49603883 Modul 1 Jpnt Matematik Tambahan

KEM SPM TERBILANG TERENGGANU 2008 (MODUL 1) ADDITIONAL MATHEMATICS PAPER 1

2008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 1

FUNCTIONS

1. Given that h(x) = 2

x, x 0 and v(x) = 3x + 2, find )(1 xhv .

Answer : .

2. Based on the above information, find the function of q.

Answer : .

QUADRATIC FUNCTIONS

3. Solve the quadratic inequality t(15 2t) 22.

Answer : .

p : t t + 2qp : t t2 + 4t + 1

MMOODDUULLEE 11 PAPER 1 (3472/1)



4. Find the range of values of k if 2x2 + 4x + k is always positive.

Answer : .

5. If and are the roots for the equation 2x2 3x 1 = 0, form a new quadratic equation if the roots are + 1 and + 1.

Answer : .

6.

Jawapan : (a) p =

n = ....

k =

m = ...

(b) ..

In the diagram on the left, (k, 4) is a turning point of a quadratic

graph with an equation in the form ( 1) py m x n . Find (a) the values of p, n, k and m,(b) the equation of the curve formed when the graph shown is

reflected on the x-axis.

O

7

(k, 4)

x

y



7. (a) Based on the above information, express f (x) in the form f (x) = (x + q)2 + r.(b) Hence, find the maximum point.

Answer : (a) ..

(b) ..

COORDINATE GEOMETRY

8. The point A(5, p) divides the straight line that joined the point E(1, 6) and F(7, 3) with the ratiom : n. Find (a) m : n(b) the value of p.

Answer : (a) ...

(b) p =

f (x) = 1

2[(x + 5)2 + (x 7)2]



9. Given that the distance between P(k, 7) and Q(2, 6) is 5 , find the possible values of k.

Answer : k =

PROGRESSIONS

10. An arithmetic progression has 20terms. Given that the 7th term is 27 and the sum of last 7 terms is 469, calculate(a) the first term,(b) the sum of the first 7 terms.

Answer : (a) ..

(b) ..

11. Given that 16

9, x, y, z,

9

16are five consecutive terms in a geometric progression, find the values of

x, y and z.

Answer : x = .

y = .

z = .



12. Given that 200

k = 2 02

where k is a positive integer, find

(a) the common ratio,(b) the value of k.

Answer : (a) .

(b) k = ..

13. In a geometric progression, the sum of the first n terms, when n is large enough for rn 0, is 8

and the second term is 2. Find the common ratio of the progression.

Answer : .



LINEAR LAW

14. Diagram A shows part of the curve y = qx + px2 where p and q are constants.

(a) Find the values of p and q.

(b) If the curve y = qx + px2 is reduced to linear form, the straight line obtained is as shown in Diagram B. Calculate the values of h and k.

Answer : (a) p =

q = ....

(b) h =

k = ....

DIFFERENTIATION15. The sides of a cube decrease from 10 cm to 994 cm. Find the small change of the volume of

the cube.

Answer : .

16. The volume of a sphere increases at the rate of 60 cm3 s 1. Find the rate of change of the surface area of the sphere when its radius is 5 cm.

(1, 4)

(4, 28)

y

xODIAGRAM A

Y

X

(k, 10)

(0, h)

DIAGRAM B

O



Answer : .

17. Evaluate 2

4

16

4limx

x

x

.

Answer : .

18. Find the value of 2

5

2 7 15

5limx

x x

x

Answer : .

INTEGRATION

19. Given that 2

1

( )h x dx = 8, find the value of k if 2

1

[ ( ) ]h x kx dx = 14.

Answer : k = .



20. Given that 3y = 4x + 11 is a normal equation of the curve at the point (1, 5) which has a gradient

function 12

x

k, find the value of k.

Answer : k = .

21.

Answer : k = .

22.

Answer : k = .

y = k

x

y

O

y = 2x2 3

x

y

y = 8

2x

O 1 k

The diagram on the left shows the shaded

region bounded by the curve y = 8

2x , the

straight line x = 1, x = k and x-axis. When the shaded region is rotated through 360

about the x-axis, the volume is 40

3 unit3.

Find the value of k.

The diagram on the left shows the shaded region bounded by the curve y = 2x2 3, the y-axis and the straight line y = k. If the shaded region is rotated through 360 about y-axis, the volume generated is 25 unit3. Find the value of k.



23. The diagram above shows part of the graph y = x 2 + 2. Evaluate 3

0

y dx + 11

2

dyx .

Answer : .

STATISTICS

Number of books 1 2 3 4 5

Number of students 5 7 4 x 8

24. The table above shows the number of reference books bought by a group of students in a period of one semester. Find (a) the minimum value of x if the mean is greater than 3,(b) the range of values of x if the median is 3.

Answer : (a) ..

(b) ..

Student The marks of OTI test

x

y

O

(3, 11)

2



25. The table above shows the marks in five Operational Targetted Incremental (OTI) Additional Mathematics test obtained by two Form Five Syukur students.(a) Find the standard deviation marks of Shasha and Fatin.(b) Determine whether Shasha or Fatin performs more consistence.

Answer : (a) Shasha : . Fatin : ......

(b) ..

CIRCULAR MEASURE

26.

Answer : = ..

Shasha 72, 54, 70, 80, 84

Fatin 65, 59, 75, 78, 83

OA B

C

6 cm

The diagram on the left shows a semi circle with centre O and the radius 6 cm. Given that the arc length BC is equal to the sum of arc length AC and the diameter AB, find the value of .



INDICES AND LOGARITHMS27. Express 2 12 2 4(2 )n n n in its simplest form.

Answer : .

28. Solve the equation 3log

9x

= 4.

Answer : .

29. Solve the equation 2 6 27 49x x = 0.

Answer : .



30. Solve the equation 12 3.x x = 6.

Answer : .

31. Given that 5 log p6 log p 96 = 4, find the value of p.

Answer : p = .

32. Given that uT = 49, express (a) log 7 u in terms of T,(b) u in terms of T.

Answer : (a) ..

(b) ..



TRIGONOMETRIC FUNCTIONS

33. Solve the equation 2 sin 2x = tan x for 0 x 180.

Answer : .

34. Solve the equation 2 3 sin = cos 2 for 90 270.

Answer : .

35. Given that tan = p and is an acute angle, express in terms of p,(a) sin 2,(b) cot ( + 45).

Answer : (a) ..

(b) ..



36. Using the space given below, sketch the graph y = | 2 sin x + 1 | for 0 2.

Answer :

37. Given that cos A = 45

and sin B = 1213

where both A and B lie in the same quadrant, find the value

of sec (A + B).

Answer : .

VECTORS38.

Answer : .

O

B

A

C

a

b

In the diagram on the left, OA

= a and

OB

= b. Find OC

in terms of a and b.



39. Given that u = 2i + 3j and w = ki + 6j, find the values of k if | w 2u | = 6.

Answer : k = .

40. Given that the coordinates of P(0, 5), Q(k, 0) and R(1, m), find

(a) the value of k if PQ

is parallel to the vector i + 2j,

(b) the values of m if |OR

| = 10 .

Answer : (a) k = ........................................

(b) m = ....................................

41. Given that a = 2

1

and b = 3

m

, find the values of m if | a + b | = 34 .

Answer : m = .



PERMUTATIONS AND COMBINATIONS42. Five alphabets from the word HISTORY is to be arranged in a row such that it should starts with a

consonant. Find the number of different arrangements that can be formed.

Answer : .

43. A number with 2 digits or 3 digits is to be formed from the digits 4, 5, 6, 8, 9 without repetition. How many numbers can be formed ?

Answer : .

44. The diagram below shows 5 alphabets and 3 digits.

A secret code is to be formed using the alphabets and the digits given. Each code must consist of 3 alphabets followed by 2 digits. How many ways the code can be formed without repetition of the alphabets and the digits ?

Answer : .

C O R A L 7 8 9



45. A Parents-Teachers Association committee which consists of 7 members is to be formed from 8 parents, 3 teachers and a principal. In how many ways can the committee be formed if it is represented by(a) exactly 5 parents,(b) at least 5 parents.

Answer : (a) ..

(b) ..

PROBABILITY

46. A, B and C shoot once at a certain target. The probability that A hits the target is 1

5. The probability

that B hits the target is 1

4. The probability that C hits the target is

1

3. If they shoot simultaneously,

find the probability that(a) all of them hit the target.(b) at least one hits the target.

Answer : (a) ..

(b) ..



PROBABILITY DISTRIBUTIONS

47. A binomial distribution has mean 12 and variance 5. If p is a probability of a success and q is a probability of failure, find (a) the values of p and q,(b) the probability of obtaining 3 success from 8 trial.

Answer : (a) p = .

q = ..

(b) .

48. It was found that one out of ten computers produced by the factory was faulty. A sample of 5computers was randomly chosen and to be tested. Find the probability that(a) 2 computers was faulty,(b) at least one computer was faulty.

Answer : (a) .

(b) .



49. The diagram above shows the standard normal distribution graph. If P (124 z k) = 07811,find the value of(a) P(z > k)(b) k.

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

(b) k = .

50. Given that X is a random variable of a normal distribution with mean 124 and variance 144, find(a) the z-score when X = 1732,(b) P(104 X 182).

Answer : (a) .

(b) .

0 z124 k

f (z)



51. A random variable X has a normal distribution with mean 14 and variance 576. Given that P(X < k) = 08258, find the value of k.

Answer : k = .

52. Given that X N(100, 2) and P(X < 106) = 08849, find the value of the standard deviation of X.

Answer : .

53. In a survey carried out in a town, it was found that the weights of 1000 residents have a normal distribution with mean 48 kg and standard deviation 5 kg. Find the probability that a resident that was randomly chosen weighs more than 52 kg.

Answer : .



2O

y

2

1

x

3

22

3

1.6

2x , x 2

2. t 2 3

3. 2 t 11

24. k > 2

5. 2x2 7x + 4 = 0

6. (a) p = 2, n = 4, k = 1, m = 3

(b) y = 3(x 1)2 47. (a) (x 1)2 + 36

(b) (1, 36)

8. (a) 2 : 1 (b) p = 4

9. k = 0, 410. (a) 3 (b) 105

11. x = 4

3, y = 1, z =

3

4

12. (a)1

100 or 001

(b) 99

13.1

2

14. (a) p = 1, q = 3(b) h = 3, k = 7

15. 18 cm3

16. 24 cm2 s 1

17. 818. 2719. k = 4

20. k =1

4

21. k = 6

22. k = 7

23. 33 unit2

24. (a) 2 (b) 1 x 725. (a) Shasha = 1075,

Fatin = 8764,(b) Fatin

26. 0571 rad27. 5 2. n or 5(2 )n

28. x = 2

29. 6, 230. 161331. p = 3

32. (a)2

T(b)

2

7T

33. 0, 60, 120, 18034. 90, 150

35. (a)2

2

1

p

p

(b)1

1

p

p

36.

37. 65

16

38. 3b 1

2a

39. k = 2, 10

40. (a) k = 5

2 (b) m = 3

41. m = 4, 242. 720

43. 80

44. 360

45. (a) 336 (b) 456

46. (a)1

60(b)

47

60

47. (a) p = 7

12, q =

5

12

(b) 0139648. (a) 00729

(b) 0409549. (a) 01114 (b) 121950. (a) 41 (b) 0952251. 162552. 5

53. 02119

ANSWERS MODULE 1

49603883 Modul 1 Jpnt Matematik Tambahan

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