MAT111 Past Questions PDF

SEN. PREMIER MAT111 STUDY QUESTIONS BY TAIWO OLALERE PREMIER 1. Express the sin4x + sin2x as product of two trigonometrical ratios. (A) 2sin3xcos2x (B) 2sin3xcosx (C) 2sin2xcos2x (D) sin3xcosx 2. Express cos4x – cos2x as product off two trigonometr...

SEN. PREMIER MAT111 STUDY QUESTIONS BY TAIWO OLALERE PREMIER 1. Express the sin4x + sin2x as product of two trigonometrical ratios. (A) 2sin3xcos2x (B) 2sin3xcosx (C) 2sin2xcos2x (D) sin3xcosx 2. Express cos4x – cos2x as product off two trigonometrical ratios. (A) -2sin3xsinx (B) 2sin3xsin3x (C) 2sinxsin3x (D) none of the above 3. Express 30o in radian (A) π/6 (B) 6/π (C) π (D) none of the above 4. Express π/2 in degree (A) 80o (B) 90o (C) 135o (D) 45o 5. Express 3.5rad in degree (A) 200.5o (B) 200o (C) 20o (D) 150o 6. The sun subtend an angle at 35degree from the centre of the earth whose distant from the centre of the earth is 382,100km. find the diameter of the sun (A) 600km (B) 650km (C) 648.6km (D) 648km 7. An arc PQ of length 20cm is marked on a circle of radius 6cm, find the area of the sector binded by this arc and the radius (A) 55cm2 (B) 60cm2 (C) 58.6cm2 (D) none of the above 8. Simplify sin75 (A) (√2 +√6)/ 4 (B) √2 + √6 (C) √6/ 4 (D) √2 9. Find the value of sin (𝛼+𝛽) without using table if sin 𝛼 = 3/5 and tan 𝛽= 5/1 and 𝛼 and 𝛽 are acute (A) 56/65 (B) 50/65 (C) 55.5/65 (D) 55/6 10. Factorize 5x2 + 9x + 4 (A) x = -4/5 or x=-1 (B) x=4/5 or x=1 (C) x=4/5 or x = -1 (D) x= -4/5 or x = 1 11. Find “a” if the equation has equal root (5a + 1)x2 – 8ax +3a = 0 (A) a = 0 or a = 3 (B) a= 0 or a = 2 (C) a=0 or a = 1 (D) a= 0 12. Find the values of “p” for which the equation (4p + 1)x2 + ( p + 3)x + 1 = 0 (A) p = 5 + 2√𝟓 or p = 5 - 2√𝟓 (B) p = 5 or p = 2 (C) p= √5 + 5√5 or p = 2 (D) none of the above 13. Find the value of K for which d roots of the equation is x2 – (4 + k)x + 9 = 0 (A) K ≤ −𝟏𝟎 or K ≥𝟐 (B) K ≤ 10 or K ≥2 (C) K ≤ 10 or K ≥−2 (D) K ≤ −10 or K ≥−2 14. If 𝛼 and β are roots of the equation 3x2 -7x – 1 = 0 find the value of (α + β)2 PREMIER  SEN. PREMIER (A) 61/9 (B) -61/9 (C) 9/61 (D) -9/61 15. If 𝛼 and β are roots of the equation 3x2 -7x – 1 = 0 find the value of α2+ β2 (A) 61/9 (B) -61/9 (C)55/9 (D) -55/9 16. Find the value of (1.02)8 correct to 5 decimal place using the first five terms of the expansion (1 + 8)8 (A) 1.02766 (B) 1.0277 (C) 1.028 (D) 1.03 17. Find the value of x for the expression (2x + 5)/(x2 –x – 6) does not exist (A) x = -3 or x = -2 (B) x = 3 or x = -2 (C) x = 3 or x = 2 (D) x = 2 or x = -3 18. Calculate “a” if the coefficient of x3 in ( a + 2x )5 is 320 (A) a = 2 (B) a= 3 (C) a = 4 (D) a = 1 19. Find the coefficient of x8 in the expansion of (2x – 5)10 (A) 288 (B) 288000 (C) 28800 (D) 2880 20. Find the 40th term of the linear sequence 6, 11, 16, 21 …… (A) 200 (B) 201 (C) 202 (D) 203 21. The 4th term of an AP is 15, the 9th term is 35. Find T15 (A) 56 (B) 57 (C) 58 (D) 59 22. If 8, x, y, z and 20 are in AP. find x, y and z (A) x = 11, y = 14, z=17 (B) x = 10, y = 13, z= 16 (C) x = 14, y= 17, z = 11 (D) x = 17, y= 14, z = 10 23. Find the value of x given that x+1, 2x , 2x + 3 are consecutive terms of AP (A) 4 (B) 5 (C) -4 (D) -5 24. The sum of nth term of a GP is for r < 1 is given as (A) a(1 – rn )/1-r (B) a(1 – rn )/r – 1 (C) (1 – rn )/1-r (D) a(1 – rn )/r 25. The third term of a G.P is 63 and the 5th term is 567. Find the sum of the 6th term of the progression. (A) 2550 (B) 2548 (C) 2540 (D) 255 26. Let p = { 1,2,3,4,5,6} and Q = { 2,4,6,8,10}. Find p – q (A) { 1,5,4} (B) { 1,3,5} (C) {1,3,8 } (D) { 1, 3, 2} Use the following information to solve question 27 and 28 Z1 = 2 – 3i Z2 = 3 + 5i 27. Find Z1 – Z2 (A) -1 – 8i (B) 1 – 8i (C) -1 + 8i (D) 1 + 8i 28. Z1/Z2 (A) -19i/34 (B) 19i /34 (C) 18i/34 (D) -18i/34 29. Determine the complex no Z which satisfies Z( 3 + 5i) = -1 – i PREMIER  SEN. PREMIER (A) -8/34, 2i/34 (B) 8/34, -2i/34 (C) 8i/34, 2/34 (D) 2i/34, 8/33 30. Express Z = 1 + i in polar form and argand form (A) √2 (cos45b+ isin45), [ √2, 45] (B) (cos45b+ isin45), [ √2, 45] (C)2 (cos45b+ isin45), [ √2, 45] (D) none of the above 31. A sequence in which each term is obtained by and addition of a constant number is ……? (A) Arithmetic progression (B) Arithmetic mean (C) Geometric progression (D) Geometric Mean 32. Given that A= { a, b } and B= { c, d}, what is n(A X B)? (A) 4 (B) 6 (C) 8 (D) 10 33. The third term in the expansion of ( 2x – 3)5 (A) -72x2 (B) 720x3 (C) 72x3 (D) -720x2 34. The equivalent of 2 + 2√3i is ……? (A) 60o (B) -4e pie/3 (C) 4e pie/3 (D) 4(cos + isin) 35. …… is the conjugate of complex number 3–i ? (A) 3+i (B) -3-i (C) –i–3 (D) -3+i 36. The symbol Z+ denotes a set of ……? (A) real numbers (B) odd numbers (C) integers (D) natural numbers 37. If A= { 1, 2, 3, 4, 5 }, B= { 2, 3, 5 }, what is B/A ? (A) {1,2} (B) {2,3,5} (C) { } (D) {0} 38. In a sequence given by Tn = a+bn, the 7th and 15th terms are 19 and 43 respectively. Find the values of a and b. (A) 3,2 (B) 2,-3 (C) -2,3 (D) 3,-2 39. In the faculty of physical sciences, there are 100 students. 85 offered MAT111 and 75 offered MAT115. How many students offered both courses? (A) 50 (B) 60 (C) 70 (D) 80 40. If 𝛼 and 𝛽 are the roots of the equation Px2 = q, what is 𝛼+𝛽? (A) p (B) –q (C) 0 (D) –q/p 41. The sum of the first eight terms of a G.P is five terms the sum of the first four terms. Find the common ratio. (A) 1 (B) 2 (C) ½ (D) 0 42. What is the 2 geometric mean, if there are 3 geometric means between 2 and 32? nd (A) 8 (B) 4 (C) 2 (D) 16 43. Find the value of m for which the equation (x-2) (x-3)=m has roots which differ by 1. (A) 3 (B) 2 (C) 1 (D) 0 44. The sum of odd numbers between 1 and 20 is ……? (A) 1533 (B) 1023 (C) 1534 (D) 1024 45. The sum of even numbers between 2 and 20 inclusive is …...? (A) 100 (B) 40 (C) 110 (D) 120 46. In a class of 24 students, 19 drink coke, 7drink Fanta, 4 drink both coke and Fanta. How many do not drink coke or Fanta? (A) 4 (B) 3 (C) 5 (D) 6 47. If P and Q are the roots of the quadratic equation 2x2 -2x +1. Find the value of P3+Q3 (A) 3/2 (B) 1 (C) -1/2 (D) ½ 48. If Z = 3+4i, what is ModZ? (A) 3 (B) 5 (C) 7 (D) 9 49. The first term of a G.P is a and the sum to infinity is a2. What is the common ratio? (A) 1/a (B) a (C) a-1 (D) a-1/a 50. For what values of P will the equation x2-2px + p+2 = 0? (A) 1 or 2 (B) -1 or -2 (C) -1 or 2 (D) 1 or -2 51. Find the sum of the 1st 20th of 2+5+8+… PREMIER  SEN. PREMIER (A) 580 (B) 610 (C) 270 (D) 330 52. solve Z+Zi if Z = 3+5i (A) 9 (B) 3 (C) 12 (D) 6 53. find the sum of the first 2n terms of the series 2+3+4+5+6+7+… (A) (2n+3)n-1 (B) 3n +21-n (C) n(2n+3) (D) n-2(n) 54. If 2, x, y, -250 is a G.P. find x:y (A) 2:5 (B) -1:5 (C) 5:4 (D) 5:0 55. Find the sum to infinity 3+2+4/3+8/9+16/2+… (A) 27 (B) 16 (C) 1/3 (D) 9 56. what is the coefficient of x2 in the expansion of (x+1/2)8 (A) 213x6 (B)28x6 (C) 7x6 (D) 81x6 57. The equation 2x2+ (k+3)x +2k=0 has equal root. Find the values of the constant k (A) 3 (B) 1/3 (C) 1 or 9 (D) none 58. Express pie/4rad in degree (A) 90o (B) 30o (C) 60o (D) 45o 59. Express 2pie/3rad in degree 3asfv (A) 120o (B) 90o (C) 270o (D) 60o 60. Express pie/6 rad in degree (A) 45o (B) 60 (C) 30 (D) 90 61. If 𝛼 and 𝛽 are the roots of the quadratic equation 3x -4x +5 =0. Find the value of 𝛼/𝛽 + 𝛽/𝛼 (A) 3/5 (B) 16/9 (C) -14/15 (D) -3/5 62. If the roots of 2x2 + 5x + 3 =0 are 𝛼 and 𝛽. What is the value of 𝛼2 + 𝛽2 (A) 4/13 (B) 14/17 (C) 13/4 (D) 17/14 63. In a science class of 42 students each student offers at least one of Maths and Physics, if 22 students offer Physics and 28 students offer Maths. Find how many students offer Physics only? (A) 19 (B) 14 (C) 21 (D) 20 64. Four members of a school first eleven cricket team are also members of the first four fourteen Rugby team. How many boys play for at least one of the two teams? (A) 19 (B) 14 (C) 21 (D) 20 65. To what sum to infinity will 0.03 be expressed (A) 3/90 (B) 8/90 (C) 7/90 (D) 11/90 66. The first four term of a G.P series are 2 and 2048 respectively. The sum of the series is 1024. Find the number of terms (A) 11 (B) 4 (C) 6 (D) 7 67. The first term of an A.P is 7, the last term is 70 and the sum of term is 385. Find the number of terns (A) 8 (B) 10 (C) 12 (D) 6 68. If x+1, 2x-1, and x+5 are in A.P. find the value of x (A) 4 (B) 9 (C) 16 (D) 8 69. If x+2, x+3, and 2x2+1 are 3 consecutive term of an A.P. find the possible values of x (A) ½ or ¾ (B) +-3\2 (C) 3\2 or -1 (D) +-1\2 70. Find the sum of the first 10th term of 1/8, ¼, ½ in G.P (A) 1025/8 (B) 527/8 (C) 548/8 (D) 610/7 71. Two or more set having element in common are said to be ……? (A) trivial (B) Disjoint (C) empty (D) none of the above 72. Express Z=-√3 + i in it polar form (A) {2, 6/5pie} (B) {4, 5/6pie} (C) {2,5/6pie} (D) 2cos5/6 PREMIER  SEN. PREMIER 73. Find the sum and of the roots of the quadratic equation 3x2-2=3/2x (A) -3/2 (B) 2/3 (C) 3/2 (D) -1/2 74. Find the quadratic equation whose root are -7 and 13/3 (A) 3y2-8y-91=0 (B) 3y2-8y+91=0 (C) 3y2+8y-91=0 (D) 3y2 -91y+8=0 75. Find the quadratic equation whose root are 5 and 3½ (A) 2y2-3y+35=0 (B) 2y2+3y-35=0 (C) 2y2-3y-35=0 (D) 2y2-+3+y35=0 76. Find the quadratic equation whose root are 4 and -5½ (A) 2y2-3y+44=0 (B) 2y2+3y-44=0 (C) 2y2-3y-44=0 (D) 2y2-+3y+44=0 77. Find the sum of the roots of the quadratic equation 5x2-3=2x (A) 2/5 (B) 5/2 (C) 2\3 (D) 3/2 78. Find the product of the roots of the quadratic equation -7x -2 = ¼x2 (A) 1/-8 (B) 1/8 (C) 8 (D) -8 79. Find the sum and the product of the roots of the quadratic equation 7x2+4=5x (A) 5/7 and 7/4 (B) 5/7 and 4/7 (C) -5/7 and 7/4 (D) 5/7 and -4/7 80. In a college of 400 students every student read 5 newspapers and every newspaper is read by 80 students. The number of newspaper is ……? (A) 25 (B) at most 20 (C) at most 25 (D) at least 25 81. If A and B are two sets then B – (B-A) (A) (A-B)-B (B) A-(A-B) (C) AnB (D) B 82. If n(A) =3, n(B)=5 and n(AnB) = 2, then n[(AXB)n(BXA)=? (A) 5 (B) 3 (C) 4 (D) 6 83. simplify cos150 (A) (√6 +√2)/ 4 (B) √2 + √6 (C) √6/ 4 (D) √2 84. Find the value of x for the expression x/x2-25 does not exist (A) 6 (B) 5 (C) 50 (D) 25 85. Find the Arithmetic mean of 4&18 (A) 12 (B) 2 (C) 11 (D) 6 86. Insert three A.M between 19&35 (A) 24, 27 & 31 (B) 23, 27 & 32 (C) 27,24 & 30 (D) 23, 27 & 31 87. Insert two Geometric mean between 12 and 324 (A) 36, 106 (B) 36, 108 (C) 37, 106(D) 37, 108 88. T2 of a G.P is 35 and the T4 is 875, Find a. (A) 7 (B) 6 (C) 5 (D) 4 89. Find three number in A.P whose sum is 3 and whose product is -15 (A) 5,-1,3 (B) 5, -1, -3 (C) 5, 1, -3 (D) -5, 1, 3 90. The first term of an A.P is 7, the last term is 70 and the sum is 385. Find the numbers of terms in the series and the common difference (A) n =10 and d=7 (B) n=7 and d=10 (C) n=-7 and d=10 (D) n=7 and d=-10 ANSWERS ARE PROVIDED IN THE OPTIONS WITH BOLD LETTERS (PREMIER – 08138361397) PREMIER  SEN. PREMIER PREMIER