Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. If find|AB| -12 12 11 -11 2. Find ∫cos2x cos 3x dx -1/10 sin 5x + 1/2 sinx + C 1/10 sin 5x + 1/2 sinx + C 1/10 sin 5x + C 1/10 sin 5x + 1/2 cosx + C 3. Solve the following equation for x 0, 3a 2a, 4a² 0, 4a 1, 2 4. A boy pulls a nail from the wall with a string tied to the nail. The string is inclined at an angle of 60° to the wall. If the tension in the string is 4N, what is the effective force used in pulling the nail? 2√3N 2N 8N 4√3N 4N 5. If (x-3) and (x+5) are factors of the expression x³ + mx² - nx - 45, what is the product of m and n 55 45 67 35 6. Which of the following pairs of graphs cannot be used to find the solution to the cubic equation x³ -3x² + 3x - 9 = 0 ? y = x² - 3x + 3and y = 9/x y = x³ -3x² + 3x and y = 9 y = x³ -3x² and y = 3x - 9 y = x³ and y = 3x² - 3x + 9 7. 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 N45,830 N10,392.30 N453,083 N5,083 8. P is a probability function of an exhaustive set S = {w, x, y, z}. If P(x) = 1/4, P(y) = 1/3, P(z) = 1/6, then P(w) is 1/12 1/72 1/4 3/4 9. Solve the following equations: 3x + 4y + 2z = 4 x - 5y + 3z = -1 2x + 3y + z = 3 x = 2, y 0, z = 1 x = 8, y= 5, z = 4 x = 0, y = 6, z = 4 x = 5, y = 6, z = -3 10. Find the value of tan (-84)° -0.294 -9.514 9.514 0.249 11. If sinθ = -5/13, where θ is an angle between 270° and 360°, calculate , without using mathematical tables, the values of cos3θ 2/3 828/2197 234/6445 22/754 12. The line 3y - x = 7 makes an angle of θ with the positive x-axis. Find the value of sin θ. 3√10 3/7 √10/10 1/3 3√10/10 13. Cards are drawn from a pack of 52 playing cards one at a time. Calculate the probability of drawing without replacement 3 diamonds 1/34 11/850 1/52 15/769 14. If x is positive, and the standard deviation of x-1, x+1, 3, 2x-1 and x+3 is 2√2, find the value of x and hence calculate the mean deviation x =4, M.D= 2.4 x =6 , M.D = 2.4 x= 4.3, M.D = 3 x=6, M.D = 4.2 15. Find the tension T in the figure below if the system is in equilibrium. 100N/√3 200N/√3 100N 300N/√3 16. Find the force parallel to the slope required to move a body of mass 2kg up a slope inclined at 30° to the horizontal with an acceleration of 2m/s² if the frictional force between the two surfaces is 10N. 10N 14N 20N 24N 17. Without using tables, evaluate (0.027)-1/3 x (0.09)3/2 0.03 0.3 0.09 0.9 18. Given thatFind the values of x for which |A| is zero. -4, 4 4, -2(twice) -2, 3 2, 3(twice) 19. Divide (2x³ - xy² + y³) by (x + y) 2x² - y² 2x² + 2xy + y² 2x² - 2xy + y² 2x² - 2xy 2x² + xy 20. The velocity of a particle, v m/s, after t s is given by v = t² + 5. Find the distance travelled at the end of 3 s. 18 m 3 m 48 m 24 m 21. In a triangle PQR, <PQR = 60°, PQ = 3 cm and QR = 4 cm. Find |PR| 2√3 cm 5 cm √13 cm 2√5 cm 22. Simplify: sec x cot x cosec x tan x 23. Differentiate the function wrt x:y = √x 1/2√x √x 2√x x² 24. The value of x which satisfies the equation is 1/2 2 -2 -1/2 25. A straight line y = ax intersects the parabola y = x² -5x + 6 at points P(1,2) and Q(m,n). The values of m and n are (3, 6) (-2, -4) (6, 12) (-1, -2) 26. Divide 2x³ + 11x² + 17x + 6 by 2x + 1 x²+5x+6 2x+1 x²+7x-2 7x-2 27. Differentiate the function wrt x: 2(x - 1/x²) 1/x² x²+2 2-3x² 28. Determine the order of the matrix: 2x3 2x4 2x2 1x2 29. Evaluate: log327 + log36 – log354 1 2 0 -21 1/3 30. A body of mass 4kg is on the point of slipping down a plane which is inclined at 30° to the horizontal. What force, parallel to the plane, will just move it up the plane? (g = 10m/s²) 5N 40N 8N 80N 31. The quadrants where abcissa and ordinate have different signs are? 2nd & 3rd quadrant 1st & 2nd quadrant 2nd & 4th quadrant 1st & 3rd quadrant 32. The expressionis equal to 3/2 9/4 2/3 4/9 33. find x and y, respectively 2, 9 2, 8 6, 9 2, 7 34. Differentiate the functions wrt x:5(3x-4)² 60x+4x² 3x²+4 60x² 30(3x-4) 35. The 2nd and 5th terms of a G.P are 2/3 and 1/12 respectively. The 1st term is 1/2 7/3 4/3 5/3 36. Change the given exponential expressions into logarithmic expressions: x2 = a a = log a a = log x (2) 2 = log x (a) 2 = log x 37. Find the value of cos (-45)° 0.4335 0.7071 -0.7071 0.8712 38. The marks scored by students in a test are recorded in the table belowCalculate semi interquartile range 3 1 0 2 39. Determine the order of the matrix 2x4 3x4 1x2 3x3 40. Find the x intercept of the graph of y = 2 log( √(x - 1) - 2) 13 10 11 12 41. In the diagram below, the resultant force along the x-axis is 14.02N 19.92N 13.46N 11.46N 42. An arithmetic sequence has five terms between 2 and 20. Determine the fourth term of the sequence. 8 18 12 14 11 43. The common ratio in the G.P log 2, log 4, log 16, ... is 2 4 3 log 2 44. Solve the equation 4 + 7cosx = 0 for 0° ≤x≤ 360° 34° 124.8° 91° 221° 45. Change the given logarithmic expressions into exponential expressions: logb (2x + 1) = 3 2x + 1 = b³ a = x c 2x³= b+ 1 a = x³ 46. The magnitude of the resultant of mutually perpendicular forces F1 & F2 is 13N. If the magnitude of F1 is 5N, what is the magnitude of F2 12N 18N 8N 2.6N 47. During the same interval, it is observed that a train travels the same distance as does a lorry. The two vehicles therefore have the same uniform acceleration initial velocity instantaneous velocity average velocity average speed 48. The diagram shows a uniform meter rule AB which balances horizontally at the 90cm mark when a mass of 0.2kg is suspended from B. Calculate the mass of the meter rule 0.05kg 1.00kg 1.20kg 0.80kg 0.20kg 49. Differentiate wrt x:x³(x - 1) 3x+2 (x²+2)x x³ + 3x²(x-1) 1+x² 50. The nth term of the A.P 10, 3, -4, ... is 17 - 7n 18 - 7n 16 - 7n 18 + 7n 51. Differentiate the function wrt x:y = x³(x²-3x+1) x²(5x²-12x+3) x²(x+3) 5x x+12 52. 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 all three balls are the same colour is 4/455 2/91 4/91 34/455 53. Given that find the value of x that satisfiesx + y -2z = 1, x+z = -1 and 2x -2y + z = 1 0 -1 2 1 54. Determine the equation of a line that cuts the y-axis at -3 that is parallel to the line with equation 3x - 2y = -5 3x - 2y = 6 2y - 3x = 6 2y + 3x = -6 x - 3y = -9 55. The gradient of a curve which passes through the point (1, -5) is given by 4x. Determine the equation of the curve. y = -2x² - 7 y = -2x² + 7 y = 2x² - 7 y = x² - 14 56. Solve the equation 4 sin x = -1 for 0° ≤x≤ 360° 23 244.2 194.5 73.4 57. A 1000kg elevator is descending vertically with an acceleration of 1m/s². If the acceleration due to gravity is 10m/s², the tension in the suspending cable is 1.0N 11000N 10N 9000N 58. Expand completely (1 - 3x)5 in ascending powers of x. 1 - 15x + 90x² + 270x3 + 405x4 - 243x5 1 - 5x + 67x² + 270x3 + 405x4 - 243x5 1 - 5x² + 270x3 + 405x4 - 243x5 1 - 5x + 67x² + 270x3 59. Given thatEvaluate |A| x³ + 24 x³ - 24 x³ + 12x + 12 x³ - 12x - 16 60. Find the value of x if1/2 log10x = 1 0.01 √10 100 1/√10 1 out of 60 Time is Up! Time's up