MT Sentuhan Akhir Paper 1,2013

8/12/2019 MT Sentuhan Akhir Paper 1,2013

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Cikgu Lin < the best of luck SPM 2> Sentuhan Akhir,{paper 1} 2013

1 Diagram 1 shows the relation

between set A and set B.

(a) Find the image of 4.

(b) State the type of relation.

2. In diagram 1, set B shows the images ofcertain elements of set A.

(a) State the type of relation between set A

and set B.(b) Using the function notation, write arelation between set A and set B.

3. Diagram 1 shows the relation between set P

and set Q.

State

a) the range of the relation,b) the type of the relation.

4. Given thatf(x) = 2x+ 3 andg(x) = 5x.fg(x) = mx+ n, find the value of mand n.

[ Ans : m =2 , n =13 ]5. Given thatf(x) = 2x3, fg (x ) = 5 + 4x.

Find functiong(x)[Ans : g(x) = 2x + 4 ]

6. Given thatg(x) = 4 + 3x, fg (x ) = 83x .find functionf(x) [Ans : f (x) = 12x ]

7. Given the function xf : 72 x , find

the values of x such that 11)x(f .

8 Given the functions 10: xxg

and35

:

x

xxh ,

5

3x , find the

value of )12(hg .

9. Given thatf(x) = 5xmand f (2) = 8find the value of

(a) m(b) value ofxthat maps to itself.

[Ans : (a) m = 2 (b) f(x) = x ; x = ]

10. (a) Solve the following quadraticequation: 08102 xx Give the answers correct to three

decimal places.b) The quadratic equation

has two equal

roots. Express m in terms of n.

11. Given that and 3 are the roots ofthe equation x

2+ 2bx+ 3a= 0 , prove

that 4a= b2.

12.One of the roots of the quadraticequation 2x

2+ 6x= 2k1 is twice the

value of the other root whereby k is aconstant. Find the roots and the value of

k. [Ans : -1, -2 ; k =2

3 ]

13. Diagram 5 shows a curve for

quadratic function f(x) = (x + p)29.

Find (a) the value of p(b) the minimum point of the curve of the

quadratic function .

B

A129641

m

n

p

r

5

4

-4

-5

25

16

Set A Set B

de

f

w x y z

SetP Set Q


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14. 34)( 2 xxxf can be

expressed in the form of

,)2()( 2 kxxf where k isconstant.

a) Find the value of k

b) Sketch the graph of the function f(x) on thegiven axes

15. Find the range of the values of x for

x2+ 7x + 10 > 0.

16. Solve the equation:xx 64 927

17. Given 243273 3 nn , find the value of

n.

18. Solve the equation 122 34 .

19. Solve the equation 4 2x-1 = 7x.

20. Given that log4x = log23 , find thevalue of x.

21 Given that log2y6 log4x = 3,express y in terms of x.

21 The first three terms of an arithmeticprogression are 3, k + 2, 11.Find

a) the value of k,b) the common difference of the

progression

22. The sum of the first n terms of thegeometric progression 8, 24, 72, is8744.Finda) the common ratio of the progression,

b) the value of n.

23. The first three terms of a geometricprogression is 6, 18, 54. Find the seventhterm.

26. The first three terms of an arithmeticprogression are 5, 9, 13.Find

a) the common difference of theprogression,

b) the sum of the first 20 terms after the

3rd term.

27. Given the geometric progression 7, ,

, . . . , find the sum to infinity of the

progression.

28. The radius, r of a circle changes from x cmto (x + 5) cm. Express, in terms of x, the

small change in the area of the circle.

29. The curve y = kx2+ 6x + p has a maximumpoint at (5, 8), where k and p are constants.Find the value of k.

30. Given that h(x) =2

)53(

1

x, evaluate

)1(h

31. Given that2

3 4( )

3

xf x

x

, find (3)f

[ Ans : 5/3 ]

32. Given ),6(2 xxy find

a)dx

dy

b) the value ofxwhenyis minimumc) the minimum value ofy

25. The n terms of an arithmetic progression

is given by .32

nn

Tn Find

a) common differentb) the sum of the first 5 terms

24. The sum of the first n terms of anarithmetic progression is given by

].13[2

nn

Sn Find

c) the sum of the first 5 terms

d) the 5th

term

13. Given ),6(2 xxy find

a)dx

dy

b) the value of xwhen yis minimum


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33.Two variables, x and y, are related by the

equationx

xy 2

3 .Given that y

increases at a constant rate of 4 units persecond, find the rate of change of x when

x= 2.

34.Find the coordinates of the turning points of

the curve 492 23 xxy .

[Ans ; min (3,23) , max (0,4)]

35.Find the equation of normal to the curve

xxy 53 at the point when 1x .[ y=1/2 x9/2 ]

36. Given that = 4, find

(a)

(b)

37. Given )(3

2xg

x

x

dx

d

, find

2

1

)( dxxg

38. Given that

dx

x(

4)1

5 = k( 1 + x) n + c,

find the values of k and n.

39. Diagram 4 shows the curve y= 3x2

and the straight line x = k.

If the area of the shaded region is 64

unit2, find the value of k.

40. A forum team consists of 3 girls and 5

boys. This team is to be chosen from 6 girlsand 7 boys.

(a) Find the number of ways to form theteam if there is no restriction

(b) How many ways the members can beseated a row such that all of the girls areto be seated next to each other?

41. The probability that Peter qualifies for the

semi-final of a badminton competition is5

4,

while the probability that Samuel qualifies is

7

5. Find the probability that

(a) all the players unqualify for the

semi-final.(b) only one of them qualify for thesemi-final

42. Justin bought 6 strawberries . The

probability that a sweet strawberry boughtby Justin is 0.80. Find the probability thatof these strawberries there is

(a) exactly one strawberry is sweet(b) more than one strawberry is sweet

43. Diagram shows a circle with centre O. Given

that the radius is 8 cm and POQ = 2 rad.

Find

[use/guna= 3.142 ](a) the length of the minor arc PQ(b) the area of the major sector OPQ

44. Diagram 16 shows a triangle OPQ. The

point R divides line PQ with ratio 3 : 2.

2 rad

OP

Q

x= k

y = 3x2

x

y

O


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Given that~

10aOP and~

15bOQ , find

the vector OR in terms of~

a and~

b .

45. The vectors a and b are nonparallel and

nonzero vectors, find the value of mand n.

bnam 263 [m =2, n = 2]

46. The points A, B and C are collinear. It is

given that AB=~~

46 ba and

BC =~~

)3(5 bna , where nis a

constant. Find

(a) the value of n, [19/3](b) the ratio of AB : BC [6 : 5]

47. Given vector u =

67 and v =

m2 .

Find the value of m such that u is parallelto u. [12/7]

48. Diagram shows a parallelogram PQRS.

Given that PQ = 3na + 4b,SR= 5amb, where mand nare constants.Find the value of mand n.

[m =4, n = 5/3]

49. Given that P(5, 2),Q(6,1) and R(n, 5),

find

a)

PQ in the form

y

x,

b) the value of n if

PQ and

QR are

parallel.

a)

13

11PQ b) 12/13

50. The variables x and y are related by theequation 3y = 5x

3+ 3px

2.

A straight line graph is obtained by

plotting

against x, as shown in

Diagram 12.

Find the value of p and of q.

51.

Diagram 2 shows part of a straight line graphdrawn to representy= 10

kx

n, wherekand nare

constants. Find the values of kand n.

52.

Express yin terms ofx.

O

P

Q

R

y

x2

xO

(q, 4)

1

P Q

RS

( 7,1)

( 3,9 )

0

0

(2 , - 3 )


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53. In a survey, the probability that a familyhaving one unit of computer is 0.6. Nfamilies were selected at random. Thestandard deviation of the numbers offamily having one unit of computer is

5

24

. Find,

(a) the value of N(b) the mean of the numbers of

family having one unit ofcomputer.

[ (a) N = 20 (b) mean =12]

Trial Melaka 2010

54. Diagram below shows a standardnormal distribution graph.

The probability represented by the area ofthe shaded region is 0.803.

(a) Find the value of P( Z > k )(b) X is a continuous random variable

which is normally distributed with amean of and a standard

deviation of 2. If the value ofXis85 when the Z-score is k, find thevalue of .

[ (a) 0.0985 (b) 82.42 ]

Trial Negeri Sembilan 2010

55. Diagram below shows a standardnormal distribution graph.

X is a continuous random variable which isnormally distributed with a mean of 30and a standard deviation of 2. It is given thatthe area of the shaded region is 0.5284.Find the value of(a) k ,(b) X [ (a) k = 0.72 (b) x = 31.44 ]

56. Xis a random variable of a normaldistribution with mean of 4.2 and avariance of 1.21. Find

(a) the z-score ifX=6.1

(b) P 6.52.4 x [ (a) 1.7273 (b( 0.3986 @ 0.3985(Cal) )

57. The probability of Siti and Kumarestraveling to London by Air Malaysia is2/3 and 1/6 respectively. Find theprobability that(a) neither of them traveling by Air

Malaysia(b) only one of them travels by Air

Malaysia[ (a) 5/18 (b) (2/3)(5/6)+(1/3)(1/6) = 11/18 ]

58. Robert and Davids favorite drink isCoca-cola. If they were to choose a drinkfrom a box that contains 4 cans of Coca-cola and 5 cans of Oranges juice.Find the probability that

(a) both of them get their favorite drink(b) only one of them got their favorite drink

[ (a) 1/6 (b) 5/9 ]

-k k z

f(z))

0.803


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59. A marble is drawn at random from a bagcontaining 2 white marbles, 3 redmarbles and 5 blue marbles.Find theprobability of(a) getting a red or blue marble

(b) not getting a red marble [ (a) 4/5 (b) 7/10 ]

60. The probability that it rains on Saturdayis 2/3 , while the probability it rains onSunday is 5/7. Find the probability thata. it rains on any one of these two daysb. there is no rain on any of these two

days[ (a) 3/7 (b) 2/21 ]

61. Table shows the number of coloured

marbles in a boxColour Number of marbles

Blue 2Green 3

Red 4

Two marbles are drawn at random fromthe box. Find the probability that bothmarbles are of same colour.

[ 5/18 ]

62. A box contains 6 black balls andpwhite balls.If a ball is taken out

randomly from the box, the probability

of getting a white ball is7

4. Find the

value of p. [ p = 8 ]

MT Sentuhan Akhir Paper 1,2013

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