1. At what time between 3 and 4 o’clock will the hand of the clock be opposite each other? A. 3:48 B. 3:50 D. 3:51 C. 3:49
2. A balot vendor sold his ballot to his first customer. The customer bought one-half of the number of balot in the basket and the vendor gave him one balot free. A second customer bought one-half of the number number of the remaining balot and again the the vendor gave one free balot. A third person bought bought half of the remaining balot and receives receives one balot free. If after the third customer all the balot were sold and each balot cost P 8.50, how much is the total sales of vendor? B. 94.50 C. 95.00 D. 93.75 A. 93.50 3. The workforce of a company was lowered by 16%, then increased by 25% of the remaining. What is the overall increase in the workforce? B. 5% A. 10% C. 9% D. 7% 4. If x is an odd integer, which of the following must also be an odd integer? A. x + 1 B. 2x C. x + 4
D. x – 1 1
5. In the system of equations 3x + 2y – z z = 5; y – z z = 2; x + 2y – 3z 3z = -1 the value of y is A. 2 B. -1 C. 4
D. 6
6. A column placed on a pedestal 20 m high subtends an angle of 45° at a point on the ground and it also subtends an angle of 45° at a point which is 20 m nearer the pedestal, find the height of the column. A. 120 m B. 140 m D. 150 m C. 100 m 7. If each interior angle of a regular polygon has a measure of 160°, how many sides has the polygon? A. 16 B. 17 C. 19
D. 18
8. A sector has a radius of 9 cm and whose central angle is 60°. If it is bent to form a cone, the radius of the cone is: A. 13 cm B. 2 cm D. 4 cm C. 1.5 cm 9. A semi-elliptic arch is 20 ft high at the center and has a span of 50 ft. Find the height of the arch at a point 10 ft from one end of the base. A. 14 ft B. 15 ft D. 17 ft C. 16 ft 10. A manufacturing firm engaged in making corrugated sheets can sell “x” sheets per day at a price of 100 – 0.02x 0.02x pesos and that it cost 20x + 10000 pesos to produce “x” sheets per day. What is the production level for maximum profit? A. 1500 B. 1700 C. 1800 D. 2000
11. From the data in the above problem, what is the price per sheet at maximum profit? A. P 40 B. P 50 C. P 60 12. ∫ ∫ ∫ B. A. C.
D. P 70
13. A light-year which is defined as the distance that light travels in 1 year is equivalent to A. 9.46 E 20 m B. 2.30 E 20 m C. 2.30 E 15 m D. 9.46 E 15 m
D.
14. Find the value of x so that the determinant given below will have a minimum value. 2 1 2 3 4 x x 3 1 C. 7 A. 5 B. 6 15. There are three candidates A, B, and C for mayor in a town. If the odds that candidate A will win are 7:5 and that of B are 1:3, what is the probability that candidate C will win? A. 0.25 B. 0.13 C. 0.17 16. A card is chosen from a deck of 52 cards. In how many ways can a spade or a te n be chosen? C. 16 A. 14 B. 15
D. 8
D. 0.21
D. 17
17. A ball is dropped from a window 64 ft above the ground. How long does it take the ball to reach the ground? What is its final velocity? B. 2 sec, 32 ft/s C. 4 sec, 64 ft/s D. 8 sec, 64 ft/s A. 2 sec, 64 ft/s 18. A ball is thrown vertically upward with an initial speed of 80 ft/s. How long will it take for the ball to return to the thrower? D. 4.97 s A. 2.25 s B. 2.62 s C. 4.06 s 19. A body weighing 40 lb starts from rest and slides down a plane at an angle of 30° with the horizontal for which the coefficient of friction is 0.3. How far will it move during the third second? How long will it require for it to move 60 ft? A. 19.02 ft, 3.87 s B. 18.75 ft, 3.50 s C. 19.33 ft, 3.94 s D. 21.50 ft, 3.56 s 20. A train whistle has a natural frequency of 1500 Hz. If the train is approaching a station at a velocity of 30 m/s, what is the frequency perceived by a person standing at the station? (Assume that the air temperature is 30°C). A. 1641.5 Hz B. 1500 Hz C. 1240 Hz 21. What is the reciprocal for sinking fund factor? A. capital recovery factor C. present worth factor
D. 2000 Hz
B. uniform series compound amount factor
D. single payment compound amount factor
22. Which of the following relationships between co mpound interest factors is NOT correct? A. Single payment compound amount factor and single payment present worth factor are reciprocals B. Sinking fund factor and uniform series compound amount factor are reciprocals C. Capital recovery factor and uniform series present worth factor are reciprocals D. Capital recovery factor and sinking fund factor are reciprocals 23. It is also known as the Toxic Substances and Hazardous Nuclear Wastes Control Act of 1990 is also known as _________. A. RA 6969 B. RA 9669 C. RA 9696 24. If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is A. an exponential B. a tangent C. a conic section D. a sinusoid 25. The minimum velocity of projection to go out from the earth’s gravitational pull is known as A. projectile velocity C. escape velocity B. angular velocity D. terminal velocity
D. RA 9669
26. When the distance of a real object from a converging lens equals the focal length of the lens, A. the image is virtual, erect and larger than the object B. the image is real, inverted and larger than the object C. the image is real, inverted and the same as the object D. no image is formed 27. A person borrows P 5000 at an interest rate of 18% compounded monthly. Monthly payments of P 167.10 are agreed upon. The length of the loan is closest to A. 12 months B. 20 months C. 24 months
D. 40 months
28. A payment of P 12,000 six years from now is equivalent, at 10% interest, to an annual payment for eight years starting at the end of this year. The annual payment is closest to B. P 1,200 A. P 1,000 C. P 1,400
D. P 1,600
29. P 25,000 is deposited in a savings account that pays 5 % interest, compounded semiannually. Equal annual withdrawals are to be made from the account, beginning one year from now and continuing forever. The maximum amount of the equal annual withdrawal is closest to A. P 625 B. P 1,000 C. P 1,250 D. P 1,265 30. If the effective interest rate per year is 12%, based on monthly compounding, the nominal interest rate per year is closes to A. 8.5% B. 9.3% C. 10.0% D. 11.4% 1. If x:y:z = 2:5:7 and 4x – y + 2z = 51, find z. B. 6 A. 21
C. 15
D. 8
2. The union of the rational numbers and the irrational numbers forms A. the set of rational numbers C. the set of real numbers B. the set of negative numbers D. the set of complex numbers 3. The ___________ of a relation is the set of second elements of the pair in the relation. C. range A. domain B. function C. graph 4. Using the discriminant, determine the type of solution for the equation: 8a2 – a + 7 = 0. A. two irrational roots C. one rational root D. two complex roots B. two rational roots 5. If a = b and b = c, then a = c. A. associative law B. transitive property
C. axiom D. reflexive property
6. Which of the following is a characteristic of all trigonometric functions? A. The values of all functions repeat themselves every 45 degrees B. All Functions have units of length or angular measure C. The graphs of all functions are continuous D. All functions have dimensionless units 7. The value of x in the equation 27 x = 94 is? A. 8/3 B. 4/3
C. 2/3
8. Given log b y = 2x + log bx. Which of the following is true? A. y = b 2x B. y = 2xb C. y = 2x/b
D. 1/3 D. y = xb2x
9. Find x if log of x to the base 2 is -6. B. -12 A. 1/64
C. 1/128
10. The log 10 (8)(6) is equal to A. log 10 8 + log 10 6 B. log 10 8 log 10 6
C. log 10 8 – log 10 6 D. log 10 8/ log 10 6
11. In 7.18 xy equals A. 1.97xy
B. 0.86
xy
D. -128
C. xy
D. 7.18xy
12. The population of a southern city is increasing at a rate of 7500 per year and the current population is 45,000. How long will it take for the population to grow to 75,000? A. 4 yrs B. 3 yrs C. 6 yrs D. 10 yrs 13. Find the missing term in the series: 1, __, 14, 30, 55, 91,…. B. 5 A. 4
C. 6
D. 7
14. Find the 347 th digit in the decimal expansion 825/999. A. 6 B. 8
C. 5
D. 2
15. The average of three numbers is 2a. If two of the numbers are -3a and 7a, the third number is? A. 4a B. -6a C. 10a
D. 2a
16. I set my video recorder to recorder to record the late film from 11:15 pm to 1:05 am. How many minutes of the new 4 hour tape remained unused? A. 50 B. 110 C. 130
D. 150
17. An administrative assistant can process a certain type of report in 25 minutes. How many such reports can she finish processing in a work-day from 9:00 am to 5:00 pm., with a 45 minute lunch break and two 10-minute c offee breaks? A. 16 B. 17 C. 18
D. 19
18. Given f(x) = (x – 4) (x + 3) + 4, when f(x) is divided by (x – k), the remainder is k. Find k. B. 4 A. -12 C. 8
D. 2
19. If x + y = m and xy = n, then the value of (x – y)2 is B. m2 – 2n A. m2 – 4n
D. m2 + n2
C. m2 + 2n
20. Ana is 5 times as old as Beth and 2 2/3 times as old as Cathy. What fraction of Cathy’s age is Beth’s? A. 1 7/8 C. 13 1/3 D. 3/40 B. 8/15 21. Rae is two years older than Al and four years younger than Nelia. If Al is “d” years old, how old is Nelia in terms of “d”? A. 2d + 2 B. d + 2 C. d + 4 D. d + 6 22. How many minutes after 2 o’clock will the hands of the clock be together for the first time? A. 11.12 B. 13.5 C. 10.91 D. 12.21
23. Susan and Peter headed for the Pizza shop. Terry joined them, but said she wasn’t really hungry. They ordered one large pizza cut into 8 slices. Peter had one more than twice as many slices of pizza as Susan. Terry had 5 less than 3 times as many slices as Susan. How many slices did Susan have? A. 1 C. 5 B. 2
D. 6
24. To pass a test with 80 questions you have to get 60% correct. Margaret was three questions short of a pass. How many questions did she answer correctly? B. 48 C. 51 A. 45
D. 77
25. The yearly change in the yield of one particular crop in our area over the past four years was 25% increase, then 25% decrease, then 25% decrease and finally a 25% increase. What was the total percentage change in yield over the four years ( to the nearest 1% )? B. -1% C. 0 D. 1 A. -12% 26. One of the most popular arithmetic books of all time ( The Scholar’s Guide to Arithmetic by Bonnycastle, 6th edition 1795) contains the exercise: If a cardinal can pray a soul in purgatory, by himself, in an hour, a bishop in three hours, a priest in five and a friar in seven, how long will it take then to pray out three souls from purgatory, all praying together? Which of these is nearest to the expected answer? C. 1 h 47.5 min A. 1 h 41.5 min B. 1 h 46 min D. an eternity 27. Two thousand kilogram of steel containing 8% nickel is to be made by mixing steel containing 14% nickel with another containing 6% nickel. How much of each is needed? A. 1500 kg steel with 14% nickel, 500 kg steel with 6% nickel B. 750 kg steel with 14% nickel, 1250 kg steel with 6% nickel C. 500 kg steel with 14% nickel, 1500 kg steel with 6% nickel D. 1250 kg steel with 14% nickel, 750 kg steel with 6% nickel 28. An arithmetic progression starts with 1, has 9 terms, and the middle term is 21. Determine the sum of the first 9 terms. A. 148 C. 112 B. 189 29. The number 0.00724 rounded off to two significant figures is A. 0.00 B. 0.0
C. 0.0072
D. 235
D. 0.72
30. The difference between 108.648 and 78.29, if expressed in the proper number of significant figures is A. 30.4 B. 30.35 C. 30.358 D. 30.36 31. The sum of 1.001 + 3.850 + 9.4, if expressed in the proper of significant figures is B. 14.25 C. 14.251 D. 14.3 A. 14 32. Ship A started sailing N40°32’E at the rate of 3 mph. After 4 hours, ship B started from the same port going S45°18’E at the rate of 4 mph. After how many hours will the second ship be exactly south of ship A. B. 2.50 hrs C. 3.58 hrs A. 8.7 hrs
33. A road run 1200 m from A to B and then makes a right angle going to C, a distance of 500 m. A new road is being built directly from A to C. How much shorter will the new road be? B. 400 m A. 600 m C. 500 m D. 300 m
D. 2.25 hrs
34. If sin α = a / ( ) , which of the following statements is true? A. tan-1 b/a = – α C. tan-1 b/a = – α B. cos-1 a / ( ) = α D. cos-1 b / ( ) = – α 35. Determine the sum of the interior angles of a hexagon. B. 720° A. 540° C. 810°
D. 630°
36. What is the height of the parabolic arch which has a span of 48 feet and having a height of 20 feet at a distance from the center of the span? A. 30 ft B. 40 ft D. 34 ft C. 36 ft 37. A circle whose center is at (6,8) passes through the origin. Which of the following points is not on the circle? D. (-2,8) A. (12,0) B. (6,-2) C. (16,8) 38. What is the middle term of the expansion of (x2 – 5)8? A. 47350 x8 B. 45370 x8 39. Find the values of x in the equation 24x 2 + 5x – 1 = 0. A. 1/8, -1/3 B. -1/8, 1/3
C. 43750 x 8
D. 47530 x 8
C. -5/8, 3/2
D. 2/3, -8/5
40. The vertices of a triangle have coordinates (1,2), (4,5) and (7,2). Find the area of the triangle. B. 9 sq. units A. 6 sq. units C. 12 sq. units
D. 16 sq. units
41. A right circular cone has an altitude of 18 cm and a radius of 5 cm. Compute the lateral area of the cone. B. 239.42 cm2 C. 329.42 cm2 A. 293.42 cm2
D. 243.42 cm2
42. What is the volume of a right circular cylinder inscribed in a cube of edge 8 cm? B. 128 A. 132 C. 120 D. 110 43. 1 -2 + 3 – 4 + 5 – 6 +…….+ 97 – 98 + 99 equals A. 0 B. 48
C. -50
44. If quadrilateral ABCD is a parallelogram and the measures of angles A and B are 2x + 4 and 3x – 4 respectively, then x = ? A. 8 B. 24 C. 36
D. 50
D. 76
45. Calculate the area of a rhombus with sides of 20 and one angle is 40°. A. 280.9 B. 275.6 D. 246.4 C. 257.1 46. Consist of all angles except right and straight angles. A. obtuse angles B. adjacent angles C. oblique angles D. reflex angles 47. When an object exerts a normal force on a surface, the force is A. equal to the object’s weight B. frictional in origin D. perpendicular to the surface C. parallel to the surface 48. What is the fifth term of the expansion of (ex + e-x)8? B. 70 A. 60
C. e4x
D. sinhx
49. Joseph is four years older than twice his sister’s age. In four years time he will be eleven year older than her. How old is Joseph now? A. 7 B. 10 C. 16
D. 18
50. How many pairs of numbers of the form x. 2x + 1 are there in which both numbers are prime numbers less than 100? A. 3 B. 4 C. 6
D. 7
51. If 6 more than x is two less than y, what is the value of y in terms of x? A. x + 2 B. (x + 2)/2 C. (x + 8)/2
D. x +8
52. If s mangoes cost 5 pesos, what is the cost of r mangoes at the same rate? A. 5r/s B. 5s C. 5s/r
D. 5r
53. Jack is twice as old as Jill and six years younger than Cathy. If Jill is h years old, how old is Cathy in terms of h? A. h - 4 B. h + 4 C. 2h - 4 D. 2h + 6 54. If 25% of the 300 students at MSA High School walk to school, and of the students who walk, one fifth are female, how many male MSA High School students walk to school? A. 15 B. 25 C. 30
D. 60
55. The price of a stereo is increased by P 420, or 6 percent of the original price. D. 7000 A. P 2520 B. P 6000 C. P 6580 56. At a sale Thiel buys a dress that was reduced by 10% from P 1000. The following week the same dress is increased by 10% over the sale price. What is the final price (in peso)? A. P 1100 B. P 1000 D. P 900 C. P 990 57. A pair of running shoes, regularly priced at P 75, is marked down 20% for a summer clearance sale. If sales tax of 8% is then added to the purchase price, how much will the shoes cost? A. P 55.20 B. P 60.00 C. P 64.80
D. P 74.88
58. In a certain high school, the number of seniors is twice the number of juniors. If 60% of the senior class and 40% of the junior class attends the last football game for the season, what fraction of the combined junior and senior class attends the game? A. 60% B. 53% C. 50% D. 47% 59. Valley High’s basketball team sponsors a refreshment table at its game each week to raise money for new uniforms. This week they sold ice cream bars, soft drinks, and homemade cookies; 355 items were bought for a total of P 253.20. The number of soft drinks sold was double the number of cookies purchased. How many cookies were sold if ice cream bars cost P 0.90 each soft drinks P 0.70 each, and cookies P 0.45 cents each? A. 187 B. 121 C. 90
D. 78
60. A 30-meter long steel cylindrical pipe of uniform constitution is cut into two pieces. One piece is 24 meters and weighs 16 kilograms. What was the weight, in kilograms, of the pipe before it was cut? B. 22 C. 24 A. 20
D. 28
61. If the ratio of red to black ribbons in a box is 8 to 9, what fractional part of the ribbon is red? A. 1/9 B. 1/8 C. 8/17
D. 9/17
62. I walk 4 km per hour and run at 6 km per hour. I find I can save 3 minutes and 45 seconds by running instead of walking to school in the mornings. How far do I live from school? A. 0.125 km B. 0.375 km C. 0.75 km
D. 6.9 km
63. Given triangle ABC whose perimeter is 8 cm. If sinA:sinB:sinC = 3:4:5, then the smallest side of the triangle ABC is: A. 1 cm C. 3 cm D. 4 cm B. 2 cm 64. A pyramid whose altitude is 4 feet weighs 600 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. 3.37 feet B. 3.55 feet C. 3.25 feet
D. 3.17 feet
65. I want to cut a long strip of metal into four shorter pieces. If each cut takes twice as long as the previous one, and the first takes one second, how long will the job take? A. 4 s B. 6 s C. 7 s
D. 15 s
66. When the cathedral clock strikes four, it takes 8 seconds between the first and last strokes. How many seconds does it take to strike twelve? D. 29 1/3 A. 18 1/3 B. 22 C. 24 67. LASER is a device for A. producing a beam of white light B. producing a beam of monochromatic and coherent light C. producing a beam of high intensity and incoherent light D. producing highly penetrating X-rays 68. Sky appears blue because A. there is more blue in sunlight than any other color B. short waves are scattered more than the long waves by the atmosphere C. eye is more sensitive to blue D. the atmosphere absorbs long wavelengths more than the short wavelengths 69. A ball is swinging in a circle on a string when the string length is doubled. At the same velocity, the force on the string will be B. one-half as much A. four times as great C. one-fourth as much D. twice as great 70. What is the inverse natural function of the cosecant? A. secant B. sine
C. cosine
71. The higher the frequency of a wave, A. the lower its speed C. the greater its amplitude
B. the shorter its wavelength D. the longer its period
D. tangent
1. The concession stand at Cinema City sells popcorn in three sizes: large, super, and jumbo. One day, Cinema City sold 240 bags of popcorn, and the ratio of large to super to jumbo was 8:17:15. How many super bags of popcorn were sold that day? A. 48 B. 90 C. 102
D. 108
2. Ben and Jen can finish a job together for 5 hrs. If Ben can do the job working alone in 8 hrs, what percent of the job Jen do in 5 hours? A. 37.5% B. 62.5% C. 60.2% D. 35.7% 3. A theatre seats 100 people. Admission is P 5 for men, P 1 for the ladies and 5 centavos each for the children. How many children should there be in a group of men, women and children in order to fill every seat and take in just P 100.00. A. 1 B. 19 C. 60 4. Find the sum of the series 1 – ½ + ¼ - 1/8 + 1/16 + …… A. 2/3 B. 4/3
C. 1.312
D. 80
D. 5/4
5. An observer wishes to determine the height of a tower. He takes sight at the top of the tower from points A and B, which are 50 ft apart, at the same elevation, and on a direct line with the tower. The vertical angle at point a is 30° and at point B is 40°. The height of the tower is B. 92.54 ft A. 89.51 ft C. 95.38 ft 6. The sides of a triangle have a total length of 100 inches. The angles are in the continued proportion 1:2:4. Find the side opposite the smallest triangle. C. 19.80 in A. 20.80 in B. 35.69 in
D. 97.33 ft
D. 17.21 in
7. Find the radius of the circle in which is inscribed in a regular nonagon whose perimeter is 417.6 cm. A. 68.37 cm C. 63.87 D. 68.73 cm B. 67.83 cm 8. If the length of each edge of a cube is increased by 3 cm, its volume is increases by 387 cm 3. Find the length of each edge of the original cube. A. 5 cm B. 6 cm C. 7 cm D. 8 cm 9. Assume that power cables hang in a parabolic arc between two poles 100 ft apart. If the poles are 40 ft high and if the lowest point on the suspended cable is 35 ft above the ground, find the height of the cable at a point 20 ft from the pole.] C. 36.8 ft A. 34.8 ft B. 35.8 ft D. 37.8 ft 10. Evaluate () . A. 0 B. 1/2
C. 1
11. A body moves so that during the first part of its motion its distance S in inches from the starting point is given by the expression S = 6.8t3 – 10.8t (t in seconds). The acceleration in 3 seconds would be A. 172.8 in/s2 C. 61.20 in/s2 B. 122.4 in/s 2
D. 2
D. 212.4 in/s2
12. A force that increases uniformly at the rate of 6 lbf/sec from a value of 1 lbf when t = 0 acts on a 32.2 lbm body initially at rest. Find s in terms of t. B. s = t 3 + 0.5t 2 A. s = 2t 3 + t2 C. s = t3 + t2 D. s = 2t3 - t2 13. A train running at 60 kph decelerated at 2 m/min2 for 15 minutes. Determine the distance traveled in km. A. 12.4 B. 20.3 C. 13.8 14. Find the inverse laplace transform of [ 2/(s + 1) ] - [ 4/(s + 3) ]. -t -3t B. e-2t – e-3t A. 2 e – 4 e 2e-3t)
C. e-2t + e-3t
D. 14.8
D. (2 e-t) (1-
15. If three sticks are drawn from 5 sticks whose lengths are 1, 3, 5, 7 and 9, what is the probability that they will form a triangle? C. 0.30 A. 0.24 B. 0.21
D. 0.36
16. Three cards are drawn from a deck of 52 cards without replacement. Find the probability that all are of the same color. B. 0.3523 C. 0.3325 D. 0.2335 A. 0.2353 17. What velocity in m/s did an airplane take off from a landing field that has a run of 500 m if it starts from rest, moves with constant acceleration and makes the run in 30 sec? A. 33.33 m/s B. 45.15 m/s C. 56.67 m/s
D. 66.67 m/s
2
18. Starting from rest a accelerated at 2 m/s for 5 seconds, then with constant velocity for 10 seconds, then accelerated again at 1 m/s2 for 15 seconds, then accelerated at 2 m/s 2 until it comes to rest. Find the total distance traveled. C. 543.75 m A. 350.25 m B. 420.75 m
D. 582.25 m
19. Find the angular acceleration of a rotating shaft if its angular speed increases from 10 rpm to 200 rpm in 30 seconds. 2 B. 0.74 rad/s2 C. 0.78 rad/s2 A. 0.66 rad/s
D. 0.81 rad/s2
20. The type of loading where failure occurs: A. high load B. repeated load 21. Sound does not travel through A. solids B. liquids
C. gases
22. In a hyperbola, which axis is parallel to the directrix? A. semi-minor axis B. conjugate axis
C. plane load
D. static load
D. a vacuum
C. semi-major axis D. transverse axis
23. Who in the Philippine Senate was the main proponent of the Chemical Engineering Law of 2004? A. Ramon Magsaysay C. Franklin Drilon B. Aquilino Pimentel D. Loren Legarda 24. Which of the following quantities is independent of the size and shape of an object composed of a given material? A. volume B. mass C. weight D. density 25. The copying of an invention of another person without his/her permission A. piracy B. plagiarism C. infringement
D. xerox
26. A piece of weighed wood just floats in water. When placed in alcohol (of lower density) it will B. float higher C. stay as before D. sink A. float lower 27. Ecological Solid Waste Management Act A. RA 6969 B. RA 8749
C. RA 9003
D. PD 984
28. A deposit of P 300 was made one year ago into account paying monthly interest. If the account now has P 320.52, the affective annual interest rate is closest to A. 7% B. 10% C. 12% D. 15% 29. A man inherited a regular endownment of P 100,000 every end of 3 months for x years. However he may choose to get a single lump of P 3,702,939.80 at the end of 4 years. If the rate of interest was 14% compounded quarterly, what is the value of x? A. 13 C. 12 B. 10
D. 11
30. A man bought an equipment which cost Php 524,000. Freight and installation expenses cost him Php 31,000. If the life of the equipment is 15 years, with an estimated salvage value of Php 120,000. Find its book value after 8 years. A. Php 323,000 B. Php 244,000 C. Php 259,000 D. Php 412,000 1. Two masses collide in a perfectly inelastic collision. Mass 1 is traveling at 10 m/s to the right while mass 2 at 20 m/s to the left. If the mass of mass 1 is 4 times the mass of mass 2, find the velocity and direction of the resulting combined mass. A. the mass is stationary C. 4 m/s to the right B. 5 m/s to the left D. 10 m/s to the right 2. A 20-kg board serves as seesaw for two children. One child has a mass of 30-kg and sits 2.5 m from the pivot point. At what distance from the pivot point must a 25-kg child place herself to balance the seesaw? Assume the board is centered at the pivot. B. 3.0 m A. 2.6 m C. 2.8 m D. 2.0 m 3. In a roadwork, 12 laborers could finished it in 17 days. After 11 days, 5 laborers quit the work and are not replaced until 4 days. How many more laborers should be added to complete the job on time? C. 15 A. 10 B. 12
D. 18
4. Two turtles A and B start at the same time towards each other at a distance of 150 m from each other. The rate f the turtle A is 10 m/s while that of B is 20 m/s. A fly named Agamemnon flies from one turtle to another at the same time that the turtle starts to move towards each other. The rate of the fly is 100 m/s. Find the total distance traveled by the fly until the two turtles meet. B. 500 m A. 400 m C. 600 m D. 700 m 5. What is the future worth of an equal quarterly payment series of $2,500 for 10 years if interest rate is 9% compounded monthly? A. F = $ 158,653 B. F = $ 151,930 C. F = $ 154,718 D. F = $ 160,058 6. What government agency supervises the Bureau of Patents, Trademarks and Technology transfer? B. DTI A. DOST C. DSWD D. DPWH 7. No one can practice Chemical Engineering in the Philippines unless licensed by A. LTO C. DOST D. PIChE B. ChE Board
8. Two cars having equal weights of 135 kN are traveling on a straight horizontal track with velocities of 3 m/s to the right and 1.5 m/s to the left respectively. They collide a nd are coupled during impact. Neglecting friction due to sliding, determine their final common velocity. A. 0.75 m/s B. 1.2 m/s C. 0.56 m/s
D. 1.5 m/s
9. The reciprocal of uniform series compound amount factor is C. capital recovery factor A. sinking fund factor B. present worth factor D. future worth factor 10. Annual maintenance costs for a particular section of highway pavement are P 2000. The placement of a new surface would reduce the annual maintenance cost to P 500 per year for the first five years and to P 1000 per year for the next 5 years. The annual maintenance after 10 years would again be P 2000. If maintenance costs are the only saving, what maximum investment can be justified for the new surface. Assume interest at 4%. A. P 5,500 B. P 7,170 C. P 10,000
D. P 10,340
11. A ball is thrown by a player from a position 2 m above the ground surface with a velocity of 40 m/s inclined at 60 to the horizontal. Determine the maximum height, H, the ball will attain. A. 63.2 m B. 61.2 m C. 30.6 m D. 31 m
12. A car starting from rest moves with a constant acceleration of 10 mi/hr 2 for 1 hour, then decelerates at a constant rate of -5mi/hr 2 until it comes to a stop. How far has it traveled? A. 10 mi C. 20 mi D. 25 mi B. 15 mi 13. Six years ago, the sum of the ages of Megie and Vince is equal to 18. Four years from now, twice Vince age is equal to Megie’s age plus 28. How old is Vince and Megie? B. 16, 14 C. 14, 16 D. 20, 12 A. 18, 12 14. The ratio of annual sales to the average of assets used in producing these sales. A. asset turnover B. inventory turnover C. operating-expense ratio D. quick ratio 15. Carlos and Juan set out to run. Carlos ran 9 kilometers per hour while Juan ran 8.5 kilometers per hour. In the same amount of time, Carlos run ½ kilometer further than Juan. How long did they run? B. 1 hr A. ½ hr C. 1 ½ hr D. 10 hr 16. Jim’s grandma gives him 36 foreign stamps to start his collection. He collects twelve more each week. How many weeks will it take for his collection to grow to 216 stamps? B. 18 C. 21 A. 15
D. 24
17. The captain of a ship views the top of a lighthouse at an angle of 60 with the horizontal at an elevation of 6 meters above sea level. Five minutes later, the same captain of the ship views the top of the same lighthouse at an angle of 30 with the horizontal. Determine the speed of the ship if the lighthouse is known to be 50 meters above sea level. A. 0.265 m/s B. 0.155 m/s C. 0.169 m/s
D. 0.210 m/s
2
2
18. Find the area bounded by the curve y = x and x = y . A. 1/3 B. 2/3
C. 8/3
D. 1
19. A bacterial population B is known to have a rate of growth proportional to B itself. If between noon and 2 PM the population triples, at what time, no controls being exerted, should B become 100 times what it was at noon? B. 10:22 PM C. 3:22 PM A. 8:22 PM
D. 6:22 PM
20. Two cars start from the same point at the same time and travel in the same direction at constant speed of 34 and 45 kph, respectively. If they start at 8:00 a.m., at what time will they be 33 km apart? B. 12:00 nn C. 11:30 a.m. A. 11:00 a.m.
D. 10:00 a.m.
21. Suppose a ball rebounds three-fourths the distance it falls. If it is dropped from a height of 40 feet, how far does it travel before coming to rest? C. 160 A. 80 B. 120
D. 280
22. 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. 6 B. 8 C. 7
D. 9
90
23. What is the units digit of 19 ? A. 0
B. 1
C. 3
D. 7
24. Find the value of k in the quadratic equation 3x 2 – kx + x – 7k = 0 if 3 is one of the roots. B. 5 C. 9 A. 3
D. 14
25. On Tuesday Joel bought 3 tank tops and 4 pairs of shorts for P 14.50 at a sidewalk sale. His cousin Bob bought 5 tank tops and 2 pairs of shorts for P 12.50. If the cost of each tank top was the same and the cost of each pair of shorts was the same, how much did one ta nk top cost? B. P 1.50 A. P 1.00 C. P 2.00 D. P 2.50 26. At approximately what time between the hours of 12:00 noon and 1:00 pm would the angle between the hour hand and the minute hand of a continuously drive clock be exactly 180 ? A. 12:25 p.m. B. 12:30 p.m. C. 12:38 p.m.
D. 12:37 p.m.
27. A number is divided into 3 parts in the ratio of 1:2:3. The number is 258. Find the largest part. C. 129 A. 43 B. 86
D. 172
28. A quiz has twenty questions with seven points awarded for each correct answer, two points deducted for each wrong answer and zero for each questions omitted. Jack scores 87 points. How many questions did he omit? B. 5 A. 2 C. 7
D. 9
29. How many pounds of peanuts should be added to 5 pounds of a 30% peanut mixture of nuts to obtain a nut mixture which is 50% peanuts? A. 1 lb C. 3 lb B. 2 lb
D. 4 lb
30. Helen cycles for 36 miles. If she had managed to go 3 mph faster she would taken one hour less. What was her average speed ( in mph )? B. 9 A. 6 C. 12
D. 18
31. If there are 50 terms in an arithmetic progression, and if the common difference is 1.5. Determine the second term if the last term is 3510. D. 3438 A. 2810 B. 3410.5 C. 2438.5
44. The intersection between the set of integers and the set of whole numbers is A. the set of natural numbers C. the set of integers D. the set of whole numbers B. the set of rational numbers
32. If the roots of an equation are zero, they are classified as C. extraneous roots A. trivial solutions B. conditional solutions D. hypergolic solutions 33. Four comrades are racing side by side down a dusty staircase. Frodo goes down two steps at a time, Gimli three, Legolas four and Aragon five. If the only steps with all four’s footprints are at the top and bottom, how many steps have just one footprint? A. 16 B. 17 C. 20
D. 22
34. In the number 0.00412 there are ______ significant figures. A. 6 B. 5
D. 4
C. 3
35. If the supplement of an angle is 5/2 of its complement, find the angle. B. 25 C. 20 A. 30
D. 15
36. The sides of a triangle are 5, 12 and 13 units respectively. Find the area of the largest circle that can be inscribed in the triangle. D. 18.5 sq. units A. 12.57 sq. units B. 15.28 sq. units C. 17.6 sq. units 37. What is true regarding the signs of the natural functions for angles between 90 and 180 ? A. the tangent is positive B. the cotangent is positive D. the sine is positive C. the cosine is negative
38. An airplane travels 209 km on a straight course, making an angle of 22.5 east of north. It then changes its course by moving 100 km north before reaching its destination. Determine the resultant displacement of the airplane, in km. B. 340 C. 403 A. 304
D. 430
39. A vertical flagpole consist of two segments, the lower being 25 feet and the upper 26 feet in length. Find the distance from the pole where the two segments will subtend equal angles at the height of 5 feet above the base of the pole. B. 187 ft C. 207 ft D. 210 ft A. 166 ft 40. In the trigonometric function 2tanx cos x = √ , the measure of the angle x is _________. A. 30 B. 45 C. 60
D. 90
41. Find x if log of 9 to the base 3 is equal to x. A. ½ B.7
D. 3
C. 2
42. The distance between centers of the two circles having radii of 4 and 8 is 15. How long is the common internal tangent segment? B. 15 C. 18 A. 9
D. 20
43. How many integers between 20 and 30 are prime? B. 3 A. 2
D. 4
C. 3
