Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Simplify : 1/3y 3y y/3 3/y None 2. If sin θ = x, the value of tan θ for 0° < θ < 90° is x/√(x²-1) 1-x x/√(x²-1) x/x-1 None 3. PQRS is a quadrilateral in which, PS is parallel to QR. PQ = 16cm, SR = 15 cm and angle QPS = 60° and angle PSQ = 44°.Calculate /QS/ 40 cm 30 cm 20 cm 50 cm None 4. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30). y = x³ + 2x² + 4 y = 6x² + 5x y = 2x³ + 5/2 x² + 4 y = 2x³ + 5/2 x² - 4 None 5. The weights to the nearest kg of a group of students are recorded in the following tableCalculate the mean weight 52.6 43 23.4 32.7 None 6. The weights to the nearest kg of a group of students are recorded in the following tableCalculate the difference between the mean deviation and the standard deviation 1.3 kg 1.6 kg 1.5 kg 1.2 kg None 7. Two cards are drawn, one after the other, with replacement from a pack of 52 cards containing four aces and four queens. The probability that the cards are either both aces or both queens is 2/13 2/221 2/169 4/13 None 8. 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 1.5kg 2.0kg 1.0kg 3.0kg None 9. Evaluate: 6/157 157/6 3/19 19/3 None 10. Find the value of x if1/2 log10x = 1 √10 0.01 1/√10 100 None 11. If (sec θ + tan θ)/(sec θ - tan θ) = 209/79, find the value of θ. 31.23 26.83 23.45 21 None 12. A car moves with an initial velocity of 25m/s and reaches a velocity of 45m/s in 10s. What is the acceleration of the car? 5m/s² 2m/s² 25m/s² 20m/s² None 13. Find the value of sin 405° 0.8453 0.7071 0.3245 0.5321 None 14. In the above diagram, the block just moves when the spring balance reads 15.0N. What is F? 10.0N 40.0N 15.0N 375.0N 0.6N None 15. Determine the order of the matrix(4 5 5 3) 2x4 4x1 1x4 3x1 None 16. Find ∫1 / x(x-1) dx In (x/ x+1) + C In (x/ x-1) + C In (x-1) + C In (x+1) + C None 17. Solve the following equation for x 0, 3a 2a, 4a² 0, 4a 1, 2 None 18. 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 (-1, -2) (-2, -4) (6, 12) (3, 6) None 19. Given that dv/dt = -64t and v = 10 when t = 0, find v when t = 2. v = 64 v = -118 v = -64 v = 118 None 20. Find the slope from the points -2/3 9 -3 2 None 21. Find ∫x sinx dx -x cosx + sinx + C sinx + C cos x + sinx + C 1/x + C None 22. Express in partial fractions 5/2(x-1) - 1/2(x+1) 5/2(x+1) - 1/(x-1) 1/(x+1) + 4/(3-x) x/(x+1) + 1/(x-1) None 23. Differentiate w.r.t x cos³x -3cos²x 3cos²xsinx -3cos²xsinx 3sinx None 24. Given that sin(A+B) = sinA cosB + cosA sinB, without using mathematical tables or calculator, evaluate sin 105°. √2/3 √6/4+ √2/4 √5/6 + √3/6 √3/2 None 25. The line 3y - x = 7 makes an angle of θ with the positive x-axis. Find the value of sin θ. 1/3 3√10 √10/10 3/7 3√10/10 None 26. The 2nd and 5th terms of a G.P are 2/3 and 1/12 respectively. The 1st term is 4/3 5/3 1/2 7/3 None 27. Find the gradients and the intercepts on the y- axis for y+3= 0 m = 3, c = 0 m = -3, c= 0 m= 0, c= -3 m = 0, c = 3 None 28. Solve for y if 5 log (y+3) = log 32 0 -1 2 1 None 29. Express in partial fractions. 7/(x+2) - 2/(x-2) 4/(3x+2) + 3/(x+1) + 1/(x+3) 4/(x+1) + 3/(x+3) 2/(x+1) + 3/(x-2) + 2/(x+2) None 30. Evaluate:log √40 + log √2 - log√8 1 2 0.5 √10 None 31. Evaluate the determinant 1 2 -1 | 2 3 -1 | -1 1 3 5 -2 -5 2 None 32. Given thatwhere A and B are constants, find the value of (A + B) 3 1 2 4 None 33. The values of tan 225° and tan 315° are respectively 1 and 1 1 and -1 -1 and -1 -1 and 1 None 34. If P = {3, 1, 0, 5}; Q = {2, 3, 8, 1, 4} and R = {7, 6, 5}, then P ∩ Q ∩ R is {1,3,5} { } {0} {1} None 35. Find the value of x if 3 1/2 2 1 None 36. 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) 8N 5N 80N 40N None 37. A 4N force acting an angle to the horizontal has a horizontal component of 1N. The vertical component of the force is 1N 3.87N 4N 0.13N None 38. Given that cosθ = 12/13, for 0°<θ<90° calculate without using tables or calculator 34/35 -6/7 -57/65 1/2 None 39. Change the given logarithmic expressions into exponential expressions: logb (2x + 1) = 3 2x + 1 = b³ 2x³= b+ 1 a = x³ a = x c None 40. Differentiate (x² - 1/x)² wrt x 4x³ -2/x³ -2 x³-3x²+2 2x²-2 2/x³ +3x +2 None 41. Find, w.r.t.x, the derivative of (2x² - x + 3)³ 7(2x² - x + 3)³ 3(4x-1)(2x² - x + 3)³ 2(2x+3) 3(4x-1) None 42. If log4p + log4q2 = 0, then p is given by 1/q q/2 q 2/q None 43. sin 38° has the same value as sin (-38) sin 218 cos 308 sin 128 None 44. Given that A =find A33 4 7 -2 5 None 45. Find the determinant of the matrix 4 5 3 4.2 None 46. In a triangle PQR, <PQR = 60°, PQ = 3 cm and QR = 4 cm. Find |PR| 5 cm 2√3 cm √13 cm 2√5 cm None 47. Solve the equation: 9(1 + 2k) = 81(2 + k) / 3k -4 -6 6 2 4 None 48. Find ∫x sin 2x dx xcos2x /2 + sin2x /2 + C cos2x /2 + C sin2x /2 + C -xcos2x /2 + sin2x /2+ C None 49. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s 56 m/s² 8 m/s² 23 m/s² 18 m/s² None 50. Solve for the determinant of 0 1 -2 -1 None 51. A curve has equation y = x³ -4x² - 3x + 18, the point P(-2, 0) lies on the curve. Find the gradient of the tangent to the curve at P. 21 25 22 29 None 52. Find the values of cos (-11π/3) 0 -1 1/2 1 None 53. Evaluate: -4 -1/4 In 3 - In 2 1/4 None 54. Find the value of √3/3 √3/2 2/√3 √3 None 55. Which of the following lines is perpendicular to the line 5x + 2y = 6? 5x - 2y = 6 5y + 2x = -6 2y - 5x = 6 5y -2x = 6 None 56. 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? 36/225 2/5 12/25 216/225 6/25 None 57. Solve for x 4 2x + 1 = 16 1/4 1/5 1/2 1/3 None 58. Find the gradient of the curve y = 2√x - 1/x at the point x = 1 2 0 3 1 None 59. Find the slope of the line 2 1/2 2/3 1 None 60. Express in partial fractions. 2/(x-4) + 3/(x-6) 5/(x-3) + 3/(x+4) 1/(x+3) + 4/(x-4) 4/(x+3) + 2/(x+1) None 1 out of 60 Time's upTime is Up!
