Math Module 2

C. 46.67

14 is 30% of what number? A. 342 B. 4.2 C. 46.67 D. 2.14

C. 46.67

14 is 30% of what number? A .- 4.2 B. 214.286 C. 46.67 D. 12.45

A .- 86

If (5x-3), (x+2), and (3x - 11) form an arithmetic progression, find the fifteenth term A .- 86 B. - 79 C .- 81 D. - 84

D. 5000

If a bus weighs 2.5 tons, how much pounds does it weigh? (1 ton = 2000 lbs) A. 5500 B. 450 C. 4500 D. 5000

C. 2x + y - 1

If log 2 = x and log 3 = y, find log 1.2 in terms of x and y. A. 2x-y + 1 B. 2x-y- 1 C. 2x + y - 1 D. x + 2y - 1

A. origin

If the equation is unchanged by the substitution of y for x, its curve is symmetrical with respect to: A. origin B. x-axis C. y-axis D. line 45° with the axis

C. Perpendicular

If the product of the slopes of any two straight lines is - 1, one of these lines are said to be A. Parallel B. Skew C. Perpendicular D. Non-intersecting

B. 19%

If the radius of a circle is reduced by 10%, its area will be reduced by A. 20% B. 19% C. 90% D. 81%

C. extremes

In a proportional of four quantities, the first and the fourth terms are referred to as: A. means B. denominators- C. extremes D. numerators

A. 4:1

In a right angle the bisector of the right triangle divides the hypotenuse in the ratio 1:2. in what ratio is the hypotenuse divided by the altitude dropped from the vertex of the right angle? A. 4:1 B. 3:2 C. 2:1 D. 4:3

C. Argand's Diagram

In complex algebra, we use a diagram to represent a complex plane commonly used: A. De Moivre's Diagram B. Funicular Diagram C. Argand's Diagram D. Venn Diagram

D. 93

In how many ways can 2 integers be selected from the integers 1, 2, 3, ... , 100 so that their difference is exactly 7? A. 69 B. 74 C.81 D. 93

B. Radius Vector

In polar coordinate system, the distance from a point to the pole is known as: A. Polar angle B. Radius vector C. x-coordinate D. y-coordinate

C. 34.3

In the chemical processing of a certain mineral, the rate of change of the amount, of mineral present varies as the amount of the mineral remaining. If after 8 hours, 100 pounds of mineral have been reduced to 70 pounds, what quantity of the mineral will remain after 24 hours? A. 53.2 B. 43.4 C. 34.3 D. 25.3

C. abscissa

It represents the distance of a point from the y axis. A. coordinate B. ordinate C. abscissa D. polar distance

A. 4

The sum of the ages of two boys is four times the sum of the ages of a certain number of girls. Four years ago, the sum of the ages of the girls was one eleventh of the sum of the ages of the boys and eight years hence, the sum of the ages of the girls will be one half that of the boys. How many girls are there? A. 4 B. 5 C.6 D. 3

A. 67

The sum of the ages of two men equals 99. If the inverted age of the elder is added to the age of the younger, the sum is 108. However, if the age of the younger is inverted and subtracted from the age of the older, the difference is 44. Find the age of the older man. A. 67 B. 53 C. 32 D. 46

B. 28

The sum of the digits of a 2-digit number is 10. If the number is divided by the unit's digit, the quotient is 3 remainder is 4. Find the number. A. 37 B. 28 C. 46 D. 19

B. 4913

The sum of the positive integers is 51. Find the greatest possible product of these 3 numbers. A. 7362 B. 4913 C. 5624 D. 9625

C. 18, 35

There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers? A. 16, 37 B. 20, 33 C. 18, 35 D. 24, 29

A. one is merely the negative of the other

Two factors are considered essentially the same if: A. one is merely the negative of the other B. one is exactly the same as the other C. both of them are negative D. both of them are positive

C. 11.25

Two positive numbers may be inserted between 3 and 9 such that the first three are in geometric progression, while the last three are in arithmetic progression. What is the sum of these two positive numbers? A. 1.25 B. 12.25 C. 11.25 D. 6.25

C. R=3-1

What equation best represents the statement Rodel (R) has 3 candies and ate one. A. R=3R-R B. R = 3/R - 1/R- C. R=3-1 D. R= 3R-1

B. (-1, 1)

What is the coordinate of the vertex of the equation x2 + 2x - y + 2 = 0. A. origin B. (-1, 1) C. (-1,-1) D. (1, -1)

C. 2

What is the sum of the coefficients of the expansion of(2x - 1)21. A. -1 B. 1 C. 2 D. 3

D. 80

What is the sum of the first 80 positive odd integers subtracted from the sum of the first 80 positive even integers? A. 50 B. 70 C. 60 D. 80

A. 50%

What part of 90% alcohol solution must be replaced by an equal amount of pure alcohol to make a 95% alcohol solution? A. 50% B. 45% C. 25% D. 5%

A. Circle

What section is formed by a cone cut by a plane perpendicular to its axis? A. Circle B. Parabola C. Ellipse D. Hyperbola

B. 13

When William was as old as Mae is now, the sum of their ages was 51. When Mae will be as old as William is now, the sum of their ages will be 103. How many years older is William than Mae? A. 25 B. 13 C. 19 D. 32

A. 1/4

Which of the following is the value of xy if x - y = 2, x2 + 2xy + y2 = 3? A. 1/4 B. 4 C. 4 D. Not in the choices

B. radicand

b in the expression cube root of b is called A. index B. radicand C. radical number D. base number

D. 8

How many terms are there in the expansion of (X+Y)7? A. 7 B. 14 C. 6 D. 8

C. 4x2- y2 = 16

Find the equation of the hyperbola whose asymptotes are y = + 2x and which passes through (5/2, 3). A. 3x2- y2 = 9 B. 5x2- y2 = 25 C. 4x2- y2 = 16 D. 2x2 - y2 = 4

D. ½

Find the positive number x that exceeds its square by the largest amount. A. 1/3 B. 1 C. 2 D. ½

B. (√2, √2, 0)

Find the rectangular coordinates of the spherical coordinate (2, π/4, π/2). A. (2, √2, 0) B. (√2, √2, 0) C. (√2, 0, √2) D. (√2, 2, √2)

C. 1/362880

Find the tenth term in the sequence 1, 1, 12, 1/6, 1/24 ... A. 1/322560 B. 1/317520 C. 1/362880 D. 1/352800

D. 489,888

Find the term independent of y in the expansion of (2y2- 3y1)^9. A. 217,728 B. - 326,592 C. - 734,832 D. 489,888

D. 96pi/5

Find the volume generated by revolving the area bounded by y = x 3, y = 8, x = 0 about the y-axis. A. 64pi/7 B. 512pV/5 C. 768pi/7 D. 96pi/5

B. 57.7 kg

Find the weight of the heaviest right circular cylinder that can be cut from a 100kg spherical shot. A. 50 kg B. 57.7 kg C. 86.6 kg D. 70.7 kg

A. 2L

How much of a 7% solution should be mixed with appropriate amount of 12% solution to get 5 liters of a 10% solution? A. 2L B. 2.5 L C. 3 L D. 4 L

D. n(n+1)^2

The simplest form of [(n+1)!]2 / [(n!)(n - 1)!] is A. n(n+1) B. n+1 C. n^2 D. n(n+1)^2

D. 275

33 is 12% of what number? A. 120 B. 263.63 C. 396 D. 275

D. 40

35% of what number is 14? A. 125 B. 4.9 C. 250 D. 40

A. ellipse

3x2 + y2 = 25 is an equation of a/an: A. ellipse B. circle C. parabola D. hyperbola

D. hyperbola

4x2- y 2 = 16 is the equation of A. circle B. ellipse C. parabola D. hyperbola

C. 45 L

9 liters of wine are taken from a container full of wine. It is then filled with water. Then 9 liters of the mixture are taken and the container is again filled with water. If the ratio of the quantity of the wine now in the container to the quantity of the water in it is 16/9, what is the capacity of the container? A. 60 L B. 54 L C. 45 L D. 36 L

B. 11

A Manila High School has 85 seniors, each of whom plays on at least one of the school's three varsity sports teams: football, baseball, and basketball. It so happen that 74 are on the football team; 26 are on the baseball team; 17 are on both the football and basketball teams; 18 are on both the baseball and football teams; and 13 are on both the baseball and basketball teams. Determine the number of seniors playing all three sports given that twice this number is members of the basketball team. A. 10 B. 11 C. 22 D. 20

C. 14

A balloon travel upwards 6 m, North and 8 m, East. What is the distance traveled from the starting point? A.7 B. 10 C. 14 D. 20

C. 126

A basketball coach has a total of 10 players. In how many ways can he field a team of 5 players if the team captain is always included? A. 42 B. 70 C. 126 D. 25

C. 22.2

A can flow the field in 4 hours less than B. If both will work together, the job is done in 10 hours. Find the number of hours for B to do the job alone. A. 25.5 B. 31.4 C. 22.2 D. 33.5

B. 5.243

A cask containing 20 gallons of wine was emptied on one-fifth of its content and then is filled with water. If this is done 6 times, how many gallons of wine remain in the cask? A. 5.121 B. 5.243 C. 6.554 D. 5.343

A. 13

A club of 40 executives, 33 like to smoke Marlboro, and 20 like to smoke Philip Morris. How many like both? A. 13 B. 10 C. 11 D. 12

C. 1/9 π

A cone with 4-in base radius and 8-in depth, if water flows inside the cone 1 cu. in/sec, find the rate on which the depth changes when the water is 2-in from the base. A. 3/34 π B. ¼ π C. 1/9 π D. 1/11 π

B. 27 cm

A figure is 30 cm high is reduced by 19% in a copier. The height of the figure in the resulting copy will be A. 5.7 cm B. 27 cm C. 24.3 cm D. 13.08 cm

B. 245 ft-tons

A hemispherical tank of radius 10 ft is full of water. Find the work done in pumping the water to the top of the tank. A. 234 ft-tons B. 245 ft-tons C. 432 ft-tons D. 135 ft-tons

D. Zero

A horizontal line has a slope of A. Negative B. Infinity C. Positive D. Zero

A. 25

A man wishes to buy a piece of land worth 15 million pesos. If it were possible for him to save one peso for the first day, two pesos on the second day, 4 pesos on the third day and so on. In how many days would he save enough money to buy the land? A. 25 B. 23 C. 24 D. 27

A. 42

A number is less than 100 and its ten's digit is 2 more than its unit's digit. If the number with the digits reversed is subtracted from the original number, the difference is 3 times the sum of the digits. Find the number. A. 42 B. 53 C. 75 D. 64

D. 64/93

A parabolic mirror has its focus 31 ft from its vertex, and the distance across the top is 64 ft. Determine the distance at the center. How deep is the center of the mirror? A. 23/45 B. 22/45 C. 32/45 D. 64/93

C. 10.24 ft

A piece of paper is 0.03 inches thick: Each time the paper is folded in half, the thickness is doubled. If the paper is folded in half 12 times, how thick to the nearest foot, would the paper be? A. 1.2 ft B. 5.3 ft C. 10.24 ft D. 4.24 ft

C. 0.19 advanced

A project activity can be done by 25 men in 60 days. At the end of the 5th day, 6 men were laid off. At the start of the 33rd day, 12 more men were hired to finish the job. How many days is the project advanced/ delayed? A. 0.81 advanced B. 0.81 delayed C. 0.19 advanced D. 0.19 delayed

B. pyramidal number

A sequence of numbers where every term is obtained by adding all the preceding terms such as 1, 5, 14, 30, ... is called: A. triangular number B. pyramidal number C. tetrahedral number D. Euler's number

D. 930

A survey was conducted to find out which of the three leading car brands they liked best. The results indicated that 500 liked Honda, 470 liked Toyota, and 430 liked Ford. But of these, 180 liked both Honda and Ford, 140 liked both Honda and Toyota, and 210 liked both Ford and Toyota. Only 60 liked all the 3 car brands. How many persons responded to the survey? A. 910 B. 980 C. 960 D. 930

B. 83

A tank is in the form of a frustum of a right circular cone is filled with oil weighing 50 pounds per cubic foot. If the height of the tank is 10 feet, base radius is 6 ft and the top radius is feet, find the work required in ft-tons to pump off to a height 10 feet above the tank. A. 232 B. 83 C. 195 D. 312

C. 631.85 cu ft

A water tank is a horizontal circular cylinder 10 feet long and 10 ft in diameter. If the water inside is 7.5 feet deep determine the volume of water contained . A. 663.44 cu ft B. 600.26 cu ft C. 631.85 cu ft D. 568.67 cu ft

C. 24.17 m/s

A woman travelled 20 m/s for 2 min., 30 m/s for 3min., and 15 m/s for 1 min., Find her average velocity. A. 21.7 m/s B. 29 m/s C. 24.17 m/s D. 20 m/s

A. 200

Given a square with 20 cm sides. Another square is to be inscribed in the given square such that the vertices of the latter lies on the midpoint sides of the former. Determine the area, in sq cm, of the smaller inscribed square? A. 200 B. 220 C. 180 D. 160

D. 6.67 ft

An arch is in the form of an inverted parabola and has span of 12 feet at the base and a height of 12 feet. Determine the equation of the parabola and give the vertical clearance 4 feet from the vertical centerline. A. 7.33 ft B. 6.00 ft C. 5.33 ft D. 6.67 ft

D. 6.67 ft

An arch is in the form of an inverted parabola and-has span of 12 feet at the base and a height of 12 feet. Determine the equation of the parabola and give the vertical clearance 4 feet from the vertical centerline. A. 7.33 ft B. 6.00 ft C. 5.33 ft D. 6.67 ft

C. it has no other integer as a factor except itself and one

An integer is said to be prime if: A. it is factorable by any value B. it is an odd integer C. it has no other integer as a factor except itself and one D. it is an even integer

C. ₱ 25,000

An investor has P 1,100 income from bonds bearing 4% and 5% if the amount at 4% and 5% were interchanged he would eam P 50 more per year. Find the total sum invested. A. ₱ 20,000 B. ₱ 30,000 C. ₱ 25,000 D. ₱ 35, 000

A. 26

An isosceles triangle of maximum area is inscribed in an ellipse with major axis 10 cm and minor axis 8 cm. so that the base is parallel to the major axis and the opposite vertex on at end of the minor axis. Find the area of the triangle. A. 26 B. 25 C. 24 D. 20

B. 2:18 6/13

At what time between 2:00 and 3:00 will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o'clock mark? A. 2:21 9/11 B. 2:18 6/13 C. 2:23 7/13 D. 2:19 7/13

B. 27.27

Boyet reads the clock differently such that he recognizes the hour hand as the minute hand and the minute hand as hour hand. How many minutes after 5 o'clock will he read the time correctly? A. 26.55 B. 27.27 C. 28.92 D. 28.66

B. 109.47°

Find the angle between adjacent faces of a regular octahedron. A. 45.5° B. 109.47° C. 35.34° D. 105°

A. 2,8

Compute the focal length and the length of latus rectum of parabola y2 + 8x - 6y +25 =0 A. 2,8 B. 4, 6 C. 16,64 D. 1, 4

B. 48 in

Convert 4 ft to in. A. 24 in B. 48 in C. 36 in D. 40 in

A. 21.33

Find the area bounded by the parabola, x2 = 4y and y = 4. A. 21.33 B. 33.21 C. 31.32 D. 13.23

C. 20

Find the area of the triangle formed by the points (5, 4), (-2,1) and (2, - 3). A. 18 B. 16 C. 20 D. 22 1/2

B. 3

Find the common ratio of a geometric progression whose first term is 1 and for which the sum of the first 6 terms is 28 times the sum of the first 3 terms. A. 4 B. 3 C. 5 D. 2

B. y = 2xy

Find the differential equation of the parabola with vertex at the origin and axis horizontal. A. x = 2y B. y = 2xy C. 2y = xy D. x = 2yy

A. x2 + y2 - 6x + 10y + 18 = 0

Find the equation of the circle whose center is at ( 3, -5) and whose radius is 4. A. x2 + y2 - 6x + 10y + 18 = 0 B. x2 + y2 + 6x + 10y + 18 = 0 C. x2 + y2- 6x - 10y + 18 = 0 D. x2 + y2 + 6x-10y + 18 = 0

A. (x/10)^2 +(v/8.66)^2 = 1

Determine the equation describing the locus of point P (x, y), such that the sum of the distances between P and (-5, 0) and between P and (5, 0) is constant at 20 units. A. (x/10)^2 +(v/8.66)^2 = 1 B. (x/10)^2+(y/5)^2 =1 C. (x/5)^2 + (10)^2=1 D. (x/8.66)^2+ (y/10)^2 = 1

B. 30/7

Equal volumes of different liquids evaporate at different but constant rates. If the first is totally evaporated in 6 weeks and the second in 5 weeks, when (week) will the second be 1/2 the volume of the first? A. 27/7 B. 30/7 C. 33/7 D. 29/7

A. 16

Express the power (1+i)^8 in rectangular form. A. 16 B. 8i C. 1-i D.-6

D. 71/8

Find k in the equation of the line 5x - 2y + k = 0 that is tangent to y =6+x2. A. 25/8 B. 5/12 C. 23/4 D. 71/8

D. 71/8

Find k in the equation of the line 5x-2x+k=0 that is tangent to y=6+x^2 A. 25/8 B. 5/12 C. 23/4 D. 71/8

C. 1/23

Find the 12th term of the harmonic progression 1, 1/3, 1/5. A. 1/9 B. 1/17 C. 1/23 D. 1/21

B. Maria bought an item worth P70.

Maria will buy in a store. In the store, if you buy at least P30, you will pay in cash. If you buy P30 to P70, you will pay in gift check. If you pay above P70, you will pay in credit card. If Maria paid through gift check, what does it mean? A. Maria bought an item worth P30. B. Maria bought an item worth P70. C. Maria bought an item above P70. D. Maria is a rich kid

B. indeterminate

One raised to infinity is: A. 1 B. indeterminate C. infinity D. zero

C. 116.67 kg

Pure tin and pure iron was added to a 50 kg of an alloy containing 10% tin and 20% iron The process produced a new alloy containing 20% tin and 50% iron. What is the weight of the new alloy? A. 66.67 kg B. 86.25 kg C. 116.67 kg D. 153.33 kg

C. 0.58 ft/min

Sand is pouring at 25x ft3/min and forming a conical pile where the radius is always twice its height. Find the rate when the height is 5ft and height is increasing at the rate of 2 in/min? A. 0.25 ft/min B. 1.32 ft/min C. 0.58 ft/min D. 0.85 ft/min

B. ellipse

The eccentricity of a given curve is less than one, the given curve is: A. parabola B. ellipse C. hyperbola D. circle

B. 3x- 2y = 12

The equation of a line that intersects the x-axis at x = 4 and the y-axis at y = - 6 is: A 3x+2y = 12 B. 3x- 2y = 12 C: 2x-3y = 12 D. 2x + 3y = 12

D. Folium of Descartes

The equation x^3 +y^3-3axy =0 represents a curve called A. stropoid B. cardioid C. lemniscate D. Folium of Descartes

A. 592.60 cu. cm

The largest volume of a rectangular box that can be made of a cardboard 20 sq. in by cutting identical squares on its edges. A. 592.60 cu. cm B. 375.63 cu. cm C. 615.53 cu. cm D. 421.94 cu. cm

B. (11,-20)

The segment from (- 1, 4) to (2, - 2) is extended 3 times its own length. The terminal point is A. (- 11, - 20) B. (11,-20) C. (11,-24) D. (11, - 18)