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2012 - MAY (MSTE) - Practice Problems for CELE
Civil Engineering (BSCE 01)
Ateneo de Davao University
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Civil Engineering Licensure Examinations CIVIL LICENSURE 2 Radius of the sphere. 18. CE Board Nov. 2011 A frustum of a sphere has diameters of 18 16 9 MATHEMATICS MAY and SURVEYING cm. and 32 cm. respectively. If the 2012 thickness is 6 cm. a 1 Find the volume of the frustum. Board May 2012 2 Find the radius of the sphere. 3. Find the area of the zone. sheet of paper measures 16 cm. Circles are to be cut from the paper, A the spherical sector has a central angle of at with a radius of 4 cm. What is the max. center of a radius R. Solution: circles that can be cut from the given Volume of the frustum. 231 cu. Find the radius the volume of segment is 1 paper? Solution: h R2 b2 (16)2 4 4 4 4 4 6 270 4 R 15 R 4 R 16 VR 85 270 6 4 R 270 4 VR2 270 43 24 141 13 R? 270 There are 6 circles that can be cut from a 15x24 cm. paper. 10 JR2 270 Solution: 6 114 R2 270 II 19 2 CE Board May 2012 R2 h 3 pyramid has a square base of side 8 cm. and is 20 cm. high. If it is cut parallel to and Area of the zone. 1 an from its base, determine the ratio of the R 14. A 2x Rh volumes of the smaller pyramid formed to the A 2x (19)(6) original pyramid. A 814 cm2 4. CE Board Solution: The diameter of two spherical bearings are in the ratio 2:5. What is the ratio of their 13 volume? 20 (13)3 (20)3 7 R 0 8 8 Civil Engineering Licensure Examinations CIVIL LICENSURE 2 Radius of the sphere. 18. CE Board Nov. 2011 A frustum of a sphere has diameters of 18 16 9 MATHEMATICS MAY and SURVEYING cm. and 32 cm. respectively. If the 2012 thickness is 6 cm. a 1 Find the volume of the frustum. Board May 2012 2 Find the radius of the sphere. 3. Find the area of the zone. sheet of paper measures 16 cm. Circles are to be cut from the paper, A the spherical sector has a central angle of at with a radius of 4 cm. What is the max. center of a radius R. Solution: circles that can be cut from the given Volume of the frustum. 231 cu. Find the radius the volume of segment is 1 paper? Solution: h R2 b2 (16)2 4 4 4 4 4 6 270 4 R 15 R 4 R 16 VR 85 270 6 4 R 270 4 VR2 270 43 24 141 13 R? 270 There are 6 circles that can be cut from a 15x24 cm. paper. 10 JR2 270 Solution: 6 114 R2 270 II 19 2 CE Board May 2012 R2 h 3 pyramid has a square base of side 8 cm. and is 20 cm. high. If it is cut parallel to and Area of the zone. 1 an from its base, determine the ratio of the R 14. A 2x Rh volumes of the smaller pyramid formed to the A 2x (19)(6) original pyramid. A 814 cm2 4. CE Board Solution: The diameter of two spherical bearings are in the ratio 2:5. What is the ratio of their 13 volume? 20 (13)3 (20)3 7 R 0 8 8 Licensure Examinations Engineering Examinations Civil Engineering formed. the Value of Solution: h A If R 70 V1 V2 R3 From his office window building, a man cu. tried to make vertical angular measurements of a utility tower in a distant field. Using crude V2 R3 instruments, he measured the angle of depression of the foot of the tower and V1 2 Radius of the sphere. recorded it be He then looked at the top V2 (25n) 63 10 CE Board May 2012 of the tower and calculated an angle of elevation of If the ground is generally L 3 Atriangle has the following given parts: level from the foot of the building to the foot of h R R hi 0 anc the tower and the eyes was R R approximately 3 m. above the ground, what B is the height of the tower? Solution: 5. CE Board May 2012 c 0 A frustum of a sphere has the following diameters 12 cm. and 20 cm. The frustum 78 is 3 cm. thick. C 1 Find the volume of the frustum of the Compute the value of c. 3 sphere. 2 Find the radius of the sphere. Compute the value of B. Find the area of the zone thus formed. Compute the value of A. Solution: Solution: 1 Value tan n 6 92 1 Volume of the frustum of the sphere. Cos C Cos 78 0 3 R R 0 29. R2 10 cm. SnB Sin 78 Licensure Examinations Engineering Examinations Civil Engineering formed. the Value of Solution: h A If R 70 V1 V2 R3 From his office window building, a man cu. tried to make vertical angular measurements of a utility tower in a distant field. Using crude V2 R3 instruments, he measured the angle of depression of the foot of the tower and V1 2 Radius of the sphere. recorded it be He then looked at the top V2 (25n) 63 10 CE Board May 2012 of the tower and calculated an angle of elevation of If the ground is generally L 3 Atriangle has the following given parts: level from the foot of the building to the foot of h R R hi 0 anc the tower and the eyes was R R approximately 3 m. above the ground, what B is the height of the tower? Solution: 5. CE Board May 2012 c 0 A frustum of a sphere has the following diameters 12 cm. and 20 cm. The frustum 78 is 3 cm. thick. C 1 Find the volume of the frustum of the Compute the value of c. 3 sphere. 2 Find the radius of the sphere. Compute the value of B. Find the area of the zone thus formed. Compute the value of A. Solution: Solution: 1 Value tan n 6 92 1 Volume of the frustum of the sphere. Cos C Cos 78 0 3 R R 0 29. R2 10 cm. SnB Sin 78 Examinations Engineering Licensure Examinations Civil Engineering 2012 15. CE Board May 2012 21. CE Board M what is the 14. CE Board May 2012 find A the value tube city of has N an outside diameter of minutes to fly from an inside diameter of hours and 15 6 cm. It takes A to city B at constant speed. how long It 3 length of 4 m. What is the total volume of a has Find Solution: the metal needed to make the tube? the journey takes The speed is 1 that of the original. Solution: The speed is of the original. The speed is 3 times the original. in N 4 Solution: B 1 The speed that of the original Vol. Ah N Board May 2012 18, 6 and ac 3. If all of the above cm2 16. CE Board May 2012 are true, what is one possible If 8 men can chop down 28 trees in one day. V(325) how many trees can 20 men chop down in one Solution: 22. CE Board May 2012 1 day? 1 hrs. DE A metal sphere weighing 24 kg is melted down 8 and recast into a solid cone which has a base Solution: with a radius of 8 cm. The metal used has a 2 The speed is of the original. No. of trees chop down in one day per man density of is lost in the D 2020 28 recasting process. The perpendicular height of the cone is not readily known. What is the diameter of the metal sphere? 0 Solution: hrs. 17. CE Board May 2012 Board 3 May 2012 The speed is 3 times the original. What is the equation in D the equation 5x 2y 8 1. and 5, what is the value of Solution: 3 Solution: 1hr. you L4 D 17 cm. Examinations Engineering Licensure Examinations Civil Engineering 2012 15. CE Board May 2012 21. CE Board M what is the 14. CE Board May 2012 find A the value tube city of has N an outside diameter of minutes to fly from an inside diameter of hours and 15 6 cm. It takes A to city B at constant speed. how long It 3 length of 4 m. What is the total volume of a has Find Solution: the metal needed to make the tube? the journey takes The speed is 1 that of the original. Solution: The speed is of the original. The speed is 3 times the original. in N 4 Solution: B 1 The speed that of the original Vol. Ah N Board May 2012 18, 6 and ac 3. If all of the above cm2 16. CE Board May 2012 are true, what is one possible If 8 men can chop down 28 trees in one day. V(325) how many trees can 20 men chop down in one Solution: 22. CE Board May 2012 1 day? 1 hrs. DE A metal sphere weighing 24 kg is melted down 8 and recast into a solid cone which has a base Solution: with a radius of 8 cm. The metal used has a 2 The speed is of the original. No. of trees chop down in one day per man density of is lost in the D 2020 28 recasting process. The perpendicular height of the cone is not readily known. What is the diameter of the metal sphere? 0 Solution: hrs. 17. CE Board May 2012 Board 3 May 2012 The speed is 3 times the original. What is the equation in D the equation 5x 2y 8 1. and 5, what is the value of Solution: 3 Solution: 1hr. you L4 D 17 cm. Licensure Examinations Licensure Examinations civil Engineering 3 23. CE Board May 2012 A diaphragm is in the form of speaker loud The end diameters h trustum of a cone. and the vertical 28 and 6 measures distance the ends is 30 The curve surface is made of felt composite of the speaker Calculate the area of fall composita material needed to cover the curved surface. material. 27. CEBoard May 2012 Solution: 4 3 A water tank has a cylindrical shape with a 7 diam. of 2 m. and a perpendicular height of 3 m. Since it was already old and leaking. it is 12 to be replaced another tank of the same capacity but in the form of a frustum of a cone. The diameters of the ends of the frustum are 30 designed to be 1 m. and 2 m. respectively. What must be its height. Solution: due to loss: 14 C V1 0 m3 31 cm. cu 3 m Surface Surface area Surface area 1705 cm2 CE Board May 2012 cone has a diameter of 80 mm and a 24. CE Board May 2012 perpendicular height of 120 mm. Calculate its voture 0 A metal sphere with a specific gravity of originally weighs 24 kg. It Solution: underwent a process of recasting and was formed into a solid cone with a base having a 25. CE Board May 2012 radius of 8 cm. Assuming of the metal was lost in the procedure, what is the A rectangular block of alloy has the following h perpendicular height of the new cone. dimensions: 4 cm. 7 cm. 12 cm. mm was melted and recast into a frustum da Solution: square pyramid, of the metal being lostin the process. If the end of the frustum are square of 3 cm. and 8 cm. respective). 1 determine the height of the frustum. r 40 mm Licensure Examinations Licensure Examinations civil Engineering 3 23. CE Board May 2012 A diaphragm is in the form of speaker loud The end diameters h trustum of a cone. and the vertical 28 and 6 measures distance the ends is 30 The curve surface is made of felt composite of the speaker Calculate the area of fall composita material needed to cover the curved surface. material. 27. CEBoard May 2012 Solution: 4 3 A water tank has a cylindrical shape with a 7 diam. of 2 m. and a perpendicular height of 3 m. Since it was already old and leaking. it is 12 to be replaced another tank of the same capacity but in the form of a frustum of a cone. The diameters of the ends of the frustum are 30 designed to be 1 m. and 2 m. respectively. What must be its height. Solution: due to loss: 14 C V1 0 m3 31 cm. cu 3 m Surface Surface area Surface area 1705 cm2 CE Board May 2012 cone has a diameter of 80 mm and a 24. CE Board May 2012 perpendicular height of 120 mm. Calculate its voture 0 A metal sphere with a specific gravity of originally weighs 24 kg. It Solution: underwent a process of recasting and was formed into a solid cone with a base having a 25. CE Board May 2012 radius of 8 cm. Assuming of the metal was lost in the procedure, what is the A rectangular block of alloy has the following h perpendicular height of the new cone. dimensions: 4 cm. 7 cm. 12 cm. mm was melted and recast into a frustum da Solution: square pyramid, of the metal being lostin the process. If the end of the frustum are square of 3 cm. and 8 cm. respective). 1 determine the height of the frustum. r 40 mm Examinations Engineering Liconsure Examinations Civil Engineering 39. CE Board May 2012 2012 43. 37. CE Board May 2012 2012 to its An angle of 125 8 is subtended Mario then must be has 4 If cone has height diameter of circle of radius many hats half as a base is 120 cm. and have 24 three together 80 what is its curved area? 1 Find the length have? does Miguel cm., Find the length of arc Solution: 3 Find the area of the circle. Solution: Solution: of that Solution: 1 Length of the minor arc. of hats that Mario has no. of hats that Miguel has L 120 S1 2 Board May 2012 125B 84 then f (x) should be equal to: Solution: cm. S2 S1 42. CE Board May 2012 44. CE Board May 2012 A particle is traveling along the Its A shipment of 3200 items is divided into 2 38. CE Board May 2012 portions such that the difference between the S1. 18 position is given portions is one half of their average. What is If ab cde is positive, which of the following the ratio of the smaller to the larger portions? must be true? Find the instantaneous rate of change of X withrespect to T when Solution: a) 2 Length of the major arc. Solution: X one portion S2 3200 X other S2 2x (8) 18 X S2 34 cm. d) 3 Area of the circle. If a (larger) (ab cde) 0 or (smaller) A 221 cm2 Ans. of Examinations Engineering Liconsure Examinations Civil Engineering 39. CE Board May 2012 2012 43. 37. CE Board May 2012 2012 to its An angle of 125 8 is subtended Mario then must be has 4 If cone has height diameter of circle of radius many hats half as a base is 120 cm. and have 24 three together 80 what is its curved area? 1 Find the length have? does Miguel cm., Find the length of arc Solution: 3 Find the area of the circle. Solution: Solution: of that Solution: 1 Length of the minor arc. of hats that Mario has no. of hats that Miguel has L 120 S1 2 Board May 2012 125B 84 then f (x) should be equal to: Solution: cm. S2 S1 42. CE Board May 2012 44. CE Board May 2012 A particle is traveling along the Its A shipment of 3200 items is divided into 2 38. CE Board May 2012 portions such that the difference between the S1. 18 position is given portions is one half of their average. What is If ab cde is positive, which of the following the ratio of the smaller to the larger portions? must be true? Find the instantaneous rate of change of X withrespect to T when Solution: a) 2 Length of the major arc. Solution: X one portion S2 3200 X other S2 2x (8) 18 X S2 34 cm. d) 3 Area of the circle. If a (larger) (ab cde) 0 or (smaller) A 221 cm2 Ans. of Civil Engineering Licensure Examinations Engineering Licensure Examinations 46. CE Board 45. CE Board May 2012 May 2012 49! law Three distinct positive integers have a sum of stipulates 15 and a product of 45. What is the largest of while flowing in of the proportional to the these integers? volts is applied across Solution: current which flows through 2 X Solution: amperes. equal Trial and error: 1 The constant voltage and current. 2 The current when 52 volts. an 3 The voltage required an 3 x amperes is required. Solution: 50 CE Board May 2012 xy 1 The constant of proportionality betwee voltage and current. Determine the sum to the first 7 terms of the series 0, 0, 2, 6 Solution: no x 10 2 The current when the voltage applied is ya 52 volts. asymptote at (52) amperes (1) y 48 CE Board 2012 3 The voltage required if a current d 3 X required then the KV Check: 51. CE Board 3 V 45 volts must be equal to: The first term of a geometric progression is 4 and the term is 128. What is the 11th 15 ok term? 47. CE Board May 2012 Solution: term) The largest integer is 9 verical ar5 128 will have a 4r5 128 2 asymptotes at 4(2110 (11thterm) Civil Engineering Licensure Examinations Engineering Licensure Examinations 46. CE Board 45. CE Board May 2012 May 2012 49! law Three distinct positive integers have a sum of stipulates 15 and a product of 45. What is the largest of while flowing in of the proportional to the these integers? volts is applied across Solution: current which flows through 2 X Solution: amperes. equal Trial and error: 1 The constant voltage and current. 2 The current when 52 volts. an 3 The voltage required an 3 x amperes is required. Solution: 50 CE Board May 2012 xy 1 The constant of proportionality betwee voltage and current. Determine the sum to the first 7 terms of the series 0, 0, 2, 6 Solution: no x 10 2 The current when the voltage applied is ya 52 volts. asymptote at (52) amperes (1) y 48 CE Board 2012 3 The voltage required if a current d 3 X required then the KV Check: 51. CE Board 3 V 45 volts must be equal to: The first term of a geometric progression is 4 and the term is 128. What is the 11th 15 ok term? 47. CE Board May 2012 Solution: term) The largest integer is 9 verical ar5 128 will have a 4r5 128 2 asymptotes at 4(2110 (11thterm) Civil Engineering Licensure Examinations Engineering Licensure Examinations Volume of the gas at 420 while keeping 61. CE Board May 2012 Board May 2012 65. ElBoard 2 applicants for civil the pressure constant engineering y and Z are integers, and construction company, A music school produced number of both even, which of the odd number of male musicians which includes 3 drummers, 4 odd integer? equal number of male and trumpet players and 5 pianists. How many 2625 liters be hired for gender different jazz trios can be formed from this a) How many men batch of musicians trio consists of a 3 Temperature when the volume is b) drummer, a trumpet player and a pianist? expanded to 2 liters: c) appled? d) Solution: 2 0(T) solution: Different jazz trios formed from this group Solution: 3(4)(5) applicants female applicants 3 lades will left out) 66. 59. CE Board May 2012 of male and female are hired) a) (equal no. A number line is divided 10 evenly spaced y, r and t are integers such that XX is thick mark. The length between each tick (even)(even) negative and is positive. If t is not a multiple mark equals X, and X is a prime number. What is the total length of the line number. b) of 2, then which of the following statements must be true? a) a multiple of 2 Solution: b) xr 0 c) 17 no. of male applicants c) even (even) even d) d) even even Solution: Total length of the line number 9x 54. CE Board May 2012 a) yis a multiple of 2 Use: a) which of the is a negative number 60. CE Board May 2012 X must be a negative number y must be an odd number to maintain If ab a b which of the following relation 62 CE Board 2012 negative results is true. If ab is positive and odo is negativa, which of y is a multiple of 2 a) (nothing suggest (not ok) the following must be true. 2 7 Assume x and (not negative) (false) b) and a) ab not ok b) because and (ok) Assume and less than 0) (false) b) c) absolute of any number (not ok) Assume and (true) d) 3kx (not d) x 0 Assume and multiple of 2) Therefore ab (false) Therefore the answer is Civil Engineering Licensure Examinations Engineering Licensure Examinations Volume of the gas at 420 while keeping 61. CE Board May 2012 Board May 2012 65. ElBoard 2 applicants for civil the pressure constant engineering y and Z are integers, and construction company, A music school produced number of both even, which of the odd number of male musicians which includes 3 drummers, 4 odd integer? equal number of male and trumpet players and 5 pianists. How many 2625 liters be hired for gender different jazz trios can be formed from this a) How many men batch of musicians trio consists of a 3 Temperature when the volume is b) drummer, a trumpet player and a pianist? expanded to 2 liters: c) appled? d) Solution: 2 0(T) solution: Different jazz trios formed from this group Solution: 3(4)(5) applicants female applicants 3 lades will left out) 66. 59. CE Board May 2012 of male and female are hired) a) (equal no. A number line is divided 10 evenly spaced y, r and t are integers such that XX is thick mark. The length between each tick (even)(even) negative and is positive. If t is not a multiple mark equals X, and X is a prime number. What is the total length of the line number. b) of 2, then which of the following statements must be true? a) a multiple of 2 Solution: b) xr 0 c) 17 no. of male applicants c) even (even) even d) d) even even Solution: Total length of the line number 9x 54. CE Board May 2012 a) yis a multiple of 2 Use: a) which of the is a negative number 60. CE Board May 2012 X must be a negative number y must be an odd number to maintain If ab a b which of the following relation 62 CE Board 2012 negative results is true. If ab is positive and odo is negativa, which of y is a multiple of 2 a) (nothing suggest (not ok) the following must be true. 2 7 Assume x and (not negative) (false) b) and a) ab not ok b) because and (ok) Assume and less than 0) (false) b) c) absolute of any number (not ok) Assume and (true) d) 3kx (not d) x 0 Assume and multiple of 2) Therefore ab (false) Therefore the answer is Liconsure Examinations Civil Engineering Licensure Examinations 68. CE Board May 2012 100 SO 67. CE Board May 2012 100 A certain curve has the equation sin A. In A sphere has a diameter of of the sphere is son ITD 31 comparison to this curve, which of the following has twice the amplitude and half the parallol planes, one IFD and the other 10 mm from the period? opposite side of it. Compute the frustum. A Distance first train have traveled: 1 D 33 24 I D 33(30) 12 D 32 2 10 Distance the 2nd traveled when its front end caught up with the tail end of the first Sin 24 2 train: D 501 3 is CE Board May 2012 D 50(30) x Solution: A train 180 m. long is chugging along a alread track going north. Along another (3) Time for the second train to overtake alroad track, very near and parallel to the completely with the first train: Solution: int another train 100 m. long is trying to overtake the first at 180 If the first train When A is larning at 120 and its tall and is 100 100 500 m. ahead of the front of the then find the following: 500 100 33 100 (ampfitude of another curve) How many meters have the first train When A when the front end of the accond caught up with its tall end? 501 100 500 160 33 Sin () How many meters have the second train 16 760 2 traveled when its front end caught up with tail and of the train? soconds How many seconds would have elapsad the initial position when the second has completely clearly overtake 70 EBoardMay 2012 cu. A tank contains 100 liters of brine with 60 kg of When Solution: salt in solution. Brine containing 1 kg per Vol. of frustum of a sphere: liter of salt flows into he tank at the rate of 2n 2 liters per minute and the mixture, kept when the end of uniform stirring, flows out at the rate of with its tail Therefore the equation of the other curve is 3 liters per minute. Find the amount of salt in 2A the tank at the end of one hour. Liconsure Examinations Civil Engineering Licensure Examinations 68. CE Board May 2012 100 SO 67. CE Board May 2012 100 A certain curve has the equation sin A. In A sphere has a diameter of of the sphere is son ITD 31 comparison to this curve, which of the following has twice the amplitude and half the parallol planes, one IFD and the other 10 mm from the period? opposite side of it. Compute the frustum. A Distance first train have traveled: 1 D 33 24 I D 33(30) 12 D 32 2 10 Distance the 2nd traveled when its front end caught up with the tail end of the first Sin 24 2 train: D 501 3 is CE Board May 2012 D 50(30) x Solution: A train 180 m. long is chugging along a alread track going north. Along another (3) Time for the second train to overtake alroad track, very near and parallel to the completely with the first train: Solution: int another train 100 m. long is trying to overtake the first at 180 If the first train When A is larning at 120 and its tall and is 100 100 500 m. ahead of the front of the then find the following: 500 100 33 100 (ampfitude of another curve) How many meters have the first train When A when the front end of the accond caught up with its tall end? 501 100 500 160 33 Sin () How many meters have the second train 16 760 2 traveled when its front end caught up with tail and of the train? soconds How many seconds would have elapsad the initial position when the second has completely clearly overtake 70 EBoardMay 2012 cu. A tank contains 100 liters of brine with 60 kg of When Solution: salt in solution. Brine containing 1 kg per Vol. of frustum of a sphere: liter of salt flows into he tank at the rate of 2n 2 liters per minute and the mixture, kept when the end of uniform stirring, flows out at the rate of with its tail Therefore the equation of the other curve is 3 liters per minute. Find the amount of salt in 2A the tank at the end of one hour.
2012 - MAY (MSTE) - Practice Problems for CELE
Course: Civil Engineering (BSCE 01)
University: Ateneo de Davao University
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