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. Solve for q:5 [2(q - 3)] = 160 6 7 9 8 10 2. Find the binomial expansion of (3.2)4 145.34 293.42 123.45 104.86 3. Point W = (5, 3). Circle J has a center at point W and radius of r = 5. This circle intersects the y-axis at one intercept and the x-axis at two intercepts. What is the area of the triangle formed by these three intercepts? 23 12 15 30 4. Solve for x in the logarithmic equation: log2 (3x + 1) = 4 25 10 5 15 5. A university undergraduate has to take 5 courses from a pool of 4 Mathematics and 3 Physics courses.In how many ways can she select her courses so that she takes exactly two courses in Physics? 7 4 24 12 6. The gradient of a curve at any point (x, y) is given by dy/dx = 2(x - 3) and the point(3, -12) lies on the curve. Find the equation of the curve. y = x² - 6x - 3 y = x² - 6x y = x - 18 y = x² - 6x - 5 7. Find the values p and q in the arithmetic progression -12, p, q, 18, ... 1, 11 -1, 8 -2, 8 0, 9 8. 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. 58.5 m/s 48 m/s 68.5 m/s 60 m/s 9. The graph of the polynomial y = a x 4 + b x 3 + c x 2 + d x + e is shown below. Find the coefficients a, b, c, d and e. a = 8, b = 0, c = 1, d = 10, e = 2 a = -1 / 7, b = 1, c = 1, d = 0, e = -4 a = -1 / 8, b = 0, c = 1, d = 0, e = -2 a = -18, b =4, c = 14, d = 0, e = -2 10. Differentiate the function wrt x:7x + √x³ 7√x x³ 4 + √x 7 + 3√x/2 11. The gradient of the curve that passes through the point (1, -10) is given by 3x² - 6. Find the equation of the curve. y = x³ - 30 y = x³ + 6x - 5 y = x³ - 6x - 5 y = x³ + 5 12. Simplify: (32y + 1 × 9y × 42y) ÷ (18y × 2y × 62y) 2y 3y 2 1 3 13. Given that (1 + 3x)10 = 1 + Px +Qx² + Rx³...find the values of the integers P, Q and R, respectively. 6, 54, 4754 98, 755, 8689 409, 67, 675 30, 405, 3240 14. From the diagram shown below, if the forces are in equilibrium, what is the value of tension T? 100.00N 241.42N 70.71N 50.00N 15. cos 65° is equal to cos 245° cos 295° sin 115° cos 115° 16. The figure below shows a block of wood resting on an inclined plane and at the point of sliding down the plane. Calculate the co-efficient of friction between the block and the plane. 0.1 0.2 0.3 0.4 0.5 17. Find, from the first principles, the derivative, with respect to x of 2x² + 1/x 1/x² 4x - 1/x 4x - 1/x² 4x 18. An object is ejected vertically upwards from the ground at 18 m/s. Find the height of the object after 3 s. 60m 84 m 48 m 54 m 19. The 5th and 10th terms of an A.P are 0 and 10 respectively. the 20th is 30 40 20 36 20. 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 20 cm 30 cm 50 cm 21. In the figure below, PT is a uniform meter rule pivoted at R, the 70cm mark. Two forces 0.1N and 0.4N are applied at Q, the 60cm mark and S, the 85cm mark. If the meter rule is kept in equilibrium by the forces and its weight, then the weight of the meter rule is 0.40N 0.30N 0.35N 0.25N 0.50N 22. Find ∫sin2x sin3x dx -1/10 sin5x + 1/2 cosx + C 1/2 cosx + C 1/10 sin5x + 1/2 sinx + C -1/10 sin5x + 1/2 sinx + C 23. A body starting from the origin O moves in a straight line, and its velocity, v m/s, after t s is given by v = 12 + 20t - 3t². Calculate the distance moved by the particle in 2 s. 44 m 32 m 56 m 78 m 24. A 1000kg elevator is descending vertically with an acceleration of 1m/s². If the acceleration due to gravity is 10m/s², the tension in the suspending cable is 11000N 1.0N 10N 9000N 25. The magnitude of the resultant of mutually perpendicular forces F1 & F2 is 13N. If the magnitude of F1 is 5N, what is the magnitude of F2 2.6N 18N 8N 12N 26. 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 13/30 1/30 1/15 27. 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 5/9 6/7 8/7 10/3 28. Find the variance and the standard deviation, respectively of the data below16, 18, 12, 14, 20, 25, 13, 15, 11 1, 13 11. 12.3 3.17, 14 17.3, 4.16 29. The value of 2cos 270° + sin 270° is -1 -2 1 0 30. The 11th term of the A.P 15, 9, 3, -3, ... is 51 75 -45 -51 31. During the same interval, it is observed that a train travels the same distance as does a lorry. The two vehicles therefore have the same initial velocity average speed uniform acceleration average velocity instantaneous velocity 32. The polynomial f(x) = 3 x 4 + 5 x 3 - 17 x 2 - 25 x + 10 has irrational zeros at + √(5) and - √(5). Find the other zeros -2, 1/3 1, 4 2, 2/3 2/3, 1/2 33. Find the value of 2.45 -1.73 -2.45 1.73 34. 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 1 1/3 1/4 4/9 7/18 35. Iffind f(A) where f(x) = x² - 5x - 2 1 0 2 -1 36. The maximum value of the function g(x) = -x² - 6x + 10 is 1 -3 19 10 4 37. The line 2y = x + 2 intersects the curve y = 1/4 (7x-x²). Calculate the area of the finite region bounded by the curve and the line 7/8 5/6 6/7 9/8 38. Evaluate the determinant of 14 12 8 17 39. 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 1.6 kg 1.2 kg 1.5 kg 1.3 kg 40. 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+ 3x - 2 y = x³ + 2x² - 2 41. A bag contains only Berries and Apples.The probability of picking a Berry at random is 0.3. Find the ratio of number of Berries to number of Apples that could be in the bag 4:7 4:9 5:7 3:7 42. When the expression pm² + qm + 1 is divided by m- 1, it has a remainder of 2 and when divided by m + 1 it has a remainder of 4. Find pq 2 -2 1 -1 43. If (2/3)x - 1 = 27/8, determine the value of 'x' -4 4 -2 8 1 44. Find the value of M if 2/3 5/3 -5/3 -2/3 45. Find ∫cos2x cos 3x dx -1/10 sin 5x + 1/2 sinx + C 1/10 sin 5x + C 1/10 sin 5x + 1/2 cosx + C 1/10 sin 5x + 1/2 sinx + C 46. Differentiate the function wrt x:y = x³(x²-3x+1) x²(x+3) x+12 5x x²(5x²-12x+3) 47. Find the derivative of <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #000000;font-family: Helvetica, Arial, Verdana, sans-serif;background-color: #ffffff" role="presentation" data-mathml="z=x(3x2−9)">z= x(3x²-9) 6x²-3 3x² 9x²-9 9x-9 48. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the origin, find the equation of the curve. y = 5x² - x³ y = 5x² + x³ y = x³ + 5x² y = x³ - 5x² 49. Find m if: 9(m + 1) × 3 = 27-m 1/3 3 3/5 -1/3 -3/5 50. Find the remainder when 12x4-9x2-2x-1 is divided by 2x+1 1/x 0 1+x x-1 51. If tan θ = 2/3, then sec²θ equals 13/9 13/4 9/13 4/13 52. The first term of an AP is -1 and the common difference is 0.5. The 6th term is 0.5 2.5 1.0 1.5 53. 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? 6/25 216/225 36/225 12/25 2/5 54. 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 white 11 13 14 12 55. Find the fourth term in the expansion of (1+x)15 455x³ 13x³ 1 13 56. For what value of k, the matrix has no inverse 2/3 1/2 3/4 3/2 57. Find the second term in the expansion of (2+3x)12 22x² 334 73728x 4096 58. A letter is chosen at random from the alphabet.Find the probability that it is one of the letters of the word INFORMATION 10/13 4/13 1/2 1/13 59. A body of mass 5kg initially at rest is acted upon by two mutually perpendicular forces 12N and 5N as shown in the figure. If the particle moves in the direction OA, calculate the magnitude of the acceleration. 0.26m/s² 2.60m/s² 3.40m/s² 0.40m/s² 1.40m/s² 60. If y = 2x², find the appropriate increase in y when x increases from 5 to 5.01 6 0.3 0.4 0.2 1 out of 60 Time is Up! Time's up