23/04/2020Senior Class WAEC/NECO/UTME Mock Exams(Mathematics) 0Comments by Gate Academy Please, fill out the information below to continue. NAME EMAIL PHONE NUMBER 1. The sine, cosine and tangent of 240° are, respectively 0.866, -1/2, 1.732 -0.866, -1/2, 1.732 -0.866, 1/2, -1.732 0.866, 1/2, 1.7322. The ratio of the sides of two similar rectangular blocks is 5 : 3. If the volume of the smaller block is 324 cm³, that of the other block is 540 cm3 864 cm3 1500 cm3 900 cm33. A rectangle is formed from a square by increasing the latter's length by 50% while reducing its width by 50%. What is the ratio of the area of the rectangle to that of the square? 3 : 2 3 : 4 4 : 3 2 : 3 4 : 94. Correct each of the numbers 38.7152 and 0.05381 to two significant figures and find their product , correct to two significant figures. 0.21 2.6 1.9 2.1 2.05. The length of a rod was given as 35cm correct to the nearest centimetre. The actual length lies within the range 34.9 - 35.1cm 34.95 - 35.05cm 34.5 - 35.5cm 34.1 - 35.9cm6. Cards are drawn from a pack of 52 playing cards one at a time. Calculate the probability of drawing without replacement at least one red card 31/102 17/102 1/102 77/1027. If y = 2x², find the appropriate increase in y when x increases from 5 to 5.01 6 0.4 0.3 0.28. In a regular pentagon ABCDE, /AC/ intersects /BD/ at F. Calculate <CBD. 60 degrees 36 degrees 72 degrees 108 degrees9. The data below shows the distribution of workers in a certain secondary school. Teacher 30 Gardeners 15Typists 9 Cleaners 6Clerks 12 Messengers 3If one of the workers is absent from work on one particular day, the probability that he is a clerk is 1/25 2/25 4/25 3/2510. sec θ sin(90° - θ) equals 90° cot θ 1 0 tan θ11. Anne spent a quarter of her food budget on provisions, half the balance on staples and one-third of the remainder on beef. If she was left with $350, how much was her food budget? $800 $1,400 $2,100 $700 $1,05012. Solve the equation:(a-7) (a+2) = 0 a = 2 or -7 a = -4 or 5 a = -2 or 7 a = -1 or 813. When the food bill for the Jackson's family increased by 20%, the mother reduced the quantity of food bought for the family by 15%. What is the fractional increase in the food bill of the family now? 13/40 1/20 7/40 7/20 1/5014. Determine the order of the matrix 1x3 2x4 3x1 1x515. The letters of the word MISSISSIPPI are cut and placed in a bag. If one letter is drawn randomly from the bag, the probability that it is neither an I nor a S is 8/11 6/11 3/11 1/216. Evaluate:log 0.225 if log 3 = 0.477 and log 5 = 0.699 -0.352 -0.648 -1.648 -1.35217. Solve for x log_{x} 0.0001 = 4 1/2 -1 1/5 1/1018. Evaluate: 2 0 20 119. Evaluate , without calculator, the logarithmic expression: Log √(10) 0 1 1/2 1/520. Solve x y^{m} = yx^{3} for m ln(x) / ln(y) 1 + 2 ln(x) / ln(y) In(x/y) 2 + In(x)21. If there is no stop-over at Dubai, and the average speed of the airplane is 500km/hr, the total time taken for the plane to fly from Lagos to Kuala Lumpur via Dubai is approximately 5 h 7 h 10 h 8 h22. Using the product rule differentiate wrt x(x²+3)(2x-1) x²+3x-1 2x² 6x+ 2 6x²-2x+623. A coin and a dice are thrown together. Find the probability of getting a head and a score greater than 4 1/12 1/4 1/6 1/224. Simplify : 2^{-3 }x 16^{3/4 }x 2^{0} 0 1/2 2 125. Simplify: 4 x 4^{-n }x 2^{2n-2}^{} 2³ 1 2 2²26. Find the determinant of the matrix 4.2 4 3 527. A storage tank in the shape of a cuboid of base 2.5 m by 2m can hold up to 7,500 litres of water. The height of the tank is 0.75 m 0.15 m 1.5 m 1.0 m28. A die is rolled 100 times with the following outcomes:Number 1 2 3 4 5 6Frequency 15 20 18 14 17 16The experimental probability of obtaining at most 4 is 0.84 0.47 0.67 0.1429. A motorist drove a distance of 90km at constant speed for the first 40km and then drove 20km/hr faster for the rest of the journey. If the whole journey took him one hour, his average speed for the first 40km was 80 km/hr 70 km/hr 40 km/hr 60 km/hr30. Two events M and N are mutually exclusive and P(M) = ¼ and P(N) = 2/3.P(M∩N) is 1/6 5/12 1/3 031. If a cube of maximum possible volume is cut off from a solid sphere of diameter d, then the volume of the remaining (waste) material of the sphere would be equal to d³/3 (π - d/2) d³/4 (√2 - π) π - d d³/3 (π/2 - 1/√3)32. Solve the equation:3x-² = 4/27 2/9 4/81 81/4 9/233. A worker's salary on appointment is N30,000 per annum. At an annual increment rate of 10%, his salary at the beginning of the third year is N39,930 N36,000 N42,000 N36,300 N39,00034. Two brothers Kameel and Kafeel owned a business in which the ratio of shares, was 3 : 2 respectively. Kafeel later sold 1/2 of his share to Kameel for £12,000. What was the value of the business? £24,000 £60,000 £48,000 £84,000 £42,00035. The bearing of a point P from an observer Q is S37°W. The bearing of Q from P is S 53° W S 37° E N 37° E N 53° W36. A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the length OP and AB respectively. Suppose ∠APB = 60° then the relationship between h and b can be expressed as x 2h²=b² 3b²=2h² 3h²=2b² 2b²=h²37. A ship leaves port A and sails on a bearing of 040°. After 15 km the ship changes direction and sails on a bearing of 070°. If the ship sails a distance of 25 km on this bearing, find its bearing from port A 289.4° 058.8° 012.3° 083.2°38. If x/y = 3/5, then (x-3)/(y-5) is 6/5 2/5 5/3 0 3/539. The sum of the first five terms of the G.P 3, -6, 12, is 33 93 -33 3140. Starting from town X(45°N, 17°E), an airplane flies to town Y(45°N, 47°E) along the parallel of latitude and later to a third town Z(60°N, 47°E) along the meridian.(R = 6,370 km, π= 22/7). The distance between Y and Z along the meridian is 5,005 km 1,668 1/3 km 3,336 2/3 km 2,502 1/2 km41. Find the variance and the standard deviation, respectively of the data below-3, -5, -7, 2, 5, 0, 4, 6 12.6, 19 4.52, 20.2 20.4, 4.52 12.3, 1742. Calculate the area under the line y = x + 2 between the limits x = 0 and x = 10 60 50 70 5543. 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 a white ball 4/9 1/3 2/3 5/944. A sum of N420 is shared among three children in the ratio 6 : 7 : 8. The largest share is N120 N180 N140 N16045. One of the roots of the equation:x² + 9 = 0 none of these -9 -3 346. The first term of an AP is -1 and the common difference is 0.5. The 6th term is 1.0 2.5 1.5 0.547. Evaluate: (3^{0 }- 9^{-1/2})^{-3} 27/8 3/2 2/3 1/948. The data below shows the distribution of workers in a certain secondary school. Teacher 30 Gardeners 15Typists 9 Cleaners 6Clerks 12 Messengers 3If one of the workers is on leave, the probability that he is either a teacher or a gardener is 3/5 2/5 1/5 3/2549. A solid cone of metal of radius r and height h cm is melted into a cube of length a. If h + r = 10 cms, and the volume of the cube formed is maximum then the radius of the cone in cms is 5 5/3 10/3 20/350. Find the value of x if 1 2 3 1/251. Differentiate wrt x:x³(x - 1) (x²+2)x 1+x² x³ + 3x²(x-1) 3x+252. The table below shows the frequency distribution of a number of pets in 25 houses Find the median of the distribution 7 3 5 453. Evaluate ∫1/x(x + 2) dx, x ≠ 0, -2 2In(x+2 / x) + C x + 2 + C x/2 + C 1/2 In(x / x+2) + C54. Factorize the polynomial x^{ 2} + 5x + 6 (x + 2)(x + 3) (x + 2)(x + 6) (x + 2)(8) (x + 5)(x + 3)55. The angle of elevation of the top of a tree from a point P and the ground is 30°. From a point Q, 10 m closer to the foot of the tree, the angle of elevation is 45°.How tall is the tree? 5(√3 + 2) m 10√3 m 10√2 m 5(√3 + 1) m56. The area of the trapezium PQRS in the figure is 36√3 cm² 36 cm² 72 cm² 18√3 cm²57. P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR? 2r+√3 r (1+√5) 2r (2+√3) 2r (1+√3)58. If log 3 = 0.4771, and 10^{x }= 0.3, find x -1.4771 -0.5229 0.4771 0.522959. Determine the order of the matrix 3x2 3x3 2x3 1x360. If X = (a, b, c), Y = (a, b, c, d, e) and Z = (a, b, c, d, e, f, g)then (X∪Y)∩(X∪Z) is (a, b, c, d, e) (a, b, c, d, e, f, g) () (a, b, c)61 out of 60Time is Up!