Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Find the coordinates of the point which will divide the line joining the points (3, 5) and (11, 8) externally in the ratio 5: 2. (49/3, 10) (5/3, 1/3) (3/49, 1/10) (3/5, 4/13) 2. 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 range N23,000 N6,000 N4,000 N31,000 3. Given that B , find B31 -2 4 2 7 4. Write the value of the angle in surd form cos 300° -√3/2 1/2 -√2 √2 5. If y = sin²x, find the rate at which y changes with respect to x sinx cosx 2cosx sinx + cosx 2sinx cosx 6. ∫(sinx- 5cosx)dx -cosx -5sinx + C sinx + C cosx + 5sinx + C cosx - 2sinx + C 7. Solve for x(1 / 3) x/2 - 2 = 9 0 -1 1 2 8. d/dx cos(3x² - 2x) is equal to -(6x-2)sin(3x² - 2x) -6x+2cosx sin(3x² - 2x) sin(3x² 9. Find the derivative of f(y) = y-2 4y 2y-4y-³ 2-2yy³ 10. 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. 68.5 m/s 48 m/s 58.5 m/s 60 m/s 11. Find constant A such that log3 x = A log5x , for all x > 0. logx5 ln(5) / ln(3) ln(5) ln(5) / ln(x) 12. Given that x is a real number and x ≠0, simplify the expression (x - 1/x)³ + (x + 1/x)³ 2x³ + 6/x x² + 2/x x³ + 3/x x + 6 13. Find the value of cosec 90° 1 -1 0 2 14. A letter is chosen at random from the alphabet. Find the probability that it is not one of the letters of the word DIAMOND 1/2 10/13 1/13 4/13 15. 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 0.7 0.8 0.9 0.6 16. Find a positive angle between 0° and 360° that is equivalent to -65.8° 342° 53.4° 386° 294.2° 17. 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 18. Two dice, one red and the other blue are rolled together. Find the probability of getting two odd numbers 1/4 1/6 1/3 1/5 19. The radius of a spherical balloon is increasing at the rate of 0.25cm/s, find the rate at which the volume is increasing when its radius is 4cm 4π cm³/s 7π cm³/s 16π cm³/s 12π cm³/s 20. 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 21. If cos θ = √3/2, evaluate (√3/2) -1 (√3-2)/ 3 (3-2√3)/ 3 1/2 22. 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 0Nm 2Nm 6Nm 8Nm 23. A figure is selected randomly from a group of figures consisting of a square, a triangle, a rectangle, a trapezium and a rhombus. The probability that the figure selected is a parallelogram is 4/5 3/5 1/5 2/5 24. Without using tables or any calculating device find the value of√2/2 cos15° + √2/2 sin15° √2/2 √2/5 √3/2 √2 25. Resolve into partial fractions 7/(x+3) - 4/(x+2) 1/(x+2) - 3/(2-x) 2/(x-3) + 2/(2-x) 1/(x+2) - 2/(4-x) 26. If find|AB| -11 12 11 -12 27. A box contains yellow, blue and white counters.The probability of picking a yellow counter is 3/8 and the probability of picking a blue counter is 35%. If there are 40 counters in the box, find the number that is blue 13 12 14 11 28. sec θ sin(90° - θ) equals 0 cot θ 90° 1 tan θ 29. Find ∫ 1/ x²+3x-10 dx C 1/7 In (x-2 / x-5) + C In (x-2 / x-5) + C 7In x + C 30. Two events M and N are mutually exclusive and P(M) = ¼ and P(N) = 2/3.P(M∪N) is 1/12 11/12 1 1/2 31. Given thatwhere A and B are constants, find the value of (A + B) 2 3 1 4 32. The values of θ for whichsin θ = cos θ are within the range 0° < θ < 360° 45° and 315° 45° and 225° 135° and 225° 45° and 135° 33. If the function f(x) = x³ + 2x² +qx - 6 is divisible by x + 1, find q -5 5 1 -2 34. Evaluate the integrals: 20 13 6 10 35. If cos θ = 3/5, find the value of (5csc θ - 4 tan θ)/(sec θ + cot θ) 2/3 3/2 11/29 29/11 36. Which of the following is a root of the equationy² + 6y = 0 ? 2 3 1 0 37. Find ∫x cos2x dx C 1/2 x sin 2x + 1/4 cos 2x + C 1/2 x sin2x + C cos4x + C 38. Without using trigonometric tables, evaluate <span id="MathJax-Element-10-Frame" class="MathJax" style="font-style: normal;font-weight: 400;line-height: normal;font-size: 15px;text-indent: 0px;text-align: left;text-transform: none;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;padding: 0px;margin: 0px;color: #000000;font-family: Verdana, Geneva, sans-serif;background-color: #ffffff" role="presentation" data-mathml="tan65°cot25°">tan65°/cot25° -1 1 2 0 39. Find the value of cos 305° 0.4435 0.6472 0.5736 -0.4732 40. Find the second term in the expansion of (2+3x)12 73728x 334 22x² 4096 41. 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. 22 21 29 25 42. The distance s metres travelled by a particle in time t seconds is given by s = 12 + 40t - 2t². Find the distance travelled by the particle before coming to rest. 120m 212m 180m 200m 43. Given that (1 + 5x)4 = 1 + Px + Qx² + Rx³ + ...find the value of P - 2Q + 3R 120 20 220 1220 44. Find, with respect to x, the derivative of sin x /(1- cos x) cos x x -1 /(1- cosx) 1 /(cosx -1) 45. In the diagram below, a lever of length 200m is used to lift a load of mass 180kg. The pivot at P is 20m from the load. What minimum force, F, must be applied at the end of the lever? 9N 20N 200N 18N 46. The line y =3x + 1 intersects thecurve y = x² -2x + 7 at the points (-1, -2) and (3, 10) (-2, -5) and (1, 4) (1, 4) and (2, 7) (2, 7) and (3, 10) 47. Evaluate: 81-1/4 × 361/2 ×100 2 3 0 10 1 48. Graph G has a line of symmetry of x = –5/2. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3? -5 -8 -7 2 49. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the minimum point on the curve (1, 7) (3, 1) (0, 6) (2, 9) 50. The chances of occurrence of three independent events X, Y and Z are 1/3, 1/4 and 2/5. What are the chances of occurrence of only Y and Z ? 1/10 1/30 13/30 1/15 51. The second term of an infinite geometric series is -1/2 and the third term is 1/4. The sum of the series is 2/3 3/2 2 1 1/2 52. Find the value of 'p' in the equation: 4(p - 1/2) = 2p² 1 3 1/2 1/3 2 53. For what value of x the matrix is a skew symmetric matrix -1 1 5 -5 54. A bag contains 6 red balls, 12 white balls and 9 green balls. A ball is selected at random. What is the probability that it is not a green ball? 2/3 1/3 5/9 4/9 55. 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 25/64 17/32 9/64 15/64 56. Evaluate: 2/3 3/2 7/6 6/7 57. Evaluate , without calculator, the logarithmic expression:logb 1 with b > 0 and b ≠ 0 b 1 0 -1 58. Find the area of the finite regions included between the curve in a curve y with gradient dy/dx = 3x² - 6x + 2 and the x-axis 2 1/3 1/4 1/2 59. The graph of the function 2y = x² - x - 6 intersects the y axis at the point (2, -3) (0, -3) (0, -6) (-2, 0) 60. A wooden block of weight 16N is placed on a rough surface. If the co-efficient of friction between both surfaces is 0.25, the least horizontal force required to move the block is 64.0N 6.4N 0.4N 4.0N 1 out of 60 Time is Up! Time's up