(ii) ADC,

(iii) area, in cm2, of quadrilateral ABCD.

[8 marks](b) A triagle ABC has the same measurements as those given for triangle ABC,

that is, AC = 12.3 cm, CB = 9.5 cm and BAC = 40.5, but which is

different in shape to triangle ABC.

(i) Sketch the triangle ABC.

(ii) State the size ofABC.

[2 marks]

Answer . (a)(i) 57.21 - 57.25 (ii) 106.07 - 106.08 (iii) 82.37 - 82.39

(b)(i) C (ii) 122.75 - 122.79

A B


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10. Table 2 shows the price indices and percentage usage of four items, P, Q, R, and S,

which are the main ingredients of a type biscuits.

Item Price index for the year 1995

based on the year 1993Percentage of usage (%)

P 135 40

Q x 30

R 105 10

S 130 20

(a) Calculate,

(i) the price of S in the year 1993 if its price in the year 1995 is RM37.70

(ii) the price index of P in the year 1995 based on the year 1991 if its

price index in the year 1993 based in the year 1991 is 120.

[5 marks](b) The composite index number of the cost of biscuits production for the year 1995

based on the year 1993 is 128.

Calculate,

(i) the value of x,

(ii) the price of a box of biscuit in the year1993 if the corresponding price in the

year 1995 is RM 32.

[5 marks]

[ Answer (a)(i) RM 29 (ii) 162 (b)(i) 125 (ii) RM 25

Section C Alternative

Answertwo questions from this section.

12. Diagram 6 shows STQ such that ST= 12.1 cm and TQ = 9.5 cm.

The area of the triangle is 45 cm2 and STQ is obtuse.

(a) Find

(i) STQ [ = 47.128STQ or '28128 ]

(ii) the length, in cm, ofSQ [19.49 cm](iii) the shortest distance, in cm, from Tto SQ. [4.613] [ 5 marks]

S

T

QDiagram 6


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Diagram 7

(b)

Diagram 7 shows a pyramid TPQR with a horizontal triangular basePQR. Tis vertically above Q. GiventhatPQ = QT= 5 cm, TR = 13 cm and = 15PRQ .Calculate two possible values of PQR

[PQR = 126.60o and 23.40o]

(c) Using the acute PQR in (i), calculate

( i) the length ofPR [7.673]

(ii) the value of PTR [29.420]

(iii) the surface area of the plane TPR [22.58] [ 5marks]

13. shows the bar chart for the monthly sales of five essential items sold at a sundry shop. Table 3 shows the

price in the year 2000 and 2006, and the corresponding price index for the year 2006 taking 2000 as th

base year.

Sugar

Rice

Salt

Cooking Oil

Flour

10 20 30 40 50 60 70 80 90 100units

Diagram 2

ItemsPrice in the

year 2000

Price in the

year 2006

Price Index for the year

2006 based on the year

2000

Cooking Oil x RM2.50 125

Rice RM1.60 RM2.00 125

R

T

Q

P

5 cm13 cm

5 cm


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Salt RM0.40 RM0.55 y

Sugar RM0.80 RM1.20 150

Flour RM2.00 z 120

TABLE 4

(a) Find the values of

(i) x,(ii) y(iii) z. [x=2.00,y=137.5,z=2.40] [3 marks]

(b) Find the composite price index for cooking oil, rice, salt, sugar and

flour in the year 2006 based on the year 2000. [131.17] [2 marks]

(c) Calculate the total monthly sales for those essential items in the year 2006,

given that the total monthly sales in the year 2000 was RM 150.[3 marks][120

(d) the composite index for the year 2008 based on the year 2000 if the monthly sales of those

essential items increased by 20% from the year 2006 to the year 2008.[157.40] [3 marks]

14. Use the graph paper provided to answer this question.

The Mathematics Society of a school is selling x souvenirs of type A and y

souvenirs of type B in a charity project based on the following constraints :

I : The total number of souvenirs sold must not exceed 75.

II : The number of souvenirs of type A sold must not exceed twice the number of souvenirs of typ

B sold.

III : The profit gained from the selling of a souvenir of type A is RM9 while th

profit gained from the selling of a souvenir of type B is RM2. The total profit must not be les

than RM200.

(a) Write down three inequilities other than x 0 dan y 0 which satisfy the above constraints.

[ Answer x + y 75 , x 2y and 9x + 2y 200]

[3 marks]

(b) Hence, by using a scale of 2 cm to 10 souvenirs on both axes, construct and shade the region R

which satisfies all the above constraints. [ 3 marks]

(c) By using your graph from (b), find

(i) the range of number of souvenirs of type A sold if 30 souvenirs of type B are sol

[ 16 number of A type souvenirs sold 45]

(ii) the maksimum which may be gained. [Answer RM 500]

[4 marks]


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15. An object, P, moves along a straight line which passes through a fixed point O.

Figure 8 shows the object passes the point O in its motion. t seconds after leaving the point O , th

velocity of P, v m s1 is given by v = 3t2 18t + 24. The object P stops momentarily for the first time

the point B.

P

O B

Figure 8

(Assume right-is-positive)

Find:

(a) the velocity of P when its acceleration is 12 ms 2 , [9 ms 1 ] [3 marks]

(b) the distance OB in meters, [20 m] [4 marks]

(c) the total distance travelled during the first 5 seconds. [28 m] [ 3 marks]

12.

(a) (i) Use area formula

45sin)5.9)(1.12(2

1=STQ

= 47.128STQ or '28128

(ii) Using cosine Rule

cmSQ

STQSQ

49.19

cos)5.9)(1.12(25.91.12222

=

+=

= 05.29TQS

(iii)5.9

05.29sinh

= or equivalent

= 4.613 cm

(b)

=

==

=

141.60,38.40@'36141,'2438

6212.015sin5

12sin

sin

12

15sin

5

QPR

p

p

PQR = 180o 15o 38.40o @

PQR = 180o 15o 141.60o

PQR = 126.60o and 23.40o


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(c) (i)

= 15sin

5

23.4sin

PR

cm7.672

4.23sin15sin

5PR

=

=

PR = 7.673 cm

(ii) Use Cosine Rule

cos PTR = 8710.0)50)(13(2

)672.7()50(13 222=

+

PTR = 29.420

(iii) Area PVR = 42.29sin)50)(13(2

1= 22.58 cm2

13.

(a) (i) x = 2.00

(ii) y = 137.5

(iii) z = 2.40

(b) Use composite index formula

17.131

30605010080

)30(120)60(150)50(5.137)100(125)80(125

=

++++

++++=

I

(c)

76.196

17.131100150

2006

2006

RMP

P

=

=

(d)

40.157

100

17.131120

120

2008

2000

2008

2006

=

=

=

I

I

14. (a) The three inequalities are

x + y 75 , x 2y and 9x + 2y 200

(b) refer by graph

(c) (i) 16 number of A type souvenirs sold 45

(ii)Maximum profit

= RM [ 9(50) + 2(25) ]

= RM500.


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1

Answer all questions.

1.

Function f is defined by

=

3,2

3

2

11

3,2

)(xx

xx

xf

Find the range corresponding to the domain 40 x [3 marks]

Answer: ..

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

2+xand fg:x

5

nmx +,

where m and n are constants , find the value of m and of n,

[2 marks ]

Answer: m =.

n =..............................

2

1

For exa

use


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2

3. Diagram 1 shows part of the mapping of x to z by the function baxxf +: followed

by the function cycy

yg

,12

: . Calculate the values of a, b, c and d.

[ 4 marks]

Answer: a=b=c=d=..

4. If the x-axis is a tangent to the curve 332

=+ ppxx , find the values of p.

[3 marks ]

Answer: p =.........

5. Given and are the roots of 0142 2 =+ xx . Form the quadratic equation with

roots 2 and2 .

[ 4 marks ]

r examiners

use only

3

4

For exam

use o

4

1

12

6 3

d

Diagram 1


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3

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

___________________________________________________________________________

6. Given the quadratic function of f(x) = 6x 1 3x2.

a) Express the quadratic function f(x) in the form k + m(x + n)2, where k, m and n are

constants.

b) write the equation of the axis of symmetry

[ 3 marks ]

Answer: (a) .........................

(b) ........................

7. Find the range of values of x if ( ) 523 2 += xxxf always positive.

[3 markah]Punca-punca bagi persamaan 033102 =+ kxx adalah dalam nisbah 2 :3.

5

6

examiners

use only


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30/101

5

[4marks]

Answer: .........

11. Solve the equation )32(loglog 93 += xx

[3marks]

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

3

8

10

11


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6

12. Given that the thn term , nTn 420= for an arithmetic progression. Find the sum of

the first 12 terms of the progression.

[3marks]

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

___________________________________________________________________________

13. Given the sum of the first 3 terms of a geometric progression is 567 and the sum of

the next three terms of the progression is 168. Find the sum to infinity of the

progression.

[4marks]

Answer: .

4

13

4

12

For

xaminers

use only


32/101

7

14. Given that the sum of the first three terms of a geometric progression is 13 times the

third term of the progression. If the common ratio, r > 0, find the common ratio.

[ 2 marks ]

Answer: .

15. Diagram 2 shows the graph of log2 y against log2 x. Values of x and values

of y are related by the equation y =x

k

n2

, where n and k are constants.

Find the value of n and the value of k.

log2 y

(5, 6)

(2, 0)

[4 marks]

Answer: n= ..k=.

16. Diagram 3 shows a semicircle KLMN, of diameter KLM , with centre L.

14

For exa

use o

r examiners

use only

log2 x

Diagram 2

0

*


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8

Given that the equation of the straight line KLM is 134=+

yxand pointN( x , y )

lies on the circumference of a circle KLMN , find the equation of the locus of the

moving

point N.

[ 3 marks ]

Answer: ......

17. If ( ) jpia 12 ++= and jib 63 += , find the value ofp if ba + is parallel to thex-axis.

[3 marks]

Answer: ......

___________________________________________________________________________

18. Given that a=020sin and b=030cos , express 050sin in terms ofa and

16

4

17

3

16

For exa

use

K N(x,y)

Diagram 3

0

y


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9

[3 marks]

Answer: ...

___________________________________________________________________________

19. Diagram below shows two sectors , OAB and OCD with centre O.

Given that COD = 0.92 rad,BC= 5 cm and perimeter of sectorOAB is 20.44 cm.Using = 3.142 , find the area of the shaded region ofABCED.

[ 3 marks ]

Answer:

19

18

r examiners

use only

O

D C

E

A B


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10

20. Given that y=2

12

x

x and

dx

dy= 2 g(x) where g(x) is a function in x .

Find1

1)( dxxg . [3 marks]

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

___________________________________________________________________________

21. The gradient of the curve y = hx +k

x 2at the point

17

2, is 2. Find the value of h

and the value of k. [3 marks]

Answer: ..

3

20

3

21


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11

22. A coach wish to choose a player from two bowlers to represent the nation in a

tournament. The following data show the number of pins scored by the two players

in six sucessive bowls:Player A: 8, 9, 8, 9, 8, 6

Player B: 7, 8, 8, 9, 7, 9

By using the values of mean and standard deviation, determine the player which

qualified to be choosen because the score is consistent.

[3 marks]

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

___________________________________________________________________________

23. In a debate competition, the probability of team A, team B and team C will qualify for

the final are5

1,

4

1,

3

1respectively. Find the probability that at least 2 teams will

qualify

for the final.

[3 marks]

Answer:

For exa

use

23

2


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12

24. The letters of the word G R O U P S are arranged in a row. Find the probability that

an arrangement chosen at random

(a) begins with the letterP,

(b) begins with the letterPand ends with a vowels.

[3 marks]

Answer: ( a)............

( b )...................................

25. The life span of certain computer chip has a normal distribution with a mean of 1500 days

and a standard deviation of 40 days.

a) Calculate the probability that a computer chip chosen at random has a life span of

more than 1540 days

b) Given that 6% of the computer chips have a life span of more than n days, find the

value of n.

[4 marks]

Answer: (a)..........

(b)..........................................

END OF QUESTION PAPER

3

24

r examiners

use only

4

25


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13


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Paper 2

Time: Two hours and thirty minutes

Instruction : This question paper consists of three sections: Section A, Section Band

Section C.Answerallquestions inSection A, four questions fromSection Bandtwo

questions fromSection C. Give onlyoneanswer/ solution for each question.All theworking steps must be written clearly. Scientific calculator that are non-programmable

are allowed.

Section A

[40 marks]

1. Given that (-1, 2k) is a solution for the simultaneous equation

x2 +py 29 = 4 =pxxy where kandp are constants. Find the value ofkand ofp.[5 marks]

Answer:

k= 4,p = 4; k= 2,p = 8

2. Given functionf:x 4 3x.(a) Find,

(i) f2(x),

(ii) (f2)1(x). [3 marks]

(b) Hence, or otherwise, find (f1)2(x) and show

(f2

)1

(x) = (f1

)2

(x). [3 marks]

(c) Sketch the graph off2(x) for the domain 0 x 2 and find its correspondingrange. [2 marks]

Answer

(a)(i) 9x 8 (ii)9

8+x(c)y

10 --------------------------

8 0 y 10

0 8/9 x

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1


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3. Diagram 3 shows five semicircles.

DIAGRAM 3

The area of the semicircles form a geometric progression. Given that area of the

smallest semicircle is1

16of the area of the largest semicircle. If the total area of the

semicircles is 302

cm , find

(a) area of the smallest semicircle(b) area of the largest semicircle

[5 marks]

Answer

(a) 10 (b) 160

4. Given that tan( ) 1x y = and 3tan4

y = , show that 1tan7

x = .

Sketch the graph of tany x= for 0 00 360x .Hence, using the same axes , draw a suitable straight line and find the number ofsolutions for the equation

3 tan 6x x+ =[6 marks]

Answer : Number of solutions = 3


2


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5. Diagram 5 shows a parallelogram OABC.

O A

P

D BC

DIAGRAM 5

Given thatAPD, OPCandDCB are straight lines. Given that

OA = 6a,

OC = 12c

and OP:PC= 3 : 1.

(i) Express

APin terms ofa and/orc.

(ii) Given the area of the ADB = 32 unit 2 and the perpendicular distancefromA toDB is 4 units, find a. [5marks]

Answer:( ) 6 9

( )2

a a c

b

+% %

6.


3

Cumulative

frequency

Length of fish

in cm

x (5.5, 6)

(10.5, 26) x

x(15.5, 58)

(20.5, 74) x

x (25.5, 80)


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O 0.5

DIAGRAM 6

Diagram 5 shows an ogive for the distribution of 80 fishes in a tank when the

cumulative frequency is plotted against upper boundaries for a certain classes. Ois the origin.

(a) Construct a frequency table with a uniform class interval from the

information given in the ogive.[2 marks]

(b) Draw a histogram and determine the mode.

[3 marks]

(c) From the frequency table, find(i) the variance,

(ii) the median

for the length of fish in the tank. [4 marks]


An experiment which involves samples of red blood cell used to trace the percentage,P, of the red blood cell which experience creanation when it is added by drops of

sodium chloride solution with different concentration,Kmol dm3. Table belowshows the results of the above experiment.

Sodium chloride

concentration (K)

0.50 0.75 1.00 1.25 1.50 1.75

Percentage of red blood

cells which experience

creanation (P)

0.4

5.0

14.5

27.6

46.2

68.9

TABLE 7

VariablesPandKare related by the equationP= 24

(K+ A)2 where and A are

constants.

(a) Draw the graph of P againstK.[5 marks]

(b) From your graph, find the value of and the value ofA.[4 marks]

(c) Find the value ofPwhenK= 1.4?

[1 mark]Answer:


4


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( ) 0.33, 0.40

( )37.21 38.44

b A

c

= =

8. y

y = x(x 1)(x + 3)

O x

(a) Diagram above shows the curve y = x(x 1)(x + 3). Calculate the areabounded by the curve, x-axis, line x = 2 and line x = 1. [6 marks]

(b) Diagram below shows the shaded region bounded by the curve y = 2 1x + , line

x = 1 and line x = k. When the region is revolved 360 at the x-axis, the volumegenerated is 18 unit3. Find the value of k. [4 marks]

[ answer (a)12

47(b) k = 4 ]

9.

y

P(0, )

Wall R(x,y)

O Q(, 0) xFloor

Diagram 9 shows thex-axis and they-axis which represent the floor and the wall.The end of a piece of woodPQ with length 9 m touches the wall and the floor at the

pointP(0, ) and point Q(, 0).

(a) Write the equation which relates and . [1 mark](b) GivenR is a point on the piece of wood such thatPR :RQ = 1 : 2.


5

Jawapan:

2 2( ) 81

2( )( ) ,5.85

3( )0.35

a

b ii

c

+ =


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(i) Show that the locus of the point R when the ends of the wood is slipping along

thex-axis and they-axis is 4x2 +y2 = 38.

(ii) Find the coordinates ofR when = 2.

(iii) Find the value of tan ORQ when = 2. [9 marks]

10.

rad

T

O

K

L

J

RQ

P

DIAGRAM 10

Answer:

2( )

3

20( )3

( )61.50

a

b

c

11. (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 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

of 58kg and variance of 25 kg2. Find

(i) the number of students with the mass of more than 90 kg.(ii) the value of w if 10% of the students in the colleges are less than w kg.


6

Diagram 10 shows a circlePQRT, centre O and radius 5 cm.JQKis a tangent to the circle at

Q. The straight lines,JO andKO, intersect the circle atPandR respectively. OPQR is a

rhombus.JLKis an arc of a circle, centre O. Calculate(a) the angle , in terms of [ 2

marks]

(b) the length, in cm, of the arc JKL [ 4 marks]

2


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[5 marks]

Answer:

(a) (i) 0.1268 (ii)400

(b) (i) 82or 83 (ii) 38.77 or 38.79

12. Diagram 12 shows the position and direction of motion for two objects,Pand Q,

which move along a straight line and passes through two fixed points,A andB

respectively.At the instant whenPpasses through the fixed pointA, Q passes through the fixed

pointB. DistanceAB is 28 m.

A C B28 m

DIAGRAM 12

The velocity ofP, vp ms1, is given by vp = 6 + 4t 2t2, where t is the time in

seconds, after passing through A, whereas Q moves with a constant velocity of

2 ms1. ObjectPstops instantaneously at the point C.(Assume towards the right is positive.)Find,

(a) the maximum velocity, in ms1, forP, [3 marks](b) the distance, in m, CfromA, [4 marks]

(c) the distance, in m, betweenPand Q at the instant whenPis at the point C.

[3 marks]

Answer:(a) 8 m/s

(b) 18

(c) 4


7


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13. . Diagram 13 shows a quadrilateralABCD such that ABCis acute.

DIAGRAM 13

(a) Calculate,

(i) ABC,(ii) ADC,(iii) area, in cm2, of quadrilateralABCD. [8 marks]

(b) A triangleABChas the same measurements as those given for triangleABC,

that is,AC = 12.3 cm, CB = 9.5 cm and BAC = 40.5, but which isdifferent in shape to triangleABC.

(i) Sketch the triangleABC.(ii) State the size ofABC. [2 marks]

Answer:

(a) (i) 57.21-57.25(ii) 106.07-106.08

(iii)82.37-82.39

(b) (ii) 122.75-122.79


8

C

12.3 cm40.50

9.8 cm

9.5 cm

5.2 cmD

B

A


47/101


ClothPreparation time (minutes) Sewing time (minutes)

T-shirt 45 50

Slack 30 70

A tailor shop received payment only for sewing T-shirt and slack. Preparation timeand sewing time for each T-shirt and slack are shown in the table above.

The maximum preparation time used is10 hours and the sewing time must be at least

5 hours 50 minutes. The ratio of the number of T-shirt to slack is not more than 4 : 5.

In a certain time, the shop is able to complete x pieces of T-shirt and y pieces ofslack.

(a) Write three inequalities, other thanx 0 andy 0, which satisfy the aboveconditions. [3 marks]

(b) By using a scale of 2 cm to I unit on the x-axis and 2 cm to 2 units on the y-axis,

draw the graphs for the three inequalities. Hence, shades the regionR whichsatisfies the above conditions. [3 marks]

(c) Based on your graph, find(i) the minimum number of slacks which can be sewn in that time if 3 pieces of

of T-shirt has been sewn..(ii) maximum total profit received in that time if the profit gained from each piece

of T-shirt and slack are RM16 and RM 10 respectively. [4 marks]

Answer:

( )45 3 600

50 70 350

5 4

( )4

(6,11), 206

a x y

x y

x y

c

RM

+

+


9


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15. (a)

Index number,Ii 105 94 120

Weightage, Wi 5 x x 4

The composite index number for the data in the table above is 108.

Find the value ofx. [4 marks]

(b) (i) In the year 1995, price and price index for one kilogram of certain grade ofrice is RM2.40 and 160 respectively. Based on the year 1990, calculate the price per kilogram of rice in the year 1990. [2marks]

Item Price index inthe year 1994

Change of price index from theyear 1994 to the year 1996

Weightage

Timber 180 Increased 10 % 5

Cement 116 Decreased 5 % 4

Iron 140 No change 2

Steel 124 No change 1

(ii) Table above shows the price index in the year 1994 based on the year 1992,

the change in price index from the year 1994 to the year 1996 and the weightage

respectively. Calculate the composite price index in the year 1996.. [4 marks]

Answer :

(a) x=3(b) (i) 1.50

(ii) RM152.90

End of question paper


10


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- 2 -

http://mathsmozac.blogspot.com Page 2

1. Given that mxxf +4: and4

3:

1 + nxxf , find the values of m and n.

Answer:- m = 3 ; n =1

4

2. Given that 12: xxf , xxg 4: and baxxfg +: , find the values ofa and b .Answer:- a = 8 ; b = 1

3. Given that 3: +xxf , 2: bxaxg + and 56366: 2 ++ xxxgf , find thevalues ofa and b .

Answer:- a = 2 ; b = 6

4. Given that xmxg 3: + and3

42:1 kxxg , find the values ofm and k.

Answer:- k=1

6; m = 4

5. Given the inverse function2

32)(1

=

xxf , find

(a) the value off(4),(b) the value of k iff1 (2k) = k 3 .

Answer:-(a)11

2(b)

1

2

6. Given the function : 2 1f x x and : 2

3

xg x , find

(a) f1 (x) ,

(b) f 1 g(x) ,

(c) h(x) such that hg(x) = 6x 3 .

Answer:-(a)1

2

x+(b)

1 1

6 2x (c) 18x + 33

7. Diagram 1 shows the function3

:2

p xg x

x

+

, 2x , wherep is a constant.

Diagram 1

Find the value ofp.

Answer:- p = 4

8.x y z

4 4 4

2 2 2

0 0 0

1

2 2 2Diagram 2

7

3

2

p x

x

+

x

g

5

g(x) = 4 3xfg(x) = 2x + 5


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- 3 -

QUADRATIC EQUATIONS

1. One of the roots of the quadratic equation is twice the other root.

Find the possible values ofp.

Answer ; 5 7,p =

2. If one of the roots of the quadratic equation is two times the other root,

find an expression that relates .

Answer : 22 9b ac=

3. Find the possible value ofm , if the quadratic equation has two equal

roots.

Answer ;

4. Straight liney = mx + 1 is tangent to the curvex2 +y2 2x + 4y = 0. Find the possiblevalues ofm.

Answer : 1

2or 2

5. Given2

and

2are roots of the equation k x(x 1) = 2mx.

If + = 6 and = 3, find the value of kand ofm.

Answer : k =2

1, m =

16

3

6. Find the values of such that the equation (3 )x2 2( + 1)x + + 1 = 0 has equalroots. Hence, find the roots of the equation base on the values of obtained.

Answer : = 1; roots: = 1, x = 1; = 1, x = 0

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- 4 -

QUADRATIC FUNCTIONS

1. Diagram 1 shows the graph of the function ( )2

2 5y x p= + , where p is constant.

Find,

(a) the value of p ,(b) the equation of the axis of symmetry,

(c) the coordinate of the maximum point.

Answer:- (a) p = 2 (b) x = 2 (c) ( 2, 5 )

2.

Diagram 2 shows the graph of the function ( ) ( ) 21 2f x p x x q= + + .(a) State the value ofq .

(b) Find the range of values ofp .

Answer:-(a) q = 2 (b)1

2p

add mth perfect score 09

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