Basic_engineering_correlation_algebra_re (1).pdf

Basic Engineering Correlation (Algebra Reviewer) 1. Three transformers are directly proportional to the KVA cost P30,000. The cost of each transformer is directly proportional to the KVA rating and each has a constant of proportionally of 0.9, 0.8 and 0.6, respectively. Find the cost of the KVA transformer. a. P7,500 b. P13,500 c. P15,500 d. P9,000 2. What is the sum of the following sequence of terms 18, 25, 32, 39, . . . ,67? a. 280 b. 380 c. 320 d. 340 3. A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at 3/5 of its former rate and arrives three hour after the time; but had the accident happened 50 miles farther on yhe line, it would have arrived one and one-half hour sooner. Find the length of the journey. a. 850/9 miles b. 800/9 miles c. 920/9 miles d. 910/9 miles 4. Ten less than four times a certain number is 14. Determine the number. a. 5 b. 7 c. 4 d. 6 5. The roots of a quadratic equation are 1/3 and 1/4. What is the equation? a. 12x2 + 7x + 1=0 b. 12x2 - 7x - 1=0 c. 12x2 - 7x + 1=0 d. 12x2 + 7x - 1=0 6. The geometric mean of 4 and 64: a. 30 b. 34 c. 24 d. 16 7. A certain company manufactures two products, X and Y, and each of these products must be processed on two different machines. Product X requires 1 minute of work time per unit on

machine 1 and 4 minutes of work time on machine 2. Product Y requires two minutes of work time per unit on machine 1 and 3 minutes of work time per unit on machine 2. Each day, 100 minutes are available on machine 1 and 200 minutes are available on machine 2. To satisfy certain customers, the company must produce at least 6 units per day of product X and at least 12 units of product Y. If the profit of each unit of product X is P50 and the profit of each unit of product Y is P60, how many of each product should be produced in order to maximize the company's profit? a. X = 20 units, Y = 40 units b. X = 30 units, Y = 40 units c. X = 20 units, Y = 50 units d. X = 40 units, Y = 60 units 8. If 4y3 + 18y2 + 8y - 4 is divided by 2y + 3, the remainder is: a. 10 b. 12 c. 11 d. 9 9. The square of a number increased by 16 is the same as 10 times the number. Find the number. a. 8, 2 b. 6, 2 c. 4, 2 d. 2, 2 10. The seating section in a coliseum has 30 seats in the first row, 32 in the second row, 34 seats in the third row and so on, until the tenth row is reached, after which there are ten rows each containing 50 seats. Find the total number of seats in the section. a. 1290 b. 1080 c. 890 d. 980 11. If the roots of an equation is zero, then they are classified as a. hypergolic solutions b. trivial solutions c. conditional solutions d. extraneous solutions 12. An airplane went 360 miles in 2 hours with the wind and, flying back the same route, it took 3 3/5 hours against the wind. What was its speed in still air? a. 120 mph

b. 150 mph c. 140 mph d. 130 mph 13. Find the fourth proportion to 3, 5 and 21. a. 27 b. 65 c. 56 d. 35 14. Two jet planes travelling towards each other take off at the same time from two airports located 3000 miles apart. If they passed each other after two hours, determine the speed of each plane if one plane is flying at a speed 100 mph faster than the other. a. 700 and 800 mph b. 600 and 700 mph c. 700 and 900 mph d. 800 and 500 mph 15. Round off 0.003086 to three significant figures. a. 0.0031 b. 0.00308 c. 0.003 d. 0.00309 16. It is sequence of numbers that successive terms differ by a constant. a. geometric progression b. arithmetic progression c. harmonic progression d. finite progression 17. At 2:00 pm, an airplane takes off at 340 mph on an aircraft carrier. The aircraft carrier moves due south at 25 kph in the same direction as the plane. At 4:05 pm, the communication between the plane and aircraft carrier was lost. Determine the communication range in miles between the plane and the carrier. a. 785 miles b. 557 miles c. 412 miles d. 656 miles 18. A manufacturing firm maintains one product assembly line to produce signal generators. Weekly demand for the generators is 25 units. The line operates for 7 hours per day, 5 days per week. What is the maximum production time per unit in hours required for the line to meet the demand? a. 3 hours b. 1 hour c. 2.25 hours

d. 0.75 hour 19. Ana is 5 years older than Beth. In5 years, the product of their age is 1.5 times the product of their product ages. How old is Beth now? a. 20 b. 25 c. 18 d. 27 20. A chemist of a distillery experimented on two alcohol solutions of different strengths, 30% alcohol and 60% alcohol, respectively. How many cubic meters of each strength must be used in order to produce a mixture of 50 cubic meters that contain 40% alcohol? a. 20, 30 m3 b. 33 1/3, 16 2/3 m3 c. 21 1/3, 28 2/3 m3 d. 10, 40 m3 21. Subtracting 2.6 x 103 from8.26 x 104 is: a. 8.0 x 104 b. 10.86 x 104 c. 8.0 x 103 d. 10.86 x 103 22. The time requires by an evaluator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for 10 hp motor to lift 100 lbs through 50 feet, what size of motor is required to lift 800 lbs in 40 seconds through a distance of 40 feet? a. 56 hp b. 50 hp c. 58 hp d. 48 hp 23. Find the 30th term of the arithmetic progression 4, 7, 10, . . . a. 94 b. 941 c. 81 d. 104 24. Convergent series is a sequence of decreasing numbers or when the succeeding term is _______ than the preceding term. a. equal b. slightly more c. greater d. lesser 25. In the equation x2 + x = 0, one root is x equal to:

a. 1 b. ¼ c. 5 d. none of these. 26. How many liters of water must be added to 35 liters of 89% hydrochloric acid solution to reduce its strength to 75%? a. 4.83 liters b. 6.53 liters c. 7.33 liters d. 5.34 liters 27. Round off 34.2814 to four significant figures. a. 34.8214 b. 34 c. 34.28 d. 34.281 28. Solve algebraiclly: 11y2 - 3x2 = 41 4x2 + 7y2 = 32. a. (-2, 2) and (2, -2) b. (± 1, ± 2) c. (± 1, ± 4) d. (2, 3)and ( -2, -3) 29. Determine the sum of the progression if there are 7 arithmetic means between 3 and 35. a. 98 b. 304 c. 214 d. 171 30. Crew No. 1 can finish installation of an antenna tower in 200 man-hour while Crew No. 2 can finish the same job in 300 man-hour. How long will it take both crews to finish the same job, working together? a. 120 man-hour b. 140 man-hour c. 100 man-hour d. 160 man-hour 31. In how many minutes after 3:00 P.M will the minute hand of a clock coincide with the hour hand? a. 15.455 b. 17.273 c. 16.364 d. 18.182 32. In a class of 40 students, 27 students like Calculus and 25 like Geometry. How many students liked both Calculus and Geometry? a. 12 b. 13

c. 11 d. 10 33. The electric power which a transmission line can transmit is proportional to the product of its design voltage and current capacity, and inversely to the transmission distance. A 115 - kilovolt line rated at 100 amperes can transmit 150 megawatts over 150 km. How much power, in megawatts can a 230 kilovolt line rated at 150 amperes transmit over 100 km? a. 595 b. 675 c. 485 d. 785 34. The electrical resistance of a wire varies as its length and inversely as the square of its diameter. If a 100 m long and 1.25 mm in diameter has a resistance of 30 ohms, find the length of the wire of the same material whose resistance and diameter are 25 ohms and 0.74 mm respectively. a. 25 m b. 35 m c. 30 m d. 40 m 35. What time after 3 o'clock will the hands of the clock be together for the first time? a. 3:02.30 b. 3:17.37 c. 3:16.36 d. 3:14.32 36. A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hours. How long will it take both pumps to pump out water in the tank? a. 6 hours b. 6 1/2 hours c. 7 1/2 hours d. 7 hours 37. If the sum is 220 and the first term is 10, find the common difference if the last term is 30. a. 3 b. 4 c. 5 d. 2 38. Equal volumes of two different liquids evaporated at different but constant rates. If the first is totally evaporated in 6 weeks and the second in 5 weeks, when will the second be onehalf the volume of the first?

a. 3.5 weeks b. 3 weeks c. 4 weeks d. 4 2/7 weeks 39. MCMXCIV is a Roman numeral equivalent to: a. 1994 b. 2174 c. 3974 d. 2974 40. Find the 100th term of the sequence 1.01, 1.00, 0.99, . . a. 0.01 b. 0.02 c. 0.03 d. 0.04 41. At what time after 12:00 noon will the hour hand and minute hand of the clock first form an angle of 120o? a. 12:21.818 b. 12:22.818 c. 12:18.818 d. 12:24.818 42. Solve the simultaneous equations: 3x - y = 6 9x y = 12. a. ( -1, 3 ) b. ( 1, -3 ) c. ( 1, 3 ) d. ( -1, -3 ) 43. A merchant has three items on sale: namely, a radio for P50, a clock fo P30, and a flashlight for P1. At the end of the day, she has sold a total of 100 of the three items and has taken exacly P1000 on the total sales. How many radios did he sale? a. 4 b. 80 c. 20 d. 16 44. What is the sum of the first 10 terms of the geometric progression 2, 4, 8, 16, . . . ? a. 1696 b. 2046 c. 1024 d. 1846 45. In a commercial survey involving 1000 persons on brand preferences, 120 were found to prefer brand x only, 200 persons prefer brand y only, 150 persons prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x, and 370 prefer either brand z or x but not y,

and none prefer all the three brands at a time. How many persons have no brand preference with any of the three brands? a. 200 b. 100 c. 280 d. 70 46. Which number has four significant figures? a. 1.414 b. 0.0014 c. 0.141 d. 0.01414 47. A club of 40 executives, 33 likes to smoke Marlboro and 20 likes to smoke Philip Morris. How many like both? a. 12 b. 13 c. 14 d. 11 48. 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. 41.25 b. 42.31 c. 44.25 d. 40.21 49. There are 9 arithmetic means between 11 and 51. The sum of the progreesion is: a. 374 b. 341 c. 320 d. 337 50. If a two digit number has X for its unit digit and Y for its tenth digit, represent the number. a. 10Y + X b. X + Y c. XY d. 10Y + Y 51. In the series 1, 1, 1/2, 1/6, 1/24, . . . , determine the 6th term. a. 1/60 b. 1/120 c. 1/150 d. 1/90 52. Round off 149.691 to the nearest integer. a. 149 b. 149.7 c. 149.69

d. 150 53. The sum of two numbers is 21, and one number twice the other. Find the numbers. a. 9 & 12 b. 7 & 14 c. 8 & 13 d. 65 & 70 54. The probability for the ECE board examinees from a certain school to pass the Mathematics subject is 3/7 and that for the Communication subject is 5/7. If none of the examinees failed in both subjects, how many examinees from the school took the examination? a. 30 b. 27 c. 29 d. 28 55. Solve for x that satisfies the equation 6x2 - 7x 5 = 0. a. 3/5 or ¾ b. 3/2 or 3/8 c. 5/3 or -1/2 d. 7/5 or -7/15 56. Three transformers are rated 5 KVA, 10 KVA and 25 KVA, respectively. The total cost of the three transformers is P15, 000.00. If the cost of each transformer is proportional to its KVA rating multiplied by the factor 1, 0.8 and 0.6 respectively, find the cost of the 10 KVA transformer. a. P4,286 b. P4,075 c. P4,101 d. P4,393 57. Solve the simultaneous equations: 2x2 - 3y2 = 6 3x2 + 2y2 = 35. a. x-3 or 3; y2 or -1 b. x3 or -3; y2 or -2 c. x3 or -3; y-2 or 1 d. x3 or -3; y-2 or 3 58. The sum of the progression 5, 8, 11, 14, . . . Is 1025. How many terms are there? a. 25 b. 24 c. 28 d. 29 59. If x varies directly as y and inversely as z, and x = 14 when y = 7 and z = 2, find the value of x when y = 16 and z = 4. a. 4

b. 8 c. 16 d. 14 60. The arithmetic means of 6 numbers is 17. If two numbers are added to the progression, the new set of the numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4? a. 18, 22 b. 23, 27 c. 10, 14 d. 31, 35 61. The sum of Kim's and Kevin's ages is 18. In 3 years, Kim will be twice as old as Kevin. What are their ages now? a. 5, 13 b. 7, 11 c. 6, 12 d. 4, 14 62. The intensity of sound varies directly as the strength of the source and inversely as the square of the distance from the source. Write the equation to the describe relation. a. I = 1/d2 + k b. I=k/d2 c. I = kd2 d. I = d2/k 63. Determine the sum of the infinite series 1/3 + 1/9 + 1/27 +. . . a. 1 b. ¾ c. ½ d. 2/3 64. For a particular experiment, you need 5 liters of 10% solution. You find 7% and 12% solutions on the shelf. How much of the 7% solution you mix with the appropriate amount of the 12% solution to get 5 liters of 10% solution? a. 2.5 b. 2 c. 1.5 d. 3 65. Find the sum of the roots of 5x2 - 10x + 2 = 0 a. -2 b. ½ c. -1/2 d. 2 66. Maria is 36 years old. Maria was twice as old as Anna was when Maria was as old as Anna is now. Jow old is Anna now?

a. 26 b. 31 c. 29 d. 24 67. Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2. a. 2/3 b. 1/6 c. ¾ d. ¼ 68. A tank is fitted with two pipes. The first pipe can fill the tank in 10 hours. But after it has been open for 3 hours, the second pipe is opened and the tank is filled up in 4 hours more. How long would it take the second pipe alone to fill tha tank? a. 12.67 hr b. 10.55 hr c. 14.89 hr d. 13.33 hr 69. How many kg of cream containing 25% butter fat should be added to 50 kg of milk containing one percent butter fat to produce milk containing 2% butter fat? a. 4.17 b. 2.174 c. 5.221 d. 3.318 70. The electrical resistance offered by an electric wire varies directly as the length and inversely as the square of the diameter of the wire. Compare the electrical resistance offered by two pieces of wire of the same material, one being 100 m long and 8 mm in diameter, and the other 50 m long and 3 mm in diameter. a. R1 = 0.28 R2 b. R1 = 0.84 R2 c. R1 = 0.57 R2 d. R1 = 0.95 R2 71. A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer, and so on until there are 10 bricks in the last layer. How many bricks are there all together? a. 458 b. 639 c. 724 d. 538 72. A 100 g of water are mixed with 150 g of alcohol (p = 790 kg/cu.m.). What is the specific

volume of the resulting mixtures? Assuming that the two fluids mix completely. a. 0.63 cu cm/g b. 0.88 cu. cm/g c. 0.82 cu cm/g d. 1.20 cu cm/g 73. One number is 5 less than another. If the sum is 135, what are the numbers? a. 65, 70 b. 60, 65 c. 75, 80 d. 70, 75 74. 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. 8/5 b. 13/5 c. 5/13 d. 3/5 75. An inexperienced statistical clerk submitted the following statistics to his manager on the average rate of production of transistorized radios in an assenbly line: "1.5 workers produced 3 radios in 2 hour." How many workers are employed in the assembly line working 40 hours per week if weekly production is 480 radios? a. 12 b. 10 c. 13 d. 14 76. Find the mean proportion of 4 and 36. a. 12 b. 8 c. 16 d. 9 77. An automobile is travelling at a velocity of 10 mph. If the automobile mileage meter already reads 20 miles, find the mileage meter reading after 3 hours. a. 60 miles b. 30 miles c. 50 miles d. 40 miles 78. Find the sum of 1, -1/5, 1/25, . . . a. 6/7 b. 7/8 c. 5/6 d. 8/9

79. A man is 41 years old and his son is 9. In how many years will the father be three times as old as his son? a. 7 b. 8 c. 6 d. 5 80. A tank is fitted with an intake pipe that will fill it in 4 hours, and an outlet pipe that will empty it in 9 hours. If both pipes are left open, how long will it take to fill the empty tank? a. 7.2 hr b. 6.8 hr c. 6.2 hr d. 7.4 hr 81. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point. a. 1 b. 5 c. 7 d. 8 82. A mechanical engineer who was awarded a P450,000.00 contract to install the machineries of an oil mill failed to finish the work on time. As provided for in the contract, he has to pay a daily penalty equivalent to one-fourth of one percent of the contract price for the first ten days of the delay, one-half percent per day for the next ten days and one percent per day for every day thereafter. If the total penalty paid was P60,750.00, how many days was the completion of the contract delayed? a. 30 days b. 26 days c. 24 days d. 28 days 83. A man started driving his car at a certain time froma certain place. On arrival at his destination at the precise appointed time, he said, "If I had averaged 6 miles per hour faster, I would have been 5 minutes early. But if I had averaged 5 mph slower, I would have been 6 minutes late." Find how far he had driven. a. 20 miles b. 10 miles c. 25 miles d. 15 miles 84. Pedro started running at a speed of 10kph. Five minutes later, Mario started running in the same

direction and catches up with Pedro in 20 minutes. What is the speed of Mario? a. 12.5 kph b. 17.5 kph c. 20.5 kph d. 15.0 kph 85. The equation whose roots are the reciprocal of the solutions of 2x2 - 3x - 5 = 0. a. 3x2 - 5x - 2=0 b. 5x2 - 2x - 3=0 c. 5x2 + 3x - 2=0 d. 2x2 + 5x - 3=0 86. In certain Board Examination, 119 examinees too the Shop Machinery subjected, 104 examinees took thye Power Plant Machinery subject and 115 examinees took the Industrial Plant Machinery subject. Seventy-eight (78) conditioned examinees took only Shop Machinery and Power Machinery subjects. Seventy-one (71) conditioned examinees took only the POwer Plant Machinery and Industrial Plant Machinery subjects. Eighty-five (85) conditioned examinees took only Industrial Plant Machinery and Shop Machinery subjects. Fifty-four took all the three subjects. How many examinees took the Certified Plant Mechanic board examination? a. 153 b. 165 c. 158 d. 176 87. If a train passes as many telegraph poles in one minute as it goes miles per hour, how far apart are the poles? a. 78 ft. b. 98 ft. c. 68 ft. d. 88 ft. 88. A man 38 years old has a son of ten years old. In how many years will the father be three times as old as his son? a. 2 b. 3 c. 4 d. 5 89. In Algebra, the operation of root extraction is called as _____. a. revolution b. resolution c. involution

d. evolution 90. Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone? a. 15 b. 13 c. 10 d. 11 91. There are 9 arithmetic means between 11 and 51. The sum of the progression is: a. 374 b. 341 c. 320 d. 337 92. The number 1.123123123. . . Is a. surd b. transcendental c. rational d. irrational 93. Which of the following numbers should be changed to make all the numbers from an arithmetic progression when properly arranged? a. 27/14 b. 45/28 c. 20/14 d. 3/28 94. How many significant digits do 10.097 have? a. 4 b. 5 c. 2 d. 3 95. Find the sum of the infinite geometric progression 6, -2, 2/3, . . . a. 9/2 b. 7/2 c. 3/2 d. 11/2 96. The time required for two examinees to solve the same problem differ by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve the problem? a. 3 minutes b. 5 minutes c. 2 minutes d. 4 minutes

97. An equipment installation job in the completion stage can be completed in 50 days of 8 hours day work, with 50 men working. With the contract expiring in 40 days, the mechanical engineer contractor decided to add 15 men on the job, overtime not being permitted. If the liquidated damages is P5,000 per day of delay, and they are paid P150 per day, will the engineer be able to complete the job on time? Would he save money with the addition of workers? a. No, P20,500 losses b. Yes, P44,750 savings c. Yes, P24,500 savings d. No, P15,750 losses 98. An airplane flying with the wind, took 2 hours to travel 1000 km and 2.5 hours in flying back. What was the wind velocity in kph? a. 40 b. 70 c. 60 d. 50 99. If a = b, then b = a. This illustrates which axiom in Algebra? a. Transitive Axiom b. Reflexive Axiom c. Symmetric Axiom d. Replacement Axiom 100. The ten's digit of a certain two digit number exceeds the unit's digit by four and is one less than twice the unit's digit. Find the number. a. 59 b. 95 c. 65 d. 85 101. One pipe can fill a tank in 6 hours and another pipe can fill the same in tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all three pipes open, how lomg will it take to fill in the tank? a. 2.18 hrs b. 2.23 hrs c. 2.81 hrs d. 2.32 hrs 102. An equipment installation job in the completion stage can be completed in 40 days of 8 hours day work with 40 men working. With the contract expiring in 30 days, the mechanical engineer contractor decided to add 10 men on the job, overtime not being permitted. If the liquidated damages is P2,000 per day of delay, and the men

are paid P80 per day, will the engineer be able to complete the job on time? a. No, there would be no savings b. No, P16,000 would be lost c. Yes, there would just be break even d. Yes, P16,000 would be saved 103. It takes Butch twice as it takes Dan to do a certain piece of work. Working together they can do the work in 6 days. How long would it take Dan to do it alone? a. 12 days b. 9 days c. 10 days d. 11 days 104. Robert is 15 years older than his brother Stan. However, "y" years ago, Robert was twice as old as Stan. If Stan is now "b" years old b.y, find the value of (b-y). a. 18 b. 17 c. 15 d. 16 105. Mike, Loui and Joy 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. 47/84 hr b. 84/47 hr c. 34/60 hr d. 45/84 hr 106. The volume of hemisphere varies directly as the cube of its radius. The volume of a sphere with 2.54 cm radius is 20.75 cm3. What is the volume of a sphere with 3.25 cm radius of the same kind? a. 4056 cm3 b. 45.98 cm3 c. 43.47 cm3 d. 39.20 cm3 107. Add the following and express in meters: 3 m + 2 cm + 70 mm. a. 3.14 m b. 2.90 m c. 3.12 m d. 3.09 m 108. From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock describe an arc of: a. 90o b. 60o c. 540o

d. 180o 109. A clock has dial face 304.80 mm in radius. The minute hand is 228.60 mm long while the hour hand is 152.40 mm long. The plane of rotation of the minute hand is 50.80 mm above the plane of rotation of the hour hand. Find the distance between the tips of the hands of the clock at 5:40 AM. a. 228 mm b. 239 mm c. 243 mm d. 233 mm 110. A certain manufactured part can be defective because it has one or more out of the three possible defects: insufficient tensile strength, a burr, or a diameter outside of tolerance limit. In a lot of 500 pieces: 19 have a tensile strength defects, 17 have a burr, 11 have an unacceptable diameter, 12 have tensile strength and burr defects, 7 have tensile strength and diameter defects, 5 have burr and diameter defects and 2 have all three defects. Determine: How many of the pieces have no defects? How many pieces have only burr defects? How many pieces have exactly 2 defects? a. 475, 2, 18 b. 490, 4, 10 c. 465, 3, 7 d. 480, 4, 6 111. Mary is 24 years old. Mary is twice as old as Ana waswhen Mary was as old as Ana is now. How old is Ana? a. 18 b. 16 c. 20 d. 19 112. The electrical resistance of wire made of a certain material varies as its length and inversely as the square of the diameter. If the wire 200 meters long and 1.25 mm in diameter has a resistance of 60 ohms, find the length of the wire of the same material, whose resistance and diameter are 5 ohms and 0.65 mm, respectively. a. 3.96 m b. 4.51 m c. 4.28 m d. 5.72 m 113. A man leaving his office on one afternoon noticed the clock at past two o'clock. Between two

three hours, he returned to his office noticing the hands of the clock interchanged. At what time did he leave the office and the time that he returned to the office? a. 2:27.08, 5:11.19 P.M. b. 2:26.01, 5:10.01 P.M c. 2:26.01, 5:10.01 P.M. d. 2:26.01, 5:12.17 P.M. 114. A medium unshaded lamp hangs 8 m directly above the table. To what distance should it be lowered to increase the illumination to 4.45 times the former value? Illumination intensity varies inversely to the square of the distance. a. 4.75 m b. 4.55 m c. 3.79 m d. 3.95 m 115. Roberto is 25 years younger than his father. However, his father will be twice his age in 10 years. Find their ages now. a. 15 and 40 b. 10 and 35 c. None of the choices d. 20 and 45 116. A storage battery discharges at a rate which is proportional to the charge. If the charge is reduced by 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge? a. 6 b. 4 c. 3 d. 5 117. Prior to the last IBP elections, a survey was conducted in a certain barangay in Metro Manila to find out which of three political parties they like best. The results indicated that 320 like KBL, 250 like LABAN and 180 liked INDEPENDENTS. But of these, 160 like both KBL and LABAN, 100 liked both LABAN and INDEPENDENTS and 70 like both KBL and INDEPENDENTS. Only 30 said they like all the three parties and none admitted that they did not like any party. How many voters are there in the barangay? a. 474 b. 525 c. 450 d. 540

118. A man left his home at past 3:00 o'clock P.M as indicated in his wall clock. Between 2 and 3 hours after, he returned home and noticed the hands of the lock interchanged. At what time the man leave his home? a. 3:24.73 P.M b. 3:18.52 P.M c. 3:31.47 P.M d. 3:28.65 P.M 119. Given: f(x) = ( x+ 3) (x - 4) +4. When f(x) is divided by (x - k), the remainder is k. Find k. a. 2 b. 6 c. 4 d. 8 120. A & B working together can finish painting the house in six days. A working alone, can finish it in five days less than B. How long will it take each of them to finish the work alone? a. 15 days for A 20 days for B b. 10 days for A 25 days for B c. 15 days for A 20 days for B d. 10 days for A 15 days for B 121. A statistical clerk submitted the following reports: "The average rate of production of radios is 1.5 units for every 1.5 hours of work by 1.5 workers." How many radios were produced in one month by 30 men working 200 hours during the month? a. 4000 b. 3500 c. 4500 d. 5000 122. A piece of paper is 0.05 in 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 will be? a. 15.2 b. 16.25 c. 17.06 d. 18.5 123. 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 number of days it took them to finish the job. a. 22.36 days b. 20.56 days c. 23.22 days

d. 21.42 days 124. Six times the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its digits, the answer is 51 and the remainder is 11. If the digits are reversed the number becomes smaller by 198, find the number. a. 825 b. 775 c. 725 d. 875 125. Given that "w" varies directly as the product of x and y and inversely as the square of z and that w = 4 when x = 2, y = 6 and z = 3. Find tha value of "w" when x = 1, y = 4 and z = 2. a. 5 b. 4 c. 3 d. 2 126. A man driving his car at a certain speed from his house will reach his office in 6 hours. If he increased his speed 15 mph, he would reach his office 1 hour earlier. Find the distance from his office to his house. a. 350 miles b. 450 miles c. 520 miles d. 250 miles 127. Determine x, so that x, 2x + 7, 10x - 7 will be a geometric progression. a. 7, -15/6 b. 7, -7/5 c. 7, -5/6 d. 7, -7/6 128. Solve for the values of x and y in 4x + 2y = 5 and 13x - 3y = 2. a. (1, 3) b. (3/2, 1/2) c. (1, 2) d. ( 1/2, 3/2 ) 129. Determine the k so that the equation 4x2 + kx + 1 = 0 will have just one real root. a. 5 b. 6 c. 4 d. 3 130. An airplane travels from points A and B with the distance of 1500 km and a wind along its flight line. If it takes the airplane 2 hours from A to B with

the tailwind and 2.5 hours from B to A with the headwind, what is the velocity? a. 700 kph b. 675 kph c. 450 kph d. 750 kph 131. How many numbers between 10 and 200 are exactly divisible by 7? Find their sum. a. 2835 b. 2840 c. 283 d. 2830 e. 27 numbers; sum f. 28 numbers; sum g. 26 numbers; sum h. 26 numbers; sum 132. A gasoline tank of a car contains 50 liters of gasoline and alcohol, the alcohol comprising 25%. How much of the mixture must be drawn off and replaced by alcohol so that the tank will contain a mixture of which 50% is alcohol? a. 10.67 liters b. 20.33 liters c. 16.67 liters d. 16.33 liters 133. In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there? a. 16 b. 14 c. 10 d. 12 134. Two thousand (2000) kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with anothercontaining 6% nickel. How much of each is needed? a. 800 kg, 1200 kg b. 500 kg, 1500 kg c. 600 kg, 1500 kg d. 400 kg, 1600 kg 135. A boat man rows to a place 4.8 miles with the stream and black in 14 hours, but that he can row 14 miles with the stream in the same time as 3 miles against the stream. Find the rate of the stream. a. 1 mile per hour b. 0.6 mile per hour c. 0.8 mile per hour

d. 1.5 mile per hour 136. Gravity causes a body to fall 16.1 ft in the first second, 48.3 ft in the 2nd second, 80.5 ft in the 3rd second. How far did the body fall during the 10th second. a. 250.1 ft b. 305.9 ft c. 529.45 ft d. 417.3 ft 137. Solve for x : 10x2 + 10 x2 + 1 = 0. a. -0.331, 0.788 b. -0.311, -0.887 c. -0.113, -0.788 d. -0.113, -0.887 138. An airplane travels from points A and B with a distance of 1500 km and a wind along its flight line. If it takes the airplane 2 hours from A and B with the tailwind and 2.5 hours from B to A with the headwind, What is the velocity? a. 700 kph b. 675 kph c. 750 kph d. 450 kph 139. A jogger starts a course at a steady rate of 8 kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take the second jogger to catch the first? a. 22 min b. 18 min c. 21 min d. 20 min 140. A rubber ball is made to fall from a height of 50 ft. and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner? a. 300 b. 200 c. 350 d. 250 141. The resistance of the 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. 144 b. 80 c. 120

d. 90 142. Ten liters of 25% salt solution and 25 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration of salt in the mixture? a. 0.1955 b. 0.2572 c. 0.2215 d. 0.2705 143. A & B can do the job in 42 days, B & C for the same job in 31 days, C & A also for the same job in 20 days. If A & C work together, how many days can they do the same job? a. 19 b. 17 c. 21 d. 15 144. A pipe can fill a tank in 14 hours. A second pipe can fill the tank in 16 hours. If both pipes are left open, determine the time required to fill the tank? a. 7.92 hr b. 8.47 hr c. 7.47 hr d. 6.53 hr 145. A man rows downstream at the rate of 5mph and upstream at the rate of 2mph. How far downstream should he go if he is to return in 7/4 hours after leaving? a. 2.5 miles b. 3.3 miles c. 2.7 mlies d. 3.1 miles 146. Solve for the value of x. 2x - y + z = 6 x - 3y - 2z = 13 2x - 3y - 3z = 16 a. 3 b. 1 c. 2 d. 4 147. Find the value of w in the following equations: 3x - 2y + w = 11 x + 5y - 2w = -9 2x + y - 3w = -6. a. 4 b. 2 c. 3 d. -2 148. A boat travels downstream 2/3 of the time as it goes going upstream. If the velocity of the river's current is 8 kph, determine the velocity of the boat in still water.

a. 70 kph b. 60 kph c. 30 kph d. 40 kph 149. A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q? a. 23 b. 22 c. 24 d. 25 Basic Engineering Correlation (Trigo Reviewer) 1. What will be the length of the two other sides of a right triangle if the opposite side of a 60 degrees angle is 4V cm _____" a. 8cm, 4 cm b. 4 cm, 3 cm c. 2 cm, 1cm d. 4cm, 5 cm 2. The expression sin16° sin14° + cos16° cos14° is equivalent to a. Cos 8° b. Sin 30° c. Sin 8° d. Cos 2° 3. If tan a = 1/2 — and tan = -3/5, then the value of tan(a +,8) is a. 5/9 b. 7/9 c. 9/7 d. 11/7 4. What is the value of sin [3 if cos p = 3/5? a. sec 0 = 0.8 b. sine=0.25 c. cot 0=0.5 d. tan@=2.5 5. A central angle of 45 degrees subtends an arc of 12 cm. What is the radius of the circle? a. 12.58 cm b. 15.82 cm c. 12.82 cm

d. 15.28 cm 6. The exact radian measure of 180o is a. π b. 3π c. 4π d. 2π 7. Solve for x by logarithm, log x2 - log (2x/5 = 7.58. a. 189675888 b. 136783520 c. 15207576 d. 13678352 8. If arctan x + arctan (1/3) = π /4, the value of x is ______. a. ½ b. 1/5 c. 1/3 d. ¼ 9. A road is tangent to a circular lake. Along the road and 12 miles from the point of tangency, another road opens towards the lake. From the intersection of the two roads to the periphery of the lake, the length of the new road is 11 miles. If the new road will be prolonged across the lake, find the length of the bridge to be constructed. a. 2.09 miles b. 6.65 miles c. 1.20 miles d. 8.89 miles 10. A strip of 640 sq. m is sold from a tirangular field whose sides are 96, 72 and 80 meters. The strip is of uniform width "h" and has one of its sides parallel to the longest side of the field. Find the width of the strip. a. 7.059 m b. 5.89 m c. 5.78 m d. 6.679 m

11. The expression sin25x sin5x is equivalent to a. 2sin10xcos5x b. Sin20x c. 2sin10xsin5x d. 2sin15xsin10x

12. The area of the sector determined by an angle of 60° in a circle of radius 5 cm is a. 49.09 cm2 b. 2812.5 cm2 c. 312.5 cm2 d. 13.09 cm2 13. Three times the sine of a certain angle is twice of the square of the cosine of the same angle. Find the angle. a. 60o b. 45o c. 10o d. 30o 14. If sin A = 2.5x and cos A = 5.5x, find the value of A in degrees. a. 24.44 b. 32.47 c. 52.37 d. 42.47 15. One leg of a right triangle is 20 cm and the hypotenuse is 10 cm longer than the other leg. Find the length of the hypotenuse. a. 10 cm b. 15 cm c. 20 cm d. 25 cm 16. Which of the following is an even function? a. f(x)=3sin x b. f (x)=4 tan x c. f (x)=5 COSx d. f (x)=4 cot x 17. The sides of a triangle lot are 130m, 180m, and 190m. This lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line (1) and the area of each lot (A). a. 1125 m, A6520 sq.m b. 1128 m, A2879 sq.m c. 1110 m, A1000 sq. m d. 1125 m, A5620 sq. m 18. If A is in the III quadrant and cos A = -15/17, find the value of cos (1/2)A.

a. -(8/17)1/2 b. -(2/17)1/2 c. -(1/17)1/2 d. -(5/17)1/2 19. Ship "A" started sailing N 40o 32' E at the rate of 3 mph. After 2 hours, ship "B" started from the same port soing S 45o 18' E at the rate of 4 mph. After how many hours wil the second ship be exactly south of ship "A"? a. 4.37 hours b. 2.37 hours c. 5.37 hours d. 3.37 hours 20. Two speedboats simultaneously sailed out from port A on a 10 km radius circle lake towards point B directly opposite of port A. The first boat took the shortest route and reached the destination in 1 hour. The boat has to pass by port C before proceeding to port B. At what speed will it run in order to arrive at port B at the same time with the first boat? a. 78.89 kph b. 67.89 kph c. 34.57 kph d. 27.32 kph

21. The reference angle of 0 = 210° is a. 15° b. 45° c. 60° d. 30° 22. If A is in the III quadrant and cos A = -15/17, find the value of cos (1/2)A. a. -(2/17)1/2 b. -(8/17)1/2 c. -(5/17)1/2 d. -(1/17)1/2 23. The angle that is supplementary to 45o 15' 25" is a. 45.257o b. 44.743o c. 134.74o d. 44o 45'

24. If 77o + 0.40x = arc tan (cot 0.25x), find x. a. 30o b. 10o c. 20o d. 40o 25. If A + B + C = 180o and tan A + tan B + tan C = 5.67, find the value of tan A tan B tan C. a. 1.89 b. 5.67 c. 1.78 d. 6.75 26. The angle of elevation of the top point D of a tower A is 23o30'. From another point B the angle of elevation of the top of the tower is 55o30'. The points A and B are 217.45 m. apart and on the same horizontal plane as the foot (point C) of the tower. The horizontal angle subtended by A and B at the foot of the tower is 90o. Find the height of the tower CD. a. 69.59 m b. 90.59 m c. 59.90 m d. 50.90 m 28. The simplified form of sin4 0 —cos4 0 is a. 0 b. 1 c. 2sin2 0-1 d. 1+2cos2 29. The simplified form of cos(A— B)—cos(A + B) is a. Cos2B b. math012-1tc. Cos2A d. 2sinAsinB 30. If cot 2A cot 68o = 1, then tan A is equal to _______. a. 0.194 b. 0.491 c. 0.491 d. 0.419 31. The exact degree measure of 0.5π is a. 45o b. 90o

c. 180o d. 145o 32. Solve for G if csc (11G - 16o) = sec (5G + 26o). a. 5 degrees b. 6 degrees c. 4 degrees d. 7 degrees 33. A ladder 5 m long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with the ground. How high od the wall does it reach? a. 3.12 m b. 2.00 m c. 12.66 m d. 3.86 m 34. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. a. 151.24 b. 153.25 c. 143.63 d. 149.08 35. The measure of 2.25 revolutions counterclockwise is a. 810 degrees b. 835 degrees c. 810 degrees d. 805 degrees 36. Determine the amplitude and the phase shift for the function f(t)= 2 sin (3x + 4) a. 2 and 4/3 b. 2 and -4/3 c. 2 and ¾ d. 2 and -3/4 37. Solve angle A of an oblique triangle with vertices ABC, if a = 25, b = 16 and C = 94 degrees and 6 minutes. a. 49 degrees and 37 minutes b. 55 degrees and 32 minutes c. 53 degrees and 40 minutes d. 54 degrees and 30 minutes 38. The terminal side of the angle θ = 500o in standard position is in quadrant.

a. III b. IV c. I d. II 39. Determine the period of the curve y = sin(1/2)x a. 540o b. 360o c. 900o d. 720o 40. Solve for x in the given equation: arc tan(x +1) +arc tan (x - 1) = arc tan (12). a. 1.5 b. 1.2 c. 1.34 d. 1.25 41. Two towers AB and CD are of equal height. At a point between them in the line AC joining their bases, the angle of elevation of the nearer tower was observed to be 60o. Then at 24 m from the same point in a direction perpendicular to AC, the angle of elevation of the top of the towers are 45o for the nearer tower and 30o for the other. Find the height of the towers (h) and their distance apart (x). a. h=29.38 m, x=71.83 m b. h=39.38m, x=61.83 m c. h=49.83, x=61.83 m d. h=29.38 m, x=61.83 m 42. If 3x = 9y and 27y = 81z, find x/z. a. 4/3 b. 8/3 c. 3/8 d. 3/5 43. Which of the following is a co terminal angle of θ = 265o? a. –95o b. 615o c. 585o d. 65o 44. The terminal side of 0 if cote > 0 and sec() >0 is in quadrant a. III b. I

c. II d. IV 45. Given: x = (cos B tan B - sin B) / cos B. Solve for x if B = D45 degrees. a. 0.5 b. 0.577 c. 0.866 d. 0 46. The perimeter of an isosceles right triangle is 6.6824. Its area is a. ½ b. 4 c. 2 d. 1 47. Simplify: 4 cos y sin y (1 - 2 sin 2y) a. sec 4y b. tan 4y c. cos 4y d. sin 4y 48. The angle of elevation of the top of the tower A from the foot of tower B is twice the angle of elevation of the top of tower B from the foot of tower A. At a point midway between the two towers, the angles of elevations of the top of the towers are complimetary. If the two towers are 120 m apart, what are the heights of the towers? a. 30 m and 50 m b. 30 m and 40 m c. 25 m and 35 m d. 40 m and 90 m 49. Find the value of x in the equation csc x + cot x = 3. a. π /2 b. π /4 c. π /3 d. π /5 50. Find the other parts of the triangle given a = 48°,1C = 57 degrees b = 47 units. a. 75 °, 36.16 units b. 75 °, 35.16 units c. 75 °, 33.16 units d. 75 °, 34.16 units

51. A clock has a dial face 12 inches in radius. The minute hand is 9 inches long while the hour hand is 6 inches long. The plane of rotation of the minute hand is 2 inches above the plane of rotation of the hour hand. Find the distance between the tips of the hands of the clock at 5:40 a.m. a. 3.89 in b. 8.67 in c. 7.78 in d. 9.17 in 52. The expression 2cos6x cos2x is equivalent to a. cos10x + cos6x b. cos5x + cos3x c. Cos8x + cos4x d. cos32x 53. The solution set of the equation(tan x) 2 — 1 = 0 on the interval [0°, 360°) is ~{30°,90°,150°1} a. {45°,135°,225°,315°1 b. {0°,30°,330° c. 160901 54. If the terminal side of angle 13 contains the point (-5, -7) then 13 is equal to a. — 35.54° b. 35.54° c. 234.46° d. 54.47° 55. Simplify the expression: (sin B + cos B tan B) / cos B. a. tan B cos B b. tan B + cos B c. 2 sin B cos B d. 2 tan B 56. A 40 m high tower stands vertically on a hillside (sloping ground) which makes an angle of 18o with the horizontal. A tree also stands vertically up the hill from the tower. An observer on top of the tower finds the angle of depression of the top of the tree to be 26o and the bottom of the tree to be 38o. Find the height of the tree. a. 59.89 m b. 89.89 m c. 35.67 m d. 10.62 m

57. Triangle ABC is a right triangle with the right angle at C. CD is perpendicular to AB. BC = 4, and CD = 1. Find the area of the triangle ABC. a. 2.7 b. 2.07 c. 2.11 d. 2.43 58. If sin A = 4/5, A is in quadrant II, sin B = 7/25, B is in quadrant I. Find sin (A + B). a. 2/5 b. ¾ c. 3/5 d. 4/5 59. A and B are summit of two mountains rise from a horizontal plain, B being 1200 m above the plain. Find the height of A, it being given that its angle of elevation as seen from a point C in the plain (in the same vertical plane with A and B) is 50o, while the angle of depression of C viewed from B is 28o58' and the angle subtended at B by AC is 50o. a. 2890.89 m b. 1002.33 m c. 1309.90 m d. 3002.33 m 60. 174 degrees is equivalent to _____ mils. a. 2044 b. 2845 c. 3421 d. 3094 61. Which of the following is arccos(n)? a. UNDEFINED b. n c. 0 d. 1 62. A cyclic quadrilateral has the sides AB = 8 cm; and CD = 12 cm. The fourth side DA forms the diameter of the circle. Find the area of the circle. a. 467.89 sq. cm b. 87.89 sq. cm c. 657.89 sq. cm d. 316.68 sq. cm

63. If tan 25 = m, find the value of tan (tan 155 - tan 115) / (1 + tan 115 x tan 155). ( Note: all angles are in degrees). a. (m2 + 1) / 2m b. m2 + 1 c. (1 - m2) / 2m d. (m2 - 1) / 2m Basic Engineering Correlation (Solid Mensuration Reviewer) 1. It is a quadrilateral two and only two of whose sides are parallel a. rectangle b. rhombus c. trapezoid d. parallelepiped 2. Five pointed figure in a a. rhombus b. star c. trapezoid d. rectangle 3. The volume of any cone is equal to a. Bh b. 1/2 Bh c. 1/3 Bh d. 4/3Bh 4. It is a polyhedron whose six faces are all squares. a. cube b. square c. frustum d. parallelepiped 5. What is the length of the diagonal of a cube of edge 7 cm a. 12.12 cm b. 18.52 cm c. 9.9cm d. 5.28cm 6. A section of a sphere when a plane passing through the center and diameter. Creating the largest section called a. medium circle b. great circle

c. big circle d. short circle 7. Each of the faces of a regular hexahedron is a a. square b. hexagon c. triangle d. rectangle 8. A cone and a cylinder have the same heightand the same volume. Find the ratio of the radius of the cone to the radius of the cylinder. a. 0.866 b. 1.732 c. 0.577 d. 1.414 9. The volume of a water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of the water in the tank. a. 1.0 m b. 1.4 m c. 1.2 m d. 1.8 m 10. It is desired that the volume of the sphere be tripled. By how many times will the raduis be increased? a. 31/3 b. 31/2 c. 33 d. 21/2 11. In Heron's formula, the symbol 's' stands for a. (a+b+c)/3 b. side c. slant height d. (a+b+c)/2 12. Find the measure of the diagonal of a rectangular parallelepiped of dimensions 2 x 3 x 8. a. 48 b. 77 c. 0.07 d. 48 13. In a plane figure, diamond is also known as a. square b. rhombus

c. trapezoid d. parallelogram

c. 21/2 d. 31/3

14. Find the weight of a snowball 1 ft. in diameter if the wet compact snow of which the ball is made weighs 25 lbs/ cu. ft. a. 1.047 lb b. 2.36 lb c. 13.09 lb d. 4.19 lb

21. The bounding cylindrical surface of a cylinder is called a. base edge b. lateral surface c. lateral edge d. edge

15. The area for a trapezoid is represented by a. (dic12)/2 b. (a+b)h/2 c. bh d. (a+b÷c)/3 16. An Egyptians pyramid of the Giza has a square base of edge 6miles. If its altitude is 15miles., determine the a. 540 cu.mi b. 90 cu.mi c. 180 cu.mi d. 270 cu.mi 17. The sum of the interior angles of a polygon is 540o. Find the number of sides. a. 8 b. 5 c. 6 d. 11 18. Prisms are named according to their? a. bases b. vertices c. sides d. diagonal 19. The approximate surface area of an ellipse is a. 211r b. 11(ab)2 c. Fir2 d. FI(ab) 20. It is desired that the volume of the sphere be tripled. By how many times will the raduis be increased? a. 33 b. 31/2

22. It is the perpendicular distance between the two bases of a frustum of a cone. a. lateral face b. altitude c. lateral edge d. element 23. Points on the same a. intersection b. congruent c. coplanar d. collinear 24. What is the area, in inches2, of a parabola with a base if 15 cm and height of 20 cm. a. 200 b. 87 c. 78.74 d. 31 25. If a lateral area of a right circular cylinder is 88 cm3 and its volume is 220 cm3, find its radius. a. 2 cm b. 5 cm c. 4 cm d. 3 cm 26. A cone has a base area of 30in? and a lateral area which is 4.5 times bigger than the base area. The surface area of the cone in in' is a. 135 b. 105 c. 75 d. 165 27. How many elements are needed in solving a truncated cylinder? a. 1 b. 4

c. 2 d. 3 28. It is a rectangle whose length is equal to its width a. square b. rectangle c. parallelepiped d. cube 29. a solid bounded by a conical surface (lateral surface) whose directrix is a closed curve, and a plane (base) which cuts all the elements. a. pyramid b. cylinder c. cone d. prism 30. The lateral area of a cylinder with a circumference of 50 cm and a height of 4 cm is a. 228.2 units b. 288.2 units c. 238.2 units d. 282.8 units 31. What is the distance, in cm, between two vertices of a cube that are farthest from each other if an edge measures 8 cm? a. 16.93 b. 12.32 c. 14.33 d. 13.86 32. If the radius of the circle is decreased by 20%, by how much is the area decreased? a. 0.26 b. 0.46 c. 0.56 d. 0.36 33. Find the volume a right circular cone to be obtained from a sector of radius 26 cm and whose central angle measure 138.5°? a. 900rt b. 800n c. 600n d. 700 n

34. A quarter circle has a radius of 8 units. What is its area? a. 18n sq. units b. 16n sq. units c. 32n sq. units d. 64n sq. units 35. A prism whose lateral edges are perpendicular to its bases; its lateral faces are rectangles a. right b. truncated c. frustum d. prismatoid 36. A window glass is 5 ft by 7 ft. What is its area? a. 17.5 ft b. 35ft c. 8.75 ft d. 11.67 ft 37. A regular hexagon pyramid has a slant height of 4 cm and the length of each side of the base is 6 cm. Find the lateral area. a. 72 cm b. 82 cm2 c. 62 cm2 d. 52 cm2 38. A central angle of 45o subtends an arc 12 cm. What is the ratio of the circle? a. 15.28 cm b. 12.58 cm c. 12.82 cm d. 15.82 cm 39. A portion of the prism included between the base and a plane not parallel to the base cutting all the edges. a. truncated cylinder b. frustum of a cone c. truncated prism d. frustum of a pyramid 40. It is a polyhedron having for bases two polygons in parallel planes and for lateral faces triangles or trapezoids a. truncated b. prismatoid c. parallelepiped

d. frustum 41. It is a part of a circle bounded by a chord and an arc. a. sector b. section c. slab d. segment 41. One of the diagonals of a rhombus is 25 units and its area is 75 units2. Determine the length of the side. a. 15.47 units b. 12.85 units c. 18.25 units d. 12.58 units 42. It is a solid bounded by a closed surface every point of which is equidistant from a fixed point called the center. a. cone b. vertex c. sphere d. circle 43. The area of a circle is 89.42 in2. What is the length of the side of a regular hexagon inscribed in a circle? a. 6.335 in b. 5.533 in. c. 7.335 in. d. 5.335 in. 44. It is a solid which is bounded by planes a. lateral face b. polyhedron c. lateral area d. plane 45. These are the intersections of the edges in a polyhedron a. Vertices b. edges c. lateral face d. lateral edge 46. The area of the rhombus is 132 m2. If its shorter diagonal is 12 m, find the longer diagonal. a. 20 m

b. 38 m c. 22 m d. 34 m 47. A regular dodecagon is inscribed in a circle of raduis 24. Find the perimeter of the dodecagon. a. 151.24 units b. 143.63 units c. 149.08 units d. 153.25 units 48. Every section of a cone made by a plane passing through its vertex & containing two points of base is a a. triangle b. square c. circle d. pyramid 49. Water flows in a pipe 1/4 ft in diameter and 24 ft in length. What is the volume of the water in the pipe? a. 8n/3 ft3 b. 3n/8 ft3 c. II/8 ft3 d. 2 n/8 ft3 50. Determine the volume of a right truncated triangular prism. The base has sides loft, 9ft and 12ft. The sides perpendicular to the base have the height of 8.6 ft, 7.1 ft, and 5.5 ft., respectively a. 391 ft3 b. 311 ft3 c. 413 ft3 d. 313 ft3 51. A certain angle has a supplement 4 times its complement. What is the angle a. 60° b. 30° c. 45° d. 90° 52. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. a. 151.24 units b. 149.08 units c. 153.25 units d. 143.63 units

53. The lateral area of the right circular water tank is 92 cm2 and its volume is 342 m3. Determine its radius. a. 6.05 cm b. 7.28 cm c. 5.56 cm d. 7.43 cm 54. The mean proportional between bases is a. bB b. sort(bB) c. 13.sort(b) d. b•scirt(B) 55. A metal washer 1-inch in diameter is pierced by a 1/2-inch hole. What is the volume of the washer if it is 1/8-inch thick? a. 0.028-inch b. 0.082-inch c. 0.047-inch d. 0.074-inch 56. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. Find the altitudes if the areas of the triangles differ by 21 units2. a. 4 and 10 b. 5 and 11 c. 3 and 9 d. 6 and 12

59. The volume of a water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of the water in the tank. a. 1.0 m b. 1.4 m c. 1.2 m d. 1.8 m 60. It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms. a. frustum b. prismatiod c. prism d. tetrahedron 61. A section of a sphere when a plane passing through the center and diameter. Creating the largest section called a. great circle b. short circle c. medium circle d. big circle 62. The ratio of the volume of the two spheres is 27:343 and the sum of their radii is 10. Find the radius of the smaller sphere. a. 5 b. 3 c. 4 d. 6

57. A right circular cone has a base radius of 10 m. and an altitude of 20 m. Determine its volume. a. 666n b. 2000n c. 1000n d. 500n

63. Find the increase in volume of a spherical balloon when its radius is increased from 2 to 3 inches. a. 74.59 in3 b. 79.59 in3 c. 74.12 in3 d. 75.99 in3

58. In plane geometry, two circular arcs that together make up a full circle are called? a. coterminal arcs b. congruent arcs c. conjugate arcs d. half arcs

64. Which formula cannot be used to compute the area for a circle a. if(ab); where a=b b. Eld2/4 c. lid2 d. n r2 65. The circumference of a great circle of a sphere is 18 π. Find the volume of the sphere.

a. 3033.6 units3 b. 3023.6 units3 c. 3053.6 units3 d. 3043.6 units3 66. Assuming that the earth is a sphere whose radius is 6400 km, find the distance along a 3o arc at the equator of the earth's surface. a. 353.10 km b. 335.10 km c. 533.10 km d. 353.01 km 67. Find the area, in cm2, of a regular octagon inscribed in a circle of raduis 10 cm. a. 283 b. 238 c. 298 d. 289 68. The side of a triangle are 8 cm. 10 cm and 14 cm. Determine the raduis of the inscribed circle. a. 2.35 cm b. 2.25 cm c. 2.45cm d. 2.55 cm 69. The side of a triangle are 8 cm. 10 cm and 14 cm. Determine the raduis of the circumscribing circle. a. 7.74 cm b. 7.14 cm c. 7.54 cm d. 7.34 cm 70. The side of a right triangle are 8, 15 and 17 units. If each side is doubled, how many units2 will the area of the new rectangle? a. 420 b. 320 c. 240 d. 300 71. What is the volume of a frustum of a cone whose upper base is 15 cm in diameter and lower base is 10 cm in diameter with an altitude of 25 cm a. 3108.87 cm3 b. 3180.87 cm3 c. 3081.87 cm3

d. 3018. 87 cm3 72. A regular hexagonal pyramid has a slant height of 4 cm and the length of each side of the base is 6 cm. Find the lateral area. a. 72 cm2 b. 52 cm2 c. 62 cm2 d. 82 cm2 73. The area of the region bounded by two concentric circles is called? a. circular disk b. annulus c. washer. d. ring 74. A cone and a cylinder have the same heightand the same volume. Find the ratio of the radius of the cone to the radius of the cylinder. a. 1.414 b. 1.732 c. 0.577 d. 0.866 75. A piece of wire of length 50 m is cut into two parts. Each part is then bent to form square. It is found that the total area of the square is 100 m2. Find the difference in length of the sides of the two squares. a. 6.62 m b. 6.16 m c. 5.32 m d. 5.44 m 76. A rectangular octagon is inscribed in a circle of radius 10. Find the area of the octagon. a. 288.2 units b. 282.8 units c. 228.2 units d. 238.2 units 77. A piece of wire is shaped to enclose a square whose area is 169 cm2. It is then reshaped to enclose a rectangle whose length is 15 cm. The area of the rectangle is? a. 175 cm2 b. 170 cm2 c. 156 cm2

d. 165 cm2 78. The apothem of a polygon is the ______ of its inscribed circle. a. circumference b. diameter c. length d. radius 79. The lateral faces are equal isosceles trapezoids. a. frustum of a cone b. cone c. frustum of pyramid d. pyramid 80. The tangent and a secant are drawn to a circle from the same external point. If the tangent is 6 inches and the external segment of the secant is 3 inches, then the length of the secant is ______ inches. a. 14 b. 15 c. 12 d. 13 81. Find the increase in volume of a spherical balloon when its raduis is increased from 2 to 3 inches. a. 75.99 in3 b. 74.59 in3 c. 74.12 in d. 79.59 in 82. The angle of a sector is 30o and the raduis 15 cm. What is the area of the sector in cm2 a. 58.9 b. 89.5 c. 85.9 d. 59.8 83. A rectangle ABCD, which measures 18 cm by 24 cm, is folded once perpendicular to diagonal AC so that the opposite vertices A and C coincide. Find the length of the fold. a. 21.5 cm b. 20.5 cm c. 22.5 cm d. 23.5 cm

84. If an equilateral triangle is circumscribed about a circle of raduis 10 cm, determine the side of the triangle? a. 34.64 cm b. 36.44 cm c. 32.10 cm d. 64.12 cm 85. If a regular polygon has 27 diagonal, then it is a? a. hexagon b. heptagon c. nonagon d. pentagon 86. The volume of a sphere is 36 π m3. The surface area of this sphere in m2 is? a. 24 π b. 12π c. 18 π d. 36 π 87. Polygons are classified according to the number of? a. diagonals b. sides c. angles d. vertices 88. One side of a regular octagon is 2. Find the area of the region inside the octagon. a. 31 b. 21.4 c. 19.3 d. 13.9 Basic Engineering Correlation (Analytic Geometry Reviewer) 1. The graph of the polar equation: r = 2cos0 is a a. Rose b. Limacon with a loop c. Circle d. Cardioid 2. Classify the conic represented by the equation x2 + 4xy + 5 y2 - x + 2y + 1 = 0 a. circle b. ellipse

c. hyperbola d. parabola 3. The graph of the polar equation: r = I l is a. a circle b. a parabola c. an ellipse d. a hyperbola 4. What is the slope of the line 4x-5y +6 = 0? a. -5/4 b. 5/4 c. 4/5 d. -4/5 5. The point of intersection of the lines x — 2y+4 0 and —3x + y —2 =0 is a. (0,2) b. (-2,0) c. (0,-2) d. (2,0) 6. The conic given by the equation? +4xy+5y2 -x+ 2y+1 =0 is a. parabola b. circle c. ellipse d. hyperbola 7. Find the slope of a line having a parametric equation of y = 4t + 6 and x = t + 1. a. 2 b. 1 c. 4 d. 3 8. Find the equation of a straight line with a slope of 3 and a y-intercept of 1. a. x + 3y + 1 b. 0 c. x - 3y - 1 d. 3x - y + 1 e. 3x + y - 1 f. 0 g. 0 h. 0 9. An equation of the line with x and y intercepts 7 and -7, respectively, is

a. x— y +7 =0 b. x —y-7 = 0 c. —x+y-7=0 d. x+y+7=0 10. The line joining the points (3, -1) and (-3, 2) has equation a. x+2y+1= 0 b. x+2y—l= 0 c. x+y-2=0 d. x-2y—I=0 11. The set of all points in a plane such that the sum of the distances of a point from some fixed points on the plane is a constant is a/an a. parabola b. ellipse c. hyperbola d. circle 12. The distance from the point (5, 2) to the line 8x - 6y +2 = 0 is a. 3 b. 4 c. 1 d. 2 13. If (3,-5) is the midpoint of (-1,-3) and (x, y), then the values of x and y are a. x=1, y=-4 b. x=7, y= -7 c. x=2, y= -1 d. x= 7, y= -1 14. The distance between the given lines 3x + 2y — 2 =0 and 3x +2y-6 =0 is a. 1.39 b. 1.12 c. 0.28 d. 0.55 15. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth. a. 94,550,000 miles b. 93,000,000 miles c. 91,450,000 milse d. 94,335,100 miles

16. A line 4x + 2y -2 = 0 is coincident with the line a. 0 b. 0 c. 4x + 4y + 2 d. 4x + 3y + 3 e. 8x + 4y - 2 f. 0 g. 0 h. 8x + 4y - 4 17. The length of the semi-transverse axis of the graph of --- 9 — 4 =1 is a. 2 b. 3 c. 5 d. 4 18. The equation of the line through (1, 2) and perpendicular to 6x - y +5 =0 is a. 6x-y-11=0 b. 6x-y+5=0 c. x+6y-13=0 d. x+6y-8=0 19. If the distance between the points (h, 2) and (0, 4) is 2 then the value of h is a. 3,J2 b. 0 c. 2,5 d. 2 20. The length of the latus rectum for the ellipse 16x2 + 25y2 = 400 is equal to1 a. 5 b. 4 c. 6.4 d. 12.5 21. The graph of the polar equation: r = 2 + 2cos9 is a a. limacon b. Circle c. cardioid d. lemniscates 22. Find the angle formed by the lines 2x + y — 8 = 0 and x + 3y + 4 = 0 a. 30°

b. 60° c. 45° d. 35° 23. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is, a. 3x + 2y b. 12 c. 2x - 3y d. 12 e. 2x - 3y f. 3x - 2y g. 12 h. 12 24. Find the distance between the lines 3x + y - 12 = 0 and 3x + y - 4 = 0 a. letter d) 8/the squareroot of 10 25. Find the polar coordinate of the point (-3,A/3 ) a. (J18, 60°) b. (412, 30°) c. (012, 150°) d. (A118, 330°) 26. To simplify the equation x2 + 4y2 + 6x +16y + 21= 0 by translation of axes, the origin must be moved to a. (-3, -2) b. (2, 3) c. (3, 8) d. (-3, -8) 27. Given the equation of the parabola x2 = 4y – 20 . Locate its vertex. a. (4, 20) b. (0, 5) c. (0, 4) d. (0, 20) 28. Find the equation of a straight line with a slope of 1/2 and y-intercept 3. a. x - 2y -3 = 0 b. 3x-y+2 =0 c. x-2y+ 6 = d. 2x-y+3 =0

29. Determine the coordinates of the point which is two-fifths of the way from the point (1,-5) to the point (6,10) a. (3, 1) b. (4, 5) c. (2, -2) d. (3, 5) 30. Find the area of the circle whose equation is x2 + y2 = 6x - 8y. a. 25 & b. 20 & c. 30 & d. 15 & 31. How far from the y-axis is the center of the curve 2x2 +2y2 + 10x - 6y - 55 = 0? a. -3.25 b. -3.0 c. -2.5 d. -2.75 32. Which of the following lines is parallel to the line 6x — 4y = 7? a. 6x + 4y = 6 b. 4x — 6y = 9 c. 3x - 2y = 15 d. 3x + 2y = 12 33. The slope of the line passing through (-2,2) and (3,12). a. -2 b. ½ c. 2 d. 10 34. A line 4x + 2y -2 = 0 is coincident with the line a. 0 b. 4x + 3y + 3 c. 0 d. 8x + 4y - 2 e. 8x + 4y - 4 f. 0 g. 0 h. 4x + 4y + 2 35. The parabolic antenna has an eqaution of y2 + 8x = 0. Determine the length of the latus rectum. a. 8

b. 12 c. 10 d. 9 36. 14. A line through (-5, 2) and (1, -4) is perpendicular to the line through (x, -7) and (8, 7). Find x. a. -4 b. -19/3 c. -6 d. -5 37. Find the eccentricity of the curve 9x2 - 4y2 - 36x + 8y = 4 a. 1.92 b. 1.86 c. 1.8 d. 1.76 38. If the points (0,0), (2, 0), and (1, k) are vertices of an equilateral triangle then a value of k is a. I b. 5 c. 0 d. 2 39. Find the inclination of the line passing through (-5, 3) and (10, 7). a. 14.63 b. 14.73 c. 14.83 d. 14.93 40. What is the equation of the line that passes thru (4, 0) and is parallel to the line x - y - 2 = 0 a. x - y b. 0 c. x + y + 4 d. 0 e. x - y - 4 f. 0 g. 0 h. x - y + 4 41. What are the coordinates of the center of the curve x2 + y2 - 2x - 4y - 31 = 0 a. (2, 1) b. (-1, -1) c. (1, 2)

d. (3, 5) 42. If a line through (-5, 2) and (1, -4) is parallel to the line through (x, -7) and (8, 7) then x = a. -5 b. -6 c. 22 d. -4 43. Find the distance between the given lines 4x 3y = 23 and 4x - 3y = -7 a. 3 b. 4 c. 6 d. 5 44. The equation of the directrix of the parabola y2 = 20x is a. x = -5 b. x = 5 c. x = 4 d. x = -4 45. The center of a circle is at (1, 1) and one point on its circumference is (-1, -3). Find the other end of the diameter through ( -1, -3). a. (3, 6) b. (2, 4) c. (1, 3) d. (3, 5) 46. Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units, the locus of the third vertex is a. x + 4y = 12 b. 4x - y =14 c. 4x + 4y = 14 d. x - 4y =-10 47. The focus of parabola y2 = 16x is at: a. (0, 3) b. (3, 0) c. (0, 4) d. (4, 0) 48. The diameter of a circle described by 9x2 + 9y2 = 16 is a. 4/3 b. 16/9

c. 4 d. 8/3 49. Find the distance between the points A (4, 7) and B (-1, -5). a. 10 b. 5 c. 13 d. 12 50. The equation 25x2 + 16y2 - 150x + 128y + 81 = 0 has its center at a. (3, -4) b. (3, 5) c. (3, 4) d. (4, -3) 51. Find the equation of the line where x-intercept is 2 and y-intercept is -2. a. x - y - 2 b. 0 c. 2x + 2y +2 d. -2 e. 0 f. -2x +2y g. 0 h. x - y - 1 52. Find the inclination of the line passing through (-2,4) and (2,7) a. 53.13 b. 90 c. 36.87 d. 70 53. A horizontal line has a slope of a. zero b. infinity c. negative d. possitive 54. To simplify the equation x2 + 4y2 + 6x +16y+ 21= 0 by translation of axes, the origin must be moved to a. (-3, -2) b. (-3, -8) c. (3, 8) d. (2, 3)

55. Find the eccentricity of the curve 9x2 –16y2 – 144 = 0 a. 0.66 b. 1.67 c. 0.88 d. 1.25 56. Find the eccentricity of the curve 9x2 —16y2 — 144= 0 a. 1.67 b. 0.66 c. 1.25 d. 0.88 57. In the equation y = x2 + x + 1, where is the curve facing? a. Downward b. Facing left c. Facing right d. Upward 58. Find the acute angle of rotation such that the transformed equation of 6x2 +31y + 4y2 + x y = 0 will have no x' y' term. a. 16.85° b. 28.15° c. 53.13° d. 53.13° 59. The equation of the line through (1, 2) and perpendicular to 6x + y — 4 = 0 is a. x+6y-4 =0 b. x+2y-4 =0 c. 6x+y+ 4 =0 d. x- 6y+ 11 = 60. The equation of the line with a slope 47 and yintercept -2 is a. —4 5x—y+2=0 b. x+y-2 =0 c. 5x-4y-20=0 d. 4x-5y-20=0 61. The polar equation r = 1 when transformed into a rectangular equation is cos° —4sin a. x2 — 4y2 =I b. 4x2 — y2 =1 c. 4x — y = 4 d. x —4y = I

62. Given three vertices of a triangle whose vertices are A(1, 1), B(3, -3) and (5, -3). Find the area of the triangle. a. 6 sq. units b. 5 sq. units c. 4 sq. units d. 3 sq. units 63. A line with slope equal to — 2 has an inclination of a. 116.57° b. —116.57° c. 63.43° d. —63.43° 64. What is the distance between the centers of the circle x2 + y2 + 2x + 4y - 3 = 0 and x2 + y2 - 8x 6y + 7 = 0? a. 7.07 b. 7.77 c. 8.07 d. 7.87 65. The area of hexagon ABCDEF formed by joining the points A(1, 4), B(0, -3), C(2, 3), D(-1, 2), E(-2, -1) and F(3, 0) is _________ square units. a. 15 b. 24 c. 22 d. 20 66. Determine B such that 3x + 2y -7 = 0 is perpendicular to 2x - By + 2 = 0. a. 4 b. 2 c. 5 d. 3 67. Find the distance between the A (4, -3) and B (2, 5). a. 10 b. 8 c. 11 d. 9 68. The equation of a line that intercepts the x-axis at x = 5 and the y-axis at y = -4 is a. 88x- l0y = 40

b. 5x + 4y = 20 c. 10x - 8y = 20 d. 4x + 5y = 20 69. Find the value of k for which the equation x2 + y2 + 4x - 2y - k = 0 represents a point circle. a. 6 b. 5 c. -6 d. -5 70. What is the length of the latus rectum of the curve x2 = 20y a. 5 b. 20 c. √ 20 d. √ 5 71. Find the acute angle of rotation such that the transformed equation of 6x2 + 3xy+ 4y2 +x-y =0 will have no x' y' term. a. 16.85° b. 28.15° c. 36.86° d. 53.13° 72. Find the coordinates of the point P(2, 4) with respect to the translated axis with origin at (1,3). a. (1, 1) b. (-1, 1) c. (1, -1) d. (-1, -1) 73. Determine the equation of the circle whose radius is 5, center on the line x = 2 and tangent to the line 3x - 4y + 11 = 0. a. (x - 2)2 + (y - 2)2=25 b. (x - 2)2 + (y - 2)2=5 c. (x - 2)2 + (y + 2)2=25 d. (x - 2)2 + (y + 2)2=5

a. (x - 3)2 + (y + 5)2 b. (x - 5)2 + (y - 3)2 c. 16 d. 16 e. (x f. 3)2 + (y - 5)2 g. 16 h. 16 i. x2 + y2 76. The line passing through the focus and is perpendicular to the directrix of the parabola. a. axis of the parabola b. latus rectum c. directrix d. tangent line 77. What is the equation of the line joining the points (3, -2) and (-7, 6)? a. 2x + 3y = 0 b. 4x + 5y - 0 c. 5x + 4y = 7 d. 4x - Sy 22= 0 78. The angle formed by the lines y = -2x +8 and y =1x- -4 is a. 45° b. 35° c. 60° d. 30° 79. In general quadratic equation, if the discriminant is zero, the curve is a figure that represents a/an _______. a. circle b. hyperbola c. ellipse d. parabola

74. The equation x2 + y1- 8x – 2y + 1 = 0 describes a. A. a circle of radius 4 centered at (4, 1) b. a circle of radius 4 centered at (-4,-1) c. an ellipse centered at (-4, -1) d. an ellipse centered at (4, 1)

80. The directrix of a parabola is the line y = 5 and its focus is at the point (4, -3). What is the length of the latus rectum? a. 18 b. 12 c. 14 d. 16

75. Find the equation of a circle whose center is at (3, -5) and whose raduis is 4.

81. A line, which is perpendicular to the x-axis, has a slope to

a. infinity b. 1 c. -1 d. 0 82. A line passes thru (1, -3) and (-4, 2). Write the equation of the line in slope-intercept form. a. y - 4 - x b. y - 2 - x c. y- x - 2 d. y - x -4 83. The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the values of x and y. a. 14, 6 b. 5, 0 c. 33, 12 d. 14, 3

84. Determine the coordinates of the point which is three-fifths of the way from the point (2, -5) to the point (-3, 5). a. (1, -1) b. (-1, 1) c. (-1, -2) d. (-2, -1) 85. Which of the following points lie on the fourth quadrant? a. (5, 57r/4) b. (-4, 27r13) c. (-4, -7rJ3) d. (5, -77r16) 86. The midpoint of the line segment between P1(x1, y1) and p2(-2, 4) is P(2, -1). Find the coordinates of P1. a. (-6, 6) b. (6, -6) c. (5, -6) d. (6, 6) 87. A locus of a point which moves so that it is always equidistat from a fixed point (focus ) to a fixed line (directix) is a _______. a. hyperbola b. ellipse

c. circle d. parabola 88. A parabola having a span of 30m and a height of 20m has an area of a. 540 b. 360 c. 400 d. 180 89. An equation of the line that is parallel to 3x-6y = —land passes through the point (2, 2) is a. 2x—y+2=0 b. x-2y-2=0 c. x-2y+2 =0 d. x+2y+2= 0 90. If the product of the slope of any two straight line is negative 1, one of these lines are said to be a. Skew b. Non-intersecting c. Parallel d. Perpendicular 91. Find the slope of the line defined by y - x = 5. a. -1/2 b. ¼ c. 1 d. 5 + x Basic Engineering Correlation (Calculus Reviewer)

1. The depth of water in cylindrical tank 4 m in diameter is increasing at the rate of 0.7 m/min. Find the rate at which the water flows into the tank. a. 6.4 b. 2.5 c. 1.5 d. 8.8 2. The volume of the sphere is increasing at the rate of 6 cm3 / hr. At what is its surface area increasing (in cn2/hr) when the radius is 50cm? a. 0.3 b. 0.24 c. 0.4 d. 0.5

3. Find the height of aright circular cylinder of maximum volume, which can be inscribed in a sphere of radius 10 cm. a. 12.81 cm. b. 11.55 cm. c. 15.11 cm. d. 14.12 cm. 4. find the area in the first quadrant bounded by the parabola y2 = 4x, x = 1 and x = 3 a. 9.955 b. 5.955 c. 5.595 d. 9.555

d. 40 kph

10. A box is to be constructed from a piece of zinc 20 sq. in. by cutting equal squarea from each corner and turning up the zinc to form the side. What is the volume of the largest box that can be so constructed? a. 592.59 cu. in. b. 622.49 cu. In c. 579.50 cu. In d. 599.95 cu. in.

5. Find the maximum point of y = x + 1/x a. (1,2) b. (2,3) c. (-1, -2) d. (2, 5/2)

11. Find the coordinates of the vertex of the parabola y = x2 - 4x + 1 by making use of the fact that at the vertex, the slope of the tangent is zero. a. (-2, -3) b. (3, -2) c. (-1, -3) d. (2, -3)

6. ___________ is the concept of finding the derivative of composite functions. a. Logarithmic differentiation b. Implicit differentiation c. Trigonometric differentiation d. Chain Rule

12. Given the function f(x) = x3 - 6x +2. Fnd the first derivative at x = 2 a. 3x2 - 5 b. 8 c. 6 d. 7

7. Find the area bounded by the curve defined by the equation x2 = 8y and its latus rectum. a. 22/3 b. 32/3 c. 16/3 d. 11/3

13. If the first derivative of the function is constant, then the function is__________. a. Linear b. Logarithmic c. Sinusoid d. Exponential

8. If y = x lnx. Find a. -1/x b. 1/x c. -1/x2 d. 1/x2

14. Using the two existing corner sides of an existing wall, what is the maximum rectangular area that can be fenced by a fencing material 30 ft. long? a. 250 sq. ft. b. 225 sq.ft. c. 200 sq. ft. d. 216 sq. ft.

9. Car A moves due east at 30 kph, at the same instant car B is moving S 30o E with the speed 60 kph. The distance from A to B is 30 km. Find how fast is the distance between them separating after 1 hour a. 38 kph b. 36 kph c. 45 kph

15. The velocity of a body is given by v(t) = sin(xt), where the velocity is given in meters per second and " t " is given in seconds. The distance covered in meters between t =1/4 and 1/2 second is close to

a. 0.5221 m b. -0.5221 m c. -0.2251 m d. 0.2551 m 16. Differentiate y = ex cos x2 a. ex(cosx2 - 2x sinx2) b. -2xex sinx2 c. -ex sinx2 d. ex cosx2 - 2x sinx2 17. Three sides of a trapezoid are each 8 cm. long. How long is the fourth side when the area of the trapezoid has the greatest value? a. 10 b. 8 c. 16 d. 12 18. Differentiate y = sec(x2 + 2) a. -cos(x2 + 2)cot(x2 + 2) b. 2xcos(x2 + 2) c. cos(x2 + 2) d. 2xsec(x2 + 2)tan(x2 + 2) 19. A statue 3 m high is standing on a base of 4 m high. If an observer's eye is 1.5 m above the ground, how far should he stand from the base in order that the angle subtended by the statue is a maximum. a. 3.41 m b. 4.41 m c. 3.51 m d. 3.71 m

22. In the curve 2 + 12x - x3, find the critical points. a. (-2,18) & (2, -14) b. (-2,18) & (-2,14) c. (2,18) & (2,-14) d. (2,18) & (-2,-14) 23. A man on a wharf 3.6 m above sea level is pulling a rope tied to a raft at 0.60 m/sec. How fast is the raft approaching the wharf when there are 6 m of rope out? a. -0.95 m/s b. -0.75 m/sec c. -0.65 m/sec d. -0.85m/sec 24. Find of y = 3sin 2x a. 3 cos 4x b. 2 sin 2x c. 6 cos x d. 6 cos 2x 25. If the distance x from the point of departure at a time t is defined by the equation x = -16t2 + 5000t + 5000, what is the initial velocity? a. 2000 b. 5000 c. 0 d. 3000 26. Find the slope of the tangent to the curve x2 + y2 - 6x + 10y + 5 = 0 at the point (1,0) a. ¼ b. 2/5 c. 2 d. 1/5

20. What is the area of the largest rectangle that can be inscribed in a semi-circle of radius 10? a. 2 √ 50 b. 100 c. 1000 d. √ 50

27. Differentiate y = arc sin cos x a. -2 b. 1 c. 2 d. -1

21. Find the partial derivative with recpect to x of the funcyion xy2 - 5y + 6 a. 2xy b. xy - 5y c. y2 - 5 d. y2

28. Evaluate the limit lnx/x as x approaches positive infinity. a. 0 b. -1 c. 1 d. infinity

29. Determine the diameter of a closed a closed cylindrical tank having a volume of 11.3 cu. m. to obtain minimum surface area. a. 1.22 b. 2.68 c. 1.64 d. 2.44 30. Divide the number 120 into two parts such that the product of one and the square of the other is maximum. a. 30 and 90 b. 60 and 60 c. 40 and 80 d. 50 and 70 31. Evaluate: Lim (2 a. b e b. e2π c. ∞ d. 0

x)tan

cm. What is the maximum possible area for the triangle? a. 14.03 sq.cm. b. 15.59 sq. cm. c. 17.15 sq. cm. d. 18.71 sq. cm. 36. The cost of a product is a function of the quantity x of the product: C(x) = x2 - 400x + 50. Find the quantity for which the cost is minimum. a. 2000 b. 3000 c. 5000 d. 0 37. Find the slope of the line tangent to the curve y = x3 - 2x + 1 at x = 1. a. 1/3 b. 1 c. 1/4 d. 1/2

32. Water is running into a hemispherical bowl having a radius of 10 cm. at a constant rate of 3 cu. cm/ min. When the water is x cm. deep, the water level is rising at the rate of 0.0149 cm./min. What is the value of x? a. 2 b. 4 c. 3 d. 5

38. Water is running out in a conical funnel at the rate of 1 cu. In. per second. If the radius of the base of the funnel is 4 inches and the altitude in 8 inches, find the rate at which the water level is dropping when it is 2 inches from top. a. in./sec b. in./sec c. -1/9πin./sec. d. in./sec

33. Find the area bounded by the line x - 2y + 10 = 0, the x-axis, the y-axis and x = 10 a. 50 b. 75 c. 100 d. 25

39. What is the area between y = 0, y = 3x2, x = 0 and x = 2? a. 24 b. 6 c. 8 d. 12

34. Find the area bounded by the y - axis and x = 4 = y2/3 a. 12.8 b. 25.6 c. 56.8 d. 30.6

40. If y = (t2 + 2)2 and t = x1/2, datermine a. x5/2 + x1/2 b. 2(x + 2) c. 3/2 d. letter b

35. A triangle has variable sides x, y, z subject to the constaint such that the perimeter is fixed to 18

41. Find the area between the curve y = cosh x and the x-axis from x = 0 and x = 1 Select one: a. 1.667 sq. units

b. 1.333 sq. units c. 1.125 sq.units d. 1.175 sq. units 42. Find the second derivative of y by implicit differentiation from the equation 4x2 + 8y2 = 36. a. 9/4y3 b. -16/9y3 c. 32xy d. 64x2 43. Find the area in sq. units bounded by the parabolas x2 - 2y = 0 and x2 + 2y - 8 = 0 a. 9.7 b. 4.7 c. 10.7 d. 11.7 44. What is the second derivative of a function y = 5x3 + 2x + 1? a. 30x b. 18 c. 30 d. 25x 45. Evaluate the limit of lim(x2 + 3x - 4) as x approaches 3. a. 54 b. 14 c. 18 d. 72 46. The rate of change of function y with respect to x equals 2-y and y = 8 when x = 0. Find y when x = ln2 a. -2 b. -5 c. 2 d. 5 47. If y = 4 cos x + sin 2x, what is the slope of the curve when x = 2 radians? a. -4.94 b. -2.21 c. 2.21 d. -3.25

48. Differentiate y = log10(x2 + 1)2 a. 4x(x2 + 1) b. log e(x)(x2 + 1) c. None of the choices None of the choices d. 2x(x2 + 1) 49. Given a cone of diameter x and altitude of h. What percent is the volume of the largest cylinder which can be inscribed in the cone to the volume of the cone? a. 2.12 b. 2.25 c. 2.86 d. 2.51 50. Find the minimum distance from the point (4,2) to the parabola y2 = 8x a. 4 √ 3 b. 2 √ 3 c. √ 3 d. 2 √ 2 51. Find the area enclosed y the curve x2 + 8y + 16 = 0, the x - axis, the y-axis and the line x - 4 = 0 a. 8.67 sq. units b. 9.67sq. units c. 10.67 sq. units d. 7.67 sq. units 52. Find the equation of the normal to x2 + y2 = 1 at the point (2,1). a. 2x +3y = 3 b. y = 2x c. x + y = 1 d. x = 2y 53. A poster is to contain 300 cm. sq. of printed matter with margins of 10 cm. at the top and bottom and 5 cm at each side. Find the overall dimensions if the total area of the poster is minimum. a. 22.24, 44.5 b. 27.76, 47.8 c. 25.55, 46.7 d. 20.45, 35.6 54. Find the equation of the normal to i>x2 + y2 = 5 at the point (2, 1)

a. x = 2y b. x + y = 1 c. 2x +3y = 3 d. y = 2x

a. 1 b. 2/3 c. 2 d. ½

55. Find the equation of the curve at every point of which the tangent line has a slope of 2x. a. y = -x2 + C b. y = x2 + C c. x = -y2 + C d. 1x = y2 + C

61. Find the area bounded by the parabola, x2 = 4y, and y = 4. a. 33.21 b. 21.33 c. 13.23 d. 31.32

56. The radius of spheres is r inches at time t seconds. Find the radius when the rates of increase of the surface area and the radius are numerically equal. a. 2π in b. 1/4π in c. π2 in d. 1/8π in

62. The area bounded by the curve y = 2x1/2, the line y = 6 and the y-axis is to be revolved at y = 6. Determine the centroid of the volume generated. a. 1.24 b. 0.56 c. 1.8 d. 1.0

57. Given a cone of diameter x and altitude of h. What percent is the volume of the largest cylinder which can be inscribed in the cone to the volume of the cone? a. 0.56 b. 0.44 c. 0.65 d. 0.46 58. The area enclosed by the ellipse (image) is revolved about the line x = 3. What is the volume generated? a. 365.1 b. 360.1 c. 370.3 d. 355.3 59. If y = 2x + sin 2x, find x if y' = 0 a. π/2 b. 3π/2 c. π/4 d. 2π/3 60. A Norman window is in the shape of a rectangle surmountedby a semi-circle. What is the ratio of the width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter?

63. Find the volume generated if the area between y = cosh x and x - axis from x = 0 to x = 1 is is revolved about the x - axis. a. 3.43 cu. Units b. 4.42 cu. Units c. 3.83 cu. Units d. 2.83 cu. Units 64. What is the area bounded by the curve y = x3, the x-axis and the line x = -2 and x = 1? a. 5.24 b. 2.45 c. 5.42 d. 4.25 65. Find the approximate increase by the use of differentials, in the volume of the sphere if the radius increases from 2 to 2.05 in one second. a. 2.12 b. 2.51 c. 2.86 d. 2.25 66. The integral of cos x wuth respect to x is a. csc x + C b. sec x + C c. -sin x + C d. sin x + C

67. Evaluate: Lim a. infinity b. 1 c. 0 d. 2 68. The distance of a body travels is a function of time t and is defined by: x(t) = 18t + 9t2.What is its velocity at t=3? a. 18 b. 54 c. 36 d. 72 Basic Engineering Correlation (Advance Mathematics and Differential Equation Reviewer) 1. Solve the equation y"+6y+9y=0subject to the conditions y(0) =-4 andy (0) = 5. a. y = (11x-4) e-3x b. y = (-7x-4) e-3x c. y = (-7x-4) e3x d. y = (-11x-4) e3x 2. Solve the homogenous equation (x2+y2) dx+2xydy=0 a. x2(x2+3y2) = c b. x(x2+2y2)=c c. x2(x2+2y2)=c d. x(x2<+3y2) =c 3. The expression equivalent to ∫01+I 6z2 dz is equivalent to a. -4+6i b. -z+Zi c. -3+3i d. 4+4i 4. What can be concluded about the function that the graph below depicts?

c. The graph is not a periodic function. d. The following shows an odd function. 5. If A = 25 eπ/42 i and B = CiS π\4 then A + B is_____" a. 39.68∠125.62o b. 40∠75o c. 53.26+ 32.11i d. 32.26+23.11i 6. Which of the following power series is a solution to the differential equation y" + y' = 0 ?

a.

b.

c.

d. 7. The differential equation dv = (y2 - 3vy)dy is said to be a. linear in y b. non linear in V c. linear in V d. non linear in x 8. The laplace transform of t is a. 1/s-1 b. 1/s c. 2/s2 d. 1/s2 9. Determine the value of the Legendre's polynomial function P2(2). a. P2 (2) = 2.5 b. P2(2) = 5.5 c. P2 (2) = 4 d. P2(2)=1

a. The following shows an even function. b. The graph shows symmetry with respect to x=0.

10. The rate at which a solid substance dissolves varies directly has the amount of undissolved solid present in the solvent and as the difference between the saturation concentration of the substance and the instantaneous concentration of the solution Five grams of A are placed in solvent B .the solution when saturated will hold ten grams of A. If 2 grams of A dossolved in 1 hr, how many grams of A will be in solution in 2 hrs? a. 7 g b. 5 g c. 4 g d. 3 g

c. second order homogenous linear different equation d. second order homogenous linear different equation

11. Find the differential equation whose general solution is y = C1x + C2 ex. a. (x + 1)y" - xy' + y = 0 b. (x - 1)y" + xy' + y = 0 c. (x + 1)y" + xy' +y = 0 d. (x - 1)y" - xy' + y = 0

17. The expression (3+2i)6 is equivalent to a. -2035- 828i b. -352+ 936i c. 729+ 64i d. 2187-128i

12. A cylindrical tank is 12ft. In diameter and 8=9 ft high. Water flows into the tank at the rate of /10 cuft/sec. It has a hole radius 1/2 inch at the bottom. The time the tank will be full if initially it is empty is a. 76 min b. 65 min c. 56 min d. 50 min 13. The indicial equation of the Bessel's equation x2 y" + xy' + (x2 - 9) y =0 is a. r2 - 9 = 0 b. r2 + 3 = 0 c. r2 + r - 9 = 0 d. r2 + r - 3 = 0

16. The series equivalent to the function a. f(x) = e3x b. f(x) = 1/1-3x c. f(x) = cos 3x d. f(x) = sin 3x

is

18. What is the order of the differential equation (4 + y")1/3 = e2x a. three b. one-third c. one d. two 19. The indicial equation of ODE 2xy"+(l+ x)y'-2y=o is a. 2r2 - r =0 b. r2 -2 +l=O c. r2-2r =0 d. r2-r =0

14. The solution to the equation x2y'+xy'+x2y=0 if x=0.5 is approximately equal to a. 0.7652 b. 0.5118 c. 0.9385 d. 0.5

20. The population of a certain municipality increases at a rate to the square root of the population. If the present population is 90,000, how long will it take for the population to reach 160,000? a. 210 years b. 150 years c. 200 years d. 180 years

15. The different equation y" + 3y' - 4y =2x is a. first order linear different equation b. second order non homogenous linear different equation

21. Find the equation of the curve at every point at which the tangent line has a slope of 2x. a. y = x2 + C b. y = -x2 + C

c. x = -y2 + C d. x = y2 + C 22. The order of the different equation

27. The expression ∫0πi cos z dz is equivalent to a. 13.098 b. 23,097i c. 13.097i d. 11.55i

a. 2 b. 4 c. 3 d. 6

28. Solve (cos x cos y - cot x)dx - sin x sin y dy = 0 a. sin x cos y = -ln(C cos) b. sin x cos y = ln (C sin x) c. sin x cos y = -ln (C sin x) d. sin x cos y = ln (C cos x)

23. A water container whose circular cross section is 6 ft in diameter and whose height is 8 ft. is filled with water. It has a hole at the bottom of radius 1 inch. The time it will take if the tank rests on support so that its 8 ft height is in a horizontal direction and the hole in its bottom is a. 25.46 min b. 29.4 min c. 28.95 min d. 24.95 min 24. Determine the values of the constants r in the indicial equations of the given ordinary differential equation (2x2 — 24"-2,942y = 0 when Frobenius' method is applied. a. ri 0,r2 = 2 b. r, = r2 = 2 c. = 1,r2= 2 d. = 0,r2 =1 25. Find a power series for the function

a. x-x3+x5 - +... b. 1+x2+x4+... c. 1- x2+x4+... d. x+x3+x5+...

29. The ganeral solution of the ordinary different equation with c = constant is a. - In(1 - 2 y) = x 22 + c b. In(1 - 2y) = x2 + c c. - 1 In(1 - 2 y) = x22 + c d. 2 y = 1 + ce-x2 30. The differential equation given is correctly described by which one of the following choices: d2y/dx2 + bxy dy/dx = f(x) a. non-linear, second order, non homogenous b. non linear, second order, homogenous c. linear,second order homogenous d. linear. Second order, non homogenous 31. Which of the following is true about the Fourier coefficients of f(x)= x if -π ≤ x ≤ π the value of f(π/2) is

a.

b.

c.

26. The order of the differential equation is d. a. 3 b. 4 c. 1 d. 2

32. Sugar decomposes in water at a rate proportional to the amount still unchanged. If there were 50 kg of sugar present initially and at the end

of 5 hours this is reduced to 20 kg, how long will it take until 90% os the sugar is decomposed. a. 12.56 hr b. 15.72 hr c. 16.41hr d. 14.12 hr 33. In the higher-order differential equation (4 — x2 )y'''-4y1+y = 0 , x = —2 is a/an point. a. focal b. ordinary c. regular d. singular 34. Evaluate cos(3 + 5i) a. -.99 + 0.28i b. 0.53-3.59i c. -73.47 -10.47i d. -3.72- 0.51i 35. A new water pump has a capacity of 60 cu m/day. If its capacity goes down by 15% every year, in how many years will the capacity go down to 20 cu m/day? a. 4.72 yrs. b. 7.32 yrs. c. 8.6 yrs d. 3.72 yrs.

37. A certain quantity increases at a rate proportional to q itself. If q = 25 when t = 0 and q = 75 when t =2, find q when t = 6. a. 675 b. 576 c. 756 d. 657 38. Calculate the time in hrs, that it will take to reach the fatal conc. Of 40% methane in a kitchen measuring 15 ft x 12.5 ft x8 ft for a leaking stove. The rate of leak is 15 cuft of 100% methane/hr. Assume no fresh air is coming in. The gas rate is measured at the rate conditions prevailing in the kitchen. a. 40 hrs. b. 50 hrs. c. 30 hrs. d. 45 hrs. 39. Determine the Fourier coefficient a() of the function f (x) = 3x2 + 4, —1 < x <1. a. ao = 5 b. ao = 1 c. a = 0 d. as=10

36. Which of the following is the solution to the Bessel's equation x2 y" + xy' + (x2 - y2) y=0

40. The differential equation (x2 +4xy+y2)dx-xydy=0 is a. variable separable b. linear differential equation c. exact d. homogenous

a.

41. The differential equation can be classified

b.

c.

d.

as a. exact b. variable separable c. linear but not homogenous d. linear and homogenous 42. A spherical tank whose inner diameter is 2 meters is filled with water (density 1 g/cc). If a tank has a hole 1 cm in diameter at the bottom, the time the tank will be totally empty is a. 3.61 hrs.

b. 2.41 hrs. c. 4.21 hrs. d. 6.31 hrs.

d.

43. The simplified form of (3 + 2i) is a. 2,034-1781i b. -2,034+1781i c. -2,035-828i d. 2,035+828i 44. The radius of conversence of the power series

(not sure yet)

a. b. c. d. 45. Which of the following is a differential equation of the first order of degree one? a. 46. Find the differential equations og the family of lines through the origin. a. xdy - ydx = 0 b. ydx + xdy = 0 c. xdx + ydy = 0 d. ydx - xdy = 0 47. Solve the equation

a. b. c.

48. Solve the different equation a. y=(2x3 + 11)2) b. y=(2x3 - 5) c. y=(x3 -5)2) d. y=(x3 +11)2 49. Determine the general solution of xdy + ydx = 0 a. ln (xy) = c b. ln x + ln y = c c. xy = c d. x + y = c 50. Find the equation of the orthogonal trajectories of the system of parabolas y2=2x+C. a. y = C ex b. y = C e-x c. y = C e-2x d. y = C e2x 51. The principal 4th root of 5 + 12i a. 1.62 + 0.39i b. 1.49 + 1.86i c. 0.73 + 1.75i d. 1.82 + 0.55i 52. Evaluate 143 - 41). a. 1.28+ j0.98 b. 1.76+ j0.54 c. 2.23+ j0.21 d. 1.61- 0.931

53. Solve a. y= -x5+cx6 b. y=x5+cx6 c. y=-x6+cx5 d. y=x6+cx5 54. What is the differential equation of a family of parabolas having their vertices at the origin and their vertices on the x-axis? a. xdy + ydx = 0 b. 2ydx - xdy = 0 c. 2xdy - ydx = 0 d. dy/dx - x = 0

55. When a simple electric circuit, containing no condensers but having inductance and resistance, has the electromotive force removed, the rate of decrease of current is proportional to the current. The current is i amperes t seconds after the cutoff, and i = 40 when t = 0. If the current dies down to 15 amperes in 0.01 sec, fid i after 0.1 sec. a. 0.003amp b. 0.001amp c. 0.004amp d. 0.002amp

(assumed uniform throughtout at any instant) and the temperature of the surrounding air, the proportionality constant being 2 Btu/minoF. If the air temperature remains constant at 70oF and if the initial temperature of the tank and its contents is 55oF, the temperature of the tank as a function of the is a. T=120+65et/25 b. T=12-6.5e-t/25 c. T=120-65e-t/25 d. T=-120+65e-t/25 61. Which of the following is a solution of the wave

56. Solve the differential equation : x(y - x = 1,determine y when x = 2. a. 1.55 b. 1.63 c. 1.48 d. 1.8 57. How can the differential equation a d2x/dt2 + B(t) dx/dt + c = D(t) best be described? a. linear, homogenous and first order b. second order and non homogenous c. homogenous and first order d. linear, second order and non homogenous 58. Evaluate sin ( 3 + 4i ) a. 0.14 -0.75i b. 3.85 - 27.02i c. -0.96 + 4i d. -0.09 + 0.75i 59. A body weighing 1960 N is pulled by a constant force of 492 N along a horizontal plane where in the coefficient of friction between the body and the plane id 0.20. Determine the velocity after 20 seconds. a. 13.1 m/s b. 10.57 m/s c. 8.25 m/s d. 9.06 m/s 60. A tank and its contents weigh 100 lbs. The average heat capacity of the system is 0.5 Btu/ lb.F. The liquid in the tank is heated by an immersion heater which delivers 100 Btu/min. Heat is lost from the system at a rate proportional to the difference between the temperature of the system

equation a. u=ex cos t b. u =(x + at)6 c. u = ln(ax-t) d. u = sin(kx)sin(at) 62. A low radioactive material is used in biochemical process to induce biological mutation. The isotope is made in the experimental reactor of the Philippine Atomic Energy Commssion, now Philippine Nuclear Research Institute, and ship to the chemical plant. It has a half life of 8.06 days. The plant receive the shipment of the radioactive material which on arrival contain 1 gram of the radioactive material. The plant uses the material at the rate of 0.1 gram per week. The time it will take for the radioactivity to last is a. 4.74 weeks b. 3.24 weeks c. 5.4 weeks d. 4.34 weeks 63. Solve the differential equation dy - xdx = 0, if the curve passes through (1, 0). a. 3x2 + 2y - 3 = 0 b. 2y + x2 - 1 = 0 c. 2x2 + 2y - 2 = 0 d. x2 - 2y -1 = 0 64. A 10-ohm resistor and a 5-henry inductor are connected in series with to a 50-volt source at time t = 0. Express the current I as a function of time. a. i = 5(1 - e)2t b. i = 5(e2t - 1)

c. i = 5(1 - e-2t) d. i = 5(1 - e2t) 65. Evaluate cosh(5 + 6i) a. 201.72 +74.21i b. 57.22-193.43i c. 71.25-2073i d. 74.20 - 0.28i 66. A 50 lb iron ball is heated to 200oF and then plunged immediately into a vessel containing 100b lbs of water whose temperature is 40oF. The specific heat of iron is 0.11 Btu/lboF. The common temperature, approached by the iron and water as time approaches infinity is a. 68.5oF b. 58.4oF c. 48.34oF d. 38.43oF 67. The rate f decay of radioactivity elements is usually assumed to be proportional to the number of atoms that have not decayed, where λ is the proportionality consatnt. If at time t=0 there are Xo atoms of a given elements, the expression for the number of atoms, X, that have not decayed (as a function of time,t,λ, and Xo) is a. Xo/(1+λt) b. Xo(1-λt) c. Xoe-λt d. Xoe(1-e-λt) 68. Which of the following is a term of the power series representation solution of the higher order differential equation 3 y" —2 x y = 0 a. a1 b. 4 c. 4a2 d. 1 69. The solution to the non homogeneous partial

differential equation a. u(x,y)=f(y)e2x-4x b. u(x,y)=f(x)e-2y+4y c. u(x,y)=f(x)e-2y+2y-1 d. u(x,y)=f(y)e-2x-2x-1

70. Find the general solution of y' = ysec x. a. y = C sec x tan x

b. y = C (sec2 x - tan y) c. y = C (sec x - tan x) d. y = C (sec x + tan x) 71. Determine the value of c such that the function u(x,t) = e -256 sin 2x will be a solution of the heat

equation given by a. 1 b. 4 c. 8 d. 2 72. The expression (5+2i)7 is equivalent to a. -15939+ 1846C1 b. -703919-68880i c. -116615+60422i d. 78125+128i 73. Find the principal 5th root of 5+121. a. 1.64 +1.38i b. 1.38+1.641 c. 1.67+0.13i d. 1.62+0.391 74. Evaluatecos(2+3i). a. -2,034+17811 b. 2,035+828i c. 2,034-1781i d. -4.19-9.11i 75. A body whose temperature is 180o is immersed in a liquid which is kept at a constant temperature of 60o. In 10 minutes the temperature of the immersed body decreased to 120o. How long will it take for the body's temperature to decrease to 90o? a. 15 min. b. 20 min. c. 25 min. d. 18 min. 76. the equation y2 = cx is the general solution of a. y' = x/2y b. y' = 2y/x c. y' = y/2x d. y' = 2x/y

77. Find the radius of the convergence of the series

a. |x| < 2 b. |x| < ½ c. |x| < 8 d. |x| < 1/8 78. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years? a. 88.6 b. 90.72 c. 92.16 d. 95.32 79. A certain subxtance increases at a rate proportional to the square of the instantaneous amount. After 5 days the amount is doubled. Determine the time before the amount is tripled. a. 40/3 b. 45/3 c. 20/3 d. 25/3 80. Evaluate sinh(6 + 5i) a. 57.22 –193.43i b. 201.71+ 74.201 c. –20.74 + 71.25i d. –0.27 – 0.96i 81. Which of the following is true about the Fourier coefficients of

a. ao=7 b. ao= 0 c. ao=10 d. ao=5 82. The solution to the homogeneous partial

differential equation

a. u(x,y)=A(y)cos 3x+B(y)sin 3x b. u(x,y)=A(y)e3x +B(y)xe3x c. u(x,y)=A(y)e3x +B(y)e-3x d. u(x,y)=A(y) +B(y)e-9x 83. Solve xy'(2y -1) = y(1-x) a. ln (xy) = x + 2y + C b. ln (xy) = 2y - x + C c. ln (xy) = x - 2y + C d. ln (xy) = 2 (x - y) + C 84. A tank initialy contains 400 liters of water. Salt solution, containing 1/8 kg of salt per liter of solution flows into the tank at the rate of 8 li/min and the solution, kept well-stirred, flows out of the tank at the rate of 4 li/min. Find the amount of salt in the tank after 100 minutes. a. 80 kg b. 85 kg c. 75 kg d. 70 kg 85. A mothball loses mass by evaporation at rate that is proportional to the surface area. If half tha mass is lost in 100 days, how long will it take the radius to decreases to half its initial value? a. 255 days b. 275 days c. 243 days d. 234 days 86. The laplace transform of et is a. 1/(s-1)2 b. 1/(s+1) c. 1/(s-1) d. 1/s 87. Evaluate cosh ( 3 + 5i) a. 2.86 + 9.61i b. 1.61 + 0.93i c. 2.08 + 1.79i d. 2.08 + 0.93 i 88. If dy = x2dx, what is the equation of y in terms of x if the curve passes through (1,1)? a. x3 - 3y + 2 = 0 b. x3 + 3y + 2 = 0 c. x2 - 3y + 3 = 0 d. 2y + x3 + 2 = 0

89. Evaluateln(5 +j3). a. 1.28+ j0.98 b. 2.54+ j0.866 c. 2.23+ j0.21 d. 1.76+ j0.54 90. Which of the following power series is a solution to the differential equation

a.

b.

c.

d.

91. Solve the equation a. y =cIe5x+ c2e3x b. y =cIe-5x+ c2e-3x c. y =(cIx+ c2)e-5x d. y =(cIx+ c2)e3x

Basic Engineering Correlation (Chemistry Reviewer) 1. Uranium-235 and uranium-238 have the same number of which of the following? a. Protons and electrons b. neutrons c. protons d. electrons

2. What is the valence (oxidation state) of carbon in sodium carbonate (Na2CO3)? a. -4 b. 4 c. 2 d. -2 3. Water and SO3 combine to sulfuric acid (H2SO4) according to the following reaction. How many grams of water must be added to 100 g of 20% oleum (20% SO3 and 80% H2SO4by weight) to produce a 95% solution ( byweight) of sulfuric acid? a. 3.3 g b. 14 g c. 5.0 g d. 7.5 g 4. During a laboratory experiment at 1.0 atm and 25oC, a student observed that oxygen gas was produced by de-composition of 15 g of sodium chlorate. What was the volume of oxygen? a. 1.27 L b. 6.54 L c. 5.17 L d. 3.85 L 5. Which of the following does a catalyst change? a. the activation energy of a reaction b. the equilibrium constant of areaction c. the concentration of product at equilibrium d. the heat of reaction of a reaction 6. What is an isomer? a. a substance containing a hydroxyl ion b. a single atom c. different arrangement of the same atoms d. a basic building block for large chemical chains 7. The reaction shown occurs in a gaseous phase. Once equilibrium has been achieved in a particular reaction vessel, additional HI gas is injected directly into the reaction vessel. Compared to the initial conditions, which of the following statemnets is correct after the new equilibrium has been achieved? a. The amount of H2 will have decreased. b. The partial pressure of H2 will have decreased. c. The amount of I2 will have increased. d. The partila pressure of HI will have decreased.

8. Which of the following compounds would be ionic, considering the electronegativities of the elements? a. I2 b. NO c. CO d. KCI 9. An unknown gas with a temperature of 25oC and a pressure of 740 mm Hg is collected in a sampling bag. The volume and mass of the gas are 24.0 L and 34.9 g, respectively. Which chemical formula could represent the gas? a. N2 b. H2S c. HCI d. Ar 10. What is the percentage (by mass) of htdrogen in glucose (C6H12O6)? a. 0.067 b. 0.093 c. 0.17 d. 0.4 11. 2.00 g of a substance dissolved in 250 g of water produces a boiling point elevation of 0.065oC. What is the molecular weight of the substance? a. 63 b. 92 c. 16 d. 8 12. A current of 0.075 A passes through a solution of silver nitrate for 10 munites. How much silver is deposited? a. 0.040g b. 0.035 g c. 0.030 g d. 0.050 g 13. How many grams of copper will be deposited at an electrode if a current of 1.5 A is supplied for 2 hours to a CuSO4? a. 7.1 g b. 3.6 g c. 48 g

d. 2.4 g 14. What is the order of reaction with respect to reactant E and the overall order of the reaction described by the following rate law? a. second order with respect to E; second order overall b. first order with respect to E; second order overall c. second order with respect to E; fourth order overall d. first order with respect to E; fourth order overall 15. What is the term for a quantity of a susbstance to which a chemical formula can be assigned and whose mass is equal to its formula weight? a. a mole b. an equivalent c. a molecule d. a one-normal solution 16. The pH of a 0.001 M HCI solution is a. 5 b. 3 c. 7 d. 1 17. The half-life of radioactive carbon is approximately 5700 years. If a sample is found to have 7000 atoms after 6000 years, how many atoms were presents initially? a. 13800 atoms b. 14500 atoms c. 14300 atoms d. 14100 atoms 18. Given the following reversible chemical reaction, assume all reactants and products are ideal gases. a. The amount of ammonia (NH3) would halve. b. There would be no change in the amount of ammonia (NH3) present. c. More ammonia (NH3) would be generated. d. The amount of ammonia (NH3) would double. 19. Which of the following statements concerning reversible reactions is false? a. Temperature affects the direction of the reaction.

b. Concentration have no effect on the direction of the reaction c. Concentration remain constant once equilibrium is reached. d. Both reactants and products are always present. 20. Which of the following reactions are not balanced? a. IV only b. I only c. II and III d. I and III 21. 2.00 g of a substance dissolved in 250 g of water produces a boiling point elevation of 0.065oC. What is the molecular weight of the substance? a. 92 b. 16 c. 8 d. 63 22. Oxygen reacts stoichimetrically with methane to form 14 g of carbon monoxide. How many moles of methane are consumed? a. 1 mol b. 0.5 mol c. 2 mol d. 1.5 mol 23. Which o fthe following chemical formulas is incorrect? a. Na2CO3 b. KOH c. Ca(OH)2 d. CaCI 24. What are the chemical formulas for the following compounds: aluminum nitrate, magnesium hydroxide, calcium oxide, and cupric carbonate? a. AINO3,Mg(OH),Ca2O3,CuCO3 b. AI(NO3)3,Mg(OH)2,CaO,CuCO3 c. AL2NO3,Mg(HO),CaO2,CuCO3 d. AINO3Mg(HO)2,CaO,Cu(CO3)2 25. Nitroglycerin is made by combining glycerol, nitric acid, and sulfuric acid. What are the

minimum coefficients needed to balance the equation of this reactions? a. 4,2,1,1,3,1 b. 1,3,1,1,3,1 c. 1,3,3,1,3,2 d. 2,6,2,2,6,2 26. Which of the following occurs when table salt (NaCI) is added to continuously heated boiling water? a. The water boils even more agitatedly. b. The temperature of the water decreases but boiling continues uninterrupted. c. The water continues to boil. d. The water momentarily stops boiling. 27. The final temperature of the hydrogen and chlorine described in Prob. 8 is 30oC. What is the final pressure in the reaction vessel? a. 80 kPa b. 320 kPa c. 240 kPa d. 160 kPa 28. A wastewater treatment plant uses chlorine gas as a reactant. A tank is filled with 800 m3 of 20oC water, and chlorine is added at a dosage of 125 g per cubic meter of water. (Assume all of the chlorine dissolves and none initially reacts chemically.) If the atmospheric pressure is 1.0 atm, what is the theoretical partial pressure of the chlorine gas at the tank surface immediately after the gas is added? a. 2.3 x 10-4 atm b. 0.11 atm c. 3.1 x 10-5 atm d. 0.039 atm 29. What family of compounds is produced from the reaction between an alcohol and a carboxylic acid? a. ether b. amine c. ester d. ketone 30. Which of the following statements pertaining to acids and bases is incorrect? a. Acids conduct electricity in aqueous solutions.

b. Bases have a pH between 7 and 14. c. Bases have a sour taste. d. Acids turn blue litmus paper red. 31. As the pressure of a gas increases, the solubility of that gas in a liquid a. always increases. b. is not changed. c. always decreases. d. cannot be determined. 32. What is a distinguishing characteristic of the halogens? a. They are phosphorescent. b. Next to the noble gases, they are the most chemicallyinactive group. c. They readily accept an electron from another atom to form compounds. d. They have a high electrical conductivity. 33. Enthalpy of formation is most closely defined as the a. potential energy of a substance. b. energy absorbed during creation of 1 grammole of a compound from pure elements. c. energy absorbed or released during a chemical reaction. d. sum of the enthalpy of reactions. 34. Assuming all of the energy goes into the reaction, what electrical power is required to produce oxygen gas at a rate of 50 mg/s?

a. 9.2 kW b. 0.89 kW% c. 3.1 kW d. 1.5 kW 35. What is the oxidation number for chromium (Cr) in the compound BaCro?

a. 2 b. 4 c. 1 d. 6 36. A transportation company specializes in the shipment of pressurized gaseous materials. An order is received for 100 L of a particular gas at STP (0oC and 1 atm). What minimum volume tank is necessary to transport the gas at 25oC and a maximum pressure of 8 atm? a. 14 L b. 12 L c. 16 L d. 10 L 37. In an experient, a compound was determined to contain 68.94% oxygen and 31.06% of an unknown element by weight. The molecular weight of this compound is 69.7 g/mol. What is this compound? a. SiO4 b. NO2 c. F2O2 d. B2O3 38. 6 g of a substance are dissolved in 1000 g of water. The solution freezes at -0.16oC. What is the molecular weight of the substance? a. 70 g/ mol b. 60 g/mol c. 75 g/mol d. 100 g/mol 39. A gaseous mixture consists of 2 kg of oxygen, 5 kg of nitrogen, and 3 kg of xenon. What is the mole fraction of the oxygen gas? a. 0.24 b. 0.17 c. 0.11 d. 0.13 40. The diameter of a spherical mothball is observed to halve in 200 days.approximately how long will it take for its remaining volume to become half of its volume at 200 days? a. 67 days b. 160 days c. 130 days

d. 200 days 41. For a given isotope of an element, the atomic number plus the atomic weight is 148, and their difference is 58. how many protons does an atom of the isotope contain? a. 45 b. 90 c. 148 d. 58 42. 10 g of solid PCI5 is heated in a 0.5 m3 container to 150oC, producing gaseous PCI3 and CI2 gas according to the following decomposition reaction: The molecule weights of the compound are What is the increase in pressure in the container when 50% (By weight) of the PCI5 is decomposed? a. 0.250 kPa b. 18 kPa c. 0.120 kPa d. 0.350 kPa 43. An alkyl radical is best defined as a. an electron that is shared in a covalent bond. b. any functional group that substitutes for a hydrogen atom in an alkane. c. the remaining portion of an alkane after it loses a hydrogen atom. d. cancer-causing molecules found in foods 44. It is known that ozone (O3) will decompose into oxygen (O2) at a temperature of 100o. One mole of ozone is sealed in a container at STP (0oC and 1 atm). What will be pressure of the container once it is heated to 100oC? a. 37 kPa b. 1.4 kPa c. 2.1 kPa d. 210 kPa 45. How much water must be added to 100 mL of a 0.75 molar solution of KCI to make a 0.04 molar solution? a. 1.88 L b. 0.188 L c. 1.78 L d. 1.98 L

46. While moving from left to right across the second row of the periodic table (i.e., from Li to Ne), the atomic radii tend to a. first increase, then decrease. b. uniformly increase. c. remain the same. d. uniformly decrease. 47. A solution is adjusted from pH 8 to pH 9. The relative concentraation of the hydrogen [H+] ion has changed by a factor of what? a. 1100 b. 5 c. 110 d. 10 48. The solubility constant of stronyium sulfate, SrSO4, is 2.8 x 10-7. How many grams of SrSO4 must be dissolved in water to produce 1 L saturated solution? a. 0.1 g b. 2 g c. 0.00005 g d. 0.0005 g 49. Which of the following elements has the largest first ionazation energy? a. CI (chlorine) b. Ar (argon) c. H (hydrogen) d. Kr (krypton) 50. How many milliters of 1 M NaOH solution will 25 mL of 2 H2SO4neutralize? a. 50 mL b. 100 mL c. 75 mL d. 25 mL 51. What is the molarity of a solution obtained by dis-solving 25 g of NaCI in enough water to produce 4 L of solution? a. 6.25 b. 0.365 c. 0.428 d. 0.107 52. What is the half-life of a substance that decays to 25% of its original amount in six days?

a. 3 days b. 0.08 days c. 8 days d. 12 days 53. Two moles of sodium react with 2 moles of water to produce which of the following? a. 1 mole of sodium hydroxide and 1 mole of hydrogen b. 2 moles of sodium hydroxide and 1 mole of hydrogen c. 1 mole of sodium hydroxide and 2 moles of hydrogen d. 2 moles of sodium hydroxide and 2 mole of hydrogen 54. When a deliquescent substance is exposed to air, it a. oxidizes. b. becomes moist c. crystallizes. d. loses water of hydration. 55. Which of the following elements does not exists as a diatomic molecule under normal (ambient) conditions? a. chlorine b. oxygen c. iodine d. sulfur 56. A given sample of radioactive material has 80% of the original substance remaining after 10 years. How much will remain after 90 additional years? a. 0.001 b. 0.017 c. 0.11 d. 0.13 57. The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is 4.5 x 109 years. In a particular rock sample, the ratio of the numbers of Pb-206 to U238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? a. 3.3x 109 yr b. 1.4 x 109 yr c. 7.0 x 109 yr

d. 9.3 x 109yr 58. How much energy is needed to convert ozone to oxygen? a. 43 kcal/mol b. 0 kcal/ mol c. 68 kcal/mol d. 140 kcal/mol 59. The group of metals that includes lithium, sodium,potassium, rubidium, and cesium forms a closely related family known as the a. rare earth group. b. halogens. c. alkali metals. d. alkaline earth metals. 60. Hydrogen and chlorine gas combine in a 35 m3 reaction vessel to produce hydrogen chloride. The masses of hydrogen and chlorine are 4.5 kg and 160 kg, respectively. How much hydrogen chloride gas is produced? a. 41 kg b. 21 kg c. 82 kg d. 160 kg 61. How many liters of 2M solution (i.e., a molarity of 2) can be produced from 184 g of enthyl alcohol (CH3CH2OH)? a. 1.5 L b. 5.0 L c. 2.0 L d. 2.5 L 62. If the current, I, is 100 A, at what rate is oxygen produced?

a. 18.7 mg/s b. 8.29 mg/s

c. 16.7 mg/s d. 9.34 mg/s 63. What mass of lead nitrate, Pb(NO3)2, must be dis-solved in 1 L of water to produce a solution that contains 20 mg of lead ions? Assume 100% ionazation. a. 43 mg b. 52 mg c. 32 mg d. 26 mg 64. A compound in gas form Has a mass of 0.377 g and occupies 191.6 mL at standard conditions (0oC and 760 mm Hg). What is the formula of the compound? a. C3H8 b. CH4 c. C5H12 d. C2H6 65. A gas mixture of N2(g) and CO2(g) contained in a volume of 10.0 L has a total pressure of 0.750 atm at a temperature of 273K. The mixture is known to contain 3.00 g N2(g). What is the partial pressure of CO2(g) in the mixture? a. 0.120 atm b. 0.630 atm c. 0.510 atm d. 0.240 atm 66. Rank the following gas according to increasing effusion rates relative to O2 (reference). a. F2< CO24 b. F<2< CH<4< CO<2 c. CH42
68. "::Add_Chem_004:: Consider a solution of water and a nonvolatile solute at some temperature. What combination of conditions would be sure to increase the vapor pressure of the solution? _____" a. Raise the temperature and add more water b. Lower the temperature and add more solute c. Raise the temperature and add more solute d. Lower the temperature and add more water 69. What is the mass of 0.01 gram-moles of Na2SO4? a. 1.42 g b. 1.19 g c. 0.71 g d. 2.38 g 70. An ideal gas occupies a volume of 4L and has a pressure of 283.71kPa (1atm=101.325kPa). Under 22.50C, what most likely is the identity of the gas if 0.01293 Kg of gas is used. a. O2 b. Cl2 c. F2 d. N2 71. The reaction shown proceeds in a gaseous state. At equilibrium, the concentration of the components X,Y, and Z are measured to be 5.73 x 10-2 mol/L, 2.67 x 10-2 mol/L and 4.59 x 10-2 mol/L, respectively. What is the equilibrium constant for this reaction? a. 9.8 x 10-4mol/L b. 1.7 x 10-2mol/L c. 3.7 x 10-1 mol/L d. 2.1 x 10-2mol/L 72. If 1.5 L of an ideal gas at 250C is heated, the new volume increases 2.5 times the original volume. The pressure and amount of substance are held constant. What is the new temperature of gas in 0F a. 882 0F b. 8800F c. 820 0F d. 8280F

73. "::Add_Chem_013::Following are three states for fluorine:1s22s12p6 1s22s22p5 1s22s22p42d1 They are, respectively: _____" a. ground, excited, impossible b. ground, impossible, excited c. excited, impossible, ground d. excited, ground, impossible 74. At what temperature in 0C will O2 has under a pressure of 2.4 atm? (ρ of O2= 1.43 g/L) a. 645.7510C b. 3810C c. 315.570C d. 318.160C 75. Macro Vee collected hydrogen gas using water displacement method. He measured the temperature of water using a thermometer and found out that it is 230C with the correponding pressure of 21.1 mmHg. Calculate the pressure of hydrogen gas under standard atmospheric pressure. a. 95.81 KPa b. 98.51 Kpa c. 98.15 Kpa d. 95.18 Kpa 76. A sample of an unknown compound is found to be 49.3% carbons, 9.6% hydrogen, 19.2% nitrogen, and 21.9% oxygen by weight. What is its molecular formula? a. C3H7NO b. C3H7NO c. C4H<><> d. C4H4NO 77. Balance the following reaction. a. HBrO3 + 5HBr 3H2O + 3bR2 b. 3HBrO3 + HBr 2H2O + 2Br2 c. 2HBrO3 + 4HBr 3H2O + 3Br2 d. HBrO3 + 4HBr 3H2O + Br2 78. Which of the following is the correct electron configuration of Pb? a. [Xe]6s24f146s2 b. [Xe]6s25d104f146p2 c. [Xe]6s25d104f145d106p2 d. [Xe]5d104f146p2

79. The mole (mol) is the amount of a substance that contains as many elementary entities as there are atoms in exactly a. 12.00 grams of C. b. average atomic mass of isotopes of C. c. 12.01 grams/mol of C. d. 12.00 grams of 12C. 80. At STP the volume of 1.5 mole N2as compared to 1.0 mole O2 is a. higher to about three fourths b. the same, 22.4L c. different by about 11.2 L d. differ by a factor of 1.25 81. "::Add_Chem_008:: How many grams of glucose, C6H12O6, are necessary to prepare 656 mL of a solution with a concentration that is 0.550 molar? _____" a. 0.00200 g b. 151 g c. 64.9 g d. 214 g 82. n the following reaction, which elements are the reducing and exidizing agents? a. Mg is the reducing agents; O2 is the oxidizing agent. b. MgO is the reducing agent; Mg is the oxidizing agent. c. Mg is the reducing agent;MgO is the oxidizing agent. d. O2 is the reducing agent; Mg is the oxidizing agent. 83. By decreasing the pressure of an ideal gas at constant temperature and amount of substance 1/3 times the original pressure, the volume of gas will a. expands two thirds the original b. increases three times the original c. multiply by a factor of 1/3 d. decreases three times the original 84. What is the gravimetric (i.e.m.,mass) percentage of oxygen in K2CrO4? a. 0.33 b. 0.66 c. 0.57

d. 0.42 85. There are 500 g of zinc sulfide (ZnS) in a load of zinc ore. The ZnS is roasted in excess air to form zinc oxide (ZnO) and sulfer dioxide (S)2). How many grams of zinc can be subsequently recovered if 5% of the zinc is lost in the roasting process? a. 340 g b. 380 g c. 320 g d. 400 g 86. What is the enthalpy of reaction at 25oC for the combustion of ethane ( C2H6)? a. -680 kcal/mol (exothermic) b. -340 kcal/mol ( exothermic) c. 130 kcal/mol (endothermic) d. 340 kcal/mol (endothermic) Basic Engineering Correlation (Physics Reviewer) (A Collaborative work of GaMbit, jay729, and airsWTP) 1. The system shown is in static equilibrium. Find W.

Select one: a. 1000 N b. 1700 N c. 1500 N d. 830 N 2. What is the force in member AF?

Select one: a. 5000 N b. 15 000 N

c. 10 000 N d. O 3. A ball is dropped from rest at a point 12 m above the ground into a smooth, frictionless chute. The ball exist the chute 2 m above the ground and at angle 45o from the horizontal. Air resistance is negligible. Approximately how far will the ball travel in the horizontal direction before hitting the ground?

Select one: a. 22 m b. 20 m c. 24 m d. 12 m

4. The structure shown is formed of three separate solid aluminum cylindrical rods, each with a 1 cm diameter. What is the -coordinate of the centroid of volume for the structure? Select one: a. 15.2 cm b. 16.0 cm c. 15.9 cm d. 14.0 cm 5. A projectile has an initial velocity of 110 m/s and a launch angle of 20o from the horizontal. The surrounding terrain is level, and air friction is to be disregarded. What is the maximum elevation achived by the projectile? Select one: a. 350 m

b. 72 m c. 140 m d. 620 m 6. What are R1 and R2? (insert question #11) Select one: a. 1250 N b. 1250 N; R2 / c. 1000 N; R2 / d. R1 / e. 3750 N f. 4000 N g. 2500 N; R2 / h. 1250 N i. R1 / j. R1 / k. 3750 N; R2 / l. R1 / 7. What is the reaction at point A?

Select one: a. 710 N b. O c. 500 N d. 290 N 8. A turntable capable of angularly accelerating at 12 rad/s2 needs to be given an initial angular velocity if it is to rotate through a net 400 radians in 6 seconds. What must its initial angular velocity be?

Select one: a. 33 rad/s b. 21 rad/s c. 200 rad/s d. 28 rad/s 9. A 550 kg mass initially at rest acted upon by a force of 50 et N. What are the acceleration, speed, and displacement of the mass at t = 4 s? Select one: a. 4.96 m/s2,4.87 m/s,19.5 m b. 4.96 m/s2,135.5 m/s,2466 m c. 4.96 m/s2,271 m/s,3900 m d. 4.96 m/s2,4.96 m/s,19.8 m 10. A constant force of 750 N is applied through a pulley system to lift a mass of 50 kg as shown. Neglecting the mass and friction of the pulley system, what is the acceleration of the 50 kg mass? Select one: a. 20.2 m/s2 b. 16.2 m/s2 c. 8.72 m/s2 d. 5.20 m/s2 11. A child keeps a 1 kg toy airplane flying horizontally in a circle by holding onto a 1.5 m long string attached to its wing tip. The string is always in the plane of the circular flight path. If the plane flies at 10 m/s, what is the tension in the string? Select one: a. 15 N b. 28 N c. 7 N d. 67 N 12. One newton is the force required to Select one: a. give a 1 g mass an acceleration of 1m/s2. b. accelerate a 10 kg mass at a rate of 0.10 m/s2. c. accelerate a 1 kg mass at a rate of 9.81 m/s2 d. accelerate a 1 kg mass at a rate of 1.00 cm/s2. 13. What is the approximate centroidal polar moment of inertia of the area?

Select one: a. 27.3cm4 b. 25.6 cm4 c. 16.2 cm4 d. 21.4 cm4 14. A 4-A current is maintained in a simple circuit with a total resistance of 2 . How much energy is delivered in 3 seconds Select one: a. 3J b. 12J c. 6 J d. 96J 15. In the pin-jointed truss shown, what is the force in member DE?

Select one: a. 3500 N b. 2500 N c. O d. 550 N 16. Link AB of the linkage mechanism shown in the illustration rotates with an instantaneous counterclockwise angular velosity of 10 rad/s. What is the instantaneous angular velocity of link BC when link AB is horizontal and link CD is vertical?

a. 1.30 m/s b. 0 m/s c. 5.20 m/s d. 1.73 m/s 20. Find the distance between position B and C.

Select one: a. 3.25 rad/s (counterclockwise) b. 2.25 rad/s (clockwise) c. 12.5 rad/s (clockwise) d. 5.50 rad/s (clockwise) 17. Why does a spinning ice skater's angular velocity increase as she brings her arms in toward her body? Select one: a. Her angular momentum is constant b. Her radius of gyration is reduced. c. Her mass moment of inertia is reduced. d. all of the above 18. A flywheel rotates at 7200 rev/min when the power is suddenly cut off. The flywheel decelerates at a constant rate of 2.1 rad/s2 and comes to rest 6 min later. How many revolutions does the flywheel make before coming to rest? Select one: a. 390 000 rev b. 18 000 rev c. 22 000 rev d. 72 000 rev 19. Two 2 kg block are linked as shown. Assuming that the surfaces are frictionless, what is the velocity of block B if block A is moving at a speed of 3 m/s?

Select one:

Select one: a. 3.23 m b. 10.1 m c. 4.78 m d. 7.78 m 21. A weekend plumber, unable to loosen a pipe fitting, slips a piece of scrap pipe (a "cheater") over his wench handle. He then applies his full mass of 100 kg to the end of the cheater by standing on it. The distance from the center of the fitting on the point where the weight acts is 0.80 m and the wrench handle and cheater make an angle of 19° with the horizontal. Find the magnitude and direction of the torque he applies about the center of the pipefitting. Select one: a. 740 N b. 120 N c. 360 N d. 520 N 22. A 1530 kg car is towing a 300 kg trailer. The coefficient of friction between all tires and the road is 0.80. How fast can the car and trailer travel around an unbanked curve of radius 200 m without either the car or trailer skidding? Select one: a. 143 km/h b. 75.2 km/h c. 40.0 km/h d. 108.1 km/h 23. A rope passes over a fixed sheave as shown. The two rope ends are parallel. A fixed load on one end of the rope is supported by a constant force on the other end. The coefficient of friction between

the rope and the sheave is 0.30. What is the ratio of tensile forces in the two rope ends?

Select one: a. 2.6 b. 1.6 c. 1.2 d. 1.1 24. If the sum of the forces on a particle is not equal to zero,the particle is Select one: a. moving with a constant velocity opposite to the direction of the resulatnt force. b. accelerating in a direction opposite to the resultant force. c. accelerating in the same direction as the resultant force. d. moving with constant velocity in the direction of the resultant force. 25. What is the -coordinate of the centroid of the perimeter line?

Select one: a. 1.66 cm b. 1.56 cm c. 1.75 cm d. 1.80 cm 26. An angle bracket is subjected to the forces and couple shown. Determine the equivalent forcecouple system at point A

Select one: a. 292 N at -5.9o ; 103 N.m b. 333 N at 42.9o ; 53 N.m c. 114 N at 15.3o ; 50 N.m d. 307 N at 10.4o ; 110 N.m 27. In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction? Select one: a. 1.33 R b. 2.00 R c. 1.67 R d. 1.50 R 28. Find the acceleration of block A after the blocks are released.

Select one: a. 2.5 m/s b. 0 m/s c. 1.4 m/s d. 5.6 m/s 29. Where can a couple be moved on a rigid body to have an equivalent effect? Select one: a. along the perpendicular bisector joining the two original forces b. along the line of action c. anywhere on the rigid body d. in a parallel plane 30. What is the reaction at point B?

a. potential energy b. total energy c. angular velocity d. linear momentum

Select one: a. 20 000 N b. 10 000 N c. 15 000 N d. 5000 N

35. A single force (not shown) is applied at point B in the y-direction, in line with points A and B. What should this force bein order for the frame to be in equilibrium in that direction?.

31. Find the -and y-coordinates of the centroid of wire ABC

Select one: a. 0.43 m ; 1.29 m b. 2.71 m ; 1.49 m c. 3.33 m ; 2.67 m d. 0.64 m ; 2.83 m 32. For a force to do work it must be ____ the displacement Select one: a. shorter than b. equal in magnitude to c. paralllel or antiparallel to d. perpendicular to

Select one: a. -280 N (down) b. 120 N (down) c. 180 N (down) d. -250 N (down) 36. A cable passes over a stationary sheave and supports a 60 kg bucket, as shown. The coefficient of friction between the cable abd the sheave is 0.10. The cable has a uniform mass per unit length of 0.4 kg/m. The cable is in the shape of a catenary due to its own weight. The tension o fthe cable at the pulley is given by T = wy, where w is the weight per unit lenght and the constant y (for this configuration) is known to be 151 m. How much more mass can be added to the4 bucket before the cable slips over the pulley?

33. For which of the following situation is the net force acting on a particle necessarily equal to zero? Select one: a. The particle has constant loinear momentum. b. The particle has constant angular momentum. c. The particle has constant kinetic energy. d. The particle is traveling at constant velocity around a circle. 34. A perfect sphere moves up a frictionless incline. Which of the following quantities increases? Select one:

Select one:

a. 12.1 kg b. 11.6 kg c. 10.0 kg d. 0 37. The moment of inertia about the -axis o fthe cross section shown is 245833 cm4. If the crosssectional area is 250 cm2 and the thickness of the web and the flanges are the same, what is the moment of inertia about the centroidal axis?

Select one: a. 600 N b. 300 N c. 100 N d. 400 N 40. What are the - and y-coordinates of the centroid of the area?

Select one: a. 2.1 x 104 cm4 b. 1.5 x 105 cm4 c. 2.5 x 105 cm4 d. 8.0 x 104 cm4 38. Assume that the centroidal moment of inertia of area A2 with respect to the composite centroidal -axis is 73.94 cm4. The moment of inertia of area A2 with respect to the composite centroidal horizontal axis is 32.47 cm4. What is the moment of inertia o fthe composite area with respect to its centroidal -axis?

Select one: a. 560 cm4 b. 460 cm4 c. 480 cm4 d. 350cm4 39. Find the tension, T, that must be applied to pulley A to lift the 1200 N weight.

Select one: a. 3.0 cm ; 4.0 cm b. 2.4 cm ; 3.4 cm c. 3.0 cm ; 3.6 cm d. 3.0 cm ; 3.8 cm 41. Determine the force in member FH for the piconnected truss shown.

Select one: a. 4130 N (tension) b. 0 c. 2320 N (compression) d. 3840 N (tension) 42. What is the period of a pendulum that passes the center point 20 times a minute. Select one: a. 0.2 s b. 3 s c. 6 s

d. 0.3 s 43. A 2kg block rests on 34o incline. If the coefficient of static friction is 0.2, how much additional force, F, must be applied to keep the block from sliding down the incline?

Select one: a. 14 N b. 9.1 N c. 7.7 N d. 8.8 N 44. A uniform rod (AB) of length L and weight W is pinned at point C. An initial impulse starts the rod accelerating with an initial angular acceleration (in rad/s2) of g/L. What is the initial reaction at point C?

Select one: a. w/3 b. w/4 c. 4w/7 d. 4w/7 45. What is the radius of gyration about a horizontal axis passing through the centroid? Select one: a. 1.7 cm b. 0.86 cm c. 3.7 cm d. 2.3 cm 46. A 153 kg car is towing a 300 kg trailer. The coefiicient of friction between all tires and the road is 0.80. The car and trailer are traveling at 100 km/h around a banked curve of radius 200 m. What is the necessary banking angle such that tire friction will not be necessary to prevent skidding?

Select one: a. 36o b. 78o c. 21o d. 8o 47. A 47.2-kg child is standing on the outer edge of a merry-go-round that has moment of inertia 543 kg · m2 and radius 2.40 m. The entire system is initially rotating at 0.180 rev/s. Find the angular velocity if the child moves to a final position 1.10 m from the center of the merry-go-round. Select one: a. 4.123 rev/s b. 0.132 rev/s c. 0.244 rev/s d. 1.324 rev/s 48. A hollow cylinder has a mass of 2 kg, a height of 1 m, an outer diameter of 1 m, and an inner diameter of 0.8 m. What is the cylinders mass moment of inertia about an axis perpendicular to the cylinders longitudinal axis and located at the cylinders end?

Select one: a. 0.79 kg m2 b. 0.87 kg m2 c. 1.49 kg m2 d. 0.41 kg m2 49. Rigid link AB is 12 m long. It rotates counterclockwise about point A at 12 rev/min. A thin disk with radius 1.75 m is pinned at its center to the link at point B. The disk rotates counterclockwise at 60 rev/min with respect to point B. What is the maximum tangetial velocity seen by any point on the disk?

53. A 2 kg mass swings in a vertical plane at the end of a 2 m cord. When = 30o, the magnitude of the tangential velo9city of the mass is 1 m/s. What is the tension in the cord at this position?

Select one: a. 45 m/s b. 28 m/s c. 33 m/s d. 6 m/s 50. A car is pulling a trailer at 100 km/h. A 5 kg cat riding on the roof of the car jumps from the car to the trailer. What is the change in the cat's momentum? Select one: a. -25 N s (loss) b. 0 N s c. 1300 N s(gain) d. 25 N s (gain)

Select one: a. 19.6 N b. 29.4 N c. 18.0 N d. 24.5 N 54. What total torque is apllied to the pulley?

51. What is the magnitude o fthe couple that exactly replaces the moment that is removed?

Select one: a. 2.5 N m b. 0.16 N m c. 15 N m d. 0.08 N m 52. Refer to a particle for which the position is defined by s(t) = 2 sin tj [tin radians]. What is the magnitude of the particles velocity at t = 4 rad? Select one: a. 3.30 b. 4.12 c. 2.75 d. 2.61

Select one: a. O b. 230 N m c. 300 N m d. 280 N m 55. A fisherman cuts his boats engine as it is entering a harbor. The boat comes to a dead stop with its front end touching the dock. The fisherman's mass is 80 kg. He moves 5 m from his seat in the back to the front of the boat in 5 s, expecting to be able to reach the dock. if the empty boat has a mass of 300 kg, how far will the fisherman have to jump to reach the dock? Select one: a. 1.3 m b. 0.0 m c. 5.0 m

d. 1.9 m 56. A cannonball of mass 10 kg is fired from a cannon of mass 250 kg. The initial velocity of the cannonball is 1000 km/h. All of the cannon's recoil is absorbed by a spring with a spring constant of 250 N/cm. What is the maximum recoil distance of the cannon? Select one: a. 0.59 m b. 0.35 m c. 0.92 m d. 0.77 m 57. The cylinder shown is acted on by couple M. Wall A is frictionless (µs = 0), but the coefficeint of static friction between the cylinder and wall B is µs = 0.3. The cylinder has a weigh of 200 N. What is the largest value of the couple M for which the cylinder will not turn?

Select one: a. 96 N m b. 31 N m c. 72 N m d. 48 N m

If the forces are in equilibrium, and F2 is 11 N, what is the magnitude of F1? Select one: a. 10 N b. 8 N c. 12 N d. 11 N 60. If the car described in Prob.72 moves along a track that is banked 5o, what is the smallest radius it can travel without skidding? Select one: a. 47 m b. 6 m c. 26 m d. 18 m 61. Find the force in member BC.

58. Whatb is the polar radius of gyration?

Select one: a. 4.2 m b. 4.9 m c. 3.6 m d. 4.0 m 59. Three concurrent forces act as shown.

Select one: a. 50 000 N (compression) b. 50 000 N (tension) c. 52 700 N (compression) d. 16 700 N (tension) 62. A projectile is fired from a cannon with an initial velocity of 1000 m/s and at an angle of 30o from the horizontal. What distance from the cannon will the projectile strike the ground if the point of impact is 1500 m below the point of release?

66. Three forces act on a hook. Determine the magnitude of the resultant of the forces. Neglect hook bending.

Select one: a. 90 800 m b. 78200 m c. 67300 m d. 8200 m 63. Quantity of inertia possessed by an object or the proportion between force and acceleration Select one: a. Mass b. Moment of inertia c. Velocity d. Momentum 64. A varying force acts on a 40 kg weight as shown in the following force versus time diagram. What is the object's velocity at t = 4 s if the object start from

Select one: a. 0.30 m/s b. 0.075 m/s c. 0.15 m/s d. 0 m/s 65. A I kg uniform rod 1 m long is suspended from the ceiling by a frictionless hinge. The rod is free to pivot. What is the product of inertia of the about the pivot point? Select one: a. 0 kg m2 b. 0.045 kg m2 c. 0.13 kg m2 d. 0.33 kg m2

Select one: a. 1250 N b. 989 N c. 1510 N d. 1140 N 67. The support force exerted on an object in contact with another stable object Select one: a. Normal force b. Weight c. Tension d. Gravity 68. Refer to a particle whose curvilinear motions is represented by the equation s = 20t + 4t2 - 3t3. What is particles initial velocity? Select one: a. 25 m/s b. 20 m/s c. 32 m/s d. 30 m/s 69. What is the tension in cable AB?

Select one: a. 250 N b. 430 N c. 870 N d. 500 N 70. A 100 kg block is pulled along a smooth, flat surface by an external 500 N force. If the coefficient of friction between the block and the

surface is 0.15, what acceleration is experienced by the block due to the external force?

Select one: a. 4.33 m/s2 b. 3.23 m/s2 c. 5.00 m/s2 d. 3.80 m/s2 71. A motorist is travelling at 70 km/h when he sees a traffic light in an intersection 250 m ahead turn red. The light's red cycle is 15 s. The motorist wanst to enter the intersection without stopping his vehicle, just as the light turns green. What uniform deceleration of the vehicle will just put the motorist in the intersection when the light turns greens? Select one: a. 0.18 m/s2 b. 1.3 m/s2 c. 0.37 m/s2 d. 25 m/s2

a. 358 rad/s2 b. 794 rad/s2 c. 126 rad/s2 d. 901 rad/s2 74. A 6.0-kg block is released from rest 80m above the ground. When it has fallen 60m its kinetic energy is approximately: Select one: a. 4800 J b. 1176 J c. 3528 J d. 120 J 75. A particle starting from rest experienced an acceleration of 3 m/s2 for 2 s. The particle then returned to rest in a distance of 8 m. Assuming all accelerations were uniform, what was the total time elapsed for the particles motion? Select one: a. 5.33 s b. 4.67 s c. 2.67 s d. 4.00 s

72. The nuts on a collar are each tightened to 18 N m torque. 17% of this torque is used to overcome screw thread friction. The bolts have a nominal diameter of 10 mm. The threads are a simple square cut with a pitch abgle of 15o. The coefficient of friction in the threads is 0.10. What is the approximate tensile force in each bolt?

76. A rope passes over a fixed sheave as shown. The two rope ends are parallel. A fixed load on one end of the rope is supported by a constant force on the other end. The coefficient of friction between the rope and the sheave is 0.30. What is the ratio of tensile forces in the two rope ends?

Select one: a. 203 N b. 1620 N c. 405 N d. 132 N

Select one: a. 1.6 b. 1.2 c. 1.1 d. 2.6

73. During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 0.250 rev. What is the angular acceleration of the CD Select one:

77. In an isolated system it does not change with time when there are no forces acting on the system Select one: a. displacement b. force c. momentum d. position

78. The coeffecicient of friction between the brqake pad and drum is 0.3. Assuming that the beam supporting the cable drum is more than adequate for the loads involved, what load,W, can be held stat5ionary?(Insert question #12) Select one: a. 100 N b. 180 N c. 33 N d. 90 N 79. The elevator in a 12--story building has a mass of 1000 kg. Its maximum velocity and maximum acceleartion ar 2 m/s and 1 m/s2, respectively. A paasenger with a mass of 75 kg stands on a bathroom scale in the elevator as the elevator ascends at its maximum acceleration. what is the scale reading just as the elevator reaches its maximum velocity? Select one: a. 886 N b. 150 N c. 75 N d. 811 N 80. The braced frame shown is constructed with pin-connected members and supports. All applied forces are horizontal. What is the force in the diagonal member AB?(Insert question #10) Select one: a. 160 N b. 250 N c. 0 d. 200 N 81. An automobile travels on a perfectly horizontal, unblanked circular track of radius r. The coefficient of friction between the tires and the track is 0.3. If the car's velocity is 10 m/s, what is the smallest radius it may travel without skidding? Select one: a. 10 m b. 50 m c. 34 m d. 68 m 82. A 10 kg block is resting on a horizontal circular disk (e.g., turntable) at a radius of 0.5 m form the

center. The coefficient of friction between the block and disk is 0.2. the disk begins to rotate with a uniform angular acceleration. What is the minimum angular velocity of the plate that will cause the block to slip? Select one: a. 4.43 rad /s b. 1.98 rad/s c. 3.92 rad /s d. 1.40 rad/s 83. A rigid body is subjecyed to three cfoncurrent, coplanar forces. What is the minimum number of independent equations that are necessary to establish the equilibrium conditions? Select one: a. 3 b. 2 c. 1 d. 0 84. Two meshing spur gears are arranged such that neither gear is turning and both are in equilibrium. Gear 1 has a radius of 4 cm. Gear 1's shaft carries a torsional moment of 65 N m from an external motor. Gear 2 has a radius of 6 cm. Assuming a 100% transmission efficiency, what torque is transmitted by the shaft of gear 2? Select one: a. 97.5 N m b. 65 N m c. 107 N m d. 101 N m 85. Determine the force in member AG for the pinconneted truss shown.

Select one: a. 37 500 N (tension) b. 31 500 N (compression) c. 25 000 N (compression) d. 50 000 N (tension)

86. What are the -and y-coordiantes of the centroid of the area?

Select one: a. 3.50 cm ; 5.50 cm b. 3.93 cm ; 4.79 cm c. 4.00 cm ; 5.00 cm d. 3.40 cm ; 5.60 cm 87. An ideal spring is hung vertically from the ceiling. When a 2.0-kg block hangs at rest from it the spring is extended 6.0 cm from its relaxed length. A upward external force is then applied to the block to move it upward a distance of 16 cm. While the block is moving upward the work done by the spring is Select one: a. -2.09 J b. -1.75 J c. -1.05 J d. -0.52 J 88. Refer to a particle for which the position is defined by s(t) = 2 sin tj [tin radians]. What is the magnitude of the particle's acceleartion at t = π? Select one: a. 2.00 b. 2.56 c. 4.00 d. 3.14 89. A satellite is placed in a circular orbit to observe the surface of Mars from an altitude of 144 km. The equatorial radius of Mars is 3397 km. If the speed of the satellite is 3480 m/s, what is the magnitude of the centripetal acceleration of the satellite? Select one: a. 2.99 m/s2

b. 2.17 m/s2 c. 3.42 m/s2 d. 2.60 m/s2 90. A motorist is travelling at 70 km/h when he sees a traffic light in an intersection 250 m ahead turn red. The light's red cycle is 15 s. The motorist wanst to enter the intersection without stopping his vehicle, just as the light turns green. What uniform deceleration of the vehicle will just put the motorist in the intersection when the light turns greens? Select one: a. 0.37 m/s2 b. 25 m/s2 c. 0.18 m/s2 d. 1.3 m/s2 91. The location of a particle moving in the -y plane is given by the parametric equations = t2 + 4t and y =(1/4)t4 - 60t, where and y are in meters and t is in seconds. What I sthe particles velocity at t = 4 s? Select one: a. 16.0 m/s b. 8.95 m/s c. 11.3 m/s d. 12.6 m/s 92. The two cables shown carry a 100 N vertical load. What is the tension in cable AB?

Select one: a. 80 N b. 60 N c. 50 N d. 40 N 93. The pedestrian bridge truss shown has 10 000 N applied loads at points I,J, and K. What is the force in member IJ?

Select one: a. 18 000 N (compression) b. 8000 N (tension) c. 8000 N (compression) d. 18 000 N (tension)

94. A projectile whose mass is 10 g is fired directly upward from ground level with an initial velocity of 1000 m/s. Neglect the effects of air resistance, what will be speed of the projectile when it impacts the ground? Select one: a. 981 m/s b. 1414 m/s c. 1000 m/s d. 707 m/s 95. The 285 kg plate shown is suspended horizontally by four wires of equal loenght, and the tension of each wire is equal. If wire D snaps, the tension in the three remaining wires is redistributed. Determined the tension in each wire after wire D snaps.

Select one: a. TA /= 699 N ; TB /= 699 N ; TC /= 1398 N b. TA /=1398 N ; TB /= 1398 N ; TC /= 0 N c. TA / d. TA /= 1398 N ; TB /= 0 N ; TC /= 1398 N e. TA = 699 N ; TB = 1398 N ; TC = 699 N 96. Identfy the zero-force members in the truss shown.

Select one: a. AB,GH,GI,HI,EG b. AB,GH c. AB,HI,GI d. GI,HI 97. Three coplanar forces are in equilibrium on the surface of a steel plate, as shown. Two of the forces are known to be 10 N. What is the angle, , of the third force?

Select one: a. 82.5o b. 26.7o c. 53.8o d. 7.50o 98. A signal arm carries two traffic signals and a sign, as shown. The siognals and sign are rigidly attached to the arm. Each traffic signal is 0.2 m2 in frontal area and weighs 210 N. The sign weighs 60 N/m2. The design wind pressure is 575 N/m2. The maximum moment that the connection between the arm and pole can withstand due to wind is 6000 N m , and the maximum permitted moment due to the loads is 4000 N m. As limited by moment on the connection, what is the maximum area of the sign?

a. 300 000N (tension) b. 50 000 N (tension) c. 37 500 N (tension) d. 350 000 N (tension)

Select one: a. 5.65 m2 b. 1.15 m2 c. 8.03 m2 d. 1.04 m2 99. A uniform thin disk has a radius of 30 cm and a mass of 2 kg. A constant force of 10 N is applied tangentially at a varying, but unknown, distance from the center of the disk. The disk accelerates about its axis at 3t rad/s2. What is the distance from the center of the disk at which the force is apllied at t = 12 s?

Select one: a. 108 cm b. 32.4 cm c. 54.0 cm d. 36.0 cm

101. A projectile has an initial velocity of 110 m/s and a launch angle of 20o from the horizontal. The surrounding terrain is level, and air friction is to be disregarded. What is the horizontal distance traveled by the projectile? Select one: a. 1200 m b. 80 m c. 800 m d. 400 m 102. QUEST032::Figure shows a uniform disk, with mass M = 2.5 kg and radius R = 20 cm, mounted on a fixed horizontal axle. A block with mass m = 1.2 kg hangs from a massless cord that is wrapped around the rim of the disk. Find the acceleration of the falling block. The cord does not slip, and there is no friction at the axle.

Select one: a. -4.8 m/s2 b. 4.8 m/s2 c. -3.2 m/s2 d. 3.2 m/s2 103. Find the velocity of block A 2.5 s after the blocks are released.

100. Four bolts (not shown) connect support A to the ground. Determine the design load for each o fthe four bolts. Select one: a. 3.5 m/s b. 0 m/s c. 4.4 m/s d. 4.9 m/s

Select one:

104. A box has uniform density and a total weight of 600 N. It is suspended by three equal-length

cables, AE,BE, and CE, as shown. Point E is 0.5 m directly above the center of the box's top surface. What is the tension in cable CE?

Select one: a. 400 N b. 200 N c. 128 N d. 370 N

Select one: a. 41 kg mo b. 16 kg mo c. 150 kg mo d. 4.1 kg mo 108. A rope is wrapped over a 6 cm diameter pipe to support a bucket of tools being lowered. The coefficient of friction between the rope and the pipe is 0.20. The combined mass of bucket and tools is 100 kg. What is the range of force that can be applied to the free end of the rope such that the bucket remains stationary?

105. The five forces shown act at point A. What is the magnitude of the resultant force? Select one: Select one: a. 720 N to 1360 N b. 560 N to 1360 N c. 720 N to 1510 N d. 670 N to 1440 N a. 234 N b. 182 N c. 156 N d. 32 N

109. A model T-beam is constructed from five balsa boards. Refer to the illustration for the as-built dimensions. What is the approximate centroidal moment of inertia about an axis parallel to the axis?

106. Determine the reaction at point C.

Select one: a. -417 N (down) b. + 83 N (down) c. +333 N (up) d. -83 N (down) 107. A 50 kg cylinder has a height of 3 m and a radius of 50 cm. The cylinder sits on the -axis and is oriented with its major axis parallel to the y-axis. What is the mass moment of inertia about the axis?

Select one: a. 660 cm4 b. 600 cm4 c. 500 cm4

d. 560 cm4 110. A 3 kg disk with a diameter of 0.6 m is rigidly attached at point B to 1 kg rod 1 m in length. The rod-disk combination rotates around point A. What is the mass moment of inertia about A for the combinanation

Select one: a. 1530 m4 b. 1020 m4 c. 2410 m4 d. 1260 m4 114. An area is a composite of a semicircle and a triangle, as shown. What is the distance between the -axis an dthe centroid?

Select one: a. 0.56 kg m2 b. 0.87 kg m2 c. 047 kg m2 d. 3.7 kg m2 111. A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision?_____" Select one: a. 27 J b. 14 J c. 5.8 J d. 8.1 J 112. A spring has a constant of 50 N/m. The spring is hung vertically, and a mass is attached to its end. The spring end displaces 30 cm from its equilibrium position. The same mass is removed from the first spring and attached to the end of a second (different) spring, and the displacement is 25 cm. What is the spring constant of the second spring? Select one: a. 63 N/m b. 56 N/m c. 60 N/m d. 46 N/m 113. What is the polar moment of nertia about the composite centroid?

Select one: a. 3.46 mm b. 3.68 mm c. 5.35 mm d. 4.28 mm 115. Find the velocity at position B.

Select one: a. 9.83 m/s b. 6.95 m/s c. 2.41 m/s d. 4.12 m/s 116. In the structure shown, the beam is pinned at point B. Point E is a roller support. The beam is loaded with a distributed load from point A to point B of 400 N/m, a 500 N m couple at point C, and a vertical 900 N force at point D. If the distributed load and the vertical load are removed and replaced with a vertical upward force of 1700 N at point F, what moment at point F would be

necessary to keep the reaction at point E at the same?.

Select one: a. -6500 N m (counterclockwise) b. 12 000 N m (clockwise) c. 3500 N m (clockwise) d. -9000 N m (counterclockwise) 117. What is the magnitude of the forces that constitute the moment?

Select one: a. 8.3 N b. 6.3 N c. 4.2 N d. 2.1 N 118. A 28 mm diameter circuit area is reduced by a 21 mm diameter circular area that is cut out. Both circles are tangent to the y-axis. What is the moment of inertia about the y-axis of the remaining (shaded) area? Select one: a. 103 000 mm4 b. 330 000 mm4 c. 1340 000 mm4 d. 20 600 mm4

Angle θ of the incline is 30°. Block A slides down the incline at constant speed. What is the mass of block B

Select one: a. 2.1 kg b. 5.0 kg c. 3.7 kg d. 3.3 kg 121. The center of gravity of a roller coaster car is 0.5 m above the rails. The rails are 1 m part. What is the maximum speed that the car can travel around an unbanked curve of radius 15 m without the inner wheel losing contact with the top of the rail? Select one: a. 8.58 m/s b. 17.2 m/s c. 24.2 m/s d. 12.1 m/s 122. Two particles are fixed to an x axis : particle 1 of charge -2.00 x 10-7 C at x=6.00 cm and particle 2 of charge +2.00 x 10-7 C at x=21.0 cm. Midway between the particles, what is their net electric field in unit vector notation? Select one: a. -3.20 X 105 N/C i ̂ b. -6.39 x 105 N/C i ̂ c. -4.00 x 105 N/C i ̂ d. -2.40 x 105 N/C i ̂

119. What is the coefficient of friction between the plane and the block? Select one: a. 0.15 b. 0.78 c. 0.22 d. 0.85

123. Find the force in member DE.

120. Two blocks are connected over a pulley. The mass of block A is 10 kg and the coefficient of kinetic friction between A and the incline is 0.20.

Select one: a. 8800 N (tension) b. 10 000 N (compresiion)

c. 0 d. 6300 N (tension) 124. A force is defined by the vector A = 3.5 i - 1.5 j + 2.0k. i,j, and k are unit vectors in the -,y-, and zdirection, respectively. What is the angle that the force makes with the positive y-axis?

b. mg c. –mx2 d. None of the choices 128. A car with a mass of 1530 kg tows a trailer (mass of 200 kg) at 100 km/h. What is the total momentum of the car-trailer combination? Select one: a. 46 000 N s b. 22 N s c. 37 N s d. 48 000 N s 129. If W = 80 N, what are the reactions at pont A?

Select one: a. 69.6o b. 20.4o c. 110o d. 66.4o 125. The position (in radians) of a car travelling around a curve is described by the following function of time (in seconds). What is the angular velocity at t = 3 s? Select one: a. -16 rad/s b. -4 rad /s c. 15 rad/s d. 11 rad/s 126. A stone is dropped down a well. 2.47 s after the stone is realeased, a splash is heard. If the velocity of sound in air is 342 m/s, find the distance to the surface of the water in the well. Select one: a. 38 m b. 2.4 m c. 28 m d. 7.2 m 127. The maximum kinetic and potential energy of a spring when stretched at various displacements is equal to Select one: a. 1 /2Kx2

Select one: a. 27 i N - 100j N b. -27 i N - 100j N c. 0 i N+ 180j N d. 0 i N + 100j N 130. A parallel-plate air capacitor is made from two plates 0.070 m square, spaced 6.3 mmapart. What must the potential difference between the plates be to produce an energydensity of 0.037 J/m3? Select one: a. 470 V b. 370V c. 270 V d. 570 V 131. Block d side freely on the homogeneous bar and experiences a gravitation force of 50 N.

Homogeneous bar AB experiences a gravitational force of 25 N. What is the force between the bar and block D?

Select one: a. 21 N b. 19 N c. 15 N d. 28 N 132. A motorist is travelling at 70 km/h when he sees a traffic light in an intersection 250 m ahead turn red. The light's red cycle is 15 s. The motorist wanst to enter the intersection without stopping his vehicle, just as the light turns green. If the vehicle decelerates at a constant rate of 0.5 m/s2, what will be its speed when the light turns green? Select one: a. 52 km/h b. 63 km/h c. 43 km/h d. 59 km/h 133. Which of the structures shown is statically determinant and stable? Select one:

134. The rotor of a steam turbine is rotating at 7200 rev/min when the steam supply is suddenly cut off. The rotor decelerates at a constant rate and comes to rest after 5 min. What was the angular deceleration of the rotor? Select one: a. 2.5 rad/s2 b. 5.8 rad/s2 c. 0.40 rad/s2 d. 16 rad/s2 135. A 6 kg sphere moving at 3m/s collides with a 10 kg sphere traveling 2.5 m/s in the same direction. The 6 kg ball comes to a complete stop after the collision. What is the new velocity of the 10 kg ball immediately after the collision? Select one: a. 0.5 m/s b. 5.5 m/s c. 2.8 m/s d. 4.3 m/s 136. Which type of load is not resisted by a pinned joint? Select one: a. compression b. moment c. shear d. axial 137. What is the resultant R of the system of forces shown?

Select one: a. I and III b. I and IV c. I only d. II and III

d. 890 N m

a.

b.

c.

d. 138. If the frame is pinned so that it rotates around point B, what counteracting moment must be applied at point A to put the frame in equilibrium?

Select one: a. 1150 N m b. 1240 N m c. 650 N m

140. An isolated parallel-plate capacitor (not connected to a battery) has a charge of Q = 2.9 × 10-5 C. The separation between the plates initially is d = 1.2 mm, and for this separation the capacitance is 3.1 × 10-11 F. Calculate the work that must be done to pull the plates apart until their separation becomes 5.3 mm, if the charge on the plates remains constant. The capacitor plates are in a vacuum Select one: a. 5 J b. 46 J c. 48 J d. 47 J 141. A wheel with a radius of 80 cm rolls along a flat surface at 3 m/s. If arc AB on the wheels perimeter measures 90o, what is the velocity of point A when point B contacts the ground? Select one: a. 3.39 m/s b. 3.75 m/s c. 4.24 m/s d. 3.00 m/s 142. A disk-shaped bofy with a 4 cm radius has a 320 N force acting through the center at an unknown angle , and two 40 N loads acting as a couple, as shown. All of these forces are removed and replaced by a single 320 N force at point B, parallel to the original 320 N force. What is the angle ?

Select one: a. 0o b. 7.6o

c. 15o d. 29o 143. A block with a mass of 150 kg is pulled over a horizontal surface by a cable guided by a pulley as shown. The coefficients of friction are 0.58 between the surface and the block, and 0.90 between the cable and the pulley. What force,F, must be applied to the cable for the block to move?

Select one: a. 2500 N b. 900 N c. 1700 N d. 2200 N 144. Refer to a particle whose curvilinear motions is represented by the equation s = 20t + 4t2 - 3t3. What is the acceleration of the particle at time t = 0? Select one: a. 2 m/s2 b. 5 m/s2 c. 3 m/s2 d. 8 m/s2 145. A playground merry-go-round has a radius of 3.0m and a rotational inertia of 600 kg m2.It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merrygo-round is Select one: a. 0.80 rad/s b. 1.04 rad/s c. 0.73 rad/s d. 0.62 rad/s 146. Traffic travels at 100 km/h around a banked high-way curve with a radius of 1000m. What

banking angle is necessary such that friction will not be required to resist the centrifugal force? Select one: a. 46o b. 2.8o c. 4.5o d. 1.4o 147. Resolve the 300 N force into two components, one along line p and the other along line Q. (F, P and Q are coplanar.) Select one: a. Fp = 126 N ; FQ /= 272 N b. Fp = 226 N ; FQ = 135 N c. Fp = 186 N ; FQ /= 232 N d. Fp = 226 N ; FQ /=212 N 148. Determine the force in member BC.

Select one: a. 1000 N (compression) b. 2500 N (tension) c. 1500 N (tension) d. 0 149. The statement “An object with constant momentum is in a state of equilibrium” is Select one: a. Insufficient data b. False c. Partly true d. True 150. The velocity (in m/s) of a falling ball is described by the equation v = 32 + t + 6t2. What I sthe acceleration at time t = 2 s? Select one: a. 25 m/s2 b. 9.8 m/s2 c. 58 m/s2

d. 32 m/s2

151. A particle has a tangential acceleration of at (represented by the equation given) when it moves around a point in a curve with instantaneous radius of 1 m. What is the instantaneous angular velocity ( in rad/s) of the particle? Select one: a. t2+cost+ 3 In |csct| b. t2-cost+ 3 In |csct| c. t2-cost+ 3 In |sint| d. t2+cost+ 3 In |sint| 152. A golfer on level ground attempts to drive a gof ball across a 50 m wide pond, hitting the ball so that it travels initially at 25 m/s. The ball travels at an initial angle of 45o to the horizontal plane. How far will the golf ball travel, and does it clear the pond? Select one: a. 58 m; the ball clears the pond b. 32 n; the ball does not clear the pond c. 45 m; the ball does not clear the pond d. 64 m ; the ball clears the pond 153. A 2000 kg car pulls a 500 kg trailer. The car and trailer accelerates from 50 km/h to 75 km/h at rate of 1 m/s2. What linear impules does the car impart on the trailer? Select one: a. 12 500 N s b. 3470 N s c. 17400 N s d. 8680 N s

pulley. The mass of block A is 10 kg and the coefficient of kinetic friction between A and the incline is 0.20. Angle θ of the incline is 30°. Block A slides down the incline at constant speed. What is the mass of block B

Select one: a. 3.7 kg b. 3.3 kg c. 2.1 kg d. 5.0 kg 156. A mass of 10 kg is suspended from a vertical spring with a spring constant of 10 N/m. What is the period of vibration? Select one: a. 6.3 s b. 0.30 s c. 0.60 s d. 0.90 s 157. What is the reaction at point A for the simply supported beam shown? Select one:

a. b. None of the choices

154. What are R1 and R2? (insert question #11) Select one: a. 1250 N b. 4000 N c. R1 / d. 1000 N; R2 / e. R1 / f. R1 / g. 3750 N; R2 / h. 1250 N 155. QUEST029::Two blocks are connected over a

c.

d. 158. A bent beam is acted upon by a moment and several concentrated forces, as shown. Find the missing force F and distance that will maintain equilibrium on the member shown.

45o from the horizontal. What is the velocity of point P at that instant? Select one: a. 10.0 m/s15.0 m/s16.2 m/s b. 18.5 m/s

Select one: a. F = 20 N ; = 0.2 m b. F = 10 N ; = 0.6 m c. F = 20 N ; = 0.4 m d. F = 5 N ; = 0.8 m 159. A car travels around an unbanked 50 m radius curve without skidding. The coefficient of friction between the tires and road is 0.3. What is the car's maximum speed? Select one: a. 54 km/h b. 25 km/h c. 44 km/h d. 14 km/h 160. A force that is directed away or towards the origin Select one: a. Frictional force b. Uniform force c. Central force d. Normal force 161. QUEST030::The small piston of a hydraulic lift has a cross-sectional area of 3.00 cm2, and its large piston has a cross-sectional area of 200 cm2 . What force must be applied to the small piston for it to raise a load of 15.0 kN? (In service stations, this force is usually generated with the use of compressed air.) Select one: a. 1.00 X 102 N b. 40 N c. 1.00 x 103 N d. 225 N 162. A disk rolls along a flat surface at a constant speed of 10 m/s. Its diameter is 0.5 m. At a particular instant, point P on the edge of the disk is

163. For the reciprocating pump shown, the radius of the crank is r = 0.3 m, and the rotational speed is n = 350 rpm. What is the tangetial velocity of point A on the crank corresponding to an angle of = 35o from the horizontal? Select one: a. 10 m/s b. 1.1 m/s c. 0 m/s d. 11 m/s 164. What is the -coordinate of the centroid of the curve y = cos between = 0 = /2? a. pi/4 b. pi/6 c. 1 – 2/pi d. pi/2 – 1 165. QUEST031::Two particles are fixed to an x axis : particle 1 of charge -2.00 x 10-7 C at x=6.00 cm and particle 2 of charge +2.00 x 10-7 C at x=21.0 cm. Midway between the particles, what is their net electric field in unit vector notation? Select one: a. -6.39 x 105 N/C i ̂ b. -2.40 x 105 N/C i ̂ c. -4.00 x 105 N/C i ̂ d. -3.20 X 105 N/C i ̂ 166. Refer to a particle whose curvilinear motions is represented by the equation s = 20t + 4t2 - 3t3. What is the maximum speed reached by the particle? Select one: a. 34.6 m/s b. 27.9 m/s c. 48.0 m/s d. 21.8 m/s 167. A torsional pendulum consists of a 5 kg uniform disk with a diameter of 50 cm attached at its center to a rod 1.5 m in length. The torsional spring constant is 0.625 N.m/rad. Disregarding the

mass of the rod, what is the natural frequency of the torsional pendulum? Select one: a. 1.0 rad/s b. 1.4 rad/s c. 1.2 rad/s d. 2.0 rad/s 168. The position (in radians) of a car travelling around a curve is described by the following function of time (in seconds). What is the angular acceleration at t = 5 s? Select one: a. 4 rad/s2 b. 26 rad/s2 c. 30 rad/s2 d. 6 rad/s2