Reviewer

Multiple ChoiceQuestionin Engineering MathematicsBy JAS Tordillo

Encoded By: Dajano, Jose Mari T. Salavante, Marc-Ian

1. A man sold a book by mistake at 120% of the marked price instead of discounting the marked price by 20%. If he sold the book for P14.40, what was the price for which he have sold the book?a) P8.00b) P8.50c) P9.00d) P9.602. In how many ways can 9 books be arranged on a shelf so that 5 of the books are always together?a) 30,200b) 25,400c) 15,500d) 14,4003. If one third of the air tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?a) 0.7122b) 0.6122c) 0.8122d) 0.91224. If 3^x = 9^y and 27^y = 81^z, find x/z?a) 3/5b) 4/3c) 3/8d) 8/35. Determine x, so that x, 2x+7, 10x-7 will be geometric progression.a) 7,-5/6b) 7, -14/5c) 7, -7/12d) 7, -7/66. A man invested part of P20,000 at 18% and the rest at 16%. The annual income from 16% investment was P620 less than three times the annual income from 18% investment. How much did he invest at 18%?a) P5,457.20b) P6,457.20c) P7,457.20d) P8,457.207. The sum of four positive integers is 32. Find the greatest possible product of these four numbers.a) 5013b) 645c) 4069d) 49138. 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 much thick in feet the folded paper be?a) 10.1 ftb) 12.1 ftc) 15.1 ftd) 17.1 ft9. A seating section in a certain athletic stadium has 30 seats in the first row, 32 seats 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) 1200b) 980c) 890d) 75010. One pipe can fill a tank in 6 hours and another pipe can fill the same tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all three pipes open, how long will it take to fill in the tank?a) 5.18 hoursb) 4.18 hoursc) 3.18 hoursd) 2.18 hours11. The tens digit of a certain two digit number exceeds the units digit by four and is one less than twice the units digit. Find the number.a) 65b) 75c) 85d) 9512. The sum of two numbers is 35 and their product is 15. Find the sum of there reciprocal.a) 2/7b) 7/3c) 2/3d) 5/213. The smallest natural number for which 2 natural numbers are factors.a) Least common divisorb) Least common denominatorc) Least common factord) Least common multiple14. Ana is 5 years older than Beth. In 5 years, the product of their ages is 1.5 times the product of their present ages. How old is Beth now?a) 30b) 25c) 20d) 1515. The time required for the 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 a problem?a) 2 minutesb) 3 minutesc) 4 minutesd) 5 minutes16. Find the value of m that will make 4x^2 4mx + 4m ) 5 a perfect square trinomial.a) 3b) -2c) 4d) 517. How many liters of water must be added to 35 liters of 89% hydrochloric acid solution to reduce its strength to 75%?a) 3.53b) 4.53c) 5.53d) 6.5318. A purse contains $11.65 in quarters and dimes. If the total number of coins is 70, find how many dimes are there.a) 31b) 35c) 39d) 4219. Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. Such equations may nonetheless determine y as a function of x or vice versa, such function called _________.a) logarithmic functionb) implicit functionc) explicit functiond) continuous function20. A piece of wire of length 50 m is cut into two parts. Each part is then bent to form a square. It is found that the total area of the square is 100 sq. m. Find the difference in length of the two squares.a) 6.62b) 7.62c) 8.62d) 9.6221. A tank is filled with an intake pipe that fills it in 2 hours and an outlet pipe that empty in 6 hours. If both pipes are left open, how long will it take to fill in the empty tank?a) 1.5 hrsb) 2.0 hrsc) 2.8 hrsd) 3 hrs22. Maria sold a drafting pen for P612 at a loss of 25% on her buying price. Find the corresponding loss or gain in percent if she had sold it for P635?a) 20.18%b) 11.18%c) 22.18%d) 28.18%23. Divide 1/8 by 8.a) 1/64b) 18c) 1d) 6424. Given 2 x 2 matrix , find its determinant.a) 31b) 44c) -20d) 2025. If the sum is 220 and the first term is 10, find the common difference if the last term is 30.a) 2b) 5c) 3d) 2/326. Find the sum of the sequence 25, 30, 35, .....a) (2/5)(n^2 + 9n)b) (5/2)(n^2 + 9n)c) (9/2)(n^2 + 9n)d) (9/2)(n^2 9n)27. Solve for x: .a) 4, -5b) -4, -5c) -4, 5d) no solution 28. Solve for x: 10x^2 + 10x + 1 =0.a) -0.113, -0.887b) -0.331, -0.788c) -0.113, -0.788d) -0.311, -0.88729. The number x, 2x + 7, 10x 7 form a Geometric Progression. Find the value of x.a) 5b) 6c) 7d) 830. Find the 30th term of A.P. 4,7,10,...a) 91b) 90c) 88d) 7531. Find the sum of the first 10 terms of the geometric progression 2, 4, 8, 16,...a) 1023b) 2046c) 225d) 159632. Find the sum of the infinite geometric progression 6, -2, 2/3,...a) 9/2b) 5/2c) 11/2d) 7/233. Find the ratio of an infinite geometric series if the sum is 2 and the first term is .a) 1/3b)1/2c) 3/4d) 1/434. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point.a) 8b) 1c) 7d) 535. What is the lowest common factor of 10 and 32.a) 320b) 2c) 180d) 9036. Ten less than four times a certain number is 14. Determine the number.a) 6b) 7c) 8d) 937. Jolo bought a second hand betamax VCR and sold it to Rudy at a profit of 40%. Rudy then sold the VCR to Noel at a profit of 20%. If Noel paid P2856 more than it cost to Jolo, how much did Jolo paid the unit?a) P4000b) 4100c) 4200d) P430038. A club of 40 executives, 33 likes to smoke Malboro, and 20 likes to smoke Philip Morris. How many like both?a) 13b) 10c) 11d) 1239. A merchant has three items on sale, namely a radio for P50, a clock for P30 and a flashlight for P1.00. At the end of the day, he has sold a total of 100 of the three items and has taken exactly P1000 on the total sales. How many radios did he sale?a) 16b) 20c) 18d) 2440. What is the sum of the coefficients of the expansion of (2x 1)^20?a) 0b) 1c) 2d) 341. Find the ratio of the infinite geometric series if the sum is 2 and the first term is 1/2.a) 1/3b) 1/2 c) 3/4 d) 1/442. A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer and sol until there are 10 bricks in the last layer. How many bricks are there together?a) 638b) 637c) 640d) 63943. Once a month a man put some money into the cookie jar. Each month he put 50 centavos more into the jar than the month before. After 12 years he counted his money; he had P5436. How much did he put in the jar in the last month?a) 73.5b) P75.50c) P74.50d) P72.5044. The seventh term is 56 and the 12th term is -1792 of the geometric progression. Find the ratio and the first term. Assume the ratios are equal.a) -2, 7/8b) -1. 5/8c) -1, 7/8d) -2, 5/845. Find the value of x in the equation 24x^2 + 5x -1 = 0.a) (1/6, 1)b) (1/6, 1/5)c) (1/2, 1/5)d) (1/8, -1/3)46. The polynomial x^3 + 4x^2 -3x +8 is divided by x 5, then the remainder is:a) 175b) 140c) 218d) 20047. Find the rational number equivalent to repeating decimal 2.3524242424...a) 23273/9900b) 23261/990c) 23289/9900d) 23264/990048. The sum of Kims and Kevins ages is 18. In three years, Kim will be twice as old as Kevin. What are their ages now?a) 4, 14b) 5, 13c) 7, 11d) 6, 1249. Ten liters of 25% salt solution and 15%liters of 35% solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration in the mixture?a) 19.55%b) 22.15%c) 27.05d) 26.72%50. Determine the sum of the infinite series: S = 1/3 + 1/9 + 1/27 + .... (1/3)^n.a) 4/5b) 3/4c) 2/3d) 1/251. Determine the sum of the positive valued solution to the simultaneous equations: xy = 15, yz = 35, zx = 21.a) 15b) 13c) 17d) 1952. The areas of two squares differ by 7 sq. ft. and their perimeters differ by 4 ft. Determine the sum of their areas.a) 25 ft^2b) 27 ft^2c) 28 ft^2d) 22 ft^253. A bookstore purchased a bestselling book at P200 per copy. At what price should this book be sold so that, giving a 20% discount, the profit is 30%?a) P450b) P500c) P375d) P40054. In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate and of the females 70% are literate. What is the female population?a) 850b) 500c) 550d) 60055. Gravity causes a body to fall 16.1 ft. in the 1st second, 48.3 ft. in the 2nd second, 80.5 ft. in the 3rd second, and so on. How far did the body fall during the 10th second?a) 248.7 ftb) 308.1 ftc) 241.5 ftd) 305.9 ft56. In a commercial survey involving 1,000 persons on brand reference, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only. 370 prefer either x or y but not z, 450 prefer brand y or z but not x, and 420 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of the 3 brands?a) 280b) 230c) 180d) 13057. The electric power which a transmission line can transmit is proportional to the total product of its design voltage and current capacity, and inversely to the transmission distance. A 115 kilovolt line rated at 1000 amperes can transmit 150 Megawatts over 150 km. How much power, in Megawatts, can a 230 kilovolt line rated 1500 amperes transmit over 100km?a) 785b) 485c) 675d) 59558. Find the geometric mean of 64 and 4.a) 16b) 34c) 32d) 2859) Factor the expression x^2 + 6x + 8 as completely as possible.a) (x + 8)(x 2)b) (x + 4)(x 2)c) (x + 4)(x + 2)d) (x 4)(x 2)60. A batch of concrete consisted of 200 lbs. Fine aggregate, 350 lbs coarse aggregate, 94 lbs cement, and 5 gallons water. The specific gravity of the sand and gravel may be taken as 2.65 and that of the cement as 3.10. What was the weight of concrete in place per cubic foot?a) 172 lbb) 236 lbc) 162 lbd) 153 lb61. Dalisays Corporation gross margin is 45% sales. Operating expenses such as sales and administration are 15% of sales. Dalisay is in 40% tax bracket. What percent of sales is their profit after taxes?a) 18%b) 5%c) 24%d) 50%62. A and B working together can finish painting a home in 6 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) 10, 15b) 15, 20c) 20, 25d) 5, 1063. Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35.a) 171b) 182c) 232d) 21664. Find the sum of 1, -1/5, 1/25,...a) 5/6b) 2/3c) 0.84d) 0.7265. Find the remainder if we divide 4y^3 + 18y^2 + 8y -4 by (2y + 3).a) 10b) 11c) 15d) 1366. What time after 3 oclock will the hands of the clock be together for the first time?a) 3:16.36b) 3:14.32c) 3:12.30d) 3:13.3767. The difference of the squares of the digits of a two digit positive number is 27. If the digits are reversed in order and the resulting number subtracted from the original number, the difference is also 27. What is the original number?a) 63b) 54c) 48d) 7368. The boat travels downstream in 2/3 of the time as it does going upstream. If the velocity of the river current is 8 kph, determine the velocity of the boat in still water.a) 40 kphb) 50 kphc) 30 kphd) 60 kph69. 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 the value of w when x = 1, y = 4, and z = 2.a) 2b) 3c) 4d) 570. The third term of a harmonic progression is 15 and 9th term is 6. Find the eleventh term?a) 4b) 5c) 6d) 771. Solve for x for the given equation, 7.4 x 10^-4 = e^-9.7x.a) 0.7621b) 0.7432c) 0.7243d) 0.733172. Find the 10th term of the geometric progression: 3, 6, 12, 24,....a) 1536b) 1653c) 1635d) 315673. Find the sum of odd integers from 1 to 31.a) 256b) 526c) 265d) 62574. Box A has 4 white balls, 3 blue balls, and 3 orange balls. Box B has 2 white balls, 4 blue balls, and 4 orange balls. If one ball is drawn from each box, what is the probability that one of the two balls will be orange?a) 27/50b) 9/50c) 23/50d) 7/2575. Solve: x^2 + y^2 = 5z and x^2 y^2 = 3z. How many and what numerical values for x, y, and z will satisfy these simultaneous equations?a) if z = 3^2, then x = 6 and y = 3b) if z = 2^2, then x =4 and y =2c) if z = 1^2, then x =2 and y = 1d) There are an infinite no. of values that will satisfy76. Two people driving towards each other between two towns 160 km apart. The first man drives at the rate of 45 kph and the other drives at 35 kph. From their starting point, how long would it take that they would meet?a) 3 hrb) 4 hrc) 2 hrd) 1 hr77. Solve x for the equation 6x 4 = 2x + 6.a) 10b) 5/2c) 5d) 2.578. The man has a total of 33 goats and chickens. If the total of their feet is 900, find the number of goats and chickens.a) 12 goats and 21 chickensb) 9 goats and 27 chickensc) 6 cats and 5 dogsd) 13 goats and 20 chickens79. Express 5y [3x (5y + 4)] into polynomial.a) 10y 3x +4b) 5y + 5x 4c) 5y + 5x + 4d) 5y 5x +480. What is the exponential form of the complex number 3 + 4i?a) e^i53.1b) 5e^i53.1c) 5e^i126.9d) 7e^i53.181. Simplify the complex numbers: (3 + 4i) (7 2i)a) -4 + 6ib) 10 + 2ic) 4 2id) 5 4i82. Solve for x: x^2 + x -12 = 0a) x = 6, x = -2b) x = 1, x = 12c) x = 3, x = -4d) x = 4, x = -383. =a) 0b) c) d) 1084. What us the value of x in the expression: x 1/x = 0?a) x = -1b) x = 1, 1/2c) x = 1d) x = 1, -185. What is the value of A: A^-6/8 = 0.001?a) 10b) 100c) 0d) 1000086. Find the value of x: ax b = cx + da) x = (a b)/(c + d)b) x = (b + d)/(a c)c) x = (a d)/(c b)d) x = (c + d)/(a c)87. Divide: 15x^4 +6x^3 + 15x + 6 by 3x^3 + 3.a) 5x + 2b) 5x^2 + 2c) 5x^2d) 5x 488. Simplify: a) b) c) d) 89. Find the value of x in the equation: csc x + cot x = 3a) /5b) /4c) /3d) /290. If A is in the III quadrant and cos A = -15/17, find the value of cos (1/2)A.a) (8/17)^1/2b) (5/17)^1/2c) (3/17)^1/2d) (1/17)^1/291. Simplify the expression: (sin B + cos B tan B)/cos Ba) 2 tan Bb) tan B + tan Bc) tan B cos Bd) 2 sin B cos B92. If cot 2A cot 68 = 1, then tan A is equal to ________.a) 0.194b) 0.419c) 0.491d) 0.91493. A ladder 5 m long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with ground. How high up the wall does it reach?a) 12.7 mb) 10.5 mc) 3.86 md) 1.55 m94. The measure of 2.25 revolutions counterclockwise is:a) -810 degb) -805 degc) 810 degd) 805 deg95. If sin A = 2.5 x and cos A = 5.5x, find the value of A in degrees.a) 14.5 degb) 24.5 degc) 34.5 degd) 44.5 deg96. Solve angle A of an oblique triangle wit vertices ABC, if a = 25, b = 16 and C = 94 degrees and 6 minutes.a) 50 deg and 40 minb) 45 deg and 35 minc) 55 deg and 32 mind) 54 deg and 30 min97. Given: x = (cos B tan B sin B)/cos B. Solve for x if B = 30 degrees.a) 0.577b) 0c) 0.500d) 0.86698. (cos A)^4 (sin A)^4 is equal to _________.a) cos 2Ab) sin 2Ac) 2tan Ad) sec A99. 174 degrees is equivalent to _________ mils.a) 3094b) 2084c) 3421d) 2800100. What is the resultant of a displacement 6 miles North and 9 miles East?a) 11 miles, N 56 Eb) 11 miles, N 54 Ec) 10 miles, N 56 Ed) 10 miles, N 54 E101. Which is identically equal to (sec A + tan A)?a) 1/(sec A + tan A)b) csc A 1c) 2/(1 tan A)d) csc A + 1102. Determine the simplified form of (cos 2A cos A)/(sin A).a) cos 2Ab) sin Ac) cos Ad) sin 2A103. Ifsec 2A = 1/sin 13A, determine the angle A in degrees.a) 5 degb) 6 degc) 3 degd) 7 deg104. Solve for x in the equation: arctan (x + 1) + arctan (x 1) = arctan (12).a) 1.50b) 1.34c) 1.20d) 1.25105. Solve for x if tan 3x = 5tan x.a) 20.705 degb) 30.705 degc) 15.705 degd) 35.705 deg106. If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x.a) 0.265b) 0.256c) 0.562d) 0.625107. The angle of inclination of ascend of a road having 8.25% grade is ______.a) 4.72b) 4.27c) 5.12d) 1.86108. A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower?a) 76. 31 mb) 73.31 mc) 73.16 md) 73.61 m109. If the sides of a parallelogram and an included angle are 6, 10, and 100 degrees respectively, find the length of the shorter diagonal.a) 10.63b) 10.37c) 10.73d) 10.23110. What is the value of log2 5 + log3 5?a) 7.39b) 3.79c) 3.97d) 9.37111. Points A and B 1000 m apart are plotted on a straight highway running east and west. From A, the bearing of a tower C is 32 degrees W of N and from B the bearing of C is 26 degrees N of E. Approximate the shortest distance of tower C to the highway.a) 364 mb) 374 mc) 394 md) 384 m112. If log of 2 to base 2 plus log of x to the base of 2 is equal to 2, then the value of x is:a) 4b) -2c) 2d) -1113. Arctan [2cos (arcsin /2)] is equal to:a) /3b) /4c) /6d) /2114. Solve A for the given equations cos^2 A = 1 cos^2 A.a) 45, 125, 225, 335 degreesb) 45, 125, 225, 315 degreesc) 45, 135, 115, 315 degreesd) 45, 150, 220, 315 degrees115. If sin A = 2/5, what is the value of 1 cos A?a) 0.083b) 0.916c) 0.400d) 0.614116. Sin A cos B cos A sin B is equivalent to:a) cos (A B)b) sin (A B)c) tan (A B)d) cos (A B)117. How many degrees is 4800 mils?a) 270 degb) 90 degc) 180 degd) 215 deg118. ln 7.18^xy equalsa) 1.97xyb) 0.86xyc) xyd) 7.18xy119. The log10 (8)(6) equal to:a) log10 8 + log10 6b) log10 8 - log10 6c) log10 8 log10 6d) log10 8 / log10 6120. 38.5 to the x power = 6.5 to the x 2 power, solve for x using logarithms.a) 2.70b) -2.10c) 2.10d) -2.02121. Given the triangle ABC in which A = 3030, b = 100 m and c = 200 m. Find the length of the side a.a) 124.64 mb) 142.24 mc) 130.5 md) 103.00 m122. An observer wishes to determine the height of the tower. He takes sight at the top of the tower from A and B, which are 50 ft apart at the same elevation on a direct line with the tower. The vertical angle at point A is 30 deg and at point B is 40 deg. What is the height of the tower?a) 85.60 ftb) 110.29c) 143.97d) 92.54 ft123. What is the value of log to the base of 1000^3.3?a) 9.9b) 99.9c) 10.9d) 9.5124. In a triangle, find the side c if angle C = 100 deg, side b = 20, and side a = 15.a) 28b) 29c) 27d) 26125. Given a triangle with an angle C = 28.7 deg, side a = 132 units and side b = 224 units. Solve for the side c.a) 95 unitsb) 110 unitsc) 125.4 unitsd) 90 units126. A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower are 13 deg and 35 deg respectively. The height of the tower is 50 m. Find the height of the monument.a) 33.51 mb) 47.3 mc) 7.48 md) 30.57 m127. Find the value of x if log12 x = 2.a) 144b) 414c) 524d) 425128. If tan x = 1/2, tan y = 1/3. What is the value of tan (x + y)?a) 1b) 2c) 3d) 4129. The logarithm of the quotient M/N and the logarithm of the product MN is equal to 1.55630251 and 0.352182518 respectively. Find the value of M.a) 6b) 7c) 8d) 9130. The angle of elevation of the top tower B from the top of the tower A is 28 deg and the angle of elevation of the top tower A from the base of the tower B is 46 deg. The two towers lie in the same horizontal plane. If the height of the tower B is 120 m, find the height of tower A.a) 87.2 mb) 90.7 mc) 79.3 md) 66.3 m131. Evaluate the log6 845 = x.a) 3.76b) 5.84c) 4.48d) 2.98132. Find the value of log8 48.a) 1.86b) 6.81c) 8.61d) 1.68133. Find the value of sin 920 deg.a) 0.243b) -0.243c) 0.342d) -0.342134. Log (x)^n =a) log xb) n log xc) 1/n log xd) n135. Sin 2 is equal to:a) 2 sin cos b) 1/2 sin c) sin cos d) 1 sin^2 136. What is the interior angle (in radian) of an octagon?a) 2.26 radb) 2.36 radc) 2.8 radd) 2.75 rad137. The trigonometric function (1 + tan^2 ) is also equal to:a) sec^2 b) cos^2 c) csc^2 d) sin 138. Derive the formula of each interior angle (in degrees).a) (no. of sides 2)180b) [(no. of sides 2)180/no. of sides]c) [(no. of sides 1)180/no. of sides]d) [no. of sides 2]/180139. What is the Cartesian logarithm of 402.9?a) 2.605b) 2.066c) 3.05d) 3.60140. What is the value of the following limit? a) 3b) 6c) 9d) 0141. Given the three sides of a triangle: 2, 3, 4. What is the angle in radians opposite the side with length 3?a) 0.11b) 0.41c) 0.55d) 0.81142. Find the area of the geometric figure whose vertices are at (3, 0, 0), (3, 3, 0), (0, 0, 4) and (0, 3, 4).a) 12 sq. unitsb) 14 sq. unitsc) 15 sq. unitsd) 24 sq. units143. A central angle of 45 degrees subtends an arc of 12 cm. What is the radius of the circle?a) 15.28 cmb) 18.28 cmc) 20.28 cmd) 30.28 cm144. It is a part of circle bounded by a chord and an arc.a) slabb) segmentc) sectiond) sector145. What is the area (in sq. inches) of a parabola with a base of 15 cm and a height of 20 cm?a) 87b) 55c) 31d) 11146. Triangle ABC is a right triangle with right angle at C. CD is perpendicular to AB. BC = 4 and CD = 1. Find the area of the triangle ABC.a) 2.95b) 2.55c) 2.07d) 1.58147. 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, the length of the secant is ________ inches.a) 15b) 14c) 13d) 12148. If a regular polygon has 27 diagonals, then it is a,a) nonagonb) pentagonc) hexagond) heptagon149. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon.a) 125b) 135c) 149d) 169150. An annulus is a plane figure, which is composed of two concentric circles. The area of the annulus can be calculated by getting the difference between the area of the larger circle and the area of the smaller circle. Also, it can be calculated by removing the hole. The method is called:a) Law of Extremitiesb) Law of Reductionc) Law of Deductiond) Sharp Theorem151. The sides of a triangle are 195, 157, and 210 respectively. What is the area of the triangle?a) 73250 sq. unitsb) 14586 sq. unitsc) 10250 sq. unitsd) 11260 sq. units152. Given a triangle of sides 10 cm and 15 cm an included angle of 60 degrees. Find the area of the triangle.a) 70b) 80c) 72d) 65153. The sides of a triangle are 8 cm, 10 cm, and 14 cm. Determine the radius of the inscribed and circumscribed circle.a) 3.45, 7.14b) 2.45, 7.14c) 2.45, 8.14d) 3.45, 8.14154. The sides of a cyclic quadrilateral are a = 3m, b = 3m, c = 4m and d = 4m. Find the radius of the inscribed and circumscribed circle.a) 1.71, 2.50b) 1.91, 2.52c) 2.63, 4.18d) 2.63, 3.88155. From the point inside a square the distance to three corners are 4, 5 and 6 m respectively. Find the length of the sides of a square.a) 7.53b) 8.91c) 6.45d) 9.31156. A regular pentagon has sides 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the larger pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.a) 430.70 cm^2b) 573.26 cm^2c) 473.77 cm^2d) 516.14 cm^2157. A rhombus has diagonals of 32 and 20 inches. Determine its area.a) 360 in^2b) 280 in^2c) 320 in^2d) 400 in^2158. In a circle with a diameter of 10 m, a regular five pointed star touching its circumference is inscribed. What is the area of the part not covered by the star?a) 60.2 m^2b) 50.48 m^2c) 45.24 m^2d) 71.28^m159. Find the area of a regular octagon inscribed in a circle of radius 10 cm.a) 186.48 cm^2b) 148.91 cm^2c) 282.24 cm^2d) 166.24 cm^2160. Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.a) 846 m^2b) 1090 m^2c) 1075 m^2d) 988 m^2161. The area of a circle circumscribing a hexagon is 144 m^2. Find the area of the hexagon.a) 374.12 m^2b) 275.36 m^2c) 415.26 m^2d) 225.22 m^2162. Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.a) 441.66 cm^2b) 467.64 cm^2c) 519.60 cm^2d) 493.62 cm^2163. Find each interior angle of a hexagon.a) 90 degb) 120 degc) 150 degd) 180 deg164. Find the length of the side of pentagon if the line perpendicular to its side is 12 units from the center.a) 8.71b) 17.44c) 36.93d) 18.47165. How many sides are in a polygon if each interior angle is 165 degrees.a) 12 sidesb) 24 sidesc) 20 sidesd) 48 sides166. Find the area of triangle whose sides are: 25, 39 and 40.a) 468b) 684c) 486d) 864167. Find the area of a regular hexagon inscribed in a circle of radius 1.a) 2.698b) 2.598c) 3.698d) 3.598168. A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft long and the goat can reach 1 ft farther than the rope length. What is the maximum area the goat can cover.a) 4840b) 4804c) 8044d) 4084169. In triangle BCD, BC = 25 m, and CD = 10 m. The perimeter of the triangle maybe:a) 79 mb) 70 mc) 71 md) 72 m170. A quadrilateral have sides equal to 12 m, 20 m, 8 m and 16.97 m respectively. If the sum of the two opposite angles is equal to 225, find the area of the quadrilateral.a) 168b) 100c) 124d) 158171. The area of a circle inscribed in a hexagon is 144 m^2. Find the area of the hexagon.a) 498.83 m^2b) 489.83 m^2c) 439.88 m^2d) 349.88 m^2172. Each angle of the regular dodecagon is equal to _________ degrees.a) 135b) 150c) 125d) 105173. If an equilateral triangle is circumscribe about a circle of radius 10 cm, determine the side of the triangle.a) 34.64 cmb) 64.12 cmc) 36.44 cmd) 32.10 cm174. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector.a) 59.8 cm^2b) 58.9 cm^2c) 89.5 cm^2d) 85.9 cm^2175. The distance between the center of the three circles which are mutually tangent to each other externally are 10, 12 and 14 units. Find the area of the largest circle.a) 72b) 64c) 23 d) 16 176. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less than its base. Find the altitude, if the areas of the triangles differ by 21 square units.a) 6 & 12b) 5 &11c) 3 & 9d) 4 & 10177. If the sides of a parallelogram and an included angle are 6, 10 and 100 degreess respectively, find the length of the shorter diagonal.a) 10.63b) 10.73c) 10.23d) 10.37178. In triangle ABC, angle C = 34 degrees, side a = 29 cm, b = 40 cm. Solve the area of the triangle.a) 324 cm^2b) 342 cm^2c) 448 cm^2d) 484 cm^2179. An oblique equilateral parallelogram.a) squareb) rectanglec) rhombusd) recession180. What is the interior angle (in radian) of an octagona) 2.26 radb) 2.36 radc) 2.8 radd) 2.75 rad181. The circumference of a great circle of a sphere is 18. Find the volume of the sphere.a) 3053.6b) 4053.6c) 5053.6d) 6053.6182. A pyramid whose altitude is 5 ft weighs 800 lbs. At what distance from its vertex must it be cut by a plane parallel to its base so that the two solids of equal weight will be formed?a) 3.97 ftb) 2.87 ftc) 4.97 ftd) 5.97 ft183. Find the increase in volume of a spherical balloon when its radius is increased from 2 to 3 inches.a) 75. 99 cu. in.b) 74.59 cu. in.c) 74.12 cu. in.d) 79.59 cu. in.184. If the lateral area of a right cylinder is 88 and its volume is 220, find its radius.a) 2 cmb) 3 cmc) 4 cmd) 5 cm185. It is desired that the volume of the sphere be tripled. By how many times will the radius be increased?a) 2^1/2b) 3^1/3c) 3^1/2d) 3^3186. A cone and a cylinder have the same height and the same volume. Find the ratio of the radius of the cone to the radius of the cylinder.a) 0.577b) 0.866c) 1.732d) 2.222187. Compute the surface area of the cone having a slant height of 5 cm and a diameter of 6 cm.a) 47.12 cm^2b) 25.64 cm^2c) 38.86 cm^2d) 30.24 cm^2188. The ratio of the volume of the lateral area of a right circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius?a) 5:2b) 5:3c) 4:3d) 4:2189. A conical vessel has a height of 24 cm and a base diameter of 12 cm. It holds water to a depth of 18 cm above its vertex. Find the volume of its contents in cubic centimeter.a) 387.4b) 381.7c) 383.5d) 385.2190. A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is 6.283 m^3. Find its altitude in m.a) 4.5b) 5.5c) 4d) 5191. The volume of water in a spherical tank having diameter of 4 m is 5.236 m^3. Determine the depth of the water in the tank.a) 1.6b) 1.4c) 1.2d) 1.0192. The corners of a cubical block touched the closest spherical shell that encloses it. The volume of the box is 2744 cm^3. What volume in cm^3 inside the shell is not occupied by the block?a) 4713.56b) 3360.14c) 4133.25d) 5346.42193. A circular cone having an altitude of 9 m is divided into 2 segments having the same vertex. If the smaller altitude is 6m, find the ratio of the volume of the small cone to the big cone.a) 0.296b) 0.396c) 0.186d) 0.486194. A frustum of a regular pyramid has an upper base of 8 m x 80 m and a lower base of 10 m x 100 m and an altitude of 5 m. Find the volume of the pyramid.a) 4066.67 m^3b) 5066.67 m^3c) 6066.67 m^3d) 7066.67 m^3195. The bases of a right prism is a hexagon with one each side equal to 6 cm. The bases are 12 cm apart. What is the volume of a right prism?a) 1211.6 cm^3b) 2211.7 cm^3c) 1212.5 cm^3d) 1122.4 cm^3196. The volume of the water in hemisphere having a radius of 2 m is 2.05 m^3. Find the height of the water.a) 0.602b) 0.498c) 0.782d) 0.865197. Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150 deg.a) 7711.82 cm^3b) 6622.44 cm^3c) 5533.32 cm^3d) 8866.44 cm^3198. A cubical container that measures 2 in on a side is tightly packed with marbles and is filled with water. All the 8 marbles are in contact with the walls of the container and the adjacent marbles are the same size. What is the volume of water in the container?a) 0.38 in^3b) 2.5 in^3c) 3.8 in^3d) 4.2 in^3199. If one edge of a cube measures12 cm, calculate for the surface area of the cube and the volume of the cube.a) 864 cm^2; 1728 cm^3b) 468 cm^2; 1728 cm^3c) 863 cm^2; 8721 cm^3d) 468 cm^2; 8721 cm^3200. A pyramid with a square base has an altitude of 25 cm. If the edge of the base is 15 cm. Calculate the volume of the pyramid.a) 1785 cm^3b) 1875 cm^3c) 5178 cm^3d) 5871 cm^3201. If a right cone has a base radius of 35 cm and an altitude of 45 cm. Solve for the total surface area and the volume of the cone.a) 10,116.89 cm^2 and 57,726.76 cm^3b) 9,116.89 cm^2 and 57,726.76 cm^3c) 10,116.89 cm^2 and 67,726.76 cm^3d) 9,116.89 cm^2 and 67,726.76 cm^3202. If the volume of a sphere is 345 cm^3. Solve for its diameter.a) 8.70 cmb) 7.70 cmc) 6.70 cmd) 9.70 cm203. A group of children playing with marbles placed 50 pieces of the marbles inside a cylindrical container with water filled to a height of 20 cm. If the diameter of each marble is 1.5 cm and that of the cylindrical container 6 cm. What would be the new height of water inside the cylindrical container after the marbles were placed inside?a) 23.125 cmb) 24.125 cmc) 22.125 cmd) 25.125 cm204. A pipe lining material silicon carbide used in a conveyance of pulverized coal to fuel a boiler, has a thickness of 2 cm and inside diameter of 10 cm. Find the volume of the material with pipe length of 6 meters.a) 45,239 cm^3b) 42,539 cm^3c) 49,532 cm^3d) 43,932 cm^3205. Given of diameter x and altitude h. What percent is the volume of the largest cylinder which can be inscribed in the cone to the volume of the cone?a) 44%b) 56%c) 46%d) 65%206. Each side of a cube is increased by 1%. By what percent is the volume of the cube increased?a) 23.4%b) 30.3%c) 34.56%d) 3.03%207. Two vertical conical tanks are joined at the vertices by a pipe. Initially the bigger tank is full of water. The pipe valve is open to allow the water to flow to the smaller tank until it is full. At this moment, how deep is the water in the bigger tank? The bigger tank has a diameter of 6 ft and a height of 10 ft, the smaller tank has a diameter of 6 ft and a height of 8 ft. Neglect the volume of water in the pipeline.a) b) c) d) 208. A pyramid has a square base of 8 m on a side and an altitude of 10 m. How many liters of water will it hold when full and inverted?a) 223,330b) 203,330c) 213,330d) 233,330209. What solid figure that has many faces?a) octagonb) decagonc) polygond) polyhedron210. If the length of the latus rectum of an ellipse is three-fourth of the length of its minor axis, find its eccentricity.a) 0.15b) 0.33c) 0.55d) 0.66211. Find the equation of a line where x-intercept is 2 and y-intercept is -2.a) 2x + 2y +2 = 0b) x y 2 = 0c) -2x + 2y = -2d) x y 1 = 0212. A point (x, 2) is equidistant from the points (-2, 9) and (4, -7). The value of x is:a) 11/3b) 20/3c) 19/3d) 3213. A parabola y = -x^2 6x 9 opens ______________.a) to the rightb) upwardc) to the leftd) downward214. A line with a curve approaches indefinitely near as its tracing point passes off infinitely is called the:a) tangentb) asymptotec) directlyd) latus rectum215. Find the eccentricity of an ellipse when the length of the latus rectum is 2/3 of the length of the major axis.a) 0.58b) 0.68c) 0.78d) 0.98216. The directrix of a parabola is the line y = 5 and its focus is at the point (4, -3).a) 20b) 18c) 16d) 12217. The radius of a sphere 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) 1/(8) inb) 1/(4) inc) 2 ind) ^2 in218. In general quadratic equation, if the discriminant is zero, the curve is a figure that represents ________.a) hyperbolab) circlec) parabolad) ellipse219. The equation of the tangent to the curve y = x + 5/x at point P(1, 3) is:a) 4x y + 7 = 0b) x + 4y 7 = 0c) 4x + y -7 = 0d) x 4y + 7 = 0220. A line 4x + 2y 2 = 0 is coincident with the line:a) 4x + 4y 2 = 0b) 4x + 3y + 33 = 0c) 8x + 4y 2 = 0d) 8x + 4y 4 = 0221. A locus of a point which moves so that it is always equidistant from a fixed point (focus) to a fixed line (directrix) is a _____________.a) circleb) ellipsec) parabolad) hyperbola222. Find the equation of the line passing through (7, -3) and (-3, -5).a) x + 5y + 22 = 0b) x + 5y 22 = 0c) x 5y + 22 = 0d) x 5y 22 = 0223. Find the vertex of the parabola, x^2 = 8ya) (0, 0)b) (0, 4)c) (4, 0)d) (0, 8)224. What type of conics is x^2 4y + 3x + 5 = 0.a) parabolab) ellipsec) hyperbolad) circle225. 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) (-2, -1)c) (-1, -2)d) (1, 1)226. A line passing through a point (2, 2). Find the equation of the line if the length of the segment intercepted by the coordinates axes is equal to the square root of 5.a) 2x y 2 = 0b) 2x + y + 2 = 0c) 2x y + 2 = 0d) 2x + y 2 = 0227. Point P(x, y) moves with a distance from point (0, 1) one half of its distance from line y = 4, the equation of its locus is:a) 2x^2 4y^2 = 5b) 4x^2 + 3y^2 = 12c) 2x^2 + 5y^2 = 3d) x^2 + 2y^2 = 4228. 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) 93,000,000 milesb) 94,335,000 milesc) 91, 450,000 milesd) 94,550,000 miles229. What is the equation of the asymptote of the hyperbola (x^2)/9 (y^2)/4 = 1.a) 2x 3y = 0b) 3x 2y = 0c) 2x y = 0d) 2x + y = 0230. Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x 6y + 25 = 0.a) 2, 8b) 4, 16c) 16, 64d) 1, 4231. Find the equation of the axis of symmetry of the function y = 2x^2 7x + 5.a) 7x + 4 = 0b) 4x + 7 = 0c) 4x 7 = 0d) x 2 = 0232. Find the value of k for which the equation x^2 + y^2 + 4x 2y k = 0, represents a point circle.a) 5b) 6c) -6d) -5233. Find the equation of the circle whose center is at (3, -5) and whose radius is 4.a) x^2 + y^2 6x + 10y + 18 = 0b) x^2 + y^2 + 6x + 10y + 18 = 0c) x^2 + y^2 6x 10y + 18 = 0d) x^2 + y^2 + 6x 10y + 18 = 0234. Determine B such that 3x + 2y 7 = 0 is perpendicular to 2x By + 2 = 0.a) 5b) 4c) 3d) 2235. In a Cartesian coordinates, the coordinates of a square are (1, 1), (0, 8), (4, 5), and (-3, 4). What is the area?a) 25b) 20c) 18d) 14236. The segment from (-1, 4) to (2, -2) is extended three times its own length. Find the terminal point.a) (11, -24)b) (-11, -20)c) (11, -18)d) (11, -20)237. Find the distance between A(4,-3) and B(-2, 5).a) 10b) 8c) 9d) 11238. Given three vertices of a triangle whose coordinates are A(1, 1), B(3, -3) and C(5, -3). Find the area of the triangle.a) 3b) 4c) 5d) 6239. The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the values of x and y.a) 33, 12b) 5, 0c) 6, 9d) 14, 6240. A line passes through (1, -3) and (-4, -2). Write the equation of the line in slope-intercept form.a) y 4 = xb) y = -x 2c) y = x 4d) y 2 = x241. What is the x-intercept of the line passing through (1, 4) and (4, 1).a) 4.5b) 5c) 6d) 4242. Find the distance between the lines, 3x + y 12 = 0 and 3x + y 4 = 0.a) 16/b) 12/c) 4/d) 8/243. Find the area of the circle whose equation is x^2 + y^2 = 6x 8y.a) 25b) 5c) 15d) 20244. Find the major axis of the ellipse x^2 + 4y^2 2x 8y + 1 = 0.a) 2b) 10c) 4d) 6245. An arch 18 m high has the form of parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64 m. Find the width of the arch at the bottom.a) 86 mb) 96 mc) 106 md) 76 m246. Find the equation of the hyperbola whose asymptotes are y = 2x and which passes through (5/2, 3).a) 4x^2 y^2 16 = 0b) 2x^2 y^2 4 = 0c) 3x^2 y^2 9 = 0d) 5x^2 y^2 25 = 0247. Find the eccentricity of the curve 9x^2 4y^2 36x + 8y = 4.a) 1.80b) 1.90c) 1.70d) 1.60248. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = - 6 is:a) 3x + 2y = 12b) 2x 3y = 12c) 3x 2y = 12d) 2x 3y = -12249. What is the radius of a circle defined by the equation x^2 6x + y^2 4y 12 = 0.a) 3.46b) 7c) 5d) 6250. Find the slope of the line defined by y x = -5.a) 1b) 1/4c) -1/2d) 5 + x251. What conic section is represented by 4x^2 y^2 + 8x + 4y = 15.a) parabolab) ellipsec) hyperbolad) circle252. What conic section is represented by x^2 + y^2 4x + 2y 20 = 0a) circleb) parabolac) ellipsed) hyperbola253. Find the equation of the straight line with a slope of 3 and a y-intercept of 1.a) 3x y + 1 = 0b) 3x + y + 1 = 0c) 3x y 1 = 0d) 3x + y 1 = 0254. What is the equation of the line that passes through (4, 0) and is parallel to the line x y 2 = 0?a) y + x + 4 = 0b) y x 4 = 0c) x y 4 = 0d) x + y 4 = 0255. Find the distance from the line 4x 3y + 5 = 0 to the point (2, 1).a) 1b) 2c) 3d) 4256. What is the center of the curve x^2 + y^2 2x 4y 31 = 0.a) (-1, -2)b) (1, -2)c) (-1, 2)d) (1, 2)257. Determine the equation of the curve such that the sum of the distances of any point on the curve from two points whose coordinates are (-3, 0) and (3, 0) is always equal to 8.a) 7x^2 + 16y^2 112 = 0b) 16x^2 + 7y^2 112 = 0c) 7x^2 + 16y^2 + 112 = 0d) 16x^2 + 7y^2 + 112 = 0258. The equation 9x^2 + 16y^2 + 54x - 64y = -1 describes:a) a hyperbolab) a spherec) a circled) an ellipse259. The sum of the distances from the two foci to any point in a/an ______________ is a constant.a) a parabolab) any conicc) hyperbolad) ellipse260. Determine the curve: 9x^2 + 6y^2 + 2x + 3y + 9 = 0.a) ellipseb) hyperbolac) parabolad) circle261. Locus of points on a side which rolls along a fixed line:a) cardoidb) epicycloidc) cycloidd) hypocycloid262. What is the radius of a circle with the following equation? x^2 6x + y^2 12 = 0a) 2b) 5c) 7d) 25253. Find the slope of the line passing to the point (-3, -4) and (2, 4).a) 0b) 5c) 10d) 1.6254. What is the slope of the line perpendicular to y = (1/4)x + 6?a) 4b) 1c) -4d) -1255. Given the polar coordinates (4, 20). Find the rectangular coordinates.a) -2, 3.46b) -3.46, -2c) 2, -3.46d) -3.46, 4256. Find the equation of the line which passes through the point (2, 1) and perpendicular to the line whose equation is y = 4x + 3.a) x 4y + 6 = 0b) y 4x + 6 = 0c) x + 4y 6 = 0d) y 4x + 6 = 0257.What is the second derivative of a function y = 5x^3 + 2x + 1?a) 25xb) 30xc) 18d) 30258. Find the height of a circular cylinder of a maximum volume, which can be inscribed in a sphere of radius 10 cm.a) 11.55 cmb) 12.55 cmc) 14.55 cmd) 15.55 cm259. Find the maximum point of y = x + 1/x.a) (2, 5/2)b) (1, 2)c) (-1, -2)d) (2, 3)260. Simplify the expression Lim(x^2 16)/(x 4) as x approaches 2.a) 8b) 6c) 4d) 2261. Evaluate the Lim (x^2 + 3x 4) as x approaches 3.a) 18b) 12c) 4d) 2262. The distance a body travels is a function of time t and is defined by: x(t) = 18t + 9t^2. What is its velocity at t = 3?a) 36b) 45c) 72d) 92263. Water running out a conical funnel at the rate of 1 cu. in per second. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top.a) -1/9 in/secb) -3/2 in/secc) -8/9 in/secd) -4/9 in/sec264. ________ is the concept of finding the derivative of composite functions.a) Logarithmic differentiationb) Chain rulec) Trigonometric differentiationd) Implicit differentiation265. The volume of the sphere is increasing at the rate of 6 cm^3/hr. At what rate is its surface area increasing (in cm^2/hr) when the radius is 50 cm?a) 0.54b) 0.44c) 0.34d) 0.24266. A man on a wharf 3.6 m above sea level is pulling a rope tied to a raft at 0.60 m per second. How fast is the raft approaching the wharf when there are 6 m of rope out?a) -0.95 m/sb) -0.85 m/sc) -0.75 m/sd) -0.65 m/s267. If the distance x from the point of departure at time t is defined by the equation x = -16t^2 + 5000t + 5000, what is the initial velocity?a) 2000b) 0c) 5000d) 3000268. Using 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) 225 sq. ftb) 240 sq. ftc) 270 sq. ftd) 335 sq. ft269. The radius of a sphere 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) 1/(8) inb) 1/(4) inc) 2 ind) ^2 in270. 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) 8 cmb) 12 cmc) 16 cmd) 20 cm271. Find the change in y = 2x 3 if x changes from 3.3 to 3.5.a) 0.1b) 0.2c) 0.3d) 0.4272. If y = arctan(ln x), find dy/dx at x = 1/e.a) eb) e/2c) e/3d) e^2273. Evaluate the limit (ln x)/x as x approaches positive infinity.a) 1b) 0c) infinityd) -1274. lim[(x^3 27)/(x 3)] as x approaches 3.a) 0b) infinityc) 9d) 27275. A box is to be constructed from a piece of zinc 20 in square by cutting equal squares from each corner and turning up zinc to form the side. What is the volume of the box that can so constructed?a) 599.95 in^3b) 592.59 in^3c) 579.50 in^3d) 622.49 in^3276. Given the function f(x) = x to the 3rd power 6x + 2, find the value of the first derivative at x = 2, f(2).a) 6b) 7c) 3x^2 5d) 8277. Water is pouring into a swimming pool. After t hours there are t + gallons in the pool. At what rate is the water pouring into the pool when t = 9 hours?a) 7/6 gphb) 1/6 gphc) 2/3 gphd) 1/2 gph278. Evaluate Lim [(x^2 16)/(x 4)] as x approaches 4.a) 1b) 8c) 0d) 16279. Evaluate Lim [(x - 4)/(x^2 x 12)] as x approaches 4.a) undefinedb) 0c) infinityd) 1/7280. Evaluate Lim [(x^3 2x + 9)/(2x^3 8)] as x approaches infinity.a) 0b) 2c) 1/2d) 1/4281. If y = 1/(t + 1) and x = t/(t + 1), find dy/dx or y.a) 1b) -1c) td) t282. Differentiate: y = [(sin x)/(1 2cos x)].a) (cos x 1)/(1 2cos x)^2b) (cos x 2)/(1 2cos x)^2c) (cos x)/(1 2cos x)^2d) (-2)/(1 2cos x)^2283. Given the curve y = 12 12x + x^3, determine its maximum, minimum and inflection points.a) (-2, 28), (2, -4), & (0, 12)b) (2, -28), (2, 4), & (0, 2)c) (-2, -28), (-2 -4) & (2, 12)d) (-2, 28), (-2, 4) & (1, 12)284. Given the curve y^2 = 5x 1 at point (1, -2), find the equation of tangent and normal to the curve.a) 5x + 4y + 3 = 0 & 4x 5y 14 = 0b) 5x + 4y 3 = 0 & 4x + 5y 14 = 0c) 5x 4y + 3 = 0 & 4x + 5y + 14 = 0d) 5x 4y 3 = 0 & 4x + 5y 14 = 0285. Find the radius of the curvature at any point on the curve, y + ln cos x = 0a) cos xb) 1.5707c) sec xd) 1286. Find the minimum volume of a right circular cylinder that can be inscribed in a sphere having a radius r.a) 1/ volume of sphereb) volume of spherec) 2/volume of sphered) volume of sphere287. Find the point in the parabola y^2 = 4x at which rate change of the ordinate and abscissa are equal.a) (1, 2)b) (-1, 4)c) (2, 1)d) (4, 4)288. What is the allowable error in measuring the edge of cube that is intended to hold 8 m^3, if the error of the computed volume is not to exceed 0.03 m.a) 0.002b) 0.003c) 0.0025d) 0.001289. Find the slope of x^2 y = 8 at point (2, 2)a) 2b) -1c) -2d) 1/2290. Water is flowing into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top. If the rate at which the water rises is 2 cm/sec, how fast is the water flowing into the conical vessel when the water is 4 cm deep?a) 6.28 m^3/sb) 2.37 m^3/sc) 4.57 m^3/sd) 5.73 m^3/s291. Find the slope of the line having a parametric equation y = 4t + 6 and x = t + 1.a) 1b) 2c) 3d) 4292. Determine the diameter of a closed cylindrical tank having a volume of 11.3 m^3 to obtain a minimum surface area.a) 1.44b) 2.44c) 3.44d) 4.44293. Determine the velocity of progress with the given equation, D = 20t + 5/(t + 1) when t = 4 sec.a) 16.8 m/sb) 17.8 m/sc) 18.8 m/sd) 19.8 m/s294. Find the slope of the curve x^2 + y^2 6x + 10y + 5 = 0 at point (1, 0).a) 1/3b) 3/4c) 2/5d) 1/5295. Two posts 10 m high and the other is 15 m high stands 30 m apart. They are to be stayed by transmission wires attached to a single stake at ground level, the wires running to the top of the posts. Where should the stake be placed to use the least amount of wire?a) 12 mb) 14 mc) 18 md) 16 m296. Find the slope of the line having the parametric equations x = t 1 and y = 2t.a) 1b) 3c) 2d) 4297. Find the second derivative of y with respect to x for: 4x^2 + 8y^2 = 36.a) 9/4y^3b) 4y^3c) -9/4y^3d) -4y^3298. Find the derivative of h with respect to u; for h = ^2u.a) ^2xb) 2u ln c) 2^2u ln d) 2^2u299. Find y if y = x ln x x.a) ln xb) x ln xc) (ln x)/xd) x/ln x300. Differentiate, y = sec x^2.a) 2x sec x^2b) 2sec x^2c) 2xtan x^2d) 2xsec x^2 tan x^2301. What is the derivative of the function with respect to x of (x + 1)^3 x^3?a) 3x + 3b) 3x 3c) 6x 3d) 6x + 3302. Evaluate the Lim [(x^2 1)/(x^2 + 3x 4)] as x approaches 1.a) 3/5b) 2/5c) 4/5d) 1/5303. Evaluate: Lim [(1 cos x)/x^2] as x approaches 0a) 0b) 1/2c) 2d) -1/2304. Evaluate: Lim [(3x^4 2x^2 + 7)/(5x63 + x 3)] as x approaches infinity.a) undefinedb) 3/5c) infinityd) 0305. Differentiate: (x^2 + 2)^1/2a) [(x^2 + 1)^1/2]/2b) x/(x^2 + 2)^1/2c) 2x/(x + 2)^1/2d) (x^2 + 2)^2306. Differentiate y = e^x cos x^2a) e^x sin x^2b) e^x (cos x^2 2xsin x^2)c) e^x cos x^2 2xsin x^2d) -2xe^x sin x307. Differentiate: y = log (x^2 + 1)^ 2a) log e (x)(x^2 + 1)^2b) 4x(x^2 + 1)c) (4xlog e)/(x^2 +1)d) 2x(x + 1)308. If y = 4cos x + sin 2x, what is the slope of the curve then x = 2.a) -2.21b) -4.94c) -3.25d) -2.22309. Find y = arcsin cos x.a) -1b) -2c) 1d) 2310. A poster is to contain 300 m^2 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 a minimum.a) 27.76 cm, 47.8 cmb) 20.45 cm, 35.6 cmc) 22.24 cm, 44.5 cmd) 25.55 cm, 46.7 cm311. Water is flowing into a conical cistern at the rate of 8 m^3/min. If the height of the inverted cone is 12 m and the radius of its circular opening is 6 m. How fast is the water level rising when the water is 4 m deep?a) 0.74 m/minb) 0.64 m/minc) 0.54 m/midd) 0.84 m/min312. An isosceles triangle with equal sides of 20 cm has these sides at variable equal angles with the base. Determine the maximum area attainable by the triangle.a) 250 cm^2b) 200 cm^2c) 180 cm^2d) 300 cm^2313. A triangle has variable sides x, y, z subject to the constraint such that the perimeter P is fixed to 18 cm. What is the maximum possible area for the triangle?a) 15.59 cm^2b) 18.71 cm^2c) 14.03 cm^2d) 17.15 cm^2314. What is the limit value of y = (x^3 + x)/(x^2 + x) as x approaches zero?a) 1b) indeterminatec) 0d) 3315. A fencing is limited to 20 ft high. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall?a) 120b) 100c) 140d) 190316. Find the point on the curve x^2 = 2y which is nearest to the point (4, 1).a) (2, 4)b) (4, 2)c) (2, 2)d) (2, 3)317. Find the largest area of a rectangle which can be inscribed in the ellipse, 4x^2 + 9y^2 = 36.a) 12b) 24c) 6d) 48318. The derivative with respect ot v of the function f(y) = is:a) (y^-2/3)/3b) 3y^2/3c) 3y^-2/3d) (y^2/3)/3319. If a is the simple constant, what is the derivative of y = x^a?a) ax xb) axc) ax to the a - 1 powerd) x to the a 1 power320. The first derivative with respect to y of the function d(y) = 3 is _____.a) 3(9/2)b) 3(9) to the 1/2 powerc) 0d) 9321. Find the derivative of f(x) = [x to the 3rd power (x 1) to the 3rd power] to the 3rd power?a) 3x 3 (x 1)b) 3[x to the 3rd power x 1] to the 3rd powerc) 9[x to the 3rd power (x 1) to the 3rd power]^2 [x (x 1)]^2d) 9[x to the 3rd power (x 1) to the 3rd power]^2 [x^2 (x 1)^2]322. Water from the filtering facility is pouring into a swimming pool. After n hours, there are n + gallons in the pool. At what rate is the water pouring into the pool when n = 16 hrs?a) 1/2 gphb) 9/8 gphc) 1 gphd) 7/6 gph323. Find the slope of the equation y = x^2 when x = 2.a) 2b) 6c) 4d) 1324. What is the value of the following limit? Lim (x^2 9)/(x 3) as x approaches 3.a) 3b) 6c) 9d) 0325. The position of an object as a function of time is describe by x = 4t^3 + 2t^2 t + 3. What is the distance traveled by an object at t = -2 and t = 2?a) 44b) 63c) 78d) 108326. Lim (x^2 0 4)/(x 2) as x approaches 2, compute the indicated limit.a) 4b) 8c) 6d) 10327. Evaluate the integral of [(3^x) /(e^x)]dx from 0 to 1.a) 1.510b) 1.051c) 1.105d) 1.510328. Evaluate the integral of tan^2 x dx.a) tan x x + cb) sec^2 x + x + cc) 2sec x x + cd) (tan^2 x)/s + x + c329. Evaluate the integral of sqrt(3t 1) dt.a) (2/9)(3t 1)^5/2 + cb) (2/9)(3t 1)^3/2 + cc) (1/2)(3t 1)^5/2 + cd) (1/2)(3t 1)^3/2 + c330. Evaluate the integral of (3t 1)^3 dt.a) (1/12)(3t 1)^4 + cb) (1/4)(3t 1)^4 + cc) (1/3)(3t 1)^4 + cd) (1/12)(3t 1)^3 + c331. Integrate the square root of (1 cos x) dx.a) -2 sqrt(2) cos (x/2) + cb) -2sqrt(2) cos x + cc) 2sqrt(2) cos (x/2) + cd) -2sqrt(2) cos x+ c 332. Find the area bounded by the parabolas x^2 2y = 0 and x^2 + 2y 8 = 0.a) 32/2b) 20/3c) 16/3d) 64/3333. Evaluate: integral of cos^8 3A dA from 0 to /6.a) 35/768b) 45/768c) 125/768d) 5/768334. Evaluate: integral of 1/(4 + x^2)^3/2 dx.a) x/(4sqrt(x^2 + 4)) + cb) -1/(4sqrt(x^2 + 4)) + cc) - x/(4sqrt(x^2 + 4)) + cd) 1/(4sqrt(x^2 + 4)) + c335. Evaluate: integral of (e^x)/(e^x + 1) dxa) ln(e^x + 1) + cb) ln(e^-x + 1) + cc) ln^2 (e^x + 1) + cd) ln^2 (e^x + 1) + c336. Evaluate: integral of (e^x 1)/(e^x + 1)a) ln (e^x -1)^2 + x + cb) ln (e^x + 1) + x + cc) ln (e^x + 1)^2 x + cd) ln (e^x + 1)^2 x + c337. Evaluate integral of ln x dx from 1 to 0.a) infinityb) 1c) 0d) e338. Find the area bounded by the line x 2y + 10 = 0, the x-axis, the y-axis and x = 10.a) 75b) 45c) 18d) 36339. Find the area bounded by the curves x^2 + y^2 = 9 and 4x^2 + 9y^2 = 36, on the first quadrant.a) 2/3b) 3/4c) 1/2d) 3/2340. Determine the integral of z sin z with respect to z, then r from r = 0 to r = 1 and from z = 0 to z = /2.a) 1/2b) 4/5c) 1/4d) 2/3341. Integrate 1/(3x + 4) with respect to x and evaluate the result from x = 0 to x = 2.a) 0.278b) 0.336c) 0.252d) 0.305342. An area in the xy plane is bounded by the following lines: x = 0 (y-axis), y = 0 (x-axis), x + 4y = 20, and 4x + y = 20. The linear function z = 5x + 5y attains its maximum value within the bounded area only at one of the vertices (intersections of the above lines). Determine the maximum value of z.a) 40b) 25c) 50d) 45343. Find the area bounded by the parabola x^2 = 4y and y = 4.a) 21.33b) 33.21c) 31.32d) 13.23344. Find the area in the first quadrant bounded by the parabola y^2 = 4x, x = 1 ad x = 3.a) 9.555b) 5.955c) 5.595d) 9.955345. Evaluate integral of 12 sin^5 x cos^5 x dx from 0 to /2.a) 0.20b) 0.50c) 0.25d) 0.35346. Evaluate integral of x(x 5)^12 dx from 5 to 6.a) 0.456b) 0.587c) 0.708d) 0.672347. What is the area bounded by the curve y^2 = x and the line x 4 = 0.a) 32/3b) 34/7c) 64/3d) 16/3348. Find the area bounded by the curve r = 8 cos 2.a) 16b) 32c) 12d) 8349. The area bounded by the curve y = 2x^1/2, the line y = 6 and the y-axis is to be resolved at y = 6. Determine the centroid of the volume generated.a) 0.56b) 1.80c) 1.0d) 1.24350. Find the area of the region bounded by the polar curve r^2 = a^2 cos 2.a) 2a^2b) 4a^2c) 3a^2d) a^2351. The area bounded by the curve y^2 = 12x and the line x = 3 is resolved about the line x = 3. What is the volume generated?a) 185b) 187c) 181d) 183352. Find the moment of inertia with respect to the x-axis of the area bounded by the parabola y^2 = 4x and the line x = 1.a) 2.35b) 2.68c) 2.13d) 2.56353. Given the area in the first quadrant bounded by x^2 = 8y, the line y 2 = 0 and the y-axis. What is the volume generated when the area is resolved about the line y 2 = 0?a) 28.41b) 27.32c) 26.81d) 25.83354. Find the area of the horizontal differential rectangle xdy by the x-axis and the line y = 4. The parabola y = 4x. Rectangle area = (4 x)dy.a) 64/2b) 32/3c) 32/4d) 32/2355. What is the approximate area bounded by the curves y = 8 x^2 and y = -2 + x^2?a) 22.4b) 29.8c) 44.7d) 26.8356. What retarding force is required to stop a 0.45 caliber bullet of mass 20 grams and speed of 200 m/s as it penetrates a wooden block to a depth of 2 inches?a) 17,716 Nb) 19,645 Nc) 15,500 Nd) 12,500 N357. A freely falling body is a body in rectilinear motion and with constant ________.a) velocityb) speedc) decelerationd) acceleration358. A ball is thrown upward with an initial velocity of 50 ft/s. How high does it go?a) 39 ftb) 30 ftc) 20 ftd) 45359. It takes an airplane one hour and forty-five minutes to travel 500 miles against the wind and covers the same distance in one hour and fifteen minutes with the win. What is the speed of the airplane?a) 342 mphb) 375 mphc) 450 mphd) 525 mph360 When the total kinetic energy of a system is the same as before and after the collision of two bodies, it is called:a) static collisionb) elastic collisionc) inelastic collisiond) plastic collision361. An airplane travels from points A to B with a distance of 1500 km and a wind along its flight. 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 kphb) 675 kphc) 450 kphd) 750 kph362. The periodic oscillations either up or down or back and forth motion in a straight line is known as ________.a) transverse harmonic motionb) resonancec) rotational harmonic motiond) translational harmonic motion363. A flywheel of radius 14 inches is rotating at the rate of 1000 rpm. How fast does a poin on the rim travel in ft/sec?a) 122b) 1456c) 100d) 39364. Pedro started running at a speed of 10 kph. 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 kphb) 15.0 kphc) 17.5 jphd) 20.0 kph365. A flywheel accelerates uniformly from rest to a speed of 200 rpm in one-half second. It then rotates at the same speed for 2 seconds before decelerating to rest in one-third second. Determine the total number of revolutions of the flywheel during the entire time interval?a) 8.06 revb) 9.12 revc) 6.90 revd) 3.05366. A ball is thrown upward with an initial velocity of 60 ft/s. Determine the velocity at the maximum height.a) 6.12 ft/sb) 2.61 ft/sc) 2.12 ft/sd) 0 ft/s367. A bullet if fired vertically upward with a mass of 3 grams. If it reaches an altitude of 100 m, what is its initial velocity?a) 54.2 m/sb) 47.4 m/sc) 52.1 m/sd) 44.2 m/s368. What is the acceleration of a point on a rim of a flywheel 0.8 m in diameter turning at the rate of 1400 rad/min?a) 214.77 m/sb) 217.77 m/sc) 220.77 m/sd) 227.77 m/s369. Impulse causes ______________.a) the objects momentum to changeb) the objects momentum to decreasec) the objects momentum to increased) the objects momentum to remain constant or to be conserve370. A DC-9 jet with a takeoff mass of 120 tons has two engines producing average force of 80,000 N during takeoff. Determine the planes acceleration down the runway if the takeoff time is 10 seconds.a) 1.52 m/s^2b) 1.33 m/s^2c) 3.52 m/s^2d) 2.45 m/s^2371. In a hydraulic press, the small cylinder has a diameter of 8 cm, while the larger piston has a diameter of 2 cm. If the force of 600 N is applied to the small piston, what is the force of the large piston, neglecting friction?a) 3895 Nb) 4125 Nc) 4538 Nd) 5395 N372. A car accelerates uniformly from standstill to 80 mi/hr in 5 seconds. What is its acceleration?a) 23.47 ft/sec^2b) 33.47 ft/sec^2c) 43.47 ft/sec^2d) 53.47 ft/sec^2373. A stone is thrown vertically upward at the rate of 20m/s. It will return to the ground after how many seconds?a) 3.67 secb) 5.02 secc) 4.08 secd) 2.04 sec374. A plane is headed due east with airspeed of 240 mph. If a wind at 40 mph is blowing from the north, find the ground speed of the plane.a) 190 mphb) 210 mphc) 243 mphd) 423 mph375. The study of motion without reference to the force that causes the motion is known as __________.a) staticsb) dynamicsc) kineticsd) kinematics376. A car accelerates from rest and reached a speed of 90 kph in 2- seconds. What is the acceleration in meter per second?a) 0.667b) 0.707c) 0.833d) 0.866377. Momentum is a property related to the objects __________.a) motion and massb) mass and accelerationc) motion and weightd) weight and velocity378. A gulf weighs 1.6 ounce. If its velocity immediately after being driven is 225 fps, what is the impulse of the bow in slug-ft/sec?a) 0.855b) 0.812c) 0.758d) 0.699379. A missile is fired with a speed of 100 fps in a direction 30 degrees above the horizontal. Determine the maximum height to which it rises?a) 60 ftb) 52 ftc) 45 ftd) 39 ft380. When the total kinetic energy of a system is the same as before and after collision of two bodies, it is called:a) plastic collisionb) inelastic collisionc) elastic collisiond) static collision381. A man travels in a motorized banca at the rate of 15 kph from his barrio to the poblacion and come back to his barrio at the rate of 12 kph. If his total time of travel back and forth is 3 hours, the distance from the barrio to the poblacion is:a) 10 kmb) 15 kmc) 20 kmd) 25 km382. A 50,000 N car travelling with a speed of 150 km/hr rounds a curve whose radius is 150 m. Find the centripetal force.a) 70 kNb) 25 kNc) 65 kNd) 59 kN383. A ball is dropped from a building 100 m high. If the mass of the ball is 10 grams, after what time will the ball strikes the earth?a) 5.61 sb) 2.45 sc) 4.52 sd) 4.42 s384. A 900 N weight hangs on a vertical plane. A man pushes this weight horizontally until the rope makes an angle of 40 with the vertical. What is the tension in the rope?a) 1286 Nb) 1175 Nc) 918 Nd) 825 N385. A plane dropped a bomb at an elevation 1000 meters from the ground intended to hit a target which is 200 m from the ground. If the plane was flying at a velocity of 300 kph, at what distance from the target must the bomb be dropped to hit the target? Wind velocity and atmospheric pressure to be disregarded.a) 1864.71 mb) 2053.20 mc) 1574.37 md) 1064.20 m386. What is the minimum distance can a truck slide on a horizontal asphalt road if it is travelling at 25 m/s? The coefficient of sliding friction between the asphalt and rubber tire is at 0.60. The weight of the truck is 8500 kg.a) 44.9b) 58.5c) 53.2d) 63.8387. A concrete highway curve with a radius of 500 ft is banked to give lateral pressure equivalent to f = 0.15. For what coefficient of friction will skidding impend for a speed of 60 mph.a) > 0.360b) < 0.310c) > 0.310d) < 0.360388. A circle has a diameter of 20 cm. Determine the moment of inertia if the circular area relative to the axis perpendicular to the area through the center of the circle in cm^4.a) 14,280b) 15,708c) 17,279d) 19,007389. An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the triangle area relative to a line parallel to the base and through the upper vertex in cm^4.a) 2,750b) 3,025c) 2,500d) 2,273390. Two electrons have speeds of 0.7c and x respectively. If their relative velocity is 0.65c, find x.a) 0.02cb) 0.12cc) 0.09cd) 0.25c391. A baseball is thrown from a horizontal plane following a parabolic path with an initial velocity of 100 m/s at an angle of 30 above the horizontal. How far from the throwing point will the ball attain its original level?a) 890 mb) 883 mc) 878 md) 875 m392. What is the speed of a synchronous earths satellite situated 4.5 x 10^7 m from the earth?a) 11,070 kphb) 12,000 kphc) 11,777.4 kphd) 12,070.2 kph393. What is the inertia of a bowling ball (mass 0.50 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds.a) 0.001 kg-m^2b) 0.002 kg-m^2c) 0.0045 kg-m^2d) 0.005 kg-m^2394. The angle or inclination of ascend of a road having 8.25% grade is ____________ degrees.a) 4.72b) 4.27c) 5.12d) 1.86395. A highway curve has a super elevation of 7 degrees. What is the radius of the curve such that there will be no lateral pressure between the tires and the roadway at a speed of 40 mph?a) 265.71 mb) 438.34 mc) 345.34 md) 330.78 m396. A shot is fired at an angle of 30 degrees with the horizontal and a velocity of 120 m/s. Calculate the range of the projectile.a) 12.71 kmb) 387.57 ftc) 0.789 miled) 423.74 yd397. A stone dropped from the top of a building 55 yd elevation will hit the ground with a velocity of:a) 37 ft/secb) 33 ft/secc) 105 ft/secd) 103 ft/sec398. What is the kinetic energy of a 4000 lb automobile which is moving at 44 ft/sec?a) 1.21 x 10^5 ft-lbb) 2.10 x 10^5 ft-lbc) 1.80 x 10^5 ft-lbd) 1.12 x 10^5 ft-lb399. Find the rate of increase of velocity if a body increases its velocity from 50 m/sec to 130 m/sec in 16 sec.a) -4.0 m/sec^2b) 80 m/sec^2c) -80 m/sec^2d) 5.0 m/sec^2400. A 20 kg sack is raised vertically 5 meters in 0.50 sec. What is the change in Potential Energy?a) 98.1 Jb) 981 Jc) 200 Jd) 490.5 J401. A 350 lbf acts on a block at an angle of 15 degrees with the horizontal. What is the work done by this force if it is pushed 5 feet horizontally?a) 1350.3 ft-lbb) 1690 ft-lbc) 1980 ft-lbd) 2002 ft-lb402. A 20 kg object moving at 10 m/sec strikes an unstretched spring to a vertical wall having a spring constant of 40 kN/m. Find the deflection of the spring.a) 111.8 mmb) 223.6 mmc) 70.7 mmd) 50.0 mm403. A 300 kg box impends to slide down a ramp inclined at an angle of 25 degrees with the horizontal. What is the frictional resistance?a) 1243.76 Nb) 9951.50 Nc) 1468.9 Nd) 3359.7 N404. A marksman fires a rifle horizontally at a target. How much does the bullet drop in flight if the target is 150 m away and the bullet has a muzzle velocity of 500 m/sec?a) 0.34 mb) 0.44 mc) 0.64 md) 0.54 m405. A ball is thrown from a building at an angle of 60 degrees with the horizontal at an initial velocity of 30 m/sec. After hiting level ground at the base of the building, it has covered a total distance of 150 m. How tall is the building?a) 230.7 mb) 756.7 mc) 692.5 md) 1089 m406. A highway curve with radius 800 ft is to be banked so that a car travelling 55 mph will not skid sideways even in the absence of friction. At what angle should the curve be banked?a) 0.159 degb) 75 degc) 6.411 degd) 14.2 deg407. An airplane flying horizontally at a speed of 200 m/sec drops a bomb from an elevation of 2415 meters. Determine the time required for the bomb to reach the earth.a) 11.09 secb) 22.18 secc) 44.37 secd) 8.20 sec408. Find the banking angle of a highway curve of 100 m radius designed for cars travelling at 180 kph, if the coefficient of friction between the tires and the road is 0.58.a) 19.23 degb) 38.5 degc) 76.9 degd) 45 deg409. A pulley has a tangential speed of 14m/sec and an angular velocity of 6/5 rad/sec. What is the normal acceleration of the pulley?a) 91 m/sec^2b) 99 m/sec^2c) 105 m/sec^2d) 265 m/sec^2410. An elevator weighing 4000 kb attains an upward velocity of 4 m/sec in 3 sec with uniform acceleration. Find the apparent weight of a 40 kg man standing inside the elevator during its ascent.a) 339 Nb) 245 Nc) 446 Nd) 795 N411. A stone is dropped from a cliff and 2 sec later another stone is thrown downward with a speed of 22 m/sec. How far below the top of the cliff will the second stone overtake the first?a) 375 mb) 507 mc) 795 md) 994 m412. How much horizontal force is needed to produce an acceleration of 8 m/sec^2 on a 75 kg box?a) 600 Nb) 500 Nc) 400 Nd) 200 N413. An elevator with a mass of 1500 kg descends with a acceleration of 2.85 m/sec^2. What is the tension in the supporting cable?a) 10,440 Nb) 12,220 Nc) 15,550 Nd) 20,220 N414. A dictionary is pulled to the right at a constant velocity by a 25 N force pulling upward at 60 degrees above the horizontal. What is the weight of the dictionary if the coefficient of kinetic friction is 0.30?a) 31 Nb) 21 Nc) 20 Nd) 63 N415. The breaking strength of a string is 500 N. Find the maximum speed that it can attain if a 1.5 kg ball is attached at one end while the other end is held stationary and is whirled in a circle. The string is 0.65 m long.a) 15.4 m/secb) 55.2 m/secc) 24.4 m/secd) 14.7 m/sec416. The position of a body weighing 72.6 kg is given by the expression S = 5t^2 + 3t + 4, where S is in meters and t is in seconds. What force is required for this motion?a) 625 Nb) 695 Nc) 726 Nd) 985 N417. Assuming a shaft output of 3,000 kW and a fuel rate of (JP-4) 34.2 lbs/min. What is the overall thermal efficiency of the machine? (HHV of JP-4 is 18,000 Btu/lb)a) 24.2%b) 28.3%c) 27.7%d) 29.1%418. g = 32.2 ft/sec^2. How is it expressed in SI?a) 9.81 m/sec^2b) 9.86 m/sec^2c) 9.08 m/sec^2d) 9.91 m/sec^2419. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. If the efficiency of the winch is 60%, calculate the energy consumed in kWh.a) 0.1718 kWhb) 0.1881 kWhc) 0.1817 kWhd) 0.218 kWh420. Cast iron weighs 640 pounds per cubic foot. The weight of a cast iron block 14 x 12 x 18 is:a) 1120 lbsb) 1000 lbsc) 1200 lbsd) 1088 lbs421. A solid disk flywheel (l = 2kg-,^2) is rotating with a speed of 900 rpm. What is its rotational kinetic energy?a) 730 x 10 to the 3rd power Jb) 680 x 10 to the 3rd power Jc) 1100 x 10 to the 3rd power Jd) 888 x 10 to the 3rd power J422. The path of a projectile is a:a) ellipseb) parabolac) part of a circled) hyperbola423. What is the name for a vector that represent the sum of two vectors?a) momentb) torquec) scalard) resultant424. Determine the super elevation of the outer rail of a 4-ft wide railroad track on a 10 degrees curve. (A 10 degrees curve is one which a chord 100 ft long subtends an angle of 10 degrees at the center). Assumed velocity of 45 mph.a) 0.90 ftb) 2.80 ftc) 2.50 ftd) 1.15 ft425. A 10 diameter helical gear carries a torque of 4000 in-lb. It has a 20 degree involute stub teeth and a helix angle of 30 degree. Determine the axial component of the load on the teeth.a) 451.4 lbb) 218 lbc) 471.5 lbd) 461.6 lb426. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. Calculate the input power in kW if the efficiency of the winch is 60%. a) 18.1 kWb) 21.8 kWc) 28.1 kWd) 13.08 kW427. A diagram which shows only the forces acting on the body:a) free body diagramb) cash flowc) forces flow diagramd) motion diagram428. One horse power is equivalent to:a) 746 wattsb) 7460 wattsc) 74.6 wattsd) 7.46 watts429. Which is a true statement about the vector? V1 = i + 2j + k and v2 = i + 3j 7ka) the vectors coincideb) the angle between them is 17.4 degreec) the vectors are paralleld) the vectors are orthogonal430. In a lifting machine, a load of 50 kN is moved by a distance of 10 cm using an effort of 10 kN which moves through a distance of 1 m, the efficiency of the machine is:a) 20%b) 50%c) 10%d) 40%431. What is the angle between two vectors A and B? A = (3, 2, 1) and B = (2, 3, 2)a) 24.8 degb) 36.7 degc) 42.5 degd) 77.5 deg432. What is the equivalent of one horsepower?a) 746 Wb) 3141 kWc) 33,000 ft-lb/mind) 2545 Btu/lb433. Two people are driving towards each other between two towns 160 km apart. The first man drives at the rate of 45 kph and the other drives at 35 kph. From their starting point how long would it take that they will meet.a) 3 hrb) 4 hrc) 2 hrd) 1 hr434. Resistance to motion, caused by one surface rubbing against another.a) inertiab) resistancec) gravityd) friction435. What happens to the acceleration if the mass is tripled and the force remains the same?a) it will be tripledb) it will be 1/3 of the originalc) it will remain the samed) it will be 3 times the original 436. Which number has five significant digits?a)0.01410b)0.00101c)1.0140d)0.01414437. The prefix of a no. 10 raise ot the power minus 6 is:a) terab)decic) centid) micro438. The length of a bar is one million of a meter is called:a) omicronb) micronc) one bard)one milli439. 120 Giga Newton is how many Mega Newton?a) 12,000b) 120c) 1,200d) 120,000440. Factor the expression ( 289x^3 - 204x^2 + 36x )a)4x( 17/2 x 3)( 17/2 x 3 )b) 4x(17x-3)(17x-3)c) 4x(4x-3)(4x+3)d)4x(17x-3)(17x+3)441. Factor the expression as completely as possible: (2x^3 -7x^2 +6x)a) x(x-2)(x-3)b) x(x-2)(x+3)c) x(x-2)(2x+3)d) x(x-2)(2x-3)442. ( (xyz)^(1/n) )^n is equal to:a) (xyz)^(1/n)b) (xyz)^nc) xyzd) (xyz)^(n-1)443. If x raise to the one half of one equals 4, x equal to:a) 24b) 8c) 12d) 16444. If the numbers one and above divided by zero the answer is:a) zerob) infinityc) indeterminated) absurd445. Solve for x and y: 4x + 3y = 11 and 8x^2 9y^2 = -7.a) x = 5/3 and y = 3/2b) x = 3/2 and y = 3/2c) x = 3/5 and y = 5/3d) x = 3/2 and y = 5/3446. If A can do the work in a days and B in b days, how long will it take to do the job working together?a) ( a + b ) / ab daysb) ( a + b ) / 2 daysc) ab / ( a + b ) daysd) a + b days447. Five hundred kg of steel containing 8% nickel to be made by mixing a steel containing 14% nickel with another containing 6% nickel. How much of each is needed?a) 125 kg and 375 kgb) 150 kg and 350 kgc) 200 kg and 300 kgd) 250 kg and 250 kg448. Logarithm of 10th root of, x raise to 10 equals to:a) log xb) ( log x^(1/10) ) / 10c) 10 log xd) log x^10449. What is the natural logarithm of e to the a plus b power?a) abb) log abc) a + bd) 2.718 ( a + b)450. What is the logarithm of negative one hundred?a) No logarithmb) Zeroc) Positive logd) Negative log451. The logarithm of 1 to base e is:a) Oneb) 2.718c) Infinityd) Zero452. What is the value of (0.101)^(5/6)?a) antilog [ log 0.101/(5/6) ]b) antilog [ 6/5 log 0.101 ]c) 6/5 antilog [ log 0.101 ]d) antilog [ 5/6 log 0.101]453. A box contains 8 black and 12 white balls. What is the probability of getting 1 black and 1 white ball in two consecutive draws from the box?a) 0.53b) 0.45c) 0.50d) 0.55454. What is the sum of the following finite sequence of terms? 28, 35, 42, ..., 84.a) 504b) 525c) 540d) 580455. Solve for x that satisfy the equation, x^2 + 36 = 9 2x^2a) 6ib) +9ic) 3id) -9i456. 35.2 to the x power = 7.5 to the x-2 power, solve for x using logarithms.a) -2.06b) -2.10c) -2.60d) +2.60457. Solve algebraically: 4x^2 + 7y^2 = 32 and 11y^2 3x^2 = 41.a) y = 4, x = 1 and y = -4, x = 1b) y = +2, x = 1 and y = -2 , x = 1c) x = 2, y = 3 and x = -2, y = -3d) x = 2, y = -2 and x = 2, y = -2458. Factor the expression 16 10x + x^2.a) (x+8)(x-2)b) (x-8)(x+2)c) (x-8)(x-2)d) (x+8)(x+2)459. What is the value of e^-4 = _____________.a) 0b) 0.183156c) 0.1381560d) 0.0183156460. A pump can pump out a tank in 15 hrs. Another pump can pump out the same tank in 20 hrs. How long will it take both pumps together to pump out the tank?a) 8.57 hrsb) 7.85 hrsc) 6.58 hrsd) 5.50 hrs461. A tank can be filled by one pipe in 9 hrs and another pipe in 12 hrs. Starting empty, how long will it take to fill the tank if water is being taken out by a third pipe at a rate per hour equal to one-sixth the capacity of the tank?a) 36 hrsb) 25 hrsc) 30 hrsd) 6 hrs462. A rubber ball was dropped from a height of 42 m and each time it strikes the ground it rebounds to a height of 2/3 of the distance from which it fell. Find the total distance travelled by the ball before it comes to rest.a) 180 mb) 190 mc) 210 md) 220 m463. From a box containing 8 red balls, 8 white balls and 12 blue balls, one ball is drawn at random. Determine the probability that it is red or white:a) 0.571b) 0.651c) 0.751d) 0.0571464. If 1/x, 1/y, 1/z are in A.P., then y is equal to:a) x-zb) (x+2z)c) (x+z)/2xzd) 2xz/(x+z)465. A class of 40 took examination in Algebra and Trigonometry. If 30 passed algebra, 36 passed Trigonmetry, and 2 failed in both subjects, the number of students who passed the two subjects is:a) 22b) 28c) 30d) 60466. Simplify: ( ab / (ab)^(1/3) )^(1/2)a) (ab)^(1/3)b) abc) (ab)^(1/2)d) (ab)^(1/5)467. Combine into a single fraction: (3x-1)/(x^2-1) (x+3)/(x^2+3x+2) 1/(x+2)a) x-1b) x+1c) 1/(x+1)d) 1/(x-1)468. Two cars start at the same time from nearby towns 200 km apart and travel toward each other. One travel at 60 kph and the other at 40 kph. After how many hours will they meet on the road?a) 1 hourb) 2 hrsc) 3 hrsd) 2.5 hrs469. A single engine airplane has an airspeed of 125 kph. A west wind of 25 kph is blowing. The plane is to patrol due to east and then return toa is base. How far east can it go if the round trip is to consume 4 hrs?a) 240 kmb) 180 kmc) 200 kmd) 150 km470. A car travels from A to B, a distance of 100 km, at an average speed of 30 kph. At what average speed must it travel back from B to A in order to average 45 kph for the round trip of 200 km?a) 70 kphb) 110 kphc) 90 kphd) 50 kph471. Two trains A and B having average speed of 75 mph and 90 kph respectively, leave the same point and travel in opposite direstions. In how many minutes would they be 1600 miles apart?a) 533b) 733c) 633d) 833472. It takes Butch twice as long 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 daysb) 10 daysc) 11 daysd) 9 days473. A man leaving his office one afternoon noticed the clock at past two oclock. Between two to three hours, he returned to his office noticing the hands of the clock interchanged. At what time did he leave the office?a) 2:26.01b) 2:10.09c) 2:30.01d) 2:01.01474. A company has a certain number of machines of equal capacity that produced a total of 180 pieces each working day. If two machines breakdown, the work load of the remaining machines is increased by three pieces per day to maintain production. Find the number of machines.a) 12b) 18c) 15d) 10475.A rectangular field is surrounded by a fence 548 meters long. The diagonal distance from corner to corner is 194 meters. Determine the area of the rectangular field.a) 18,270 m^2b) 18,720 m^2c) 18,027 m^2d) 19,702 m^2476. Solve for x: (x+2)^(1/2) + (3x-2)^(1/2) = 4a) x = 1b) x = 3c) x = 2d) x = 4477. Solve for x: (1/x) + (2/x^2) = (3/x^3).a) x=1,x=-3b) x=3,x=1c) x=-1,x=3d) x=2,x=3478. Solve for x: x^(2/3) + x^(-2/3) = 17/4a) x=-4,x=-1/4b) x=8,x=-1/4c) x=4,x=1/8d) x=8,x=1/8479. A rectangular lot has a perimeter of 120 meters and an area of 800 square meters. Find the length and width of the lot.a) 10m and 30mb) 30m and 20mc) 40m and 20md) 50m and 10m480. A 24-meter pole is held by three guy wires in its vertical position. Two of the guy wires are of equal length. The third wire is 5 meters longer than the other two and is attached to the ground 11 meters farther from the foot of the pole than the other two equal wires. Find the length of the wires.a) 25m and 30mb) 15m and 40mc)20m and 35md) 50 and 10m481. In a racing contest, there are 240 cars which will have fuel provisions that will last for 15 hours. Assuming a constant hourly consumption for each car, how long will the fuel provisions last if 8 cars withdraw from race every hour after the first?a) 20 hoursb)10 hoursc) 15 hoursd) 25 hours482. A pile of boiler pipes contains 1275 pipes in layers so that the top layer contains one pipe and each lower layer has one more pipe than the layer above. How many layers are there in the pile?a) 50b) 45c) 40d) 55483. A production supervisor submitted the following report on the average rate of production of printed circuit boards(PCB) in an assembly line: 1.5 workers produce 12 PCBs in 2 hours. How many workers are employed in the assembly line working 40 hours each per week with a weekly production of 8000 PCBs/a) 50 workersb) 60 workersc) 55 workersd) 70 workers484. A man bought 20 calculators for P20,000.00. There are three types of calculators bought, business type costs P3,000 each, scientific type costs P1,500 each and basic type costs P500 each. How many calculators of each type were purchased?a) 3, 6, 11b) 2, 6, 12c) 1, 4, 15d) 2, 5, 13486. A veterans organization in cebu city consists of men who fought in World War II and men who fought in Korea. The secretary noted that 180 members had fought in Korea and that 70% had taken part in World War II, while 10% of the members had fought in both World War II and Korea. How many members are there together?a) 400b) 500c) 450d) 700487. An angle greater than a straight angle and less than two straight angles is called:a) Right angleb) Obtuse anglec) Reflex angled) Acute angle488. A line segment joining two points on a circle is called:a) Arcb) Tangentc) Sectord) Chord489. All circles having the same center but with unequal radii are called:a) encircleb) tangent circlesc) concyclicd) concentric circles490. A triangle having three sides equal is called:a) equilateral trianglesb) scalene trianglesc) isosceles trianglesd) right triangles491. In a regular polygon, the perpendicular line drawn from the center of the inscribed circle to any one of the sides is called:a) radiusb) altitudec) mediand) rhombus492. A quadrilateral with two and only two sides of which are parallel is called:a) parallelogramb) trapezoidc) quadrilaterald) rhombus493. A polygon with fifteen sides is termed as:a) dodecagonb) decagonc) pentedecagond) nonagon494. A statement the truth of which is admitted without proof is called:a) an axiomb) a postulatec) a theoremd) a corollary495. A rectangle with equal sides is termed as:a) rhombusb) trapezoidc) squared) parallelogram496. The sum of the sides of a polygon is termed as:a) circumferenceb) altitudec) apothemd) perimeter497. A line that meets a plane but not perpendicular to it, in relation to the plane, is:a) parallelb) collinearc) coplanard) oblique498. A quadrilateral whose opposite sides are equal is generally termed as:a) a squareb) a rectanglec) a rhombusd) a parallelogram499. A part of a line included between two points on the line is called:a) a tangentb) a secantc) a sectord) a segment500. Lines which pass through a common point are called:a) collinearb) coplanarc) concurrentd) congruent501. Points which lie on the same plane is called:a) collinearb) coplanarc) concurrentd) congruent502. In two intersecting lines, the angles opposite to each other are termed as:a) opposite anglesb) vertical anglesc) horizontal anglesd) inscribed angles503. A normal to a given plane is:a) perpendicular to the planeb) lying on the planec) parallel to the planed) oblique to the plane504. Which of the following statements is correct?a) all equilateral triangles are similarb) all right-angled triangles are similarc) all isosceles triangles are similard) all rectangles are similar505. A polygon is ________ when no side, when extended, will pass through the interior of the polygon.a) equilateralb) isoperimetricc) congruentd) none of the above506. The sum of the sides of a polygon:a) perimeterb) hexagonc) squared) circumference507. What are the exact values of the cosine and tangent trigonometric functions of the acute angle A, given sin A = 5/8?a) cos A = 8 / 39^(1/2) and tan A = 39^(1/2) / 5b) cos A = 39^(1/2) / 5 and tan A = 8 / 39^(1/2)c) cos A = 39/8 and tan A = 5/ 39^(1/2)d) cos A = 8/5 and tan A = 5/8508. Given a triangle with angle C=290, side a =132 units and side b=233.32 units. Solve for angle B.a) B=1200b) B=122.50c) B=125.20d) B=1300509. Simplify: cos2 ( 1 + tan2 )a) tan 2b) 1c) sin 2d) cos 510. What is the cosine of 1200?a) -0.500b) -0.450c) -0.866d) 0.500511. What is the sine of 8400?a) -0.866b) -0.500c) 0.866d) 0.500512. If the sine of angle A is given as k, what would be then tangent of angle A? Symbol h for hypotenuse, o for opposite and a for adjacent.a) hk/ob) hk/ac) ha/kd) ok/a513. Which is true regarding the signs of the natural functions for angles between 900 and 1800?a) The tangent is positiveb) The cotangent is positivec) The cosine is negatived) The sine is negative514. What is the inverse natural function of the cosecant?a) secantb) sinec) cosined) tangent515. What is the sum of the squares of the sine and cosine of an angle?a) 0b) 1c) 3^(1/2)d) 2516. What is an equivalent expression for sin 2x?a) sin x cos xb) 2 sin x cos xc) -2 sin x cos xd) 2 sin x/sec x517. A transit set-up 112.1 feet from the base of a vertical chimney reads 32030 with the crosshairs set on top of the chimney. With the telescope level, the vertical rod at the base of the chimney is 5.1 feet. How tall is the chimney?a) 66.3 ftb) 71.4 ftc) 76.5 ftd) 170.9 ft518. If sin cos = 1/3, what is the value of in 2?a) 1/3b) 1/9c) 8/9d) 4/9519. If cos = 3^(1/2)/2, then find the value of x if x = 1 tan2 :a) -2b) -1/3c) 4/3d) 2/3520. Solve for x: x = 1-(sin -cos )^2a) sin cos b) -2cos c) cos 2 d) sin 2 521. A mobiline tower and a Nipa Hut stand on a level plane. The angles of depression of the top and bottom of the Nipa Hut viewed from the top of the mobiline tower are 150 and 400, respectively. The height of the tower is 100m. Find the height of the Nipa hut.a) 78.08 mb) 87.08 mc) 68.07 md) 77.08 m522. Ship A started sailing N40032E at the rate of 3 mph. After 2 hours, ship B started from the same port going S45018E at the rate of 4 mph. After how many hours will the second ship be exactly south of ship A?a) 2.25 hrsb) 2.97 hrsc) 3.73 hrsd) 4.37 hrs523. Solve for the value of x in the equation: ln (2x+7) ln (x-1) = ln 5a) x=4b) x=5c) x=6d) x=8524. Two ships started sailing from the same point. One travelled N200E at 30 mph while the other travelled S500E at 20 mph. After 3 hrs, how far apart are the ships?a) 124 milesb) 129 milesc) 135 milesd) 145 miles525. A quadrilateral ABCD is inscribed in a semi-circle such that one of the sides coincides with the diameter AD. AB = 10 meters, and BC = 20 meters. If the diameter AD of the semi-circle is 40 meters, find the area of the quadrilateral.a) 350 m^2b) 420 m^2c) 470 m^2d) 530 m^2526. Solve for x: Arcsin 2x - Arcsin x = 150a) 0.1482b) 0.2428c) 0.3548d) 0.4282527. Solve for x: 2^x + 4^x = 8 ^xa) 0.694242b) 0.692424c) 0.964242d) 0.742420528. Given: Triangle ABC whose angle A is 320 and a = 75 m. The opposite side of angle B is 100m. Find angle C.a) 1000b) 1030c) 1100d) 1150529. Given triangle ABC with sides AB=210 m, BC=205 m, and AC=110 m. Find the largest angle.a) 72.7510b) 75.7210c) 77.1570d) 82.5170530. A pole which leans 10015 from the vertical towards the sun casts a shadow 9.43m long on the ground when the angle of elevation of the sun is 54050. Find the length of the pole.a) 12.5mb) 14.2mc) 15.4md) 18.3m531. Two points lie on a horizontal line directly south of a building 35 m high. The angles of depression to the points are 29010 and 43050, respectively. Determine the distance between the points.a) 26.3 mb) 28.7 mc) 30.2 md) 36.4 m532. Two points lie on a horizontal line directly south of a building 35 m high. The angles of depression to the points are 29010 and 43050, respectively. Determine the distance between the building and the farthest point.a) 62.7 mb) 36.5 mc) 26.5 md) 72.6 m533. Given triangle ABC with sides AB=210 m, BC=205 m, and AC=110 m. Find the largest angle.a) C = 1100b) C = 85.20c) C = 77.10d) C = 43.50534. Given triangle ABC whose angle A is 320 and opposite side of A is 75 meters. The opposite side of angle B is 100 m. find the opposite side of angle C.a) c = 137.8 mb) c = 181.2 mc) c = 117.7 md) c = 127.8 m535. A point P within an equilateral triangle has a distance of 4m, 5m, and 6m respectively from the vertices. Find the side of the triangle.a) 8.53mb) 6.78mc) 9.45md) 17.8m536. The diagonal of the floor of a rectangular room is 7.50 m. The shorter side of the room is 4.5 m. What is the area of the room?a) 36 sq. mb) 27 sq. mc) 58 sq. md) 24 sq. m537. A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose length is 1 cm more than its width, find the area of the rectangle.a) 256.25 sq. cmb) 323.57 sq. cmc) 386.54 sq. cmd) 452.24 sq. cm538. The length of the side of a square is increased by 100%. Its perimeter is increased by:a) 25%b) 100%c) 200%d) 300%539. A piece of wire of length 52 cm is cut into two parts. Each part is then bent to form a square. It is found that total area of the two squares is 97 sq. cm. the dimension of the bigger square is:a) 4b) 9c) 3d) 6540. A sector has a radius of 12 cm. If the length of its arc is 12 cm, its area is:a) 66 sq. cmb) 82 sq. cmc) 144 sq. cmd) 72 sq. cm541. The perimeter of a sector is 9 cm and its radius is 3 cm. What is the area of the sector?a) 4 sq. cmb) 9/2 sq. cmc) 11/2 sq. cmd) 27/2 sq. cm542. An iron bar 20 cm long is bent to form a closed plane area. What is the largest area possible?a) 21.56 sq. mb) 25.68 sq. mc) 28.56 sq. md) 31.83 sq. m543. A swimming pool is to be constructed in the shape of partially-overlapping identical circles. Each of the circles has a radius of 9 cm, and each passes through the center of the other. Find the area of the swimming pool.a) 302.33 sq. mb) 362.55 sq. mc) 398.99 sq. md) 409.44 sq. m544. A circle of radius 5 cm has a chord which is 6 cm long. Find the area of the circle concentric to this circle and tangent to the given chord.a) 14 b) 16 c) 9 d) 4 545. The diagonals of a rhombus are 10 cm and 8 cm, respectively. Its area is:a) 10 sq. cmb) 50 sq. cmc) 60 sq. cmd) 40 sq. cm546. The diagonals of a parallelogram are 10 cm and 16 cm, respectively, if one of its side measures 6 cm, what is the area?a) 59.92 sq. cmb) 65.87 sq. cmd) 69.56 sq. cmd) 78.56 sq. cm547. Given a cyclic quadrilateral whose sides are 4 cm, 5cm, 8cm and 11cm. its area is:a) 40.25 sq. cmb) 48.65 sq. cmc) 50.25 sq. cmd) 60.25 sq. cm548 How many cubic meters is 100 gallons of liquid?a) 1.638b) 37.85c) 3.7850d) 0.37854549. How many cubic meters is 100 cubic feet of liquid?a) 3.785b) 28.31c) 37.85d) 2.831550. The volume of a sphere is 904.78 m^3. Find the volume of the spherical segment of height 4 m.a) 234.57 m^3b) 256.58 m^3c) 145.69 m^3d) 124.58 m^3551. A sector of radius of 6 cm and central angle of 600 is bent to form a cross. Find the volume of the cone.a) (35)^(1/2) / 3b) (35)^(1/2)c) 35 / 3^(1/2)d) 35 / 3552. A spherical wedge of a sphere of radius 10 cm has an angle of 400. Its volume is:a) 523.42 cm^3b) 465.42 cm^3c) 683.42 cm^3d) 723.45 cm^3553. If a solid steel ball is immersed in an eight cm diameter cylinder, if displaces water to a depth of 2.25 cm. The radius of the ball is:a) 3 cmb) 6 cmc) 9 cmd) 12 cm554. The volume of a cube is reduced by how much if all sides are halved?a) 1/8b) 5/8c) 6/8d) 7/8555. If 23 cm^3 of water are poured into a conical vessel, it reaches a depth of 12 cm. How much water must be added so that the depth reaches 18 cm?a) 95 cm^3b) 100 cm^3c) 54.6 cm^3d) 76.4 cm^3556. A cylindrical tank, lying horizontally, 0.90 m in diameter and 3 m long is filled to a depth of 0.60 m. How many gallons of gasoline does it contain?a) 250b) 360c) 300d) 270557. A closed cylindrical tank is 8 ft long and 3 ft in diameter. When lying in a horizontal position, the water is 2 feet deep. If the tank is in the vertical position, the depth of the water tank is:a) 5.67 mb) 5.82 mc) 5.82 ftd) 5.67 ft558. The surface area of a sphere is 4r^2. Find the percentage increase in its diameter when the surface area increases by 21%.a) 5%b) 10%c) 15%d) 20%559. Find the percentage increase in volume of a sphere if its surface area is increased by 21%.a) 30.2%b) 33.1%c) 34.5%d) 30.9%560. Determine the estimated weight of steel plate size x 4 x 8.a) 184.4 kgb) 148.7 kgc) 327 kgd) 841 kg561. The no. of board feet in a plank 2 in. thick, 6 in. wide and 20 ft long is:a) 15b) 30c) 20d) 25562. Determine the volume of a right truncate triangle prism with the following dimensions: Let the corners of the triangular base be defined by A, B ad C. The length AB=11ft, BC=10ft and CA=13ft. The sides at A, B and C are perpendicular to the triangular base and have the height of 8.6ft, 7.1ft and 5.5ft, respectively.a) 377 ft^3b) 337 ft^3c) 358 ft^3d) 389 ft^3563. A right circular conical vessel is constructed to have a volume of 100,000 liters. Find the diameter if depth is to be 1.25 times the diameter.a) 6.736 mb) 7.632 mc) 8.24 md) 9.45 m564. A hollow sphere with an outer radius of 32 cm is made of a metal weighing 8 grams per cubic cm. The weight of the sphere is 150 kg so that the volume of the metal is 24,000 cubic cm. Find the inner radius.a) 30 cmb) 35 cmc) 40 cmd) 45 cm565. A circular cylindrical tank, axis horizontal, diameter 1 meter, and length 2 meters, is filled with water to a depth of 0.75 meters. How much water is in the tank?a) 2.578 m^3b) 2.125 m^3c) 1.2638 m^3d) 1.0136 m^3566. A machine foundation has the shape of a frustrum of a pyramid with lower base 6m x 2m, upper base 5.5m x 1.8m, and altitude of 1.5m. Find the volume of the foundation.a) 12.5 m^3b) 14.2 m^3c) 15.6 m^3d) 16.4 m^3567. An elevated water tank is in the form a circular cylinder with diameter of 3