Q1 – ALGEBRA QUIZ MATHEMATICS 1. A collection of 32 coins amounted to $5.15. If it consists of dimes and quarters, how many quarters are there? a. 11 b. 19 c. 13 d. 17 2. The number 0.123123123123……… is a. Irrational b. surd c. rational d. transcendental 3. Solve for x if 8^x = 2^(y + 2) and 16^(3x – y) = 4^y. a. -4 b. -2 c. -3 d. -1 4. What is the first four terms of the sequence whose general terms is n^3 + 1? a. 5, 10, 17, 26 b. 2, 9 28, 65 c. 2, 5, 10, 17 d. 0, 3, 8, 15 5. An experienced carpenter works three times as fast as his helper. Working together, it would take them 6 hours to finish a certain job. How long would it take the helper to do the job alone? a. 20 hrs b. 8hrs c. 24hrs d. 15hrs 6. Joey will be x years old y years from now. How old is she now? (REE SEPT 2019) a. y – x b. x c. x – y d. y 7. A 10-kg salt solution originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated? a. 2.5 b. 2.0 c. 15 d. 20 8. What is the remainder when the polynomial 𝑥 4 − 5𝑥 3 + 5𝑥 2 + 7𝑥 + 6 is divided by x + 2. a. 16 b. 32 c. 48 d. 68 9. In a hydrographic survey, a certain point below the surface of the water measures 12 fathoms. It is equivalent to a deep of how many feet? a. 72 b.60 c. 48 d. 36 10. The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers? a. 42.31 b. 50 c. 38.62 d. 57.12 11. At approximately what time after 1 o’clock will the hour and the minute hands of a clock form an angle of 120 degrees for the second time? a. 30 minutes b. 43 minutes c. 50 minutes d. 49 minutes 12. A speed boat can make a trip of 100 miles in one hour and 30 minutes if it travels upstream. If it travels downstream, it will take one hour and 15 minutes to travel the same distance. What is the river current? a. 193.45 mph b. 73.33 mph c. 293.33 mph d. 6.67 m Q1 - ALGEBRA QUIZ MATHEMATICS Page 1 13. If a two-digit number has x for its unit’s digit and y for its ten’s digit, represent the number a. 10x + y b. 10y + x c. yx d. xy 14. How many minutes after 4:00 PM will the minute hand of the clock overtakes the hour hand? a. 23 mins b. 19 mins c. 24 mins d. 22 mins 15. A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed? a. 1 hr b. 1/2 hr 16. If x + y = 2 and x^2 + y^2 = 1, find x^4 + y^4. a. -7/2 b. 4 c. 2 hr d. 3/2 hr c. 1/2 d. 7/2 17. The sum of three consecutive odd integers is 87. What is the largest integer? a. 24 b. 26 c. 31 d. 29 18. On one job, two power shovels excavate 20,000 m3 of earth, the larger shovel working for 40 hours and the smaller for 35 hours. Another job, they removed 40,000 m3 with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can the larger shovel move in one hour? a. 368.12 b. 173.91 c. 162.22 d. 347.8 19. 7 + 0i is a. Irrational number b. real number 20. Which of the following pairs of numbers are prime twins? a. (1, 3) b. (7, 9) c. imaginary number d. a variable c. (2, 4) d. (17, 19) 21. A pound of alloy of lead and nickel weighs 14.4 ounces in water, where lead losses 1/12 of its weight and nickel losses 1/8 of its weight. How much of each metal is in the alloy? a. Lead = 7.2 oz.; Nickel = 8.8 oz. c. Lead = 9.6 oz.; Nickel = 6.4 oz. b. Lead = 8.8 oz.; Nickel = 7.2 oz. d. Lead = 6.5 oz.; Nickel = 5.4 oz. 22. A job could be done by eleven workers in 15 days. Five workers started the job. They were reinforced with four more workers at the beginning of the 6th day. Find the total numbers of days it took them to finish the job. a. 20.56 b. 22.36 c. 21.42 d. 23.22 23. One pipe can fill a tank in 5 hours and another pipe can fill the same tank in 4 hours. A drainpipe can empty the full content of the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank? a. 2.5 hours b. 1.92 hours c. 2 hours d. 1.8 hours 24. Find the coefficient of the term involving b^5 in the expansion of (a^2 – 2b)^10 a. 3360 b. -3360 c. -960 d. -8064 25. Find the value of m that will make 4x^2 – 4mx + 4m + 5 a perfect square trinomial. a. 5 b. -2 c. 3 d.4 ALGEBRA QUIZ (Q1) MATHEMATICS Page 2 26. Find the coefficient of the term involving 𝑏4 in the expansion of (𝑎2 − 2𝑏)10 . a. -3360 b. 10! c. -960 d. 3360 27. How many terms of the progression 3, 5, 7 should there be so that their sum will be 3135. a. 65 b. 50 c. 55 d. 60 28. The selling price of TV set is double that of its cost. If the TV set was sold to a customer at a profit of 25% of the net cost, how much discount was given to the customer? a. 33.7 % b. 35.7 % c. 37.5 % d. 34.7 % 29. A and B can do a piece of work in 42 days, B and C in 31 days, and A and C in 10 days. Working together, how many days can all of them finish the work? a. 19 b. 20 c. 13 d. 18 30. A father is three times as old as his son. Four years ago, he was four times as old as his son was at that time. How old is his son? a. 24 b. 12 c. 36 d. 18 31. Solve for x in the following equation x + 4x + 7x + 10x + … + 64x = 1430 a. 3 b. 1 c. 2 d. 4 32. An iron bar 8 meters long has a 50 lb boy on one end and a 150 lb man at the opposite end. How far from the man should the fulcrum be located to balance the bar. a. 6m b. 2m c. 3m d. 5m 33. A rich man left his entire estate to his wife, daughter, son and bodyguard. His daughter and son got half the total value of the estate sharing in the ratio of 3:2. His wife got twice value as much as the share of the son. If the bodyguard received one million pesos, what is the total value of the estate? a. 10 million b. 9 million c. 5 million d. 6 million 34. The second term of an infinite geometric sequence is 4/9, and the sixth term is 1/36. What is the sum of all the terms of this sequence? a. 128/27 b. 64/27 c. 72/23 d. 16/9 35. If a piece of paper is 0.05 inches thick. Each time the paper is folded into half the thickness is doubled. If the paper was folded 12 times, how thick in feet the folded paper be? a. 12.34 b. 10.24 c. 17.07 d. 11.25 36. A 40-gram alloy containing 35% gold is to be melted with a 10-gram alloy containing 50% gold. How much percentage of gold is the resulting alloy? a. 30 % b. 38 % c. 45 % d. 40 37. Twice the middle digit of three-digit number is the sum of the other two. If the number is divided by the sum of its digit, the answer is 56 and the remainder is 12. If the digits are reversed, the number becomes smaller by 594. Find the number. a. 147 b. 741 c. 852 d. 258 ALGEBRA QUIZ (Q1) MATHEMATICS Page 3 38. The geometric mean and the arithmetic mean of the two numbers are 8 and 17, respectively. Find one of the numbers. a. 32 b. 16 39. What is the sum of all even integers from 10 to 500? a. 65955 b. 62730 c. 3 d. 4 c. 87950 d. 124950 40. If kx^3 – (k + 3)x^2 + 13 is divided by x – 4, and the remainder is 157. Then the value of k is _____. a. 3 b. 5 c. 6 d. 4 41. A building contractor buys 525 metal bars. Because he is buying more than 500 bars, the wholesaler gives him a discount of $420. If he paid $3,780, write an equation to find the cost per bar. a. 3780=420+525b c. 525b+420=3780 d. 525b-420=3780 b. -420-525b=3780 42. The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction. a. 13/5 b. 3/5 c. 5/13 d. 5/3 43. At exactly what time after 2 o’clock will the hour hand and the minute hand extend in opposite directions for the first time? a. 2:43 and 0.63 sec b. 2:43 and 3.82 sec c. 2:43 and 38.2 sec d. 2:43 and 6.3 sec 44. Find the sum of the roots of 5x2 – 10x + 2 = 0 a. 1/2 b. -1/2 c. 2 d. -2 45. Matthew, Luis and Eric can mow the lawn in 4, 6 and 7 hours respectively. What fraction of the yard can they mow in 1 hour if they work together? a. 17/84 b. 84/17 c. 84/47 d. 47/84 46. What are the values of n if (2n – 6) is greater than 1 but less than 14? a. 3, 4, 5, 6, 7, 8, 9 b. 3, 4, 5, 6, 7, 8, 9, 10 c. 4, 5, 6, 7, 8, 9 d. 4, 5, 6, 7, 8, 9, 10 47 It takes an airplane one hour and forty-five minutes to travel 500 miles against the wind and covers the same distance in one hour and fifteen minutes with the wind. What is the speed of the airplane? a. 342.85 mph b. 375.50 mph c. 450.50 mph d. 285.75 mph 48. What was the marked price of a shirt that sells at ₱ 300 after a discount of 20%? a. ₱ 280 b. ₱ 300 c. ₱ 340 d. ₱ 37 49. The resistance of a wire varies directly with its length and inversely with its area. If a certain piece of wire 10 m long and 0.10 cm in diameter has a resistance of 100 ohms, what will its resistance be if it is uniformly stretched so that its length becomes 12 m? a. 80 b. 90 c. 144 d. 120 50. If 16 is 4 more than 4x, find 5x -2. a. 14 b. 13 ALGEBRA QUIZ (Q1) c. 3 d. 5 MATHEMATICS Page 4