Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Solve the inequality:18 < x² - 3x -3 < x < 6 x 6 x > -3 or x > 6 x < -3 or x < 6 None 2. Express in partial fractions. 4/(x+3) + 2/(x+1) 1/(x+3) + 4/(x-4) 2/(x-4) + 3/(x-6) 5/(x-3) + 3/(x+4) None 3. Differentiate, with the respect to x: cosx - x sinx 2sinx -xcosx xcosx -2sinx - xcosx -2sinx + xcosx None 4. Find in square units, the area of the finite region bounded by the curve y = x³ - x and the x-axis, from x = -1 to x =1 1/3 1/2 1/4 2 None 5. A uniform meter rule QR is balanced on a knife edge which is 55cm from R. When a mass of 10g is hung at P as shown below, the mass of the meter rule is 350g 550g 70g 35g None 6. Evaluate , without calculator, the logarithmic expression:logb 1 with b > 0 and b ≠ 0 0 1 b -1 None 7. A curve y has gradientdy/dx = 3x² - 6x + 2.If the curve passes through the origin, find its equation. y = x + 2 y = x(x-1)(x-2) y = x(x+5) y = 1-x None 8. Find the gradients and the intercepts on the y- axis for 3y-2x+5 = 0 m = 2/3, c=-5/3 m= 3, c = -5 m = 1, c = -1 m = 1/3, c = 5/3 None 9. Solve for x the equation 2 x b4 logbx = 486 1 3 2 4 None 10. Differentiate the function w.r.t x: y = 4(x² - 3) 8x² 8x 6x x²-3 None 11. sec θ sin(90° - θ) equals 90° 1 tan θ 0 cot θ None 12. Which of the following is a root of the equationy² + 6y = 0 ? 0 2 3 1 None 13. Find the binomial expansion of (1.04)5 1.2167 2.4342 1.4633 1.5332 None 14. Find angle a° 50.1° 40.3° 27° 72° None 15. Find the value of sec 210° -1/√2 1/√2 √2 -√2 None 16. Evaluate: 0.658 0.563 0.163 0.777 None 17. Given that V = 4/3 πr³ and A = 4πr², find dA/dV 3/r 2/r r/2 r/3 None 18. Find the value of x if 4 log x + 5 log x - 7 log x = log 16 4 2 16 8 None 19. Solve the equation: 6z² - 7z - 5 = 0 z = -5/3 or 1/2 z = 1/3 or 5/2 z = 5/3 or -1/2 z = 1/2 or -5/2 None 20. Given that cosθ = 12/13, for 0°<θ<90° calculate without using tables or calculator -6/7 34/35 -57/65 1/2 None 21. The first term of an AP is -1 and the common difference is 0.5. The 6th term is 2.5 0.5 1.0 1.5 None 22. If log 4 = 0.6021, evaluate:log 40 - 3log 400 -7.7958 -6.2042 -7.2042 -6.7958 None 23. Factorize completely 3x3 + 4x2 – 13x + 6 completely, given that x-1 is a factor (x-1)(x+3)(3x-2) 3x+1 2x-5 (x+2)(3x-1) None 24. Divide 2x³ + 11x² + 17x + 6 by 2x + 1 2x+1 x²+7x-2 x²+5x+6 7x-2 None 25. What is the least possible value of 9/(1 + 2y²) if 0 ≤ y ≤ 2? 0 2 1 9 None 26. A letter is chosen at random from the alphabet. Find the probability that it is not one of the letters of the word DIAMOND 4/13 1/2 10/13 1/13 None 27. Solve the simultaneous equations2/x + 1/y = 33/x - 2/y = 8 x = 1/2, y = 1 x = 1, y = -2 x = 1/2, y = -1 x = 1, y = 2 x = -1, y = 2 None 28. If X = ( -1, 2 ) and Y = ( 0, 1 ), which of the following points lies on the line XY produced? ( -3, 4 ) ( 3, 4 ) ( 2, -2 ) ( 1, 3 ) ( 3, -2 ) None 29. The radius of a circle s increasing at the rate of 0.05 cm/s. Find the rate of increase of the circumference when the radius of the circle is 4 cm. 8π cm/s 10π cm/s 0.2π cm/s 4π cm/s None 30. In how many different ways can the letters of the word GEOLOGY be arranged in order? 1,260 5,040 2,520 720 None 31. A particle moves in a straight line with a velocity v in m/s at time t is given by v = 3t² +10. Calculate the distance it travels from t = 2s to t = 5s. 147 m 132 m 32 m 47 m None 32. Solve the equation 3tan(x + 25°) = -0.8391 for 0° ≤x≤ 360° 45° 319.4° 213° 12.6° None 33. A curve passes through the point (3, -1). If its gradient function is 2x + 5, find the equation of the curve y = x² + 5x - 25 y = 3x³ + x² + 5x - 25 y = 3x³ + x² + 5x + 25 y = 3x³ + 5x - 25 None 34. In a certain class, 37 students take at least one of Chemistry, Economics and History. 8 students take Chemistry, 19 take Economics and 25 take History. 12 students take Economics and History but nobody takes Chemistry and Economics . How many students take both Chemistry and History? 3 6 5 4 None 35. Evaluate: log327 + log36 – log354 0 1/3 -21 2 1 None 36. Evaluate: 7/3 2/3 -7/3 -3/2 None 37. The graph of a cubic polynomial y = a x 3 + b x 2 + c x + d is shown below. Find the coefficients a, b, c and d. a = 2 , b = 10, c = 3/2 and d = 1 a = 1/2 , b = 5, c = -3/2 and d = 1/3 a = 2 , b = 1/4, c = 3/2 and d = 1 a = 1/2 , b = 0, c = -3/2 and d = 1 None 38. A force of 10N, drags a mass of 10kg on a horizontal table with an acceleration of 0.2m/s². If the acceleration due to gravity is 10m/s², the co-efficient of friction between the moving mass and the table is 0.80 0.02 0.08 0.20 None 39. If log 7 = 0.8451,find the value of log (1/70) -1.1549 -2.8451 -2.1549 -1.8451 None 40. Evaluate the integrals: 6 10 13 20 None 41. Find the slope of the tangent to the curve y = 3x² - 2x + 5 at the point (-1, 10) 8 -4 -8 4 None 42. Determine the turning point of the curve y = x² + 250/x (-2, 7) (-5, 35) (2, 7) (5, 35) None 43. The value of 2cos 270° + sin 270° is -2 -1 0 1 None 44. Line Q has the equation 5y – 3x = 45. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.) 41 25 33 36 None 45. Find, from the first principles, the derivative, with respect to x of 2x² + 1/x 4x - 1/x 4x - 1/x² 1/x² 4x None 46. 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 2x³-3x²+11x-60 11x-60 3x²+11x-60 2x³+11x-60 None 47. If cos θ = 3/5, find the value of (5csc θ - 4 tan θ)/(sec θ + cot θ) 11/29 3/2 2/3 29/11 None 48. Factorize the polynomial x 3 - x 2 - 25x + 25 (x-5)² (x - 1)(x + 5)(x - 5) (x - 1)(x + 5)² x²-1(x-5) None 49. Write the value of the angle in surd form sin 240° -√3/2 √3/2 -√2 √2 None 50. The matrices A and B are given by: A =and B =where a ≠ 0, b ≠ 0If BA =kA, where k is a scalar, Find another equation satisfied by a and b a + 3b = 0 2a + 5b = 3 3a + kb =1 2a + (1 - k)b = 0 None 51. Find the remainder when4x³ + 5x² - 11x + 10 is divided by x+2 19 20 18 21 None 52. In which quadrant does the point (-3,4) lie? 4th quadrant 1st quadrant 2nd quadrant 3rd quadrant None 53. Evaluate the integrals: 1 -1 2 0 None 54. If sin p = 3/5, where 0° < p < 90°, find the value of 1 2 0 7 None 55. Find the value of x if log4x = 3.5 256 128 14 64 None 56. If P = {3, 1, 0, 5}; Q = {2, 3, 8, 1, 4} and R = {7, 6, 5}, then P ∩ Q ∩ R is {1} {1,3,5} { } {0} None 57. 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 58. Find m if: 9(m + 1) × 3 = 27-m -1/3 3 3/5 1/3 -3/5 None 59. Find the limit of (x³ - 1)/(x² - 1) as x → 1. 1 1.5 ∞ 0 2.5 None 60. If sin 49° = 3/4, find the value of sin 581°. √7 √3 √7/4 √2 None 1 out of 60 Time's upTime is Up!