Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. The points of intersection of the graphs of y = x² + 2 and y = 2x + 5 when drawn on the same set of axes are (3, 0) and (-1, 0) (-1, 3) and (3, 11) (1, 0) and (-3, 0) (-1, 11) and (3, 3) 2. The gradient of a curve which passes through the point (1, 2) is 3+2x. Find its equation. y = x³ + 2x² - 2 y = x³ + 2x²+ 3x y = x³ + 2x²+ 3x - 2 y = x²+ 3x - 2 3. Find ∫ (2+x)/x dx, x > 0. In 2x + x + C In x² + x + C In 2x + C ln x³ +x + C 4. For what value of x the matrix is a skew symmetric matrix -5 1 5 -1 5. Evaluate the integrals: 14/3 12/3 14 12 6. The distance s metres after time t second covered by a particle moving along a straight line is given by s = t³ - t² - t - 2Find the average acceleration between t = 2 and t = 4 2ms-² 6ms-² 4ms-² 3ms-² 7. Evaluate the definite integral: 27 32/5 33/4 45/2 8. 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 0.08 0.20 0.02 0.80 9. Which of the following have the same value as sin 15°?I. sin 165°II. sin 285°III. sin (-15°)IV. sin (-195°) I and II only III and IV only I and III only I and IV only 10. 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 M1g / M2 M2 / M1 M2g / M1 11. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the area of the finite region enclosed by the curve, the lines x = 1, x = 3 and y = 0 8/7 5/9 6/7 10/3 12. 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 mean deviation N4,290.23 N7,354.34 N353 N8,888.89 13. Find the angles between 0° and 360° whose sine is -0.9781 23° 258° 235° 443° 14. Find the derivative of y = sin(2x³ + 3x - 4) wrt x cos(2x³ + 3x - 4) 6xsin(2x³ + 3x - 4) (6x²+3)cos(2x³ + 3x - 4) sin4x+x 15. Find the value of cos 200° sin 160° + sin (- 340°) cos (- 380°) 0 -1 1 2 16. One of the roots of the equation: 6y² = 5 - 7y is 5/3 -1/3 1/2 -1/2 17. Evaluate: (3^{0 }- 9^{-1/2})^{-3} 2/3 27/8 3/2 1/9 18. Differentiate w.r.t x sin³x 3sin²xcosx -3sin²xcosx -3cos²xsinx 3sin²x 19. An object of mass 80kg is pulled on a horizontal rough ground by a force of 500N. Find the coefficient of static friction. (g = 10m/s²) 0.625 1.00 0.40 0.80 20. Differentiate wrt x 2/3x³ 3x³ 2 - 2/3x³ 1-3x 21. Solve for x the equation ln (x - 1) + ln (2x - 1) = 2 ln (x + 1) 4 -5 5 -4 22. A bag containing 5 red balls and 3 green balls. Two balls are picked, one after the other, with replacement. The probability that both are the same colour is 9/64 17/32 25/64 15/64 23. A letter is chosen at random from the alphabet. Find the probability that it is not one of the letters of the word DIAMOND 1/13 1/2 10/13 4/13 24. In a game involving two dice, Kamsi will win if she throws at least one six, or the sum of the numbers is 10. The probability of Kamsi winning at the next throw is 4/9 1 1/4 1/3 7/18 25. Write the value of the angle in surd form sin 300° √3/2 -√3/2 -√2 √2 26. Use the binomial theorem to expand (1 + 4x)^{4}. Hence, find the value of (1.04)^{4} correct to 4 decimal places 1 + 96x² + 256x3 + 256x4; 1.169 1 + 16x + 96x² + 256x4; 1.16 1 + 16x + 96x² + 256x3 + 256x4; 1.1699 1 + 16x + 96x² + 256x3 + 256x4; 1.1 27. Find the remainder whenx³- 2x²-5x+6 is divided by x-1 24 3 0 -64 28. The roots of the equation ay² + by + c = 0 are 1/2 and -3. The values of a, b and c are, respectively 1, 5, 3 2, 5, -3 2, 5, 3 2, -5, -3 29. If x= 2 is a root of the equation 2x³-2x²-5x+2 find the other roots 0.366 1.7433 0.566 3.446 30. A binary operation * is defined over the set of real numbers such thata * b = a (b + 2). Find 3 * (4 * 2). 18 80 72 60 54 31. Simplify 3 1/3 1/9 9 32. Simplify:log_{5}25^{x }- log_{5}(0.04) x/2 2x+1 2x-2 2x+2 33. Subtract the polynomials: (xy + 3x + 2) - (3x^{2} + y) -3x²+xy+3x-y+2 3x²+4xy+2 -3x²+3x-y+2 34. Calculate the area under the line y = x + 2 between the limits x = 0 and x = 10 55 50 70 60 35. Divide (2x³ - xy² + y³) by (x + y) 2x² + xy 2x² - y² 2x² - 2xy 2x² - 2xy + y² 2x² + 2xy + y² 36. Find the mean and mean deviation, respectively of the following 16, 18, 12, 14, 20, 25, 13, 15, 11 37. Find the value of tan (-84)° -0.294 -9.514 9.514 0.249 38. If (2/3)^{x - 1 }= 27/8, determine the value of 'x' 1 4 8 -2 -4 39. If (3/4)^{x}(2/3)^{y }= 32/27, the values of x and y respectively are 2, -2 2, 2 -2, 1 1, 2 40. Evaluate: -3/2 5 -2/3 1/5 41. Given that sin(θ+α) = sinθcosα + cosθsinα, find the value of sin 75° 2 (√6+√2) 1/4 (√6+√2) 1/2 (√6+√2) 4 (√6+√2) 42. Simplify: (3^{2y + 1 }× 9^{y }× 4^{2y}) ÷ (18^{y }× 2^{y} × 6^{2y}) 3 3y 2 2y 1 43. Without using trigonometric tables, evaluate sin 35° sin 55° - cos 35° cos 55° 2 0 -1 1 44. Solve the following equations: 3x + 4y + 2z = 4 x - 5y + 3z = -1 2x + 3y + z = 3 x = 5, y = 6, z = -3 x = 8, y= 5, z = 4 x = 2, y 0, z = 1 x = 0, y = 6, z = 4 45. The integral values of z which satisfy the inequalitiy -1 < 2z - 5 ≤ 5 are 2, 3, 4, 5 2, 3, 4 3, 4, 5 2, 5 46. Use binomial theorem to expand (1 - 4x)³ in ascending powers of x 1 - 2x + 8x2 + 14x3 1 - 12x + 64x3 1 - 12x + 48x2 1 - 12x + 48x2 + 64x3 47. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the point (-1, 10), find the equation of the curve y = x² -4 y = 5x³ - x² + 8 y = 5x² - x³ y = 5x² - x³ + 4 48. The integral values of y which satisfy the inequality -1 < 5 - 2y ≤ 7 are -1, 0, 1, 2, 3 -1, 0, 2, 3 -1, 0, 1, 2 0, 1, 2, 3 49. 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. 29 22 25 21 50. Divide 6x² - 13x + 5 by 2x -1 2x+5 x+7y 5x-3 3x-5 51. Tireni throws a coin twice. The coin is biased so the probability of landing a head is 2/5. Find the probability that she throws two tails 1/5 3/25 9/25 1/4 52. Find the value of sin 405° 0.7071 0.5321 0.3245 0.8453 53. 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 34/455 4/91 4/455 2/91 54. A bag contains only gala and royal apples. The probability of picking a gala at random is 0.3. Find the probability of picking a royal apple 0.6 0.9 0.8 0.7 55. Differentiate the function wrt x:y = √x 1/2√x x² √x 2√x 56. If (2/3)^{a-1 }= 27/8, what is a? -4 -2 2 6 57. Solve the equation 4 cosx - 3 = 0 for 0° ≤x≤ 360° 234° 12.5° 63° 41.4° 58. Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7. Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have? 8 6 7 9 59. Given that cos θ = -0.3420, where 180° ≤θ≤ 360° , find θ 190° 345° 320° 250° 60. Solve the equation 4sinθ - 1 = -3 for 0° < θ < 2π 240 or 300 degrees 30 or 150 degrees 210 or 330 degrees 210 or 300 degrees 1 out of 60 Time is Up! Time's up