Math Flashcards by John Paul Bicalan

A farmer is to plant rice in a rectangular field 30 meters by 40 meters. He started on the
edge and plant around the perimeter. How wide a strip around he plant for each side in
order to do half the work?

A. 5 m
B. 2.5 m
C. 3 m
D. 5.5 m

A. 5 m

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If a mechanical engineer borrowed money from his girl friend with simple interest of
12%, determine the present worth of P75,000.00 which is due at the end of 7 months.

A. P72,200.20
B. P70,200.20
C. P73,900.50
D. P70,093.20

D. P70,093.20

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An Electrical Engineer obtained a loan of P50,000 at the rate of 6% compounded annually in order to repair his mistress’
house. How much must the Electrical Engineer pay monthly to amortize the loan within a period of ten years?

A. P605.20
B. P550.90
C. P505.90
D. P508.90

B. P550.90

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What is the value of 1 radian in degrees?

A. 89.55 deg
B. 57.3 deg
C. 60.3 deg
D. 45.58 deg

B. 57.3 deg

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How many degrees are 4800 mills?

A. 180 deg
B. 315 deg
C. 90 deg
D. 270 deg

D. 270 deg

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A force of 200 lb acts on a block at an angle of 28 deg with respect to horizontal. The block is pushed 2 ft horizontally. Find the work done by this force.

A. 480 J
B. 408 J
C. 840 J
D. 804 J

A. 480 J

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A truck starts from rest and moves with a
constant acceleration of 6 m/s2. Find the speed of the truck after 4 seconds.

A. 18 m/s
B. 28 m/s
C. 24 m/s
D. 35 m/s

C. 24 m/s

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A car starts from rest and has a constant
acceleration of 3 ft/s2. Determine the average
velocity during the first 10 seconds of motion.

A. 15 fps
B. 20 fps
C. 12 fps
D. 18 fps

A. 15 fps

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Determine the value of each interior angle of
a regular pentagon.

A. 108 deg
B. 120 deg
C. 98 deg
D. 135 deg

A. 108 deg

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Determine the first derivative with respect to
x of the functions g(x) = √10 - 35

A. 3⁄4
B. 0
C. 4(9)3/4
D. 35

B. 0

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Determine the slope of a curve y = -x^2 at the point (2, 3).

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

B. -4

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What is the sum of the roots of the equation
2x^2 + 5x + 5 = 0?

A. -2.5
B. 2.5
C. 2.25
D. -2.25

A. -2.5

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Determine the distance travelled by a particle
between a time interval of 0.2 seconds to 0.30
seconds if its velocity is v = 12t^4 + 7/t, where v
is in cm/s and t is in seconds.

A. 3.75 cm
B. 2.84 cm
C. 2.75 cm
D. 3.84 cm

B. 2.84 cm

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Compute the arithmetic mean of the
following set of numbers: 18, 24, 27, 30, 35,
42, 50.

A. 31.82
B. 32.29
C. 30
D. 29.96

B. 32.29

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Find the root mean square of 11, 23 and 35.

A. 25
B. 27
C. 26
D. 24

A. 25

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Five years ago the father is three times as old
as his son. Ten years from now, the father will
be twice as old as his son. How old is the son
twelve years from now.

A. 32 years old
B. 20 years old
C. 50 years old
D. 38 years old

A. 32 years old

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The sum of P15,000, deposited in an account
earning 4% per annum compounded
quarterly, will become P18,302.85.
Determine the effective rate of interest per
year.

A. 3.06%
B. 4.06%
C. 5.06%
D. 6.06%

B. 4.06%

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If a machine is purchased on instalment and
the buyer makes an P80,000.00 down payment and owes a balance of P150,000 in 2 years. Determine the machine cash value if money is worth 14% compounded quarterly.

A. P199,312.00
B. P183,912.00
C. P193,912.00
D. P139,912.00

C. P193,912.00

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A machine was purchased under these terms:
P30,000 down and P5,000 each month for 5
years. If money is worth 12% compounded
monthly, what is the cash price of the
machine?

A. P144,775.19
B. P245,775.19
C. P542,775.91
D. P254,775.19

D. P254,775.19

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Find ∫(7x^3 + 4x^2) dx?

A. 7x^2 /3 + 4x^2 /2 + C
B. 7x^4 /4 + 4x^3 /3 + C
C. 7x^4 /4 + 4x^2 /5 + C
D. 7x^4 /5 + 4x^3 /5 + C

B. 7x^4 /4 + 4x^3 /3 + C

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What is the least common denominator or
simply LCD of 1/12 and 1/18?

A. 24
B. 36
C. 72
D. 54

B. 36

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How many two digit numbers can be formed
from the number 1, 2, 3, and 4 if repetitions is
not allowed?

A. 8
B. 12
C. 16
D. 20

B. 12

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How many two digit numbers can be formed
from the number 1, 2, 3, and 4 if repetitions
is allowed?

A. 6
B. 12
C. 18
D. 64

D. 64

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The volume of the cube is increasingly at the
rate of 5 cu. M per minute. Determine the
rate at which the surface area is increasing in
m^2/min, when its side is 10 m.

A. 1⁄2
B. 1.75
C. 1.5
D. 2

D. 2

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The segment from (-1, 4) to (2, -2) is extended three times its own length. What is the terminal point? A. (11, -18) B. (11, -24) C. (11, -20) D. (-11, -20)

C. (11, -20)

The midpoint of the line segment between P_1 (x_1, y_1) and P_2 (-2, 4) is P_m (2, -1). Find the coordinate of P_1 . A. (6, -5) B. (11, -24) C. (6, -6) D. (-6, 6)

C. (6, -6)

Find the coordinates of the point P(2, 4) with respect to the translated axis with origin at (1,3). A. (1, -1) B. (1, 1) C. (-1, -1) D. (-1, 1)

B. (1, 1)

What is the area bounded by y = 0, y = e^x, x =0, x = 2 A. 2.27 B. 6.389 C. 1.79 D. 1.27

B. 6.389

The salary of an employee’s job has five levels, each one 5% greater than the one below it. Due to circumstances, the salary of the employee must be reduced from the top (fifth) level to the second level, which means a reduction of 3000.00 per month. What is the employees present salary per month? A. P22,032.50 B. P23,022.50 C. P22,320.50 D. 22,302.50

A. P22,032.50

Twice the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its digit, the answer is 56 and the remainder is 12. If the digits are reversed, the number becomes smaller by 594. Find the number. A. 852 B. 285 C. 825 D. 582

A. 852

Lucy sold 100-pirated DVD. Eighty of them were sold at a profit of 30% while the rest were sold at a loss of 40%. What is the percentage gain or loss on the whole stock? A. 15% B. 20% C. 16% D. 12%

C. 16%

A pole cast a shadow 15 m long when the angle of elevation of the sun is 61 deg. If the pole has lean 15 deg from the vertical directly toward the sun, what is the length of the pole? A. 54.23 m B. 48.64 m C. 36.84 m D. 64.84 m

A. 54.23 m

A man finds the angle of elevation of the top of the tower to be 30 deg. He walks 85 m nearer the tower and finds angle of elevation to be 60 deg. What is the height of the tower? A. 76.31 m B. 73.31 m C. 73.16 m D. 73.61 m

D. 73.61 m

How many 3 digit numbers may be formed from the digits 0, 1, 2, 3, 4 and 5 if no digit may be repeated in a given number?

120

In how many ways can you line-up 4 marines and 6 army soldiers must be side by side with each other and the army soldiers are likewise? A. 35,460 B. 34,560 C. 36,450 D. 30,546

B. 34,560

A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the positions? A. 540 B. 480 C. 680 D. 840

A. 540

A bag contains 3 white and 5 red balls. If two balls are drawn at random, find the probability that both are white. A. 0.375 B. 0.10714 C. 0.46667 D. 0.28571

B. 0.10714

A certain job can be done by Jobelle and TJ in 10 hours, by Jobelle and Jessyl in 12 hours and TJ and Jessyl in 20 hours. Find how long would it take by Jobelle to do the job alone. A. 30 hours B. 60 hours C. 15 hours D. 25 hours

C. 15 hours

In 1995, little cute Jobelle had a pocket contains P11.65 of twenty five and ten centavo coins. If the total number of coins is 70. Find how many twenty five coins did she has? A. 31 B. 39 C. 21 D. 29

A. 31

A bullet weighing 4 grams was fired from a gun with the barrel measuring 12 cm long. If the bullet was fired with a speed of 380 m/s solve the energy of the bullet in Joules. A. 289 B. 345 C. 798 D. 1009

A. 289

A pipe lining material of silicon carbide used in the conveyance of pulvurized coal to fuel a boiler, has a thickness of 2 cm and inside diameter of 10 cm. Find the volume of the material of a pipe length of 6 meters in liters. A. 45.24 B. 47.45 C. 51.47 D. 68.97

A. 45.24

A missile is fired with a speed of 100 fps in a direction of 30 deg above the horizontal. Determine the maximum height to which it rises in feet. A. 38.85 B. 19.43 C. 377.33 D. 1509.32

A. 38.85

What time between 2 and 3 o’clock will the hands of the clock be opposite one another. A. 2:43 7/11 B. 2:44 7/11 C. 2:37 8/11 D. 2:46 7/11

A. 2:43 7/11

From a deck of ordinary cards, what is the probability of drawing a heart or face card?

43.75%

A perfect gas is expanded polytropically with an initial volume and temperature of 0.06 m^3 and 147 degC respectively. If the final volume and temperature are 0.21 m^3 and 21 degC respectively, what is the index of the expansion? A. 1.285 B. 1.212 C. 1.333 D. 4.400

A. 1.285

If the loan was for 15 months at 16.8% interest a year and the repayment on a loan was P12,100.00, how much was the principal? A. P8,500.00 B. P9,500.00 C. P10,000.00 D. P10,500.00

C. P10,000.00

The sum of P15,000, deposited in an account earning 4% per annum compounded quarterly, will become P18,302.85. Determine the effective rate of interest per year. A. 3.06% B. 4.06% C. 5.06% D. 6.06%

B. 4.06%

Find the number of years when P2,500.00 is compounded to P5,800.00 at 12% compounded quarterly. A. 6.12 years B. 7.12 years C. 8.12 years D. 5.12 years

B. 7.12 years

What is the effective rate equivalent of 12% compounded quarterly? A. 12.55% B. 11.55% C. 12.98% D. 13%

A. 12.55%

What rate compounded quarterly is equivalent to 14% compounded semi-annually? A. 10.76% B. 11.76% C. 12.76% D. 13.76%

D. 13.76%

Celestino owes P500, due in 3 years and P800 due in 7 years. He is allowed to settle these obligations by a single payment on the 6th year. Find how much he has to pay on the 6th year if money is worth 14% compounded semi-annually. A. P1,449.12 B. P1,559.12 C. P1,339.12 D. P1,669.12

A. P1,449.12

Determine the amount that must be deposited every 3 months in a fund earning 12% compounded quarterly in order to have P25,000 in 8 years. A. P716.71 B. P476.17 C. P674.71 D. 1700.00

B. P476.17

What is the value of 1 radian in degrees? A. 89.55 deg B. 57.3 deg C. 60.3 deg D. 45.58 deg

B. 57.3 deg

If the density of gas is 0.003 slug/ft^3, what is the specific weight of the gas? A. 15.2 N/m^3 B. 9.04 N/m^3 C. 98.2 N/m^3 D. 76.3 N/m^3

A. 15.2 N/m^3

If the specific weight of a liquid is 58.5 lb per cubic foot, what is the specific volume of the liquid? A. 1.0675 cm^3/g B. 0.5321 cm^3/g C. 1.5502 cm^3/g D. 0.9504 cm^3/g

A. 1.0675 cm^3/g

The atomic weight of hydrogen is 1 gram per gram-atom. What is the mass of a hydrogen atom? A. 1.66 x 10^-24 g/atom B. 6.02 x 10^-23 g/atom C. 1 g/atom D. The mass is too small to calculate

A. 1.66 x 10^-24 g/atom

A ball is dropped from a height of 60 meters above ground. How long it take to hit the ground? A. 4.5 seconds B. 3.5 seconds C. 2.5 seconds D. 1.5 seconds

B. 3.5 seconds

A 5 meter extension ladder leans against the wall; the bottom is 3 m from the wall. If the bottom stays at the same place, how much should the ladder be extended so that the top would lean against the wall 1 meter higher? A. 1.2 m B. 1.5 m C. 0.5 m D. 0.83095 m

D. 0.83095 m

If a stone is dropped from a balloon while ascending at the rate of 7.5 m/s reaches the ground in 6 seconds, what was the height of the balloon when the stone was dropped? A. 110.12 m B. 120.25 m C. 131.81 m D. 140.12 m

C. 131.81 m

A cubical container that measures 50.8 mm on a side is tightly packed with marbles and is filled with water. All eight marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are same size. What is the volume of water in the container? A. 434,096.51 mm^3 B. 62,454.54 mm^3 C. 431,960.51 mm^3 D. 68,641.97 mm^3

B. 62,454.54 mm^3

What is the determinant of the 2 x 2 matrix, │7 6 │? │5 9 │ A. -33 B. 33 C. -43 D. 43

B. 33

What is the determinant of the 3 x 3 matrix, │1 2 -1│? │2 -1 1│ │1 1 1 │ A. 6 B. 7 C. -6 D. -7

D. -7

Given the following vectors A = 3i + 2j, B = 2i + 3j + k, C = 5i + 2k. Simplify the expression (A x B).C. A. 20 B. 0 C. 60i + 24k D. 5i + 2k

A. 20

Determine the rationalized value of the complex number (6 + 2.5i)/(3 + 4i). A. 1.12 – 0.66i B. 0.32 – 0.66i C. -32 + 0.66i D. -1.12 + 0.66i

A. 1.12 – 0.66i

Determine the type of flow of fluid flowing inside 25.4 cm radius pipe at a velocity of 10 m/s and a viscosity of 1.131 Pa-s. A. Laminar flow B. Turbulent flow C. Critical flow D. Transition flow

A. Laminar flow

What is the probability of an examinee to pass or fail the board exam? A. 50% B. 0% C. 100% D. 75%

C. 100%

How many even numbers of three different digits each can be formed from the digits 1, 2, 3, 4, 5 and 7? A. 20 B. 40 C. 36 D. 28

B. 40

What is the measure of 1 1⁄2 revolutions counter-clockwise? A. +540 deg B. -540 deg C. +90 deg D. -90 deg

A. +540 deg

If the hypotenuse of a right triangle is 34 cm. What is the length of the shortest leg if it is 14 cm shorter than the other leg. A. 17 cm B. 15 cm C. 16 cm D. 18 cm

C. 16 cm

If AB = 15 cm, BC = 18 cm and CA = 24 cm, find the point of intersection of the angular bisector from the vertex C. A. 11.3 cm B. 13.4 cm C. 12.1 cm D. 14.3 cm

D. 14.3 cm

A car travels from point M northward for 30 minutes then eastward for one hour, then shifted N30 deg W. If the constant speed is 40 kph, how far directly from M will be it after 2 hours? A. 41.6 km B. 47.9 km C. 43.5 km D. 45.2 km

B. 47.9 km

If the sides of a triangle are 18 cm, 24 cm and 34 cm, respectively. What is the length of the median to the 24-cm side? A. 21.4 cm B. 24.4 cm C. 20.4 cm D. 23.4 cm

B. 24.4 cm

From the third floor window of a building, the angle of depression of an object on the ground is 35o58’, while from a sixth floor window, 9.75 m above the first point of observation the angle of depression is 58o 35’. How far is the object from the building? A. 15.3 m B. 9.3 m C. 10.7 m D. 11.9 m

C. 10.7 m

In the following identities, which one is different from the others? A. 2cos²x – 1 B. Cos⁴x – sin⁴x C. Cos³x – sin³x D. 1 – 2sin²x

C. Cos³x – sin³x

Estimate the median of the following set of numbers: 18, 24, 27, 30, 35, 42, 50. A. 31.82 B. 32.29 C. 30 D. 29.96

C. 30

How many permutations can be made from the letters a, b, and c taken two at a time? A. 6 B. 8 C. 18 D. 64

A. 6

Solve for the length of the hypotenuse of a right triangle if length of the two legs are 7 m and 16 m, respectively. A. 10.363 m B. 12.567 m C. 15.648 m D. 17.464 m

D. 17.464 m

A car in overtaking a trailer, uniformly accelerated its speed from 40 km/hr to 90 km/hr in 8 seconds. Calculate the distance travelled during the period of acceleration in meters. A. 144.44 B. 156.09 C. 346.9 D. 500.78

A. 144.44

An area of 25.6 cm² on the map represents a lot having an area of 640 m² . If the scale on the map is 1:x, what is the remainder is 10. Determine the value of x? A. 50 B. 100 C. 500 D. 900

C. 500

When the expression x⁴ + ax³ + 5x² + bx + 6 is divided by (x – 2), the remainder is 16. When it is divided by (x + 1) the remainder is 10. Determine the value of the constant a. A. 6 B. 9 C. 5 D. 7

D. 7

What is the simple interest rate if an investment of P37,500.00 accumulates to P45,937.5 in 18 months? A. 0.15 B. 0.20 C. 0.21 D. 0.3

A. 0.15

The JRF Corporation manufactures bookcases that sells for P65.00 each. It costs JRF corporation P35,000.00 per year to operate its plant. The sum includes rentals, depreciation charges on equipment, and salary payments. If the cost to produce one book case is P50.00, how many bookcases must be sold each year for the corporation to avoid taking a loss? A. 539 Bookcases B. 750 Bookcases C. 2333 Bookcases D. 2334 Bookcases

D. 2334 Bookcases

A machine is purchased for P500,000.00. The salvage value in 25 years is P100,000.00. What is the depreciation in the first three years using straight line method? A. P24,000.00 B. P32,000.00 C. P48,000.00 D. P16,000.00

D. P16,000.00

How much must be deposited at 6% each year on January 1, year 1, in order to accumulate P5,000.00 on the date of the last deposit, January 1, year 6?

716.813

Jeffrey made a loan from a bank. The bank charges him 12% simple interest on a P300.00 loan. How much will be repaid if the loan is paid in one lump sum after three years? A. P425.00 B. P408.00 C. P551.00 D. P450.00

B. P408.00

My P5,000 shall accumulate for 10 years at 8% compounded quarterly. What is the compound interest of my money at the end of 10 years? A. P6,005.30 B. P6,040.20 C. P6,000.00 D. P6,010.20

B. P6,040.20

What is the effective rate corresponding to 18% compounded daily? A. 17.72% B. 18.72% C. 19.72% D. 20.72%

C. 19.72%

The management of a certain company deposits P1,500.00 for each of its employees in a retirement fund at the end of each year for the next 12 years. How much is each employee’s fund at the end of 12 years if it accumulates 8% for the first 8 years and 6% for the last 4 years? A. P27,705 B. P26,705 C. P24,705 D. 23,705

B. P26,705

What is the least number of years needed to triple a certain amount of money at 5% per annum compounded interest to the nearest year? A. 20.5 years B. 18.5 years C. 22.5 years D. 16.5 years

C. 22.5 years

The roots of the quadratic equation are 1/3 and -3/2. What is the equation? A. 6x² + 5x + 3 = 0 B. 6x² – 7x – 3 = 0 C. 6x² + 7x – 3 = 0 D. 6x² + 7x + 3 = 0

C. 6x² + 7x – 3 = 0

What is the sum of the numerical coefficient in the expansion of ( x – 2y)⁷? A. -1 B. 1 C. -2187 D. 2187

A. -1

Mr. PME covered a distance of 55 km in 4 hrs by driving his car 40 kph, part of the way, and by walking the remainder of the way at 5 kph. What part of the total distance did Mr PME go by car? A. 7/11 B. 8/11 C. 9/11 D. 10/11

B. 8/11

The water tank in Calamba Water District can be filled by pipe A in half the time the pipe B can empty the tank. When both pipes are operating, the tank can be filled in 1 hour and 12 minutes. Determine the time, in hours, for pipe A to fill the tank alone. A. 0.6 B. 0.7 C. 0.75 D. 0.8

A. 0.6

Of the 316 people attending the party, there are 78 more children than women and 50 more women than men. Determine the number of men in the party. A. 46 B. 96 C. 112 D. 178

A. 46

A house can be constructed in as many days as there are men in the group of construction personnel. If the number of men is reduced by 4, the project is delayed by 5 days. Determine the original number of number of construction personnel. A. 18 B. 16 C. 20 D. 24

C. 20

Determine the distance between points A(2, - 3, 5) and B(7, 2, -6). A. 11.08 units B. 12.08 units C. 13.08 units D. 14.08 units

C. 13.08 units

What are the two positive numbers whose sum is 8, if the product of one number by the cube of the other number is to be maximum? A. 1 & 7 B. 2 & 6 C. 3 & 5 D. 4 & 4

B. 2 & 6

Forty liters of a 60% salt solution are produced to a 45% solution. How much solution must be drained off and replaced with distilled water so that the resulting solution contains only 45% solution. A. 6 liters B. 8 liters C. 10 liters D. 12 liters

C. 10 liters

If ln y = 5 and ln x = 3, what is the value of ln(x²/y½)? A. 2.5 B. 3.5 C. 4.5 D. 1.5

B. 3.5

A river is 580 ft wide. The bridge construction cross the river is banked 1/7 of its length in the east and 1/6 of the length in the west. What is the length of the bridge? A. 660 ft B. 750 ft C. 840 ft D. 1670 ft

C. 840 ft

What is the area of the circle whose equation is x² + y² – 6x + 8y = 0? A. 25π B. 5 π C. 15 π D. 20 π

A. 25π

Math Flashcards

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