23/04/2020Senior Class WAEC/NECO/UTME Mock Exams(Further Maths) 0Comments by Gate Academy Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Factorize completely xy(y + x)((y + x) x(y - x)y(y + x) xy(y - x)(y + x) xy(x -y)(x + y)2. Solve for x in the logarithmic equation: log_{x} 8 = 3 2 4 5 33. The variance for the set of numbers 3, 6, 9, 12, 15 is 24 12 18 15 364. Find the coefficient of a^{17}b^{3} in the expansion (a+b)^{20} 1120 1140 345 5705. Evaluate the determinant of 12 8 -10 -126. Simplify: 2 3 0 17. Find the values of x for whichis equal to zero 4 or 1/2 -3 or 5 4 or -3/2 2 or 68. Find the third term in the binomial expansion of (2-a)^{10} 11520a² 11520a 45332a 45332a²9. 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 / M110. Given that sin θ = √3/2 and cos θ = -½. The value of θ is 150 degrees 300 degrees 120 degrees 240 degrees11. Use matrix method to solve the following system of equations : 5x-7y = 2, 7x-5y = 3 x = 11/24, y = 1/24 x = 3/18, y = 5/18 x = 1/24, y = 16/19 x= 1/25, y = 412. If 3 tan θ = 4, evaluate (3sin θ + 2 cos θ)/(3sin θ - 2cos θ). 1 2 4 313. The integral values of y which satisfy the inequality -1 < 5 - 2y ≤ 7 are 0, 1, 2, 3 -1, 0, 1, 2, 3 -1, 0, 1, 2 -1, 0, 2, 314. Solve the equation: 6z² - 7z - 5 = 0 z = 5/3 or -1/2 z = -5/3 or 1/2 z = 1/2 or -5/2 z = 1/3 or 5/215. If sec θ = 17/8 and θ is a positive acute angle, find the value of csc θ using Pythagoras theorem. csc θ = 27/15 csc θ = 16/15 csc θ = 17/19 csc θ = 17/1516. Find the value of tan 158° 1.3732 0.9362 -0.7071 -0.404017. 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 I and III only III and IV only I and IV only18. Differentiate the function wrt x: 3x + 1/4x² 1/2 - 1/4x² 1/4x² 1/2 + 3x + 1/4x²19. Find the value of √3 √3/2 2/√3 √3/320. Solve the equation 4sinθ - 1 = -3 for 0° < θ < 2π 240 or 300 degrees 210 or 300 degrees 30 or 150 degrees 210 or 330 degrees21. Find the values of cot (- 855°) -1 0 2 122. 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. 25 29 22 2123. A body rolls down a slope from a height of 100m. Its velocity at the foot of the slope is 20m/s. What percentage of its initial potential energy is converted into kinetic energy? 40% 35% 15% 20%24. Solve the equation 3tan x - 5 = 2 for 0° ≤x≤ 360° 88.6° 212° 18.94° 246.8°25. 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 3/25 1/4 1/5 9/2526. Solve for the determinant of 1 -2 0 -127. Decompose into partial fractions : (5x + 10) / x(x + 5) x/2 x/2 + 3/(x+3) 2/x + 3/(x + 5) 3/ (x+5)28. Find the remainder when 3x³ + 5x² - 11x + 4 is divisible by x + 3 1 -1 2 029. Given that sin(A+B) = sinAcosB +cosAsinB, express sin(120°+45°) in the form p(√x + √y) where p, x and y are rational numbers 1/4 (√6 - √2) 6(√8 + √5) 1/6 (√7 - √9) 4 (√4 + √6)30. The value of (sin35°/cos 55°) + (cos 15°/ sin 75°) is 2 -2 1 031. A coin and a dice are thrown together. Find the probability of getting a head and a score greater than 4 1/2 1/4 1/6 1/1232. If sec 5θ = csc (θ - 36°), where 5θ is an acute angle, find the value of θ 45° 46° 36° 21°33. Evaluate: 3/19 157/6 19/3 6/15734. Given that tan θ = -2.361, where 0° ≤θ≤ 360° , findθ 54.4° 113° 9° 23°35. 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 58.5 m/s 60 m/s 48 m/s36. 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? 12/25 36/225 216/225 6/25 2/537. If a = x^{1/n}, log_{a}x^{n} is n-¹ n-² n n²38. Find n if 9^{1+n }x 3 = 27^{-n} 3/5 1/3 -1/3 -3/539. Find the co-ordinates of the point of intersection of the medians of triangle MNO; given M = (-2, 3), N = (6, 7), O = (4, 1). (5/3, 17/3) (3/8, 3/11) (5/3, 1/3) (8/3, 11/3)40. Find the value of P, such that the matrix is singular -8 8 7 -941. If y = x³ + 3x², find 2(dy/dy) - x(d²y/dx²) 6x 4x 5x 2x42. At what rate in cm² per cm is the area of the circle changing w.r.t its radius when the radius is 5cm? 10πcm²/cm 3πcm²/cm 20πcm²/cm 5πcm²/cm43. In how many different ways can the letters of the word GEOLOGY be arranged in order? 720 2,520 1,260 5,04044. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to 5/3 5/4 3/4 4/345. 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 distance from 0 at this instant 54.75 m 21.54 m 43.45 m 12.47 m46. Find the value of sin 250° -0.9397 0.4328 -0.2232 -0.423847. Given that x and t are two variables such that dx/dt = 3t² - 4t, and x = 1 when t = 4, express x in terms of t. x = 3t³ + 2t² - 31 x = t³ - 2t² - 31 x = t³ - 2t - 31 x = 3t³ - 2t² - 3148. Evaluate ∫ x / x+3 dx x-3 + C C In(x + 3) + C x - 3 In(x+3) + C49. What is the least possible value of 9 / (1 + 2y²) if 0 ≤ y ≤ 2 ? 0 1 2 950. 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 1.5 kg 1.3 kg 1.6 kg 1.2 kg51. A bag containing 5 red balls and 3 green balls. Two balls are picked, one after the other, with replacement. The probability that the two balls selected are of different colours is 17/32 15/32 1/8 15/6452. Find ∫ 1/ x²+3x-10 dx C 1/7 In (x-2 / x-5) + C In (x-2 / x-5) + C 7In x + C53. If cos θ = √3/2, evaluate (3-2√3)/ 3 1/2 √3/2 -1 (√3-2)/ 354. Given that x is a real number and x ≠0, simplify the expression (x - 1/x)³ + (x + 1/x)³ x³ + 3/x x + 6 x² + 2/x 2x³ + 6/x55. The twelfth term of the sequence (x - a), x, (x + a), ... is x + 12a x + 11a x + 10a x + 9a x - 12a56. If , what is |A| 2 1 0 -157. Use the product rule to differentiate wrt xx³(2x+5)³ 2x+20 4x+5 10x(2x+5)² 3x²(4x+5)(2x+5)²58. Find, from the first principles, the derivative, with respect to x of 2x² + 1/x 4x - 1/x² 4x 1/x² 4x - 1/x59. 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 5N, 37° north of east 7N, 37° west of north 5N, 53° east of north 7N, 37° south of west60. If -1 is a root of the equation -ax² + 6x + 8 = 0, the value of 'a' 1 -2 -1 261 out of 60Time is Up!