MODULE 1 PAPER 1 (347/1) FUNCTIONS 1. Given that h(x) =, x 0 and v(x) = 3x +, find hv 1 ) x ( x. p : t t + qp : t t + 4t + 1. Based on the above information, find the function of q. QUADRATIC FUNCTIONS 3. Solve the quadratic inequality t(15 t). 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 1
4. Find the range of values of k if x + 4x + k is always positive. 5. If and are the roots for the equation x 3x 1 = 0, form a new quadratic equation if the roots are + 1 and + 1. 6. y 7 O (k, 4) x In the diagram on the left, (k, 4) is a turning point of a quadratic graph with an equation in the form y m( x 1) p 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. Jawapan : (a) p = n =... k = m =... (b).. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu
f (x) = 1 [(x + 5) + (x 7) ] 7. (a) Based on the above information, express f (x) in the form f (x) = (x + q) + 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 ratio m : n. Find (a) m : n (b) the value of p. Answer : (a)... (b) p = 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 3
9. Given that the distance between P(k, 7) and Q(, 6) is 5, find the possible values of k. PROGRESSIONS Answer : k = 10. An arithmetic progression has 0terms. Given that the 7 th term is 7 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 and z., x, y, z, 9 16 are five consecutive terms in a geometric progression, find the values of Answer : x =. y =. z =. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 4
1. Given that 00 k = 0 (a) the common ratio, (b) the value of k. where k is a positive integer, find Answer : (a). (b) k =.. 13. In a geometric progression, the sum of the first n terms, when n is large enough for r n 0, is 8 and the second term is. Find the common ratio of the progression. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 5
LINEAR LAW y (4, 8) Y (k, 10) O (1, 4) DIAGRAM A x O (0, h) DIAGRAM B X 14. Diagram A shows part of the curve y = qx + px where p and q are constants. (a) Find the values of p and q. (b) If the curve y = qx + px is reduced to linear form, the straight line obtained is as shown in Diagram B. Calculate the values of h and k. DIFFERENTIATION Answer : (a) p = q =... (b) h = k =... 15. The sides of a cube decrease from 10 cm to 9 94 cm. Find the small change of the volume of the cube. 16. The volume of a sphere increases at the rate of 60 cm 3 s 1. Find the rate of change of the surface area of the sphere when its radius is 5 cm. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 6
17. Evaluate 16 x lim x 4 x 4. 18. Find the value of x x lim x 5 7 15 5 x INTEGRATION 19. Given that h( x) dx = 8, find the value of k if 1 [ h( x) kx] dx = 14. 1 Answer : k =. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 7
0. Given that 3y = 4x + 11 is a normal equation of the curve at the point (1, 5) which has a gradient k function 1, find the value of k. x Answer : k =. 1. y y = 8 x The diagram on the left shows the shaded 8 region bounded by the curve y =, the x 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. O 1 k x Answer : k =.. y O y = x 3 x y = k The diagram on the left shows the shaded region bounded by the curve y = x 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 5 unit 3. Find the value of k. Answer : k =. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 8
y (3, 11) O x 3 3. The diagram above shows part of the graph y = x +. Evaluate y dx + 0 11 x dy. STATISTICS Number of books 1 3 4 5 Number of students 5 7 4 x 8 4. 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 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 9
Shasha 7, 54, 70, 80, 84 Fatin 65, 59, 75, 78, 83 5. 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 6. C 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. A O 6 cm B Answer : =.. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 10
INDICES AND LOGARITHMS 7. Express n n n 1 4( ) in its simplest form. log3 x 8. Solve the equation 9 = 4. 9. Solve the equation x 6 x 7 49 = 0. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 11
30. Solve the equation x x 1 = 6.. 3 31. Given that 5 log p 6 log p 96 = 4, find the value of p. Answer : p =. 3. Given that u T = 49, express (a) log 7 u in terms of T, (b) u in terms of T. Answer : (a).. (b).. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 1
TRIGONOMETRIC FUNCTIONS 33. Solve the equation sin x = tan x for 0 x 180. 34. Solve the equation 3 sin = cos for 90 70. 35. Given that tan = p and is an acute angle, express in terms of p, (a) sin, (b) cot ( + 45 ). Answer : (a).. (b).. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 13
36. Using the space given below, sketch the graph y = sin x + 1 for 0. Answer : 37. Given that cos A = 4 5 of sec (A + B). and sin B = 1 13 where both A and B lie in the same quadrant, find the value VECTORS 38. A In the diagram on the left, OA = a and OB = b. Find OC in terms of a and b. a B C b O 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 14
39. Given that u = i + 3j and w = ki + 6j, find the values of k if w u = 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 + j, (b) the values of m if OR = 10. Answer : (a) k =... (b) m =... 41. Given that a = 1 and b = 3 m, find the values of m if a + b = 34. Answer : m =. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 15
PERMUTATIONS AND COMBINATIONS 4. 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. 43. A number with digits or 3 digits is to be formed from the digits 4, 5, 6, 8, 9 without repetition. How many numbers can be formed? 44. The diagram below shows 5 alphabets and 3 digits. C O R A L 7 8 9 A secret code is to be formed using the alphabets and the digits given. Each code must consist of 3 alphabets followed by digits. How many ways the code can be formed without repetition of the alphabets and the digits? 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 16
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. The probability 5 that B hits the target is 1. The probability that C hits the target is 1. If they shoot simultaneously, 4 3 find the probability that (a) all of them hit the target. (b) at least one hits the target. Answer : (a).. (b).. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 17
PROBABILITY DISTRIBUTIONS 47. A binomial distribution has mean 1 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 5 computers was randomly chosen and to be tested. Find the probability that (a) computers was faulty, (b) at least one computer was faulty. Answer : (a). (b). 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 18
f (z) 1 4 0 k z 49. The diagram above shows the standard normal distribution graph. If P ( 1 4 z k) = 0 7811, 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 1 4 and variance 1 44, find (a) the z-score when X = 17 3, (b) P(10 4 X 18 ). Answer : (a). (b). 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 19
51. A random variable X has a normal distribution with mean 14 and variance 5 76. Given that P(X < k) = 0 858, find the value of k. Answer : k =. 5. Given that X N(100, ) and P(X < 106) = 0 8849, find the value of the standard deviation of X. 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 5 kg. 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 0
ANSWERS MODULE 1 1.. t 3 6, x x 1. k = 6. k = 7 3. 33 unit 37. 65 16 38. 3b 1 a 3. t 11 4. (a) (b) 1 x 7 39. k =, 10 4. k > 5. x 7x + 4 = 0 6. (a) p =, n = 4, k = 1, m = 3 (b) y = 3(x 1) 4 7. (a) (x 1) + 36 (b) (1, 36) 8. (a) : 1 (b) p = 4 9. k = 0, 4 10. (a) 3 (b) 105 11. x = 4, y = 1, z = 3 3 4 1. (a) 1 or 0 01 100 (b) 99 13. 1 14. (a) p = 1, q = 3 (b) h = 3, k = 7 15. 18 cm 3 16. 4 cm s 1 17. 8 18. 7 5. (a) Shasha = 10 75, Fatin = 8 764, (b) Fatin 6. 0 571 rad 7. 5 8. x = 9. 6, 30. 1 613 31. p = 3 y 3 1 O. n n or 5( ) 3. (a) T (b) 33. 0, 60, 10, 180 34. 90, 150 p 35. (a) 1 p 36. (b) 1 p 1 p 7 T 3 40. (a) k = 5 41. m = 4, 4. 70 43. 80 44. 360 x (b) m = 3 45. (a) 336 (b) 456 46. (a) 1 60 (b) 47 60 47. (a) p = 7, q = 5 1 1 (b) 0 1396 48. (a) 0 079 (b) 0 4095 49. (a) 0 1114 (b) 1 19 50. (a) 4 1 (b) 0 95 51. 16 5 5. 5 53. 0 119 19. k = 4 0. k = 1 4 008 Hak Cipta Jabatan Pelajaran Negeri Terengganu 1