MACAPAGAL MATH EXAM 1.pdf

1. A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n. A. 55 B. 100 C. 110 D. 8 2. Which of the following is not a multiple of 11? A. 133...

1. A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n. A. 55 B. 100 C. 110 D. 8 2. Which of the following is not a multiple of 11? A. 1331 B. 88 C. 221 D. 122 3. Binoy, Boboy, and Bata are hired to paint signs. In 8 hours Binoy can paint 1 sign, Boboy can paint 2 signs, and Bata can paint 1 1/3 signs. They all come to work the first day, but Bata doesn’t like the job and quits after 3 hours. Boboy works half an hour longer than Bata and quits. How long will it take Binoy to finish the two signs they were supposed to paint? A. 1 1/2 hrs B. 2 hrs C. 3 hrs D. 2 1/3 hrs 4. Bonnie has twice as many cousins as Robert. George has 5 cousins, which is less than Bonnie has. How many cousins does Robert have? A. 8 B. 21 C. 4 D. 17 5. The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find the width of the rectangle. A. 37.5 inches C. 13.5 inches B. 15 inches D. 14.5 inches 6. Melissa is four times as old as Jim. Pat is five years older than Melissa. If Jim is y years old, how old is Pat? A. 4y + 5 B. y + 5 C. 5y D. 4y 7. Find the value of x in the equation 24x^2 + 5x - 1 = 0. A. (1/6, 1) C. (1/2, 1/5) B. (1/8, -1/3) D. (1/2, -1/5) 8. In the vicinity of a bonfire, the temperature T in deg C at distance of x meters from the center of the fire was given by: T = 762,500 / (x^2 + 300). At what range of distances from the fire’s center was the temperature less than 500 deg C? A. More than 35 meters C. More than 25 meters B. More than 45 meters D. More than 30 meters 9. Find the sum of the first 10 terms of the GP 2, 4, 8, 16,.... A. 2046 B. 225 C. 1024 D. 1023 10. A student already finished 70% of his homework in 42 minutes. How many minutes does he still have to work? A. 18 B. 20 C. 24 D. 16 11. A line segment is a side of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle? A. 1:1 B. 4:1 C. 3:2 D. 2:1 12. The plane rectangular coordinate system is divided into eight parts which are known as A. octants C. axis B. coordinates D. quadrants 13. Jeff burns 500 calories per hour bicycling. How long will he have to bike to burn 750 calories? A. 1.5 hours B. 3 hours C. 2 hours D. 0.5 hour 14. How many ancestors does a set of triplets have in the eleven generations before them? Assume there are no duplicates. A. 4085 B. 4009 C. 4095 D. 4005 15. A boat can travel 10 miles downstream and at the same time can travel 6 miles upstream. If the current of water is 3 mph, find the speed of a boat in still water. A. 9 mph B. 7 mph C. 12 mph D. 8 mph 16. Evaluate 1 – 2/3 + 4/9 – 8/27 + 16/81 – 32/243 + … A. 0.666 B. 1.333 C. Divergent D. 0.6 17. Mrs. Farrell’s class has 26 students. Only 21 were present on Monday. How many were absent? A. 5 B. 4 C. 16 D. 15 18. Joseph gave of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally? A. 50 B. 30 C. 20 D. 40 19. Evaluate arc cot [2cos (arc sin 0.5)]. A. 60o B. 30o C. 45o D. 90o 20. If the polynomial x^3 + 4x^2 – 3x + 8 is divided by x – 5, determine the remainder. A. 42 B. 210 C. 218 D. 45 21. The areas of two squares differ by 7 sq. ft and their perimeters differ by 4 ft. Determine the sum of their areas. A. 27 B. 22 C. 25 D. 28 22. On a particular morning, the temperature went up 1 degree every 2 hours. If the temperature was 53 degrees at 5 A.M. at what time was it 57 degrees? A. 11 AM B. 1 PM C. 2 PM D. 12 NN 23. Suppose two radar stations located 20 miles apart each detect an aircraft between them. The angle of elevation measured by the first station is 35 degrees, whereas the angle of elevation measured by the second station is 15 degrees. Determine the height of the airplane. A. 3.876 B. 4.279 C. 5.521 D. 2.871 24. Three circles of radii 3, 4, and 5 inches, respectively are tangent to each other externally. Find the largest angle of a triangle formed by joining the centers. A. 73.4° C. 72.6° B. 74.3° D. 76.2° 25. Divide 1/8 by 8. A. 64 B. 1/18 C. 18 D. 1/64 26. The tangent of an angle of a right triangle is 0.75. What is the cosecant of the angle? A. 1.667 B. 1.333 C. 1.414 D. 1.732 27. 42% of 997 = A. 418.74 B. 450.24 C. 990.24 D. 499.44 28. A container is in the form of a right circular cylinder with an altitude of 6 in and a radius of 2 in. If an asbestos of 1 in thick is inserted inside the container along its lateral surface, find the volume capacity of the container. A. 12.57 cu.in C. 18.58 cu.in B. 18.85 cu.in D. 12.75 cu.in 29. At exactly what time after 5 o’clock will the hour hand and the minute hand be perpendicular for the first time? A. 5:10 and 54 sec C. 5:30 and 24 sec B. 5:15 and 24 sec D. 5:20 and 54 sec 30. How many positive real roots are there in the polynomial: x^4 – 4x^3 + 7x^2 – 6x – 18 = 0. A. 1 or 2 B. 3 or 1 C. 3 or 0 D. 1 or 0 31. If f(x) = 10^x + 1, then f(x + 1) – f(x) is equal to A. 10(10^x) C. 1 B. 9(10^x) D. 9(10^x + 1) 32. After having a meal at a restaurant, Jared is charged 9% of the cost of the meal in sales tax. In addition, he wants to leave 15% of the cost of the meal before tax as a tip for the server. If the meal costs $24.95 before tax and the tip, what is the total amount he needs to pay for the meal, tax, and tip? A. $5.99 B. $28.69 C. $47.41 D. $30.94 33. A contractor has 50 men of the same capacity at work on a job in 30 days, the working day being 8 hours, but the contract expires in 20 days, how many workers should he add? A. 30 B. 15 C. 20 D. 25 34. Solve for x in the equation, 7.4 x 10^-4 = e^-9.7x A. 0.7243 B. 0.7432 C. 0.7331 D. 0.7621 35. What are the values of n if (2n – 6) is greater than 1 but less than 14? A. 4,5,6,7,8,9 C. 4,5,6,7,8,9,10 B. 3,4,5,6,7,8 D. 2,3,4,5,6,7 36. z varies directly as x and inversely as \(y^2\). If x = 1 and y = 2 then z = 2. Find z when x = 3 and y = 4. A. 3.5 B. 1.5 C. 2.5 D. 3 37. What is the value of x in Arctan 3x + Arctan 2x = 45 degrees? A. −1/6 B. 1 C. −1 D. 1/6 38. A four-pound mixture of raisins and nuts is \(2/3\) raisins. How many pounds of nuts are there? A. 2.6 pounds B. 1.6 pounds C. 1.3 pounds D. 2.4 pounds 39. Larry finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower? A. 73.61 m B. 63.61 m C. 53.61 m D. 83.61 m 40. What time after one o’clock will the hands of the clock coincide for the first time? A. 1:5-5/11 B. 1:6-5/11 C. 1:4-5/11 D. 1:7-5/11 min min min min 41. Susan starts working at 4:00 and Dy starts at 5:00. They finished at the same time. If Susan worked x hours, how many hours did Dy work? A. x + 2 B. x – 1 C. x D. x + 1 42. A ball is dropped from a height of 18 m. On each rebound, it rises 2/3 of the height from which it last fell. What distance has it traveled at the instant it strikes the ground for the 5th time? A. 37.89 m B. 73.89 m C. 75.78 m D. 57.78 m 43. The drivers at F and M trucking must report the mileage on their vehicle each week. The mileage reading of Ed’s vehicle was 20,907 at the beginning of one week, 21,053 at the end of the same week. What is the total number of miles driven by Ed that week? A. 235 B. 146 C. 1046 D. 145 44. Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. A. 1 mil B. 2.5 mils C. 2.04 mils D. 4 mils 45. Justin weighed 8 lbs 12 oz when he was born. At his two-week check-up, he had gained 8 ounces. What was his weight in pounds and ounces? A. 9 lb 4 oz B. 10 lb 2 oz C. 8 lb 15 oz D. 9 lb 46. Find the sum of all odd integers between 100 and 1000. A. 247500 B. 148500 C. 374200 D. 454500 47. Four is added to the quantity two minus the sum of negative seven and six. This answer is then multiplied by three. What is the result? A. 57 B. -21 C. 21 D. 15 48. Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486. A. 844 B. 748 C. 984 D. 540 49. The dimensions of a rectangular prism can be expressed as x + 1, x – 2 and x + 4. In terms of x; what is the volume of the prism? A. x^3 + 3x>> - 6x + 8 C. x^3 + 5x>> - 2x + 8 B. x^3 + 3x>> - 6x - 8 D. x^3 - 5x>> + 2x + 8 50. A laboratory keeps two acid solutions on hand. One is 20% acid and the other is 35% acid. How many liters of distilled water should be added to a liter of 35% acid solution in order to dilute it to a 20% acid solution? A. 0.57 B. 0.25 C. 0.45 D. 0.75