Math Looks Fam

79. A solid has a circular base of radius 20 cm. Find the volume of the solid if every plane section perpendicular to a particular fixed diameter is an equilateral triangle. A. 12453. 57 cm^3 B. 18475. 21 cm^3 C. 21342. 56 cm^3 D. 15453. 67 cm^3

b

86 These are solutions that satisfy a transformed equation but do not satisfy the original equation. A. pertinent solutions B. extraneous solutions C. intrinsic solutions D. primitive solutions

b

87 A graph with one vertex and no edges is called a __. A. multigraph B. trivial graph C. digraph D. isolated graph

b

99 The Boolean function [~(~p^q)^~(~p^~q)] v (p^r) is equal to the Boolean function __. A. q B. p C. p ^ r D. p v r

b

99 Which of the following functions is onto? A. Injection B. Surjection C. Bijection D. Relation

b

10 In a quadratic problem, one student made a mistake in copying the coefficient of x and got a root of +3 and -2. Another student made a mistake in copying the coefficient of x and got a root of +3 and +2. Which one of the correct roots? A. 3 B. 4 C. -3 D. 6

d

100 A radioactive material, such as the isotope thorium-234 disintegrates at a rate proportional to the amount currently present..... A. 0.3833/day B. 0.2833/day C. 0.0383/day D. 0.0283/day

d

12 A wallet contains the same number of .... total $1.44. How many of each type of coin does the wallet contain? A. 10 B. 7 C. 12 D. 9

d

34 An aircraft is flying horizontally at a constant height of 4000 ft above a fixed observation point.... A. 2.1 deg/s B. 1.1 deg/s C. 2.6 deg/s D. 1.6 deg/s

d

39 A statue 3.2 m high stands on a pedestal such that its foot is 0.4 m above an observer's eye level. How far from the statue must the observer stand in order that the angle subtended by the statue will be maximum? A. 1.1 m B. 1.5 m C. 1.6 m D. 1.2 m

d

49 Find the moment of inertia with respect to the x-axis of the area bounded by y2 = 4x.y = 4 and x = 0. A. 21.2 B. 31.2 C. 41.2 D. 51.2

d

51. A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n. a. 80 b. 55 c. 110 d. 100

d

54 Given a function y=f(x) from set A to set B, denoted as f.A -> B, B is called ___ of f. A. domain B. limit C. range D. codomain

d

54 If a 10 lb weight could be lifted from the surface of the earth to a height of 4000 miles above the surface of the earth, how much work would have to be done? Assume the force of gravitation to vary inversely as the square of the distance.... A. 22 000 mi-lb B. 21 000 mi-lb C. 23 000 mi-lb D. 20 000 mi-lb

d

56 It is the type of graphs that has no multiple edges and no multiple loops. A. pseudo graph B. multi graph C. counter graph D. simple graph

d

59 Let the probability density function of the random variable X be defined as f(x) =5(1-x)4 for 0 ≤ x ≤ 1. Determine P(X<2). A. 0 B. 5/8 C. 3/8 D. 1

d

70. A mixture of 40 kg of candy worth P6/kg is to be made up by taking some worth P4.50/kg and some worth P8.50/kg. How many kilograms of each should be taken? A. 23 and 20 B. 34 and 15 C. 25 and 12 D. 25 and 15

d

78 A bag contains an assortment if red and blue balls. If two ball are drawn..... How many red balls are there in the bag? A. 3 B. 4 C. 5 D. 6

d

88 Transitivity and irreflexivity imply A. Symmetric B. Reflexive C. Irreflexive D. Asymmetric

d

89 It is a polyhedron containing triangular lateral faces with a common vertex and a base which is a polygon. A. pyramid B. triangular prism C. dodecahedron D. icosahedron

d

9 Find the Taylor polynomial.... for ln x about x=2 A. 1/2...1/12...1/24 B. 1/2...1/8...1/16 C. 1/2...1/4...1/24 D. 1/2...1/8...1/24

d

91. The equation r = a is the polar equation of a A. Line B. Hyperbola C. Circle D. None

d

94 It is the locus of points at which tangents drawn to both circles have the same length. A. rotation axis B. imaginary axis C. true axis D. radical axis

d

97 Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L..... A. 440.5170 min B. 470.5170 min C. 450.5170 min D. 460.5170 min

d

66. A mechanical engineer bought 24 boxes of screws for P2200. There were three types of screws bought. Screw A cost P300 per box, screw B cost P150 per box and screw C cost P50 per box. How many boxes of screw A did he buy? A. 2 boxes B. 4 boxes C. 3 boxes D. 5 boxes

b

69. A tank can be filled in 48 minutes by two pipes running simultaneously. By the larger pipe, it can be filled in 5 minutes less time than by the smaller. Find the time required for the larger pipe to fill it. A. 109. 8 minutes B. 93. 6 minutes C. 45. 2 minutes D. 90. 65 minutes

b

70 The following are equivalent statement for p -> q except ___. A. "p implies q" B. "q is necessary for p" C. "if p then q" D. "p follows from q"

b

71 Give the contrapositive of the statement. If a triangle is right then it has a 90deg angle. A. If a triangle has 90deg angle then it is right. B. If a triangle is not right then it does not have a 90deg angle. C. If a triangle has a 90deg then it is not right. D. If a triangle does not have a 90deg angle then it is not right.

b

72 For damped motion, there are three separate cases to consider depending in whether the roofs of the characteristic equation are real & distinct, equal or complex conjugate. When the roots are real and distinct, it can be classified as ___. A. Undamped B. Overdamped C. Critically damped D. Oscillatory damped

b

88 A partial ordered relation is transitive, reflexive, and ___. A. antisymmetric B. bisymmetric C. anti-reflexive D. asymmetric

a

89 A minimal spanning tree of a graph G is __. A. all of the choices B. minimum weights C. a spanning sub graph D. a tree

a

93 Limits at infinity are associated with ___. A. vertical asymptotes B. vertical axis C. horizontal asymptotes D. horizontal axis

a

95 An electrical system consists of four components as illustrated......(block diagram) A. 0.7776 B. 0.4532 C. 0.4563 D. 0.7423

a

95 The graph of r= a/θ is called ___. A. hyperbolic spiral B. logarithmic spiral C. lituus D. limacon

a

63. If three sides of a trapezoid are each 10 cm long, how long must the fourth side be if the area is maximum? A. 15 B. 20 C. 10 D. 30

b

57 A spherical iron ball 8 inches in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 20 cu in per min, how fast is the outer surface of the ice decreasing when the ice is 1 in thick? A. -3.39 in2/min B. -3.33 in2/min C. -3.36 in2/min D. -3.30 in2/min

b

57 It is the formula which is always true for every value of its propositional variables. A equivalence B. tautology C. synthesis D. contingency

b

58 It is a finite sequence of precise instructions for performing a computation or for solving problem. A. time complexity B. algorithm C. quick counting D. sorting

b

61 A tank contains 100 L of pure water. Brine that contains 0.1 kg of salt per liter enters the tank.... A. 5.28 B. 4.51 C. 5.51 D. 4.28

b

62 In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to A. singular matrix B. Upper triangular matrix C. Diagonal matrix D. Lower diagonal matrix

b

63 Find the sum of the coefficients of a cubic polynomial whose graph passes through the points (1,3),(2,-2),(3,-5) and (4,0). A. 5 B. 3 C. 7 D. 4

b

100 Which of the following function is the constant 1 function? A. (p ^ q) v (~p v (p ^ ~q)) B. ~p v (p ^ q) C. (p ^ ~q) ^ (~p vq) D. (~p v q) v (p ^ q)

a

11. x=1−√1−√1−√1−√1−⋯ A. 0.382 B. 0.618 C. 0.482 D. 0.218

a

15 A fisherman 12 km from the shore desires to reach a point on the shore 20 km from his present position. If he can walk 4 km/hr and rows 2 km/hr. In what direction θ should he row in order to reach his destination the shortest possible time? A. 30deg B. 60deg C. 40deg D. 10deg

a

2 A resistor and inductor are connected in series in a circuit containing an impressed volage of 100 V. If R=10 ohm, L=2 H, and i=0 when t=0 , find I when t=0.2s. A. 0.9516 A B. 0.8016 A C. 0.9016 A D. 0.8516 A

a

23. Candle A and Candle B are of equal length are to be lighted at the same time and burning until candle A is twice as long as candle B, candle A is designed to fully burn in 8 hours A. 2hrs 40.2 mins B. answer C. is D. letter A

a

24. A pipe can fill up a tank with the drain open in three hours. If the pipe runs with the drain open for one hour and then the drain is closed, it will take 45 more minutes for the pipe to fill the tank. If the drain will be closed right at the start of filling, how long will it take for the pipe to fill the tank? A. 1. 125 hours B. 1. 450 hours C. 1. 324 hours D. 1. 512 hours

a

26 the slope of the surface z=xy2 in the x-direction at the point (2,3) is __. A. 9 B. 10 C. 12 D. 7

a

4 Water leaks from a cylinder at a rate proportional to the square root of the volume remaining at any time. If initially there are 64 gallons present and 15 gallons leak out on the first day, how much will be left after 4 days? A. 14 gallons B. 20 gallons C. 15 gallons D. 16 gallons

a

4 When two rows are interchanged in position, the value of the determinants will be A. Unchanged B. Multiplied by C. Become zero D. Unpredictable

a

49. In how many ways can you express 47 as a sum of two primes? a. 0 b. 2 c. 1 d. none

a

51 Find the perimeter of the curve x2/3+y2/3=4. A. 48 B. 49 C. 47 D. 46

a

54. A television antenna 20 m high stands on top of a house which is 12 m high. At what distance from the base of the house will the antenna and the house subtend equal angle? A. 24 m B. 31 m C. 15 m D. 28 m

a

55 The variance of a standard normal random variable Z is equal to ___. A. 1 B. 1/2 C. 0 D. 2

a

62 A __ occurs when all possible cases in which the given conditions are satisfied. A. proof by cases B. exhaustive proof C. proof by contraposition D. proof by equivalence

a

65 A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mh/cm3 of the drug enters the patient's bloodstream at a rate of 100 cm3/h.... A. dq/dt = 500 + 0.4q; q in mg, t in h B. dq/dt = 500 - 0.4q; q in mg, t in h C. dq/dt = 500 - 0.04q; q in mg, t in h D. dq/dt = 500 + 0.04q; q in mg, t in h

a

68 It is a proof technique used to prove propositions involving the set of natural numbers or its subset. A. Mathematical Induction B. Proof by cases C. Proof by contraposition D. Proof by equivalence

a

69 For what values of k does the function y = coskt satisfy the differentia equation 4y'' = 25y? A. ±5/2 B. ±25/4 C. ±5 D. ±5/4

a

71 For damped motion, there are three separate cases to consider depending in whether the roofs of the characteristic equation are real & distinct, equal or complex conjugate. When the roots are complex conjugates of each other, it can be classified as ___. A. Undamped B. Overdamped C. Critically damped D. Oscillatory damped

a

73 The compound proposition ( p ^ q) ^ ~(p v q) is an example of __. A. contradiction B. tautology C. contingency D. eventuality

a

84 In an undirected graph, the number of nodes with odd degree must be __. A. even B. prime C. at least one D. odd

a

100 Which of the following correspondence is invertible? A. Onto B. One-to-one C. One-to-many D. Many-to-one

b

14 Am investment of Php125000 is made at an annual simple interest rate of 5.5. How much additional money must be invested at an annual simple interest of 8% so that the total interest rate is 7% if the total investment? A. Php 180,500 B. Php 187,500 C. Php 197,500 D. Php 190,500

b

16 At 3:00 PM, a boat is 12.5 miles due west of a radar station and travelling at 11 mph in a direction that is 57.3deg south of an east-west line. At what time will the boat be closest to the radar station? A. 3:26 PM B. 3:41 PM C. 3:37 PM D. 3:11 PM

b

2 Solve the different equation x(y−1)dx+(x+1)dy=0 if y = 2 and x =1. Determine y when x = 2. A. 1.80 B. 1.55 C 1.48 D. 1.63

b

35 For a continuous function at a critical point x =c, a/an __ occurs at x = c whenever the derivative changes from negative to positive going from left to right of x = c. A. Relative maximum B. relative minimum C. inflection point D. relative extremum

b

36 If ln(lny)+lny=lnx, find y' A. x/(x + y) B. y/(x + y) C. x/(x - y) D. y/(x - y)

b

4 What is the range of f(x) = sec-1x? A. (-inf, -1) U (1,+inf) B. (-inf, -1] U [1. =inf) C. [0, pi/2) U (pi/2, pi) D. (0, pi/2) U (pi/2, pi)

b

40 Find the area enclosed by the curve r2=4cosɸ. A. 4 B. 8 C. 2 D. 16

b

45 Determine the coordinates of the centroid for the plane bounded by the graphs of y=-x2 and y= x - 6. A. (-1/2, -4) B. (-1/2, -5) C. (-1, -4) D. (-1,-5)

b

45 The area in the second quadrant of the circle x2+y2=36 is revolved about the line y+10=0. What is the volume generated? A. 2218.63 B. 2228.83 C. 2233.43 D. 2208.53

b

45 Two lead firefighter (Beth and Tim) are 300 yards apart and they estimate each of their distances to the fire as approximately 150 yards (Beth) and 200 yards (Tim)... A. 28deg B. 26deg C. 30deg D. 32deg

b

46 Find the area of the surface generated by revolving the arc of 3y = 4x from x=0 to x=3 about the x-aix. A. 10pi B. 20pi C. 25pi D. 15pi

b

5 A series circuit has a capacitor of 10-5 F, a resistor of 300 ohms and an inductor of 0.2 H. The initial charge on the capacitor is 10-6 and there is no initial current. Find the charge Q on the capacitor at any time t. A. Q = 10-4(e-500t - 2e-1000t) C in : t in s B. Q = 10-6(2e-500t - e-1000t) C in : t in s C. Q = 10-4(2e-500t - e-1000t) C in : t in s D. Q = 10-4(e-500t - 2e-1000t) C in : t in s

b

52 The angle θ, made by swinging pendulum with the vertical direction, is given at tie t by the equation θ = asin(bt + c) where a, b and c are constants. Find the angular acceleration at time t. A. -a2θ B. -b2θ C. -aθ D. -bθ

b

11 A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many dimes are there? A. 6 B. 10 C. 9 D. 18

c

12 Determine x, so that: a, 2x+4, 10x-4 will be a geometric progression. A. 6 B. 2 C. 4 D. 5

c

22 A transmitter with a height of 15 m is located on top of a mountain, which is 3.0 km high. What is the furthest distance on the surface of the Earth that can be seen from the top of the mountain? Take the radius of the Earth to be 6400 km. A. 196 km B. 255 km C. 205 km D. 156 km

c

25. A two-digit number is chosen randomly. What is the probability that it is divisible by 7? A. 13/90 B. 11/90 C. 12/90 D. 17/90

c

28 A wire with a length of 54 inches is cut into two unequal lengths. Each part is bent to form a square. If the sum of the area for the two squares is 97 square inch, what is the area of the smaller square? A. 34 B. 23 C. 16 D. 10

c

29 A gambler throws two fair dice twice. Let A be the event that the first toss is a 7 or an 11 and let B be the event that the second toss is an 11. What is P (A or B)? A. 41/162 B B. 45/162 C. 43/162 D. 47/162

c

38 A landscaper has planted a rectangular garden that measure 8 ft by 5ft. He has ordered 2 cubic yard of stones for a border along the outside of the garden. If the border needs to be 4 inches deep and he wants to use all of the stones, how wide should the border be? A. 2.2 ft B. 3.1 ft C. 2.3 ft D. 3.2 ft

c

41 When a certain polynomial p(x) is divided by (x-1), remainder is 12. When the same polynomial is divided by (x-4), the remainder is 3. Find the remainder when the polynomial is divided by (x-1) (x-4). A. x + 5 B. -2x - 8 C. -3x + 15 D. 4x - 1

c

47 A delivery company accepts only rectangular boxes of the sum of whose length and girth.... A. 11,668 in3 B. 11,644 in3 C. 11,664 in3 D. 11,688 in3

c

52 The ___ of a proposition p, is the statement "It is not the case that p" A. implication B. conjunction C. negation D. disjunction

c

53 It is the value of the observation in a dataset that appears most frequently. A. median B. mean C. mode D. disjunction

c

58. How many sides have a polygon if the sum of the interior angles equals twice the sum of the exterior angles? A. 7 B. 4 C. 6 D. 5

c

59 It is the maximum number of linearly independent row vectors of matrix A A. Zero of A B. Span of A C. Rank of A D. Basis of A

c

62 Use Euler's method with step size 0.1 to approximate... A. 1.262 B. 1.220 C. 1.362 D. 1.528

c

65 A merchant paid P360 for some crates of Bananas. Four crates were spoiled and had to be thrown away, but he sold the rest at an increase in price in price of P2 per crate, gaining P88.00. How many crates did he buy? A. 70 B. 65 C. 60 D. 55

c

66 Consider the following propositions. p: Today is Monday q: It is raining today Express ~p ^ q in simple English A. Today is Monday and it is raining. B. Today is Monday or it is not raining. C. Today is not Monday and it is raining. D. Today is Monday or it is not raining.

c

67 Let p: John learns math logic q: John gets a good grade Express ~q <-> ~p A. If John learns math logic then he gets a good grade. B. John gets a good grade if and only if he learns math logic. C. John does not get a good grade if and only if he does not learn math logic. D. If John does not learn math logic then he does not get a good grade.

c

68 Find the radius of curvature of r = 2 cost t i + 3 sin t j at t= pi/2. A. 3/2 B. 3/4 C. 4/3 D. 2/3

c

72 A compound proposition that is always false for all possible truth values of the constituent propositions is called a/an ___. A. contingency B. tautology C. contradiction D. contingency

c

73 An experiment that can result in different outcomes, even though it is repeated in the same manner every time is called A. classical experiment B. controllable experiment C. random experiment D. repetitive experiment

c

75. Find the angle between the hour and minute hands at 7:49. A. 60° B. 58.5° C. 59.5° D. 59°

c

82 This method for solving linear systems is a systematic process of elimination that reduces to triangular form because the system can be easily solved by back substitution. A. Runge-Kutta Method B. Gaussian Elimination C. Gauss-Jordan Elimination D. Gauss-Seidel Method

c

85 A/an ___ equation that is true for any number substituted to the variable. A. consistent B. independent C. identity D. conditional

c

91 If B is a Boolean Algebra, then which of the following is true? A. B is finite, distributive but not complemented lattice B. B is not distributive lattice C. B is a finite, complemented and distributive lattice D. B is a finite but not complemented

c

94 A lottery has a first prize of P10,000,000. Suppose only 8,000,000 tickets are sold... A. P30 B. P40 C. P50 D. P60

c