Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Simplify: (9^{-1/2 }× 81^{3/4}) ÷ (9^{1/2}) 3 1/3 1/9 1 9 2. By solving equation √x + 3 = 0, value of 'x' will be 9 -9 3 -3 3. If (sec θ + tan θ)/(sec θ - tan θ) = 209/79, find the value of θ. 21 31.23 26.83 23.45 4. Evaluate: 81^{-1/4 } × 36^{1/2 }×10^{0} 2 1 3 0 10 5. 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 6. Two of the angles of a triangle are 120° and 45°. If the side facing the angle 45° is 10cm long,then the side facing the angle 120° is 10√2 cm 5√3 cm 5√6 cm 20 cm 7. A G.P has a common ratio of 3.If the difference between the 1st term and 5th term is 160, the 5th term is 160 120 180 162 8. Without using tables, evaluate (0.027)^{-1/3} x (0.09)^{3/2} 0.3 0.03 0.9 0.09 9. Find n if 9^{1+n }x 3 = 27^{-n} -3/5 3/5 1/3 -1/3 10. The values of tan 225° and tan 315° are respectively -1 and 1 1 and 1 1 and -1 -1 and -1 11. The value of is -2 0 2 1 12. Evaluate: 12/7 12/5 1/2 14/3 13. Find the derivative of f(y) = 2-2yy³ 2y-4y-³ 4y y-2 14. Find the values p and q in the arithmetic progression -12, p, q, 18, ... 1, 11 -1, 8 -2, 8 0, 9 15. A body is projected from a point O in a straight line with an initial velocity of 10 m/s. If the acceleration is 5t² + 3t, find the velocity after 3 seconds. 60 m/s 48 m/s 58.5 m/s 68.5 m/s 16. Given that 2sin(θ-45°) = cos(θ+45°),find the value of tanθ 1/2 1 0 -1 17. If log_{4}p + log_{4}q^{2 }= 0, then p is given by 2/q 1/q q/2 q 18. Determine the order of the matrix: 2x3 2x2 1x2 1x1 19. If the point (m, -n) lies in the second quadrant, which of the following is true? m > 0, n < 0 m 0 m < 0, n < 0 m > 0, n > 0 20. Find ∫ sin x cos 3x dx 1/8 cos4x + 1/4 sin2x + C -1/8 cos4x + 1/4 cos2x + C 1/4 cos2x + C -1/8 cos4x + 1/4 sin2x + C 21. If sin θ = x, the value of tan θ for 0° < θ < 90° is 1-x x/√(x²-1) x/x-1 x/√(x²-1) 22. If sinθ = -5/13, where θ is an angle between 270° and 360°, calculate , without using mathematical tables, the values of sin2θ 2/5 169/120 120/169 -120/169 23. If (3/4)^{m} (2/3)^{n } = 32/27, then find the values of 'm' and 'n'. 2, -2 -2, 1 1, 2 2, -1 2, 2 24. A body starting from the origin O moves in a straight line, and its velocity, v m/s, after t s is given by v = 12 + 20t - 3t². Calculate the distance moved by the particle in 2 s. 56 m 44 m 32 m 78 m 25. The maximum value of the function g(x) = -x² - 6x + 10 is 19 4 1 -3 10 26. In the diagram below, MN is perpendicular ON and MP. What is the difference between the moment about N of the force 20N, applied along MP and its moment about O? 4Nm 8Nm 0Nm 6Nm 2Nm 27. Use the product rule to differentiate wrt xx³(2x+5)³ 10x(2x+5)² 2x+20 3x²(4x+5)(2x+5)² 4x+5 28. Find the value of x if log_{4}x = 3.5 256 14 64 128 29. Two events M and N are mutually exclusive and P(M) = ¼ and P(N) = 2/3.P(M∪N) is 1/2 1 1/12 11/12 30. Ifis a symmetric matrix, find x 4 5 2 3 31. Find the value of x such that the points (0, 2), (1, x), and (3, 1) are collinear 5/3 2/5 3/5 5/2 32. Using the product rule differentiate wrt x(3x + 4)(x - 3) x²+12 9x-12 6x-5 6x² 33. Find the differential coefficient of y = -5/(x²+4) at the point (1, -1) 5/2 -2/5 -5/2 2/5 34. The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the distance traveled by the body between the two instants at which the acceleration is zero 34/3 m 56 ,m 123 m 184/3 m 35. Subtract the polynomials: (-x^{2} + 5 x) - (6 x^{2} + x - 2) -7x²+4x+2 5x²+6x 5x²+6x-2 -5x²+6x+2 36. Differentiate w.r.t x sin³x -3cos²xsinx 3sin²x -3sin²xcosx 3sin²xcosx 37. If 5 cot θ = 3, find the value of (5 sin θ - 3 cos θ)/(4 sin θ + 3 cos θ) 16/35 13/48 13/46 16/29 38. Given that I is a (2x2) unit matrix and If BA = I, where B is a (2x2) matrix, deduce that B may be expressed in the form αA + λI, stating the values of the constants α and λ, respectively 1/5, - 4/5 - 1/5, 4/5 2, 5 -1, 4 39. Calculate the apparent weight loss of a man weighing 70kg in an elevator moving downwards with an acceleration of 1.5m/s². (g = 10m/s²) 581N 105N 686N 595N 40. 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 41. If sinθ = 1/2 and 0° < θ < π/2, evaluate √3/2 4/√3 √3/4 4√3 42. Find the determinant of the matrix 3 4 4.2 5 43. If sin p = 3/5, where 0° < p < 90°, find the value of 1 2 7 0 44. Find the equations of the straight lines passing through the point (2, -1) and the gradient 2 y = 4x + 9 y = 2x - 5 y = x +1 y = x + 7 45. Find the mean and mean deviation, respectively of the following 5, -3, 6, -2, 4, -8, 4, 7, -10, 10 2.3, 4.64 1.3, 5.64 3.3, 3.64 4.3, 2.64 46. Find the angles between 0° and 360° whose sine is 0.4226 25° 422.3° 113° 324° 47. Find m if: 9^{(m + 1)} × 3 = 27^{-m} 1/3 -1/3 3 -3/5 3/5 48. Using the trapezoid rule with five ordinates at x = 1, 2, 3, 4, 5, estimate the value of 13 sq. units 12 sq. units 11 sq. units 10 sq. units 49. Write the value of the angle in surd form sin 240° √2 -√3/2 -√2 √3/2 50. Find a positive angle between 0° and 360° that is equivalent to -74° 286° 462° 336° 125° 51. If a = x^{1/n}, log_{a}x^{n} is n-² n n² n-¹ 52. Find the minimum value of the function3x²-x³ 2 0 -1 1 53. Solve for x the equation ln (x - 1) + ln (2x - 1) = 2 ln (x + 1) 4 -4 -5 5 54. Without using tables or any calculating device find the value of√2/2 cos15° + √2/2 sin15° √2/5 √2/2 √2 √3/2 55. Iffind dy/dx (x+1)³ (x-1)³ 1/(x+1)³ 1/(x-1)³ 56. 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. 1/2s, 2.4s 3s, 5s 0s, 4s -2s, 9s 57. The twelfth term of the sequence (x - a), x, (x + a), ... is x + 11a x + 10a x + 9a x + 12a x - 12a 58. P = and Q = If PQ =Find (a, b) (1, 2) (1/2, 1/3) (4, 7) (2, 3) 59. Two matrices P and Q are given by P = (x, y), Q =where x ≠ 0, y ≠ 0.Given that PQ =λP, where λ is a scalar, obtain the roots of the equation inλ² -6λ + 5 = 0 1 or -5 -3 or 5 1 or 5 2 or 7 60. A mass of 2kg on a surface (μ = 1/2) is connected to a second mass of 4kg over a frictionless pulley as shown in the diagram. If the acceleration due to gravity is 9.8m/s², then the masses will accelerate at 39.2m/s² accelerate at 4.9m/s² remain stationary accelerate at 19.6m/s² accelerate at 9.8m/s² 1 out of 60 Time is Up! Time's up