Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curve y = 3x³ + x² + 5x + 25 y = 3x³ + x² + 5x - 25 y = 3x³ + 5x - 25 y = x² + 5x - 25 None 2. If y = x³ + 3x², find 2(dy/dy) - x(d²y/dx²) 4x 6x 5x 2x None 3. Evaluate 3 log√2 + log√3 - log√6 log√2 log 3 log 6 log 2 None 4. Find the derivative of y = sin(2x³ + 3x - 4) wrt x sin4x+x (6x²+3)cos(2x³ + 3x - 4) cos(2x³ + 3x - 4) 6xsin(2x³ + 3x - 4) None 5. Differentiate the function wrt x:y = x³(x²-3x+1) 5x x²(5x²-12x+3) x²(x+3) x+12 None 6. A bag contains 6 red balls, 9 blue balls and 5 green balls. Two balls are chosen one after the other with replacement. What is the probability that they are of the same colour? 9/100 27/100 71/100 19/100 None 7. If x² - 5x + 6 = (x-a)² + b, what is the value of b? 3 - 2 0 -1/4 5/2 None 8. Change the given exponential expressions into logarithmic expressions: x^{2} = a a = log a 2 = log x (a) 2 = log x a = log x (2) None 9. Factorize completely 3x^{3} + 4x^{2} – 13x + 6 completely, given that x-1 is a factor 3x+1 (x-1)(x+3)(3x-2) (x+2)(3x-1) 2x-5 None 10. Determine the order of the matrix: 2x2 2x3 2x4 1x2 None 11. From the diagram shown below, if the forces are in equilibrium, what is the value of tension T? 241.42N 70.71N 50.00N 100.00N None 12. In the diagram below, the resultant force along the x-axis is 19.92N 14.02N 13.46N 11.46N None 13. If log 3 = 0.4771, and 10^{x }= 0.3, find x -1.4771 0.4771 0.5229 -0.5229 None 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 None 15. Find the value of x if 3 2 1/2 1 None 16. Add the polynomials: (-x^{2} + 5 x + 2) + (6 x^{2} + x) 5x² 5x²+6x+2 5x²+6x 7x²+6x+2 None 17. If y = 2xcos2x - sin2x, find dy/dx when x = π/4 π/2 π/4 π -π None 18. Find the angles between 0° and 360° whose sine is 0.4226 25° 324° 422.3° 113° None 19. If sin p = 3/5, where 0° < p < 90°, find the value of 2 0 7 1 None 20. Solve the equation: 3y^{-2} = 4/27 81/4 4/81 2/9 9/2 81 None 21. Solve the equation: 9^{(1 + 2k)} = 81^{(2 + k) }/ 3^{k} 6 4 -6 2 -4 None 22. Evaluate:∫ 1 / x²(1-4x) 4(x / 1-4x) + C Inx + C C 4In(x / 1-4x) - 1/x + C None 23. Evaluate:log √40 + log √2 - log√8 2 0.5 1 √10 None 24. The marks scored by students in a test are recorded in the table belowCalculate semi interquartile range 2 3 1 0 None 25. The length of each of a metal cube increases at the rate of 0.025cm²s-¹ when heated. Find the rate of increase in cm²s-¹ of the total surface area of the cube, when the length of each side is 6cm 1.5 1.8 1.6 1.0 None 26. Evaluate the definite integral: 456.43 324.87 2456.63 1658.57 None 27. The seventh term of the G.P 16/9, -8/3, 4, ... is 81/4 16 -32/3 -9/2 None 28. Evaluate: 124/3 123/3 11/2 19/3 None 29. Find the value of x if log_{3}x^{2} = -4 1/√3 9/16 1/9 3/4 None 30. The 2nd and 9th terms of an A.P are 391 and 328 respectively. The 7th term is 346 373 355 400 None 31. Solve the equation:(log_{3}a) – 6log_{3}a + 9 = 0 27 9 81 18 None 32. 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 3g/4 g 2g/5 g/2 8g/25 None 33. 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 M1 / M2 M2g / M1 M1g / M2 M2 / M1 None 34. Given thatwhere A and B are constants, find the value of (A + B) 3 2 1 4 None 35. An object dropped from rest has position s = 7t² metres below its starting point. At what time does the object have velocity of 35 m/s. 3 s 14 s 2 s 2.5 s None 36. Differentiate the function wrt x:7x + √x³ 7√x x³ 7 + 3√x/2 4 + √x None 37. Find the point (x, y) on the Euclidean plane where the curve y = 2x² -2x + 3 has 2 as gradient (1, 3) (5, 7) (2, 9) (3, 4) None 38. If cos θ = sin 50°, then θ is 45 degrees 90 degrees 50 degrees 40 degrees None 39. Find, without using mathematical tables, the value ofcos30°sin120° + sin30°cos120° 0 2 1/2 1 None 40. The velocity of a particle is given by v =3t² + 8t. Find the distance travelled by the particle between t = 3 s and t = 5 s. 224 m 144 m 162 m 158 m None 41. The sine, cosine and tangent of 240° are, respectively 0.866, -1/2, 1.732 -0.866, -1/2, 1.732 -0.866, 1/2, -1.732 0.866, 1/2, 1.732 None 42. Find a positive angle between 0° and 360° that is equivalent to -250° 283° 110° 34° 74° None 43. Use Bionomial Theorem to find the first three terms in the expansion of (1 + x)^{15} 45 + 46x² +342x³ 2 + 45x + 735x² 3x+ 536x³ 1 + 15x + 105x² None 44. Find the gradients and the intercepts on the y- axis for 5x = 6y m = 1, c = -1/2 m = 5/6, c= 0 m = 1/6, c= -1 m = -1, c= -1 None 45. If f(1/x) = x² - 2x + 3, then f(2) = 2 1/2 9/4 3 3/2 None 46. Differentiate the functions wrt x:(x-2)(3x+5) 4x+4 3x² 6x-1 3x+2 None 47. Evaluate: (3^{0 }- 9^{-1/2})^{-3} 3/2 2/3 27/8 1/9 None 48. Simplify without calculator: ((3^{-1} - 9^{-1}) / 6)^{1/3} 1/7 1/2 1/3 1/9 None 49. Solve for y: 27^{y/2 }= 3^{3/4} × 9^{-1/4} 1/6 3 1/3 1/2 6 None 50. Find the value of x for which 3^{2x} + 6(3^{x}) = 27 -3 1 3 -1 None 51. The graph of the polynomial y = a x^{ 4} + b x^{ 3} + c x^{ 2} + d x + e is shown below. Find the coefficients a, b, c, d and e. a = -1 / 7, b = 1, c = 1, d = 0, e = -4 a = 8, b = 0, c = 1, d = 10, e = 2 a = -18, b =4, c = 14, d = 0, e = -2 a = -1 / 8, b = 0, c = 1, d = 0, e = -2 None 52. Find the derivative of f(y) = 2y-4y-³ 2-2yy³ y-2 4y None 53. If tanx = 12/5, find the value of sinx, 0° ≤ x ≤ 90° 22/45 17/18 12/13 2/3 None 54. Simplify without calculator: log_{6}(216) + [ log(42) - log(6) ] / log(49) 5/2 1/2 3/2 7/2 None 55. A bowl contains two white, one blue and two red balls. A ball is drawn randomly from the bowl, replaced and another ball is drawn. What is the probability that exactly one of the balls is white? 6/25 36/225 2/5 12/25 216/225 None 56. Simplify:log_{5}25^{x }- log_{5}(0.04) 2x+1 2x-2 2x+2 x/2 None 57. If Find |M| 11 12 10 17 None 58. A force of 16N is applied to a 4kg block that is at rest on a smooth horizontal surface. What is the velocity of the block at t = 5s? 10m/s 20m/s 50m/s 80m/s 4m/s None 59. Find the value of θ (0° ≤ θ ≤ 90°), when sin^{2} θ - 3 sin θ + 2 = 0 60° 80° 90° 70° None 60. Two forces 3N and 4N act on a body in directions due north and due east respectively. Calculate their equilibrant. 5N, 53° west of south 5N, 53° east of north 7N, 37° west of north 5N, 37° north of east 7N, 37° south of west None 1 out of 60 Time's upTime is Up!