23/04/2020 Senior Class WAEC/NECO/UTME Mock Exams(Further Maths) 23/04/2020 0Comments by Gate Academy Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. If sin (x + y) = 1 and cos (x - y) = <span id="MathJax-Element-21-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="32">3√232, find x and y. x = 30° and y = 90° x = 21° and y = 48° x= 60° and y =30° x = 45° and y = 45° 2. What is the slope of the line passing through the points J (-2, 3) and (2, 7)? 4 1 2 3 3. Find the value of x if 4 log x + 5 log x - 7 log x = log 16 2 8 4 16 4. Solve for x(1 / 3) x/2 - 2 = 9 2 1 0 -1 5. What is the coefficient of static friction between a load of mass 0.75kg and a horizontal surface, if the limiting frictional force is 5N? (g = 10m/s²) 1.50 0.66 0.15 0.066 3.75 6. Without using tables or any calculating device find the value of √2-2 √3-1 √2-1 √2-3 7. The hypotenuse of a right-angled isosceles triangle is 8 units. The length of each of the other sides are 4√2 4 4(√2-1) 4/√2 8. Simplify: 1/2 2 1/4 1/8 9. Evaluate: 81-1/4 × 361/2 ×100 1 0 3 10 2 10. Find the coefficient of a17b3 in the expansion (a+b)20 1120 1140 570 345 11. Solve for n : log25 + log26 + log2n = 1 10 30 3 15 12. The value of x which satisfies the equation is -2 1/2 2 -1/2 13. The finite are enclosed by the curve y² = 4x and the line x = 4 is rotated through 360° about the x-axis. Find the volume of the solid generated in cubic units. 27 27π 32π 32 14. 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? -8 2 -5 -7 15. Find ∫ 1/ x²+3x-10 dx 1/7 In (x-2 / x-5) + C In (x-2 / x-5) + C 7In x + C C 16. The gradient of a curve which passes through the point (1, 2) is 3+2x. Find its equation. y = x³ + 2x²+ 3x y = x²+ 3x - 2 y = x³ + 2x² - 2 y = x³ + 2x²+ 3x - 2 17. Given that the quadratic expression 3m² - 7m + K is a perfect square, the value of K is 49/24 49/36 49/12 49/4 18. Evaluate: 1/3 1/2 -1/3 -1/2 19. Find the values p and q in the arithmetic progression -12, p, q, 18, ... 0, 9 1, 11 -1, 8 -2, 8 20. When a polynomial f(x) is divided by (2x - 3), the quotient is x² - x + 2 and the remainder is -1. Find f(x) 2x³ + 5x² - 7x + 5 2x³ - 5x² + 7x - 7 can't be gotten 2x³ - 5x² + 7x - 7 2x³ + 5x² - 3x + 7 21. If θ is a positive acute angle and sec θ = 25/7, find the value of csc θ using trigonometric identity. csc θ = 1/4 csc θ = 25/27 csc θ = 23/24 csc θ = 25/24 22. Given that V = 4/3 πr³ and A = 4πr², find dA/dV 2/r r/3 r/2 3/r 23. 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 0.4N 4.0N 6.4N 64.0N 24. 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 14 11 12 13 25. A moving object has a uniform acceleration. Its displacement increases at a constant rate velocity increases by equal amounts in equal time velocity varies inversely with time speed is directly proportional to time 26. Find the resultant 5N, N 65° W 15N, S 43.4° W 3N, N 75.2° E 17N, S 61.9° E 27. Given that k²= log2 512, find k 5 4 3 2 28. The distance s metres after time t second covered by a particle moving along a straight line is given bys = t³ - t² - t - 2Find the acceleration when the velocity is zero 5ms-² 6ms-² 4ms-² 4ms 29. The distance S (m) covered in time t (s) by a body iss = 5(1 -e-4t). Find its speed, in m/s, when t = 0 14 30 10 20 30. Find the value of x at which the function y = x³ - 7x² + 15x has the greatest value 3 5 5/3 3/5 31. Decompose into partial fractions : (8x + 14) / (x + 1)(x + 5) 3/2(x+5) 3/(2(x + 1)) + 13/(2(x + 5)) 13/(2(x + 5)) 3/(2(x + 5)) + 13/(2(x + 6)) 32. Solve for y: 25y + 3(5y) = 4 -4 or 0 1 or 4 1 0 33. Differentiate the function w.r.t x: y = 4(x² - 3) 6x x²-3 8x² 8x 34. Find the value of tan 240° √2 1/√3 1/√2 √3 35. Evaluate : 2 6 1/2 1/3 36. Change the given logarithmic expressions into exponential expressions: logb (2x + 1) = 3 2x³= b+ 1 a = x c a = x³ 2x + 1 = b³ 37. The value ofsin (870°) is -1/2 1/2 -0.866 0.866 38. Find the force parallel to the slope required to move a body of mass 2kg up a slope inclined at 30° to the horizontal with an acceleration of 2m/s² if the frictional force between the two surfaces is 10N. 24N 10N 14N 20N 39. cos 65° is equal to cos 245° cos 295° cos 115° sin 115° 40. If a graph of the function y = 3x² -5x - 7 is provided, the roots of the equation 3x² - 2x -5 = 0 are given by the points of intersection of the curve y = 3x² -5x - 7 and the line y = -7x - 2 y = -3x - 2 y = 3x - 2 y = 7x - 12 41. Evaluate the definite integral: 4 5 -4 3 42. If y = x³ + 3x², find 2(dy/dy) - x(d²y/dx²) 4x 2x 6x 5x 43. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s 23 m/s² 18 m/s² 56 m/s² 8 m/s² 44. Given that I is a (2x2) unit matrix and If BA = I, where B is a (2x2) matrix, deduce that B maybe expressed in the form αA + λI, stating the values of the constants α and λ, respectively. -1 and 4/5 - 1/5 and 4/5 1/5 and 2/5 1 and 1/5 45. Tara received a cash gift from her parents on her 10th birthday. On each succeeding birthday, she received twice the amount received in the previous year. If she had received a total of £31,500 by the time she was 15, the cash gift for her 12th birthday was £1,000 £4,000 £3,000 £5,000 £2,000 46. Find the values p and q in the arithmetic progression -12, p, q, 18, ... 0, 9 -1, 8 -2, 8 1, 11 47. Determine the order of the matrix: 2x2 1x1 1x2 2x3 48. Find the value of x for which 32x + 6(3x) = 27 3 -3 -1 1 49. Two forces 3N and 4N act on a body in directions due north and due east respectively. Calculate their equilibrant. 5N, 53° west of south 7N, 37° south of west 5N, 53° east of north 7N, 37° west of north 5N, 37° north of east 50. 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 = 5x² - x³ + 4 y = 5x² - x³ y = x² -4 y = 5x³ - x² + 8 51. Solve the equation 7 = 2 + 4tanx for 0° ≤x≤ 360° 124° 87° 51.3° 23.7° 52. PQRS is a quadrilateral with dimensions shown belowCalculate the length of the diagonal PR 7 cm 10 cm 6cm 4 cm 53. Evaluate: log327 + log36 – log354 2 1 -21 1/3 0 54. Express cos (- 1555°) in terms of the ratio of a positive angle less than 30°. sin 15° -sin 25° cos 15° cos 25° 55. Given that 2sin(θ-45°) = cos(θ+45°),find the value of tanθ 0 -1 1/2 1 56. The expressionis equal to 2/3 9/4 4/9 3/2 57. Determine the order of the matrix 3x4 1x2 2x4 3x3 58. If (1 + 2x)6 = 1 + Px + Qx² + ...., find the values of the constant P and Q, respectively. 12, 60 14, 72 10, 50 8, 55 59. In the figure below, the three forces F1 , F2 & F3 acting at O are in equilibrium. If the magnitude of F1 is 10.0N and the magnitude of F2 is 5.0N; find the magnitude of F3 26.4N 13.2N 15.0N 10.0N 60. Find the value of 1.73 -2.45 2.45 -1.73 1 out of 60 Time is Up! Time's up