Ramon is r years old. His father is one year more than four times as old as Ramon.

How old is his father

5 years ago?

A. 4r B. 4r – 1 C. 4r – 4 D. 4r – 2

Determine the SUM of the positive-valued solutions to the simultaneously equations:

xy = 24 yz = 32 xz = 48

A. 18 B. 16 C. 15 D. 17

If the surface area of a cube is increasing at the rate of 3 sq. m per minute, find the rate at which the
volume is increasing in cu. m per minute when its side is 12 m.

A. 6 B. 7 C. 8 D. 9

A side and a diagonal of a parallelogram are 14 inches and 24 inches respectively. The angle between
the diagonals, opposite the given side is 120o. Find the length of the other diagonal.

A. 6.76 inches B. 17.48 inches C. 8.48 inches D. 9.48 inches

The daily wage of a RME and a CPM are in the ratio 3:1. In a day, a RME has to work 8 hours but the
CPM only 5 hours. The hour wages of a RME and a CPM are in the ratio of _____.

A 14:3 B. 15:8 C. 3:2 D. 8:13

A group of fishermen chartered a boat for 4,500 pesos. Five members of the group were unable to go
the trip and as a consequence, each of the other had to pay 150 pesos more. How many were there in
the original group?

A. 5 B. 10 C. 15 D. 20

In how many minutes after 2:00 pm will hour hand and the minute hand of the clock first form an angle
of 140 degree? A. 11.82 min B. 22.82 min C. 28.28 min D. 36.36 min

The difference of the cubes of two positive numbers is 1647 and the cube of their difference is 27. Find
the larger number.

A. 15 B. 18 C. 21 D. 24

In the expression of (x + 2y)8, the numerical coefficient of the fifth term is _______.

A. 2,360 B. 1,120 C. 3,540 D. 3,810

Solve the differential equation whose general solution is y = C1e-x + C2e2x.

A. y” - y’ - 2y = 0 B. y” + y’ – 6y = 0 C. y” – 5y’ + 6y = 0 D. y” – y’ – 6y = 0

Simplify the following expression: i3217 - i438 + i18

A. 1 + 2i B. –i C. i D. 1 + i

Find the two positive numbers whose sum is 10 if the product of one number by the cube of the other
number is to be maximum.
 A. 3 and 7 B. 3 and 8 C. 7.5 and 2.5 D. 4.5 and 5.5

Two ships leave a dock at the same time. One sails northeast at the rate of 10 mph, the other sails
north at the rate of 13 mph. How many miles apart are they at the end of 2 hours?

A. 11.4 B. 18.5 C. 13.4 D. 24.4

Solve the differential equation: (D3 - 8)y = 0

A. y = C1e-2x + ex(C2 + C3x) B. y = C1e2x + e-x(C2 + C3x)

C. y = C1e-2x + ex(C2sin1.732x + C3cos1.732x) D. y = C1e2x + e-x(C2sin1.732x + C3cos1.732x)

What is the integral of 20 sin7x cos6x dx if the lower limit is zero and the upper limit is π/2?

A. 0.057 B. 0.106 C. 0.158 D. 0.209

Find the ∫ 𝑒 𝑥 𝑠𝑖𝑛𝑥 𝑑𝑥

A. –e-x(sinx – cosx) + C B. ex(sinx – cosx) + C

C. -1/2 ex(sinx – cosx) + C D. ½ ex (sinx – cosx) + C

. If y = 4 tanh x + sinh 2x, what is the slope of the curve when x = 3?

A. -154.9 B. -228.2 C. 354.9 D. 403.47

𝑥 2 −1
Find lim
𝑥→∞ 𝑥 3 −1

A. 0 B. 2/3 C. 1 D. indeterminate

Find the derivative of the function: f(x) = ln coshe2x

A. 2e2xcothe2x B. -2e2xcothe2x C. 2e2xtanhe2x D. -2e2xtanhe2x

Given: A = 3i – 4j + 5k, B = 2i + 3j – 6k, C = -4i + 7j – 3k. Determine (𝐴𝑥𝐶) ∙ 𝐵

A. 85 B. 93 C. -109 D. 109

What is the probability that of 6 cards dealt from a well-shuffled deck, 4 will be face card and two will be
non-face card?

A. 0.01897 B. 0.02897 C. 0.03897 D. 0.04897

Find the variance of the following data: 3, 7, 6, 4, 8, 10, 12, 5

A. 9.267 B. 9.91 C. 10.86 D. 11.52

Determine the area of the triangle bounded by the straight lines x + 2y – 6 = 0, 3x – 4y – 2 = 0, 2x – y + 5

= 0.

A. 11.88 sq units B. 20 sq units C. 16.20 sq units D. 25 sq. units

Express in gradient the angle between the hands of a clock at 6:50 PM.
 A. 65.3 B. 72.5 C. 105.6 D. 180.6

Find the possible factors of x4 – x3 – 7x2 + x + 6.

A. (x – 1) B. (2x – 1) C. (x - 3) D. A or C

The function f(x) = (x – 4)/(x3 – 2x2 – 5x + 6) is discontinuous at x = ?

A. -2 B. 1 C. 3 D. All of these

During a rain, 3 mm of water fell. Find how many gallons of water fell on a level 10-acre park.

A. 21,381 B. 25,381 C. 27,381 D. 32,076

Find the distance between the given line and point 3x – y = 0 and P(2, 4).

A. 0.153 unit B. 0.345 unit C. 0.496 unit D. 0.632 unit

Find the area bounded by connecting the points (1, 1), (4, 5), (0, 8) and (-3, 4).

A. 20 sq. units B. 25 sq. units C. 30 sq. units D. 35 sq. units

Find the abscissa of point of inflection of y = 2x6 – 6x4.

A. 1.095 B. 2.095 C. 3.095 D. 4.095

Find the equation of normal line to the graph y = x2 + 1 at point (1, 2).

A. 2y + x – 5 = 0 B. 2y + x + 5 = 0 C. 2y + 5x – 5 = 0 D. 8y + x – 5 = 0

Find the equation of tangent line to the graph y = 2x3 + 4x2 – 5x – 3 at point (-1, 4).

A. 3y + 7x + 3 = 0 B. y - 7x + 3 = 0 C. y + 7x + 3 = 0 D. y + 7x + 6 = 0

Find the 5th term of (m – 2p)12.

A. 5920 m8p4 B. 3920 m8p4 C. 7920 m8p4 D. 9920 m8p4

Tom can run 6 miles per hour, while Roy runs 4 miles per hour. If they start running at the same time
and same point in opposite direction, how long would it take them to be ¾ mile apart?

A. 3.0 min B. 3.5 min C. 4.0 min D. 4.5 min

A stereo on sale for 15% off. The sale price is $425. What was the original price?

A. $450 B. $500 C. $550 D. $600

A triangle has a perimeter of 30 cm. Two sides of the triangle are both twice as long as the shortest
side. Find the length of the shortest side.

A. 6 cm B. 8 cm C. 10 cm D. 12 cm

Helen can paint the room in 5 hr. Jay can paint the same room in 4 hr. How long will it take them to
paint the room together?
 A. 1.11 hrs B. 2.22 hrs C. 3.33 hrs D. 4.44 hrs

What is the addendum of a gear having a module of 3?

A. 0.234 in B. 0.198 in C. 0.345 in D. 0.118 in

Find the length of the side of heptagon whose perimeter is 28 inches.

A. 1 B. 2 C. 3 D. 4

The parabola y2 – 6y + 4x – 14 = 0 opens _________.

A. Right B. Left C. Upward D. Downward

Find the area of circle x2 + y2 -8x – 6y - 11 = 0

A. 32π B. 34π C. 36π D. 38π

Find the slope of line y = 4x + 3.

A. 3 B. 4 C. 5 D. 6

What is the geometric mean of 4 and 9?

A. 3 B. 4 C. 5 D. 6

A 75 mm diameter shaft is transmitting 300 KW at 600 rpm. A flange coupling is used and has 6 bolts,
each 18 mm in diameter. Find the required diameter of the bolts circle based on an average shearing
stress of 27.5 Mpa.

A. 227.4 mm B. 477.2 mm C. 274.7 mm D. 247.7 mm

A 1200 mm cast iron pulley is fastened to 112.5 mm shaft by means of a 28.13 mm square key 175 mm
long. The key and shaft have a shearing stress of 14,000 psi. Determine the force acting at the pulley
that will shear the key.

A. 10,015 lb B. 11,005 lb C. 11,050 lb D. 10,501 lb

A 4 inches shaft using a flat key, whose width is 1 inch, is transmitting a torque of 63,000 in-lb. If the
designed shearing stress is 5000 psi, determine the safe length of key.

A. 6.3 inches B. 5.3 inches C. 4.3 inches D. 7.0 inches

A steel rod 30 mm & 800 mm long has an allowance elongation not to exceed 1.5 mm, find the
allowable load in kN.

A. 274 B. 248 C. 316 D. 236

A round steel shaft rotates at 200 rpm and is subjected to a torque of 275 N-m and a bending moment
of 415 N-m. Determine the equivalent twisting moment.

A. 597.84 N-m B. 456.42 N-m C. 546.43 N-m D. 497.85 N-m

A flange bolt coupling has 10 steel 25.4 mm diameter bolts evenly tighten around a 415 mm bolt circle.
Determine the torque capacity of the connection if the allowable shearing stress in the bolt is 50
MN/m2.

A. 59.95 KN-m B. 52.6 KN-m C. 46.15 KN-m D. 43. 8 KN-m

A hollow steel shaft 80 mm outside diameter and 60 mm inside diameter is designed to deliver 80 kw
power at 450 rpm. Find the torsional deflection per meter length. Use G = 79.3 GPa

A. 0.426o B. 0.328o C. 0.583o D. 0.755o

The total force of 125 KN is required for a flange coupling that has 5 bolts has also a shearing stress of 30
Mpa for bolt. Determine the required bolt diameter.

A. 62.54 mm B. 54.21 mm C. 45.62 mm D. 32.57 mm

A main transmitting shaft transmits 350 KW to drive a generator at 2500 rpm, what is the required
diameter of the shaft?

A. 58.5 mm B. 62.7 mm C. 65.3 mm D. 56.2 mm

Find the angular acceleration of the shaft whose speed changes from 0 to 2500 rpm in 5 seconds.

A. 23.47 rad/s2 B. 34.23 rad/s2 C. 52.36 rad/s2 D. 65.34 rad/s2

A 12 ft length steel lineshaft has no bending action except it own weight. What power in Hp can the
shaft deliver at a speed of 2000 rpm. Consider a torsional deflection of 0.08o/ft length.

A. 25.95 B. 12.34 C. 17.34 D. 98.23

A steel shaft has an angular deflection of 5o. The shaft torque is 2.5 KN.m. If the shaft length is 20 times
the shaft diameter, find the shaft diameter.

A. 32.17 mm B. 41.92 mm C. 87.56 mm D. 56.34 mm

A line shaft is to transmit 200 HP at 900 rpm. Find the diameter of the shaft.

A. 2.18 in B. 2.28 in C. 3.18 in D. 3.28 in

Compute the working strength of 1 1/2 in bolt which is screwed up tightly in packed joint when the
allowable working stress is 13,000 psi.

A. 11,465.5 lbs B. 13,860.5 lbs C. 11,212.5 lbs D. 11,854.5 lbs

A 10 inches diameter gear is use to transmit 20 kw at 900 rpm. Determine the tangential force on each
gear. A. 1.761 KN B. 1.671 KN C. 1.842 KN D. 2.614 KN

An air cylinder has a bore of 25 mm and is operated with shop air at a pressure of 90 psi. Find the push
force exerted by the piston rod, in N.

A. 127 B. 70 C. 402 D. 305

Find the distance between centers of a pair of gears, one of which has 12 teeth and the other 37 teeth.
The diametral pitch is 7.
 A. 3.0 in B. 3.5 in C. 4.0 in D. 4.5 in

What is the addendum of a gear having a module of 3?

A. 0.234 in B. 0.198 in C. 0.345 in D. 0.118 in

A square thread screw has an efficiency of 70% when friction of threads is 0.10 and collar friction is
negligible. Determine the lead angle.

A. 12.6o B. 16.5o C. 14.3o D. 18.3o

A thrust washer has an inside diameter of 0.5 inch and an outside diameter of 3 in. For an allowable
bearing pressure of 90 psi, how much axial load can it sustain?

A. 618.5 lb B. 537.2 lb C. 702.2 lb D. 871.2 lb

Find the clearance of a 14.5o involute gear having a module of 2.5

A. 0.0534 in B. 0.0246 in C. 0.0154 in D. 0.1345 in

An internal gear has a center distance of 20 in. If speed ratio is 3, find the diameter of internal gear.
A. 18 in B. 22 in C. 20 in D. 24 in

A thermometer reading 75oF is taken out where the temperature is 20oF. The thermometer reading is
30oF after 4 minutes later. Find the thermometer reading in oF, 6 minutes after the thermometer was
brought outside.

A. 21.8 B. 22.8 C. 23.8 D. 24.3

A weight of 100 lbs strikes a coil spring from a height of 18 inches and deflects the spring of 6 inches.
Find the average force acting on the spring.

A. 600 lbs B. 800 lbs C. 400 lbs D. 900 lbs

An internal gear has a center distance of 20 in. If speed ratio is 3, find the diameter of internal gear.
A. 18 in B. 22 in C. 20 in D. 24 in

Find the clearance of a 14.5o involute gear having a module of 2.5

A. 0.0534 in B. 0.0246 in C. 0.0154 in D. 0.1345 in

A thrust washer has an inside diameter of 0.5 inch and an outside diameter of 3 in. For an allowable
bearing pressure of 90 psi, how much axial load can it sustain?

A. 618.5 lb B. 537.2 lb C. 702.2 lb D. 871.2 lb

A square thread screw has an efficiency of 70% when friction of threads is 0.10 and collar friction is
negligible. Determine the lead angle.

A. 12.6o B. 16.5o C. 14.3o D. 18.3o

What is the geometric mean of 4 and 9?

A. 3 B. 4 C. 5 D. 6
Find the slope of line y = 4x + 3.

A. 3 B. 4 C. 5 D. 6

Find the area of circle x2 + y2 -8x – 6y - 11 = 0

A. 32π B. 34π C. 36π D. 38π

The parabola y2 – 6y + 4x – 14 = 0 opens _________.

A. Right B. Left C. Upward D. Downward

Find the length of the side of heptagon whose perimeter is 28 inches.

A. 1 B. 2 C. 3 D. 4

Which of the following has four significant figures?

A. 0.0014 B. 0.01414 C. 0.141 D. 1.4140

𝑖𝜋
What is the product of the complex numbers 2 − 2𝑖 and √32𝑒 4

A. 16 B. 16i C. e D. 14

The numbers has a ratio of 2 : 5 : 8. If the sum of the numbers is 60, what is the larger number?

a. 36

b. 32

c. 24

d. 22

A car travels 100 miles to city A in 3 hours, then travels 200 miles to city B in 4 hours. What is the
average speed of the car for the trip?

a. 45 mph

b. 58.3 mph

c. 60 mph

d. 42.85 mph

Tukmol can paint a fence of 50% faster than Kikoy and 20% faster than Tiburcio and together they can
paint a given fence in 4 hours. How long will it take Tukmol to paint the same fence if he had to work
alone?

a. 11

b. 8

c. 9

d. 10
Crew A can clean the Megadome in 8 hours and crew B can clean it in 12 hours. After a night game,
Crew A began a cleanup at midnight and was joined by crew B at 2:00 am. When was the job
completed?

e. 4:23 AM

f. 5:36 AM

g. 6:00 AM

h. 6:30 AM

John is four times as old as Harry. In six years, John will be twice as old as Harry. What is the age of
Harry now? (April 2004)

a. 2

b. 3

c. 4

d. 5

Two thousand (2000) kg of steel containing 8% nickel is to be made by mixing a steel containing 14%
nickel with another containing 6% nickel. How much of each is needed?

a. 1300 and 700

b. 1200 and 800

c. 1000 and 1000

d. 500 and 1500

Two runners run in a 500 m diameter circular track field at the same point and opposite direction. If one
runner has a rate of 1 m/sec and the other has 1.5 m/sec, find the time they will meet.

a. 10.47 minutes

b. 16.48 minutes

c. 20.47 minutes

d. 24.67 minutes

Karen drove a certain distance at an average speed of 80 km/hr and then another distance at 84 km/hr.
If the total distance traveled was 450 km and the total traveling time was 5.5 hr, find the distance she
traveled at 84 km/hr.

a. 200 mph

b. 210 mph

c. 220 mph
 d. 230 mph

A man can row 6 mph in still water. If it takes him 3 hours to row 8 miles downstream and then back,
what is the rate of the current?

a. 1 mph

b. 2 mph

c. 3 mph

d. 4 mph

A radiator contains 8 liters of a 40% anti freeze solution. How many liters of pure anti freeze must be
added to obtain a 50% solution?

a. 1.6 li

b. 1.8 li

c. 2.0 li

d. 2.2 li

Four different colored flags can be hung in a row to make coded signal. In how many ways can have a
display of two or more flags?

a. 30

b. 40

c. 50

d. 60

How many different committees of 6 can be formed from 12 boys and 8 girls if each committee is
consisting of 4 boys and 2 girls? (April 2007)

A. 2970

B. 13860

C. 15820

D. 27720

What is the probability of picking an orange ball and a white ball out of a bag containing seven orange
balls, eight green balls, and two white balls?

a. 0.071
 b. 0.10

c. 0.3

d. 0.53

What is the probability that either two heads or three heads will be thrown if six fair coins are tossed at
once?

a. 0.35

b. 0.55

c. 0.5

d. 0.63

Three standard 52-card decks are used in a probability experiment. One card is drawn from each deck.
What is the probability that a diamond is drawn from the first deck, an ace from the second, and the ace
of hearts from the third?

a. 0.000062

b. 0.00015

c. 0.00037

d. 0.0062

Two die are rolled. Find the probability that the sum of the two die is 9?

a. 0.11111

b. 0.12345

c. 0.2222

d. 0.3345

A bag contains 100 balls numbered 1 to 100. One ball is drawn from the bag. What is the probability that
the number on the ball selected will be odd or greater than 80?

a. 0.10

b. 0.50

c. 0.60

d. 0.70

For the given numbers 4, 5, 6, 6, 6, 8, 7, 7, 9. What is the mode?

a. 6

b. 7
 c. 8

d. 5

For the given numbers 4, 5, 6, 6, 6, 8, 7, 7, 9. What is the median?

a. 6

b. 7

c. 8

d. 5

For the given numbers 4, 5, 6, 6, 6, 8, 7, 7, 9. What is the mean?

a. 6.44

b. 7.44

c. 8.44

d. 5.44

For the given numbers 4, 5, 6, 6, 6, 8, 7, 7, 9. What is the RMS value?

a. 6.60

b. 7.60

c. 8.60

d. 5.60

For the given numbers 4, 6 and 8. What is the standard deviation?

a. 1.63

b. 4

c. 2.5

d. 6

For the given numbers 4, 6 and 8. What is the standard deviation of sample?

a. 1.63

b. 4

c. 2.5

d. 2

For the given numbers 4, 6 and 8. What is the standard variance?

a. 1.63
 b. 4

c. 2.5

d. 6

What is the sum of the following finite sequence of terms? 18, 25, 32, 39, …., 67

a. 300

b. 320

c. 310

d. 340

What is the sum of the following finite sequence of terms? 32, 80, 200, ….., 19531.25

a. 32035.50

b. 32530.75

c. 53230.75

d. 23570.50

In a survey of 10 smokers, it was disclosed that 7 smokes M, 5 smoke H, 3 smoke W, it was further
disclosed that 3 smoke M & H, 2 M & W , 2 H & W, 1 M,H,W. How many smoke M only?

a. 1

b. 2

c. 3

d. 4

In a survey of 10 smokers, it was disclosed that 7 smokes M, 5 smoke H, 3 smoke W, it was further
disclosed that 3 smoke M & H, 2 M & W , 2 H & W, 1 M,H,W. How many smoke W only

a. 1

b. 2

c. 0

d. 4

In a survey of 10 smokers, it was disclosed that 7 smokes M, 5 smoke H, 3 smoke W, it was further
disclosed that 3 smoke M & H, 2 M & W , 2 H & W, 1 M,H,W. How many smoke M, H and W

a. 1

b. 2

c. 3
 d. 4

In a survey of 10 smokers, it was disclosed that 7 smokes M, 5 smoke H, 3 smoke W, it was further
disclosed that 3 smoke M & H, 2 M & W , 2 H & W, 1 M,H,W. How many smoke M or H nor W

a. 1

b. 2

c. 3

d. 6

In a survey of 10 smokers, it was disclosed that 7 smokes M, 5 smoke H, 3 smoke W, it was further
disclosed that 3 smoke M & H, 2 M & W , 2 H & W, 1 M,H,W. How many smoke M and H nor W

a. 1

b. 2

c. 3

d. 4

The capsule orbits the earth 160 km above the surface. In what velocity in m/s necessary for a circular
orbit consider the earth radius at 6400 km and at 9.6 m/s2?

A. 8864 B. 7016 C. 7780 D. 7936

A simply supported beam is 50 mm by 150 mm in cross section and 5 m long. If the flexural stress is not
to exceed 8.3 Mpa, find the maximum mid-span concentrated load.

A. 0.623 KN B. 0.987 KN C. 0.0345 KN D. 1.245 KN

A vertical load of 1000 N acts at the end of a horizontal rectangular cantilever beam 3 m long and 30
mm wide. If the allowable bending stress is 100 Mpa, find the depth of the beam.

A. 23.45 mm B. 38.43 mm C. 77.46 mm D. 45.34 mm

Two shafts 3.6 m between centers carry pulleys 1.2 m in diameter and 0.91 m in diameter in diameter
respectively, connected by a cross belt. It is desired to put the belt on as an open belt. How long a piece
must be cut of it?

A. 300 mm B. 350 mm C. 400 mm D. 250 mm

A pulley has a belt pull of 2.5 KN. If 20 Hp motor is use to drive the pulley, determine the belt speed.

A. 19.58 ft/sec B. 5.97 ft/sec C. 7.42 m/sec D. 10.86 m/sec

A pulley have an effective belt pull of 3 KN and an angle of belt contact of 160 degrees. The working
stress of belt is 2 Mpa. Determine the thickness of belt to be used if width is 350 mm and coefficient of
friction is 0.32. A. 6.42 mm B. 7.24 mm C. 8.68 mm D. 9.47 mm
A pulley 600 mm in diameter transmits 50 KW at 600 rpm by means of belt. Determine the effective
belt pull. A. 2.65 KN B. 3.65 KN C. 4.65 KN D. 5.65 KN

The cone angle of pinion and the gear are 25o and 65o respectively. Find the speed ratio.

A. 1.5 B. 5.2 C. 4.23 D. 2.14

The cone angle of pinion of a pair of bevel gear is 30o while for the gear 60o. If the pinion turns at 300
rpm, find the speed of the gear.

A. 173.21 rpm B. 183.21 rpm C. 193.21 rpm D. 203.21 rpm

What modulus of elasticity in tension is required to obtain a unit deformation of 0.00105 from a load
producing a unit tensile stress of 45,000 psi?

A. 40 x 106 psi B. 43 x 106 psi C. 45 x 106 psi D. 46 x 106 psi

A spring has load of 50 lb with a spring index of 8. If stress induced is 90,000 psi, determine the wire
diameter.

A. 0.058 in B. 0.452 in C. 0.828 in D. 0.1157

A shear pin is to be shear at 15 hp and 1000 rpm. The pin attaches a hub to a shaft 1.5 inches in
diameter and ultimate shearing stress of 50,000 psi. Find the diameter of the pin.

A. 1/8 in B. ¼ in C. ¾ in D. 1 in

A beam of circular cross-section is 7 inches in diameter. It is simply supported at each end and loaded by
two concentrated loads of 20,000 lb each, applied 12 in from the ends of the beam. Determine the
maximum bending stress in the beam in lb/in2.

a. 7,127

b. 10,690

c. 14,254

d. 3, 563

A cantilever of rectangular section is 100 mm broad by 150 mm deep and carried a concentrated load of
15 KN at its free end. Neglecting the weight of the beam, find the distance from the free end where the
stress at the outer fiber is 75 MN/m2.

a. 1.875 m

b. 0.875 m

c. 2.785 m

d. 3.785 m

A beam of regular rectangular-section is 64 mm broad by 100 mm deep and 1.6 m long. It is simply
supported at each end and carries a concentrated load of 10 KN at its mid-length. Neglecting the weight
of the beam, find the maximum stress in the material.
 a. 35.7 Mpa

b. 57.3 Mpa

c. 53.7 Mpa

d. 37.5 Mpa

The flow rate of water through a cast iron is 5000 gallons per minute. The diameter of the pipe is 1 foot,
and the coefficient of friction is f = 0.0173. What is the pressure drop over a 100 foot length of pipe?

a. 21.078 lb/ft2

b. 23.78 lb/ft2

c. 337.26 lb/in2

d. 337.23lb/ft2

A rigid container is closed at one end and measures 8 in diameter by 12 in long. The container is held
vertically and is slowly moved downward until the pressure in the container is 17 psia. What will be the
depth of the top of the water in the container from the free water surface?

a. 63.69 in

b. 73.69 in

c. 83.69 in

d. 93.69 in

A gourmet ice cream store has fixed expenses (rent, utilities, etc) of $50,000/year. Its two full- time
employees each $25,000 per year. There is also a part-time employee who makes $14,000 plus $6000 in
overtime if sales reach $120,000 in a year. The ice cream costs $4/L to produce and sells for $7/L. What
is the minimum number of liters the store must sell to break-even?

a. 40000

b. 30000

c. 38000

d. 35000

A steel drum manufacturer incurs a yearly fixed operating cost of $220,000. Each drum manufactured
costs $150 to produce and sells for $200. What is the manufacturer’s break-even sales volume in drums
per year?
 a. 4400

b. 3200

c. 2600

d. 2650

For the effective rate of 12%, find the nominal interest rate if compounded semi-annually.

a. 11.66%

b. 12.13%

c. 13.56%

d. 15.99%

What is the effective rate equivalent of 12% compounded quarterly?

a. 12.55%

b. 11.55%

c. 12.98%

d. 13%

Cleofatra borrowed P2,000.00 from a bank and agreed to pay the loan at the end of one year. The bank
discounted the loan and give P1950 in cash. Determine the rate of discount.

a. 3.75%

b. 3.12%

c. 2.5%

d. 1.2%

Determine the exact simple interest on P5,500.00 for the period from January 10,1996 to October
28,1996 at 11% interest

a. P482.68

b. P287.00

c. P532.88

d. P498.58

Find the area of ellipse x2/9 + y2/16 = 1

 A. 10π B. 11π C. 12π D. 13π

A bacteria culture grows exponentially so that the initial number is double in 2 hours. How many times
the initial number will be present after 12 hours?

A. 36 B. 48 C. 52 D. 64

Find the compound amount if P7500 is invested at 15% compounded quarterly for 7 years and 6
months.

A. P18,204.47 B. P22,631.00 C. P38,204.47 D. P48,204.47

A sum of money is deposited now in a savings account. The effective annual interest rate is 12% and
interest is compounded monthly. How much money must be deposited to yield P1,500.00 at the end of
10 months?

A. P1364.83 B. P1551.99 C. P2351.99 D. P3351.99

What is the present worth of 60,000 due in 5 years if money is worth 12% and is compounded semi-
annually?

A. P33,504.00 B. P29,111.63 C. P39,111.63 D. P49,111.63

What is the capitalized cost of a project that will cost P20,000,000 now and will require P3,000,000 in
maintenance annually? The effective annual interest rate is 12%.

A. P30,000,000 B. P45,000,000 C. P50,000,000 D. P60,000,000

If P20,000 is invested now, and P40,000 four years from now (all at 5%), what will be the total amount in
nine years?

A. P82,078.00 B. P130,505.37 C. P230,505.37 D. P330,505.37

A savings certificate that costs P5000 now will pay P9000 in five years. What is the interest rate?

A. 9.85% B. 11.85% C. 12.47% D. 25.55%

A company pays 2.5% interest quarterly. What is the effective annual interest rate?

A. 10.38% B. 14.75% C. 17.45% D. 24.75%

What is the working strength of a 1.5 inches bolt which is screwed up tightly in a packed joint when the
allowable working stress is 15,000 psi.

A. 12,937.5 lbs B. 10,345.6 lbs C. 14,345.6 lbs D. 16,345.5 lbs

An eye bolt is lifting a weight of 1000 lbs. The eyebolt has an ultimate stress of 70 ksi and Sy = 60 ksi.
What is the required stress area of this bolt in in2.

A. 0.082 B. 0.172 C. 0.215 D. 0.534

Compute how many 1/4 inch diameter set screws required to transmit 5 hp at a shaft speed of 900 rpm.
The shaft diameter is 1.5 in.
 A. 1 B. 2 C. 3 D. 5

Determine the stress area in in2 of a 2-4UNC bolt.

A. 1.42 in2 B. 1.86 in2 C. 2.42 in2 D. 2.58 in2

A keyed gear deliver a torque of 1.2 KN-m thru its shaft of 65 mm outside diameter. If the key has
thickness of 16 mm and width of 12 mm, find the length of the key. Assume the permissible stress
values of 62 Mpa for shear and tension of 99.8 MPa.

A. 4.624 cm B. 3.23 cm C. 4.96 cm D. 5.34 cm

A flange coupling has ten (10) steel 25.4 mm diameter bolt evenly tightened around a 450 mm bolt
circle. Determine the torque capacity if allowable shearing stress is 50 Mpa.

A. 27 KN-m B. 37 KN-m C. 47 KN-m D. 57 KN-m

A coupling whose bolt circle diameter is 80 cm contains 10 bolts. The torsional shearing stress of the 100
mm diameter shaft is 40 Mpa and for the bolt is 35 Mpa. The compressive stress of the bolt is 70 Mpa.
Find the flange thickness of the coupling.

A. 1.23 mm B. 5.23 mm C. 3.32 mm D. 7.23 mm

A flange coupling has eight (8) steel 25.4 mm diameter bolt evenly tightened around a 450 mm bolt
circle. Determine the torque capacity if allowable shearing stress is 50 Mpa.

A. 32.34 KN-m B. 45.60 KN-m C. 54.23 KN-m D. 64.56 KN-m

A 25.4 mm diameter shaft with 2 m length has a modulus of rigidity of 80 Gpa. If maximum twist is 2o,
find the maximum torque developed by the shaft.

A. 57.056 N-m B. 45.237 N-m C. 60.234 N-m D. 49.340 N-m

A hollow steel shaft has an inner diameter of 70 mm and wall thickness of 12 mm. If torque transmitted
is 3 KN-m, find the torsional deflection in rad/m.

A. 0.00713 rad B. 0.0243 rad C. 0.0343 rad D. 0.0443 rad

Find the horsepower needed for a steel line shaft of 24 ft turning at 450 rpm subjected no bending
action except its own weight. Consider 0.08 deg/ft length.

A. 45.67 B. 373.68 C. 234 D. 595

A steel line shaft has a length of 10 ft with no bending action except its own weight. Find the shaft
diameter.

A. 1.02 in B. 1.18 in C. 1.23 in D. 1.45 in

A bolt made of carbon steel has an applied load of 500 lbs. Find the stress area of the bolt.

A. 0.845 in2 B. 0.453 in2 C. 0.234 in2 D. 0.197 in2

A shaft is used to transmit 30 hp at 450 rpm. If deflection of shaft is 0.08 deg/ft length of shaft, find the
shaft diameter. Using G = 11.5 x 106 psi
 A. 1.72 B. 2.38 in C. 3.21 in D. 4.23 in

A shaft whose length is 20 times its diameter has an angular deflection of 1 degree. If torque
transmitted is 3000 in-lb. Find the shaft diameter.

A. 1.44 in B. 2.34 in C. 0.253 in D. 4.34 in

A force tangent to 60 cm diameter pulley is 5 KN and is mounted on a 5 cm shaft. Determine the

torsional deflection per meter if G = 83 x 106 Kpa.

A. 0.804o B. 0.786 C. 0.654 D. 1.69

A hollow shaft that has 110 mm outside diameter and 80 mm inside diameter is used to transmit 120
KW at 600 rpm. Determine the shaft stress.

A. 13.73 MPa B. 10.15 MPa C. 16.82 MPa D. 17.21 Mpa

The shaft of a motor has a length of 20 times its diameter and has a maximum twist of 1 degrees when
twisted at 2.5 KN-m torque. If the modulus of rigidity of the shaft is 80 Gpa, find the shaft diameter.

A. 71.45 mm B. 64.23 mm C. 73.23 mm D. 66.33 mm

A shaft has an ultimate stress of 350 Mpa and has a factor of safety of 5. The torque developed by the
shaft is 2 KN-m and the diameter outside diameter is 80 mm. Find the inside diameter of the shaft.

A. 83.45 mm B. 73.58 mm C. 76.45 mm D. 66.34 mm

A short shaft is use to transmit 45 hp at 300 rpm. Find the diameter of short shaft.

A. 1.09 in B. 2.34 in C. 0.53 in D. 1.79 in

A shaft is use to transmit 50 kw at 600 rpm. If shearing stress of shaft is 42,000 kpa, find the diameter of
main shaft.

A. 23.45 mm B. 27.45 mm C. 34.23 mm D. 45.87 mm

A 2.5 inches diameter line shaft has a speed of 750 rpm. Find the shaft horsepower.

A. 123 B. 187 C. 219 D. 231

A steel shaft transmit 60 hp at 1400 rpm. If allowable stress is 5000 psi, find the shaft diameter.

A. 3.58 in. B. 1.65 in. C. 2.84 in. D. 1.40 in.

What is the speed of 50 mm shaft transmitted 75 KW if stress is not to exceed 26 Mpa.

A. 550 rpm B. 650 rpm C. 1122.33 rpm D. 1700.75 rpm

Find the diameter of a steel shaft which will be used to operate a 110 KW motor rotating at 5 rps if
torsional stress is 80 Mpa.

A. 60.63 mm B. 38.30 mm C. 58.30 mm D. 46.20 mm

Two cylinders 30 cm and 70 cm diameter turning in opposite direction has a center distance of:
 A. 50 cm B. 55 cm C. 60 cm D. 65 cm

An air cylinder has a bore of 25 mm and is operated with shop air at a pressure of 90 psi. Find the push
force exerted by the piston rod, in N.

A. 127 B. 70 C. 402 D. 305 N

A 4 KN load acts at the end of a 3 m cantilever beam. The section modulus of the steel beam is 131,000
mm3. How much is the stress induced?

A. 91.6 N/mm2 B. 96.1 N/mm2 C. 92.3 N/mm2 D. 94.5 N/mm2

A U-bolt support a load of 2730 kg. The cross-section of the bolt has a diameter of 12.7 mm. How much
stress is induced in the sides of the bolt?

A. 103.5 Mpa B. 105.71 Mpa C. 101.5 Mpa D. 109.5 Mpa

If the ultimate shear stress of a 1/8 inch thick drawn steel plates is 40 ksi what force is required to punch
a 1½ inch diameter hole?

A. 10,011 lbs B. 23,562 lbs C. 11 Mtons D. 20620 lbs

A rail having a coefficient of linear expansion of 11.6 x 10-6 m/mC increases its length when heated
from 70F to 150F. Determine the strain.

A. 5.15 x 10-4 B. 6.05 x 10-4 C. 4.06 x 10-4 D. 2.77 x 10-4

An iron rod 6 m long and 0.5 cm2 in cross section stretches 1 mm when a mass of 225 kg is hang on it.
Compute the modulus of elasticity of the iron.

A. 176.58 GPa B. 169.81 Gpa C. 264.87 GPa D. 180.26 Gpa

A hollow shaft with outside diameter of 1.5 in a wall thickness of 0.25 in. If tensile load of 4000 lbs is
applied both ends, find the stress in the shaft occur.

A. 42910.26 psi B. 5810.26 psi C. 4074.37 psi D. 2610.37 psi

A steel wire having 0.5 in diameter and 100 ft long has an applied load of 1000 lbs. Find the length of
wire after the load application.

A. 100.204 ft B. 100.0169 ft C. 100.304 ft D. 100.404 ft

A rod with a stress of 60 Mpa and strain of 0.0003 has a modulus of elasticity of.

A. 180 Gpa B. 190 Gpa C. 195 Gpa D. 200 Gpa

A 50 m steel rod is heated from 26oC to 66oC. Find the total elongation of the rod.

A. 54.60 mm B. 36.78 mm C. 23.40 mm D. 17.34 mm

A 3.5 inches diameter journal bearing with 4 inches long has a load of 50 KN. Find the stress developed.

A. 5535.70 kpa B. 7834.56 kpa C. 8364.55 kpa D. 9374.33 kpa

A wire 120 m long with negligible weight has a load of 16 KN and a modulus of elasticity of 207 Gpa. If
the wire elongation is 10 mm, find the diameter of rod.

A. 34.36 mm B. 35.98 mm C. 40 mm D. 25 mm

Find the force needed to punch a 1.8 inches diameter hole from a 0.5 inch thick plate if ultimate
shearing stress is 20,000 psi and factor of safety of 5.

A. 67,495 lb B. 56,549 lb C. 73,585 lb D. 91,155 lb

Compute for the load in KN on a 3 cm diameter, 100 cm long steel rod if its maximum elongation exceed
0.12 cm.

A. 175.4 B. 196 C. 148 D. 287

The equation of three lines are given as follows:

I. y = 0.75x II. 4x + 3y = 10 III. 3x – 4y = 11; which lines are parallel?

A. I and II B. I and III C. II and III D. I, II and III

What is the value of k if the line joining (4, k) and (6, 8) and the line joining (-1, 4) and (0, 8) are
perpendicular?

A. 8.5 B. 1 C. 0 D. none of the above

The last test that an examiner gave was so hard that he decided to scale the grade upward. He decided
to raise the lowest score of 47 to 65 and the highest score of 78 to 90. Find a linear function, that would
gave a fair way to convert the other test scores.

A. y = 25x/31 +840/31 B. y = 23x/13 + 453/13 C. y = 23x/432 + 34 D. y = 17x/32 + 453

Supposed that the radioactive material isotope decays so that the radioactive present decreases by 15%
per day. If 40 kg are present now, find the amount present 6 days from now?

A. 23.7 kg B. 15.1 kg C. 12.98 kg D. 8.76 kg

Find a quadratic equation with roots 2 ± 3i.

A. x2 – 4x + 13 = 0 B. x2 + 4x + 13 = 0 C. x2 – 13x + 4 = 0 D. x2 + 13x + 4 = 0

The solution to the inequality 3x – 4 ≤ 10 + x.

A. x ≤ -7 B. x ≥ -7 C. x ≤ 7 D. x ≥ 7

A north-south bridle path intersects an east-west river at point O. At noon, a horse and rider leave O
travelling north at 12 kph. At the same time, a boat at A is 25 km east of O travelling west at 16 km/h.
What is the minimum distance between the boat and the horse?

A. 15 B. 10 C. 5 D. 1
Suppose a car presently worth $8200 depreciates 20% per year. About how much will it be worth 2
years and 3 months from now?

A. 3241 B. 4321 C. 2341 D. 4963

A house bought five years ago for P1,000,000 was just sold for P1,350,000. What was the annual growth
rate?

A. 14.81% B. 6.19% C. 35% D. 9.87%

A radiation isotope has a half life of 5 days. At what rate does the substance decay each day?

A. 13% B. 87% C. 21% D. 31%

Solve for x: Log2 x + log2 (x – 2) = 3

A. 2, 4 B. -2, 4 C. 2, -4 D. -2, -4

The equation of the parabola with vertex (0, 0) and directrix at x = 2.

A. x2 = 8y B. x2 = -y C. y2 = 8y D. y2 = -8x

The circles x2 + y2 = 20, and (x – 6)2 + (y – 3)2 = 5 are tangent. Determine the equation of the common
tangential line of the two circles.

A. 3x + 2y = 4 B. y = -2x + 10 C. 3y = 5x -2 D. -5x + 2y = 5

Let the focus F be (0, 3) and the directrix D have equation y = 12. What conic is form for the set of
points P if PF/PD = 0.5.

A. parabola B. hyperbola C. Ellipse D. Circle

Earth’s orbit is an ellipse with the sum almost at one focus. During January, Earth is closed to the sun, a
distance of 9.14 x 107 miles. During July, Earth is farthest from the sun, a distance of 9.44 x 107 miles.
Find the eccentricity of the earth’s orbit.

A. 0.016 B. 0.023 C. 0.32 D. 0.12

A sector of circle has arc length 6 cm and area 75 cm2. What is the radius?

A. 50 cm B. 7.5 cm C. 25 cm D. 12.5 cm

Suppose you can ride a bicycle a distance 5 miles in 15 min. If you ride at a constant speed and if the
bicycle’s wheels have diameter 27 in, find the wheels approximate rate of turn (in rpm).

A. 41.5 B. 83 C. 249 D. 1244

Jupiter has an apparent size of 0.01o when it is 8 x 108 km from earth. Find the approximate diameter of
Jupiter.

A. 130,000 km B. 8,000,000 km C. 140,000 km D. 1273239 km

The reference angle for an angular measure of 695o is _______.

A. 5o B. 65o C. 85o D. 25o

Solve 2sinθ - cosθ = 1 for 0 < θ < 360o

A. 53.1 and 180 B. 53.1 and 306.9 C. 180 and 306.9 D. 306.9

The highest tower in the world is in Toronto, Canada and is 553 m high. An observer at point A, 100 m
from the center of the tower’s base, sights the top of the tower. What is the angle of elevation of the
top of the tower?

A. 5.53 B. 79.7 C. 29.8 D. 43.7

From a shift offshore, the angle of elevation of a hill is 1.1o. After the ship moves inland at 4.5 knots for
20 min, the angle of elevation is 1.4o. How high is the hill? (1 knot = 6080 ft/hr)

A. 1324 ft B. 765 ft C. 181 ft D. 816.97 ft

Two sides of a triangle have lengths 7 cm and 4 cm. The angle between the sides measures 73o. Find
the area of the triangle.

A. 28 cm2 B. 14 cm2 C. 35.2 cm2 D. 13.4 cm2

Find the angles between the lines y = 3x + 1 and y = 5 – 2x.

A. 135o B. 45o C. 45o and 225o D. 45o and 135o

A sphere has points A (8, -2, 3) and B(4, 0,7) as endpoints of a diameter. What is the equation of the
sphere?

A. (x + 6)2 + (y + 1)2 + (z – 5)2 = 9 C. (x - 6)2 + (y - 1)2 + (z – 5)2 = 9

B. (x - 6)2 + (y + 1)2 + (z + 5)2 = 9 D. (x - 6)2 + (y + 1)2 + (z – 5)2 = 9

Find the area of the triangle with vertices P(1, 2), Q(3, 6) and R(6, 1).

A. 22 B. 11 C. 32 D. 35

Determine the formula of the nth term of the arithmetic progression 3, 5, 7, ………..

A. 3n + 1 B. 2n – 1 C. 3n + 1 D. 2n + 1

Find the area of the triangle with vertices P(1, 2), Q(3, 6) and R(6, 1).

A. 22 B. 11 C. 32 D. 35

A car travelling on a horizontal unbanked circular track of radius rand the track is 0.35. Determine the
cars velocity while travelling at a radius of 34 m, without skidding.

A. 15 m/s B. 14 m/s C. 12.45 m/s D. 10.80 m/s

A force of 400 lbf acts on a block at an angle of 30o with the horizontal. The block is pushed 8 ft
horizontally. What is the work done by this force?

A. 2439 J B. 3259.52 J C. 2689 J D. 3757.56 J

Trailer travels at 85 mi/hr around a banked highway curve with a radius of 1100 ft. What banking angle
is necessary such that friction f = 0.3 to resist the centrifugal force?

A. 7o B. 10o C. 9o D. 12o

Given the component velocities, what is the resultant accelerationwhen t = 5? Vx = t4 – t, Vy = 6 – t3

A. 240 B. 504.60 C. 459.62 D. 310

A 10 kg block was dropped 4 meters high. What is the velocity of the block upon reaching the ground?

A. 7.67 m/s B. 7.76 m/s C. 8.86 m/s D. 6.67 m/s

A shot is fired at an angle of 38o with the horizontal and velocity of 300 fps. Calculate to the nearest,
the range of the projectile.

A. 350 ft B. 1200 m C. 400 mi D. 904 yards

What is the density of a stone in kg/m3 that weighs 90 N in air and 60 N in water?

A. 3259 B. 3000 C. 2205 D. 2270

Two forces B1 and B2 act at a point. The magnitude of B1 is 8 lb and its direction is 600 above the x-axis in
the first

quadrant. The magnitude of B2 is 5 lb and the direction is 530 below the x-axis in the fourth quadrant.
What are the horizontal and vertical components of the resultant force?

A. Bx = 7 lbs, By = 2.9 lbs B. Bx = 7 lbs, By = 3 lbs

C. Bx = 6.95 lbs, By = 2.9 lbs D. Bx = 6.95 lbs, By = 3 lbs

Find the magnitude of the resultant of two 10-lb forces applied at the same point when the angle
between the forces is130o.

A. 7.8 lbs B. 18.1 lbs C. 19.8 lbs D. 8.5 lbs

Two boys, B1 and B2 act at a point. The magnitude of B1 is 8 lbs and its direction is 60 degrees above the
horizontal axis in the first quadrant. The magnitude of B2 is 5 lbs and its direction is 53 degrees below
the horizontal axis in the fourth quadrant. What is the magnitude of the resultant force?

A. 7.0 lbs B. 6.9 lbs C. 7.6 lbs D. 8.6 lbs

A roller whose diameter is 20 in weighs 72 lb. What horizontal force is necessary to pull the roller over a
brick 2 in high when the force if applied at the top?

A. 20 lbs B. 30 lbs C. 24 lbs D. 28 lbs