Please, fill out the information below to continue. Note: This is a sample test, and you can only take it for a limited period, after which you will be required to subscribe to a plan NAME EMAIL PHONE NUMBER 1. 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 7/18 1 1/3 1/4 4/9 2. 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 0.67 0.47 0.14 0.84 3. A ______ of books. (Fill in the blanks) liberty course group pack 4. If Sin θ = -0.6 and Tan θ > 0, then Sec θ is equal to 1.25 -0.8 -1.25 -5/3 0.8 5. Choose the word that best completes the sentence:In the factory, men are getting paid more than women and we need to do away with this __________. anger animosity announcement angle anomaly 6. The locus of a point which is equidistant from the lines y - x = 0 and y + x = 0, for x > 0, is the line x = y x-axis line y = 1 y-axis line x = 1 7. A square pyramid and a cuboid have the same height and the areas of their bases are equal. Find the ratio of their volumes 1/6 1/2 1/4 1/8 1/3 8. The quantity x varies inversely as y, and y varies directly as the square of z. If z is halved, then the value of x is doubled reduced by a factor of 4 halved tripled quadrupled 9. The graph of the function 2y = x² - x - 6 intersects the y axis at the point (0, -3) (-2, 0) (0, -6) (2, -3) 10. Choose the word that best completes the sentence:We need to find a new site with _________ access to the European motorway network. pronounced outright widespread wholehearted ready 11. A sector of a circle of radius 14 cm which subtends an angle of 120° at the center is bent to form a cone. The base radius of the cone is 14 cm 7/2 cm 28/3 cm 14/3 cm 12. Choose the word that best completes the sentence:Many of the headlines in the newspaper ______ hard to believe. were seem is seems 13. A regular polygon with (2m + 1) sides has each interior angle equal to 144°. The value of m is 9/2 10 8 5 14. Correct adjectival order?A plastic black bag. True False 15. Choose the option that best completes the sentence:The girl needs _____________ balls for that activity. both ten small cotton small ten cotton ten cotton small 16. Jasmin invested a total of $200,000 in two companies which paid dividends of 5% and 7% respectively. How much did she invest at 7% if she received a total of $11,600? $160,000 $100,000 $120,000 $80,000 $140,000 17. The 8th term of the A.P -4, -2, 0... IS 8 -10 12 10 18. cos 65° is equal to cos 245° sin 115° cos 115° cos 295° 19. A ladder of length 5m rests against a vertical wall and makes an angle 30° with the wall. How far is the foot of the ladder from the wall? 7.07 m 5/2 m 4.33 m 5 m 20. If tan θ = 5/12,then the value of sin θ - cos θ is 5/13 12/13 7/13 - 7/13 21. The difference in longitude betweenP(55°N, 12°W) and Q(15°S, 65°W) is 40° 77° 70° 53° 22. A bag contains 4 red, 8 green and 6 blue ball of identical size. The probability that a ball selected randomly is either red or green is 2/3 2/9 4/9 1/3 23. Solve the equation: 3y^{-2} = 4/27 9/2 81 2/9 4/81 81/4 24. Two men and six boys can cut a field in 3 hours. If the men work at 3/2 times that of the boys, how many men are required to cut the field in 2hrs? 4 9 6 8 25. Four books whose authors' surnames start with the letters A, J, P, and W are placed randomly on a shelf. The probability that the books will be arranged in the alphabetical order of the authors' last names is 1/24 1/6 4/18 1/12 1/4 26. What is the lowest common multiple of the prime numbers between 1 and 10? 35 210 70 105 90 27. Find m if: 9^{(m + 1)} × 3 = 27^{-m} 3 -1/3 3/5 -3/5 1/3 28. Sorry, she can't come to the phone. She _______ a bath (Fill in the blanks) have having is having has 29. The standard deviation of the set of numbers -3, -2, -1, 0, 1, 2, 3, is 0 4 2 2√2 4√2 30. The population of a school is 1,376. Express this to three significant figures. 1,370 1,470 1,380 138 1,376 31. The line 3y - x = 7 makes an angle of θ with the positive x-axis. Find the value of sin θ. 3/7 3√10/10 3√10 √10/10 1/3 32. A ladder resting against a vertical wall makes an angle tan-¹(2.4) with the ground. If the foot of the ladder is 1 m from the wall, what is the length of the ladder? 2.6 m 2.4 m 1 m 5.2 m 33. A motorist drives Lagos to Abuja at an average speed of 80km/hr and immediately returns from Abuja to Lagos through the same route at an average speed of 50 km/hr. The average speed for the round trip journey is 62.5km/hr 65.0km/hr 53.3km/hr 60.0km/hr 34. GATE Academy registers 300 candidates for an examination. 180 of the candidates offer Economics and 70 offer Geography. 80 candidates offer neither Economics nor Geography.The number of candidates offering both Economics and Geography is 30 50 60 40 35. Choose the word that best completes the sentence:I don`t think we can succeed without the __________ acceptance of the unions. wholehearted careless polite pronounced average 36. A girl walks 30 m from a point P on a bearing of 040º to a point Q. She then walks 30 m on a bearing of 140º to a point R. How far is R from P 42.4 km 38.6 km 25.2 km 30 km 37. Two events M and N are mutually exclusive and P(M) = ¼ and P(N) = 2/3.P(M∩N) is 1/3 0 1/6 5/12 38. Solve the simultaneous equations2/x + 1/y = 33/x - 2/y = 8 x = 1, y = -2 x = 1/2, y = -1 x = -1, y = 2 x = 1/2, y = 1 x = 1, y = 2 39. If 2 log_{4}P + log_{4}Q² = 0 , then P = ? 2/Q Q 1/Q Q/2 PQ 40. If the lengths of the sides of a right-angled triangle are given as (x-1), x and (x+1), then the hypotenuse is 7 3 5 13 4 41. 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 3/11 1/2 8/11 6/11 42. Find the mean and the modal marks respectively given the following data: 3, 4, 9, 3, 5, 5, 2, 4, 4, 6, 6, 6, 8, 7, 5, 7, 7, 6, 5, 6 5.5, 5.5 5, 6 5.4, 6 5.25, 6 5.4, 5 43. An arithmetic sequence has five terms between 2 and 20. Determine the fourth term of the sequence. 14 11 8 18 12 44. Two years ago, a woman was six times as old as her son. Four years from now, she will be three times as old as the son. Find their present ages 40, 10 30, 7 26, 6 32, 8 28, 7 45. If (x-y)² = 1 and xy = 2, the positive value of 1/x + 1/y is 2/3 1 1/2 3/2 1 out of 45 Time is Up! Time's up