Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Solve for x0.01 ^{x} = 100 -1 2 0 1 2. Find m if: 9^{(m + 1)} × 3 = 27^{-m} 1/3 -1/3 3/5 3 -3/5 3. If log_{10}x = 0.5,the value of x is √5 5.0 √10 0.05 4. If f ( x+ 2 ) = x² + 3x + 1, then f ( -2 ) is 5 11 0 -1 1 5. A bag contains 6 red balls, 12 white balls and 9 green balls.A ball is selected at random. What is the probability that it is a red or green ball? 2/3 4/9 1/3 5/9 6. The gradient of a curve at any point (x,y) is 6x² - 6x + 11. If the curve passes through the point (3, 0), find its equation 3x²+11x-60 2x³-3x²+11x-60 2x³+11x-60 11x-60 7. If (2/3)^{a-1 }= 27/8, what is a? 2 -2 -4 6 8. Solve the equation: 4^{(w - 1)} × 5^{(2w - 2) }× 10^{w }= 1 4/3 5/4 3/4 1 2/3 9. In the figure below, the three forces F_{1 , }F_{2} & F_{3} acting at O are in equilibrium. If the magnitude of F_{1} is 10.0N and the magnitude of F_{2} is 5.0N; find the magnitude of F_{3} 15.0N 26.4N 13.2N 10.0N 10. If X = ( -1, 2 ) and Y = ( 0, 1 ), which of the following points lies on the line XY produced? ( 3, 4 ) ( 3, -2 ) ( 2, -2 ) ( -3, 4 ) ( 1, 3 ) 11. Tireni stands on a spring scale placed in a lift. The lift descends at constant velocity. As a result, the scale reads a weight of zero greater than the weight of Tireni by 1kg less than the weight of Tireni greater than the weight of Tireni the same as the weight of Tireni 12. The 8th term of the A.P. -4, -2, 0... is 12 -10 8 10 13. Factorize the polynomial x^{ 3} - 1 2x+1 (x-1)² x-1 (x - 1)(x² + x + 1) 14. The distance s metres travelled by a particle in time t seconds is given by s = 12 + 40t - 2t². Find the distance travelled by the particle before coming to rest. 120m 212m 180m 200m 15. The prices of computers in a catalogue are: N125,000, N99,000, N125,000, N120,000, N110,000, N115,000, N130,000, N120,000, N100,000.Calculate the standard deviation N5,083 N10,392.30 N453,083 N45,830 16. Given that k²= log_{2 }512, find k 3 4 5 2 17. Find the equation of the line passing through (2, -1) and parallel to the line 2x – y = 4. y = 5x-2 y = x+1 y = 2/ 5x-1 y = 2x-5 18. Two events M and N are mutually exclusive and P(M) = ¼ and P(N) = 2/3.P(M∪N) is 1/12 11/12 1 1/2 19. In the diagram below, the hanging mass M_{2} is adjusted until M_{1} is on the verge of sliding. The co-efficient of static friction between the mass M_{1} and the table is M2 / M1 M2g / M1 M1g / M2 M1 / M2 20. The integral values of z which satisfy the inequalitiy -1 < 2z - 5 ≤ 5 are 2, 5 2, 3, 4 3, 4, 5 2, 3, 4, 5 21. Which of the following have the same value as sin 15°?I. sin 165°II. sin 285°III. sin (-15°)IV. sin (-195°) I and II only III and IV only I and III only I and IV only 22. If x² > 4x - 3, then x 3 3 < x < 1 x < 1 x > 3 1 < x < 3 23. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s 23 m/s² 8 m/s² 18 m/s² 56 m/s² 24. The masses are hanging from a light rod 1.0m long as shown in the diagram below. To keep the rod horizontal, the mass of X must be 2.0kg 1.5kg 1.0kg 3.0kg 25. Find the derivative of <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #000000;font-family: Helvetica, Arial, Verdana, sans-serif;background-color: #ffffff" role="presentation" data-mathml="z=x(3x2−9)">z= x(3x²-9) 9x-9 3x² 6x²-3 9x²-9 26. Subtract the polynomials: (xy + 3x + 2) - (3x^{2} + y) 3x²+4xy+2 -3x²+xy+3x-y+2 -3x²+3x-y+2 27. What integral values of x satisfy the inequality-2 ≤ x < 2 ? -2, -1, 1, 2 -1, 0, 1 -2, 0, 1, 2 -2, -1, 0, 1 28. Find the values of x for whichis equal to zero 4 or 1/2 2 or 6 -3 or 5 4 or -3/2 29. A body of mass 10kg on a smooth inclined plane is connected over a smooth pulley to a mass of 15kg as shown. The acceleration of the system in terms of g is g 2g/5 3g/4 8g/25 g/2 30. Given thattanx = 5/12, what is the value of sinx + cosx? 17/13 13/17 17 13 31. Divide 2x³ + 11x² + 17x + 6 by 2x + 1 x²+5x+6 7x-2 2x+1 x²+7x-2 32. The maximum value of the function g(x) = -x² - 6x + 10 is 10 -3 1 4 19 33. Find the angles between 0° and 360° whose tan is -2.1445 124° 295° 23° 97° 34. Four books whose authors' surnames start with the letters A, J, P, and W are placed randomly on a shelf. The probability that the books will be arranged in the alphabetical order of the authors' last names is 1/4 1/6 1/24 4/18 1/12 35. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the origin, find the equation of the curve. y = x³ + 5x² y = x³ - 5x² y = 5x² - x³ y = 5x² + x³ 36. Three boys play a game of luck in which their respective chances of winning are 1/2, 1/3 and 1/4. What is the probability that one and only one of the boys wins the game? 11/24 16/19 12/21 1/2 37. If sinθ = -5/13, where θ is an angle between 270° and 360°, calculate , without using mathematical tables, the values of sin2θ 2/5 -120/169 120/169 169/120 38. Given thatwhere A and B are constants, find the value of (A + B) 4 2 1 3 39. Solve for x the equation 2 x b^{4 logbx} = 486 4 2 1 3 40. The 2nd and 5th terms of a G.P are 2/3 and 1/12 respectively. The 1st term is 5/3 4/3 7/3 1/2 41. If f(1/x) = x² - 2x + 3, then f(2) = 1/2 3 2 9/4 3/2 42. If y = log_{e}(1/x) find dy/dx 43. Find the value of sin 250° -0.9397 -0.4238 -0.2232 0.4328 44. The distance s metres after time t second covered by a particle moving along a straight line is given by s = t³ - t² - t - 2Find the average acceleration between t = 2 and t = 4 4ms-² 2ms-² 6ms-² 3ms-² 45. Evaluate : 6 2 1/3 1/2 46. Find the lower and upper quartiles for the set of numbers 4, 7, 8, 10, 12, 15, 17, 20, 26, 32, 40 8, 20 7, 32 7, 20 10, 20 8, 26 47. The values of tan 225° and tan 315° are respectively 1 and -1 1 and 1 -1 and -1 -1 and 1 48. The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the values of t at which the acceleration of the particle is zero. 0s, 4s 3s, 5s -2s, 9s 1/2s, 2.4s 49. The integral values of y which satisfy the inequality -1 < 5 - 2y ≤ 7 are -1, 0, 1, 2 0, 1, 2, 3 -1, 0, 1, 2, 3 -1, 0, 2, 3 50. Solve for a :27^{a/2} = 3^{3/4 }x 9^{-1/4} 6 3 1/6 1/3 51. If sinθ = -5/13, where θ is an angle between 270° and 360°, calculate , without using mathematical tables, the values of cos3θ 22/754 2/3 234/6445 828/2197 52. Using the product rule differentiate wrt x(x²+3)(2x-1) 6x+ 2 6x²-2x+6 x²+3x-1 2x² 53. Three balls are drawn one after the other, without replacement from a bag containing 4 blue, 6 white and 5 red identical balls.The probability that the three balls are: one blue, one white and one red is 4/91 16/225 8/225 1/3 54. Differentiate w.r.t x cos³x 3cos²xsinx 3sinx -3cos²x -3cos²xsinx 55. A box contains 5 blue balls, 3 black balls and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining one black and one red ball in any order 3/25 3/5 2/5 3/7 56. IfA = , write the value of det A x-y x+y 1 0 57. If the point (m, -n) lies in the second quadrant, which of the following is true? m 0 m > 0, n < 0 m > 0, n > 0 m < 0, n < 0 58. The value of (sin35°/cos 55°) + (cos 15°/ sin 75°) is -2 0 1 2 59. Which point is the reflection of the point (–7, 5) over the line y = –x? (7, -5) (5, -7) (-5, 7) (7, 5) 60. In the figure below, PT is a uniform meter rule pivoted at R, the 70cm mark. Two forces 0.1N and 0.4N are applied at Q, the 60cm mark and S, the 85cm mark. If the meter rule is kept in equilibrium by the forces and its weight, then the weight of the meter rule is 0.50N 0.35N 0.40N 0.25N 0.30N 1 out of 60 Time is Up! Time's up