Math
c
1) Mary was four times as old as Lea ten years ago. If she is now twice as old as Lea, how old is Mary? a. 25 b. 40 c. 30 d. 15
a
1. Find the mode for the following numbers: 16,29,19,27,18,20,27,24,19,27. a. 27 b. 19 c. 18 d. 24
a
1.A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was a. 14 b. 33 c. 19 d. 38
d
1.What is the derivative with respect to x of (x + 1)3 - x3? A. 3x + 6 B. 3x - 3 C. 6x - 3 D. 6x + 3
c
10. The positive square root of the variance is equal to a. Quartile deviation b. Mean deviation c. Standard deviation d. Average deviation
a
10. The probability that the Ginebra basketball team will win the championship is assessed as being 1/3. Find the odds that the team will win. a. 1:2 b. 2:1 c. 1:3 d. 3:1
a
10. What theorem is used to solve for centroid? a. Pappus' Theorem b. Varignon's Theorem c. Castiglliano's Theorem d. Pascal's Theorem
c
10. Which of the following numbers is not a prime number. a. 2 b. 5 c. 9 d. 7
a
10.A tank contained brine of which 1.5% was salt. When 100 pounds of water had been evaporated, 2.5% of the brine was salt. How many pounds of the solution remained? a. 150 lb b. 4lb c. 300 lb d. 200 lb
c
2) The terms of a sum may be grouped in any manner without affecting the result. This law is known as: a. Commutative Law b. Distributive Law c. Associative Law d. Reflexive Law
b
2. MCMXCIV is equivalent to what number? A. 1964 B. 1994 C. 1984 D. 1974
d
2. What is the area of the kite whose diagonals have lengths 12 and 7? a. 24 b. 30 c. 40 d. 42
b
3. Express 45° in mils A. 80 mile B. 800 mils C. 8000 mils D. 80000 mils
b
4) Which of the following is equivalent to (x)(x)(x)(x3), for all x? a. 6x b. x6 c. 4x6 d. 4x4
c
4. Find the distance between (1,2,-5) and (-1,-1,4). a. Sqrt(92) b. Sqrt(93) c. Sqrt(94) d. Sqrt(95)
a
5) The graph of r = 10cos(Θ), where r and Θ are the polar coordinates, is a. a circle b. an ellipse c. a horizontal line d. a hyperbola
c
5. The sum of two logarithms of two numbers is 1.748188 and the difference of their logarithms is -0.0579919. One of the numbers is: A. 9 B. 6 C. 8 D. 5
b
6) At the maximum point, the second derivative of the curve is a. 0 b. Negative c. Undefined d. Positive
a
6. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? a. 15 days b. 10 days c. 5 days d. 1 day
c
6. All board reviewees are not more than 25 years old. This statement implies that they are: a. less than 25 years old b. at least 25 years old c. 25 years old or less d. 25 years old or more
a
6. Consider the series Sn =1 -1 +1 -1 +1 + -... If n is even, the sum is zero and if n is odd, the sum is 1. What do you call this kind of infinite series? a. Oscillating series b. Geometric series c. Bilateral Series d. Di-valued Series
a
6. The mean deviation is a measure of a. Dispersion b. Distribution c. Central tendency d. Frequency
c
6. The two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26°. What is the third side? A. 197.49 m B. 218.61 m C. 341.78 m D. 282.15 m
b
7) Solve for x if log5 x = 3. logb x = y <-----> x = by x= 53 x=125 a. 115 b. 125 c. 135 d. 145
c
7. The number 0.123123123123 .. . is A. irrational B. surd C. rational D. transcendental
b
8. A man and a boy can dig a trench in 20 days. It would take the boy 9 days longer to dig it alone than it would take the man. How long would it take the boy to dig it alone? a. 54 days b. 45 days c. 35 days d. 36 days
c
9) If a=b and b=c, then a=c. This property of real number is known as: a. Reflexive Property b. Symmetric Property c. Transitive Property d. Addition Property
d
A spherical triangle which contains at least one side equal to a right angle is called a. Right angle b. An isosceles triangle c. Polar triangle d. A quadrantal triangle
a
A/n ______ is the set of all points P in a plane such that the sum of the distances of P from two fixed points F and G of the plane is constant. a. Ellipse b. Circle c. Paraboloid d. Conic
b
Consider the series Sn =1 -1 +1 -1 +1 + -... If n is even, the sum is zero and if n is odd, the sum is 1. What do you call this kind of infinite series? a. Geometric Series b. Oscillation Series c. Bilateral Series d. Di-valued Series
a
Determine the period and amplitude of the function y = 2sin5x. a. 2π/5, 2 b. 3π/2, 2 c π/5, 2 d. π/5, 2
c
Determine the slope of the curve y = x^2 - 3x as it passes through the origin a. -4 b. 2 c. -3 d. 0
a
Differentiate the equation y = (x^2)/(x + 1). a. (x^2 + 2x)/(x + 1)^2 b. x/(x + 1) c. 2x^2/(x + 1) d. 1
a
Establish the identity: □csc csc θ-□cot cot θ= 1/(□sin sin θ )-(□cos cos θ )/(□sin sin θ ) a. sinθ/(1+cosθ) b. sinθ/(1-cosθ) c. sinθ/(1+sinθ) d. cosθ/(1+sinθ)
b
Evaluate the limit of (x + 2)/(x - 2) as x approaches α a. α b. -1 c. 1 d. 4
d
Given vectors A = i + j + k and B = 2i - 3j + 5k, find A∙B. a. 2i- 3j+ 5k b. 2i+ 3j+ 5k c. 6 d. 4
b
How many edges are there in a graph with 12 vertices each of degree six? a. 12 b. 36 c. 64 d. 72
d
How many relations are there on set A = {a, b, c, d}? a.4 b. 16 c. 256 d. 65536
a
Let the interval (a, + ∞) be the range of function f. The range of f(x) -4 is given by a. The interval (a - 4, + ∞) b. The interval (a + 4, + ∞) c. The interval (a, + ∞) d. None of these
d
Solve (x^2+ y^2 )dx-2xdy=0 a. x^2+ y^2=cx b. x^2-y^2/x=c c. x^2-y^2=c d. 〖 x〗^2-y^2=cx
c
The derivative of an increasing function f(x) must be a. Strictly positive b. Always positive c. Non-negative d. Negative
d
The derivative with respect to x of 2cos^2 (x^2 + 2) a. 4 sin (x^2 + 2) cos (x^2 + 2) b. -4 sin (x^2 + 2) cos (x^2 + 2 c. 8x sin (x^2 + 2) cos (x^2 + 2 d. -8x sin (x^2 + 2) cos (x^2 + 2)
b
The radius of the inscribed circle of a polygon is? a. Abscissa b. Apothem c. Asymptote d. Directrix
c
What is the Laplace Transform of a unit step function? a. 1 b. s c. 1 / s d. u(t)
a
9. According to Newton's law of cooling, the rate at which a substance cools in air is directly proportional to the difference between the temperatures of the substance and that of air. If the temperature of the air is 30° and the substance cools from 100° to 70° in 15 minutes, how long will it take to cool 100° to 50°? A. 33. 59 min B. 43.60 min C. 35.39 min D. 45.30 min
b
9. If the value of the discriminant of a quadratic equation is 1.25, then the roots of the equation are: a. real and equal b. real and unequal c. complex and unequal d. imaginary and distinct
b
9. Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy? a. 100 grams b. 200 grams c. 300 grams d. 500 grams
b
9. The odds that a reviewee will not pass the board exam are 1:4. Find the probability that the reviewee will not pass the exam. a. 0.80 b. 0.20 c. 0.25 d. 0.75
c
Find the angle between the vectors u=(-2,5) and v=(3,2) a. θ= 168.1° b. θ= 7.81° c. θ= 78.1° d. θ= 75.1°
a
Find the coordinate of the vertex of the parabola y = x^2 - 4x + 1 by making use of the fact that at the vertex, the slope of the tangent is zero. a. (2,-3) b. (3,2) c. (-1,-3) d. (-2,-3)
b
Find the derivative of y = x^x a. x^x (2 + ln x) b. x^x (1 + ln x) c. x^x (4 - ln x) d. x^x (8 + ln x)
a
Two sides of a triangle are 5 and 10 inches, respectively. The angle between them is increasing at the rate of 5◦ per minute. How fast is the third side of the triangle growing when the angle is 60deg? a. 5π/36 in/min b. 5π/25 in/min c. 6π/5 in/min d. 6π/25 in/min
d
What are the odds of getting 2 ones in a single throw of a pair of dice? a. 25 to 36 b. 35 to 36 c. 1 to 36 d. 1 to 35
c
What is the Laplace transform of sinh (wt)? a. 1 / (s2 + w2) b. 1 / (s2 - w2) c. s / (s2 + w2) d. s/ (s2 - w2)
d
What is the transverse axis on the x-axis, a=4, latus rectum 32? a. x^2-4y^2=64 b. 4x^2+y^2=64 c. x^2+〖4y〗^2=64 d. 4x^2-y^2=64
a
Which of the following is an odd function? a. f(x)=xcosx b. f(x)=xsinx c. f(x)=e^cosx d. f(x)=〖sin〗^2 x
c
2. A ladder leans against the wall of a building with its lower end 4m from the building. How long is the ladder if it makes an angle of 70o with the ground? a. 12.3 m b. 13.5 m c. 11.7 m d. 10.8 m
c
2. A line which a curve approach infinity but will never intersect. a. Parallel line b. Inclined line c. Assymptote d. Skew line
b
2. Differentiate √((x^2 + 2) ) A. ((x2 + 2)1/2) / 2 B. x / (x2 + 2)1/2 C. (2x) / (x2 + 2)1/2 D. (x2 + 2)3/2
a
3. In how many ways can 8 persons be seated at a round table if a certain 2 are to sit next to each other? a. 1, 440 b. 1,008 c. 4, 140 d. 5, 040
c
4. Find tan Ѳ if sin Ѳ = 2/3 and Ѳ is not in the first quadrant. a. -√5/3 b. -√5/2 c. -2/√5 d. -3/√5
a
4. Find the radius of curvature of a parabola y2 - 4x = 0 at point (4, 4). A. 22.36 units B. 25.78 units C. 20.33 units D. 15.42 units
a
4. If 16 is 4 more than 4x, find 5x - 1. A. 14 B. 3 C. 12 D. 5
c
4. If x:y:z =4: - 3:2 and 2x+4y-3z = 20, find the value of x. a. 6 b. -4 c. -8 d. 7
d
5. Solve logx2=(logx)2 a. 103 b. 102 c. 101 d. 100
b
6. If the inclination θ of a line is an obtuse angle, then the tangent of θ is a. Positive b. Negative c. Zero d. Infinity
d
7. Two prime numbers, which differ by two, are called prime twins. Which of the following pairs of numbers are prime twins? a. (1,3) b. (7,9) c. (13,15) d. (17,19)
d
8) The logarithm of a negative number is a. Irrational number b. Real number c. Imaginary number d. Complex number
d
8. .A plane is headed due to east with airspeed 240 mph. if a wind at 40 mph from the north is blowing. find the groundspeed of the plane. a. 342 mph b. 532 mph c. 4123 mph d. 243 mph
a
8. A committee of 5 people is to be selected from a group of 6 men and 7 women. What is the probability that the committee will have at least 3 men? a. 59/143 b. 140/429 c. 84/145 d. 37/429
c
8.One ounce of the mixture containing an unknown percentage of salt is to be mixed with 2 ounces of a mixture which is 15% salt, in order to obtain a solution which is 12% salt. What was the percentage of salt in the first solution? a. 12% b. 5% c. 6% d. 24%
d
8. The integral of any quotient whose numerator is the differential of the denominator is the: a. product b. derivative c. cologarithm d. logarithm
c
9. Which of the following relations is true? a. sin(-A) = sin A b. tan(-A) = tan A c. cos(-A) = cos A d. csc(-A) = csc A
b
5. What is the sum of the coefficients in the expansion (x + y - z)8? A. 0 B. 1 C. 2 D. 3
c
6. Getting an odd number by throwing a die is called: a. an experiment b. an outcome c. an event d. a trail
a
6. K/(s2+k2) is inverse laplace transform of: a. cos kt b. sin kt c. tan kt d. sec kt
a
6. Solve for the value of "a" in the equation a8 - 17a4 + 16 = 9 A. ± 2 B. ± 3 C. ± 4 D. ± 5
c
If 〖f(x)=e〗^(-x+1), then f'(1) is equal to a. 0 b. 1 c. -1 d. ∞
a
3. If the distance between (8,7) and (3,y) is 13, what is the value of y? a. -5 or 19 b. 5 or 19 c. 5 or -19 d. -5 or -19
a
3. In an oblique triangle, a=25, b=16, angle C=94˚06'. Find the measure of angle A. a. 54.5˚ b. 45.5˚ c. 24.5˚ d. 54.5˚
a
3. It is a sequence of numbers such that successive terms differ by a constant a. Arithmetic progression b. Infinite progression c. Geometric progression d. Harmonic progression
d
3. Peggy guesses on all 10 questions on a true-false quiz. What is the probability that exactly half of the answers are correct? a. 1/2 b. 1/32 c. 1/8 d. 63/256
c
3. The L'Hopital's Rule was formulated by __. a. Marquis de L'Hopital b. Marrione de L'Hopital c. Johann Bernoulli d. Isaac Newton
c
8. Find the term involving y5 in the expansion of (2×2 + y)10. A. 8064 x10y5 B. 8046 x5y5 C. 8046 x10y5 D. 4680 x5y5
b
1. A function wherein one variable is not yet readily expressed as function of another variable is said to be: a. Symmetric b. Implicit c. Explicit d. Exponential
c
1. A pair of dice is thrown. Find the probability that their sum is greater than 7 given that the numbers are match. a. 6/36 b. 3/36 c. 1/2 d. 1/11
a
1. Find the probability of a sum of 6 or a sum of 9 on a single throw of two dice. a. 1/4 b. 5/324 c. 5/9 d. 15/36
d
1. Find the value of k so that 4×2 + 6x + k is a perfect square. A. 36 B. 2.5 C. 9 D. 2.25
b
1. How many horsepower are there in 800 kW? a. 2072. hp b. 1072.4 hp c. 746 hp d. 3072.4 hp
b
1. In a regular hexagon, the measure of each interior angle is _______. a. 100o b. 120o c. 140o d. 160o
a
1. In how many ways can a picture be painted by using two or more of 7 different colors? a. 120 b. 110 c. 128 d. 131
d
1. What is the temperature in degree Celsius of absolute zero? A. -32 B. 0 C. 273 D. -273
b
1. The arc length equal to the radius of the circle is called: a. 1 grad b. 1 radian c. π radian d. 1 quarter circle
c
1. The number 0.123123123123 .. . is A. irrational B. surd C. rational D. transcendental
b
10) The logarithm of 1 to any base is: a. indeterminate b. zero c. infinity d. one
a
10. Consider the series Sn =1 -1 +1 -1 +1 + -... If n is even, the sum is zero and if n is odd, the sum is 1. What do you call this kind of infinite series? a. Oscillating series b. Geometric series c. Bilateral Series d. Di-valued Series
c
10. Evaluate the determinant: A. 4 B. 2 C. 5 D. 0
c
10. Find the equation of the curve at every point of which the tangent line has a slope of 2x. A. x = -y2 + C B. y = -x2 + C C. y = x2 + C D. x = y2 + C
d
10. Find the quadratic mean of {1.3, 1.5, 1.7, 1.0, 1.1} a. 9.04 b. 1.1 c. 1.8 d. 1.34
d
10. Find the sum of the roots 5x^2 -10x + 2 = 0 a. -2 b. 1/2 c. -1/2 d. 2
d
10. How many feet difference is 1 nautical mile and 1 statute mile? A. 100 feet B. 200 feet C. 400 feet D. 800 feet
c
10. How many sides are there in a regular polygon if it has a sum of 1,800o in its interior angle? a. 10 b. 11 c. 12 d. 13
d
10. If P(n+1, 4) = 2P(n, 4) a. 4 b. -7 c. 10 d. 7
b
10. If the radius of the circle is decreased by 20%, by how much is its area decreased? a. 46% b. 36% c. 56% d. 26%
c
2. Find the median of the following set of data: {4,10,1,6} a. 4 b. 10 c. 7 d. 5.25
d
2. Find the value of x which will satisfy the following expression: A. 3/2 B. 9/4 C. 18/6 D. No real solution
c
2. Given vectors A = i + 2j and B = 3i - 2j + k, find the angle between them. a. 0° b. 36.575° c. 96.865° d. 127.352°
a
2. If the roots of an equation are zero, then they are classified as: a. Trivial solution b. Hypergolic solution c. Zeros of function d. Extraneous roots
b
2. John and Jack can do a job in 4 hours and the working rate of John is twice that of Jack. How many hours would it take John to work alone? a. 5 b. 6 c. 7 d. 10
b
2. What is the probability of getting a number "4" thrice in five tosses of a die? a. 0.0232 b. 0.0322 c. 0.3220 d. 0.2330
b
3) The ratio of the circumference of any circle to the diameter of the circle is: a. An integer b. An irrational number c. A rational number d. A whole number
a
3. A ______ is a collection of objects, and these objects are called the elements. a. set b.subset c.venn diagram d.union
c
3. A clock has a minute hand 16cm long and an hour hand 11cm long. Find the distance between the outer tips of the hands at 2:30 o'clock. a. 19.6 cm b. 20.6 cm c. 21.6 cm d. 22.6 cm Hint: The angle between the minute and hour hand is 105o.
a
3. Find the slope of the line tangent to the curve y = x^3 - 2x + 1 at x = 1. A. 1 B. 1/2 C. 1/3 D. 1/4
b
3. What is defined as the locus of point that moves in a plane so that its distance from a fixed point is equal to its distance from a fixed line? a. Hyperbola b. Parabola c. Ellipse d. Circle
a
3. What is the height of the old College of Engineering building if the shadow of the building is 20 meters and the angle of elevation of the sun is 30o? a. (20√3)/3 b. (√3)/20 c. (2√3)/3 d. (√3)/3
d
4. A spherical triangle which contains at least one side equal to a right angle is called ___. a. Right Triangle b. Isosceles Triangle c. Polar Triangle d. Quadrantal Triangle
d
4. It can be defined as the set of all points on a plane whose sum of distances of any of which from two fixed points is constant. a. Circle b. Hyperbola c. Parabola d. Ellipse
b
4. It is an equation that contains one or several derivatives of an unknown function called y(x) and which we want to determine from the equation. a. homogeneous differential equation b. ordinary differential equation c. partial differential equation d. linear constant coefficient differential equation
b
4. Suppose that three dice are thrown at the same time. Find the probability that at least one 4 will show. a. 1/216 b. 91/216 c. 25/36 d. 1/12
b
5. A number which can be expressed as the quotient of two integers is a. rational b. irrational c. natural d. prime
c
5. A parabolic arch has a span of 20 m and a maximum height of 15m. How high is the arch 4m from the center of the span? a. 10.6 m b. 11.6 m c. 12.6 m d. 13.6 m
c
5. At a Math Contest, the judges eliminate 1/3 of the contestants after each half hour. If 81 contestants were present at the start, how many would be left after 2 hours? a. 18 b. 12 c. 16 d. 10
c
5. Evaluate the limit of (8−3x+12x2) as x approaches to 2, if it exists. a. 0 b. 1 c. 50 d. 56
d
5. Find the value of A between 270° and 360° if sin 2 A - sin A = 1. A. 300° B. 320° C. 310° D. 330°
b
5. The graph of r=a+bcos θ is a : a. Lemniscates b. Limacon c. Cardioids d. Lituus
d
5. Two cars begin a trip from the same point P. If car A travels north at the rate of 30 mi/h and car B travels west at the rate of 40 mi/h, how fast is the distance between them changing 2 hours later? a. 20 mi/h b. 30 mi/h c. 40 mi/h d. 50 mi/h
a
5. What is the Laplace transform of sin (wt)? a. 1/(s2+w2) b. 1/(s2-w2) c. s/(s2+w2) d. s/(s2-w2)
a
5. What is the equation whose roots are the reciprocal of the roots of 2x2 - 3x - 5 = 0? A. 5×2 + 3x - 2 = 0 B. 2×2 + 3x - 5 = 0 C. 3×2 - 3x +2 = 0 D. 2×2 + 5x - 3 = 0
b
5. What is the probability of drawing a king or a black card? a. 15/25 b. 7/13 c. 1/2 d. 6/13
d
5. _________ is the concept of finding the derivative of an exponential expression. a. Logarithmic derivative b. Trigonometric derivative c. Implicit derivative d. Chain rule
a
6. Each side of a cube is increased by 1%. By what percent is the volume of the cube increased? a. 3% b. 23.4% c. 33.1% d. 34.56%
b
6. Evaluate the first derivative of V(t) = (t+1)/(t+4). a. ¼ b. 3/(t+4)2 c. 3/(t+4) d. 3/(t+1)(t+4)
b
6. The graphs of the equations of the forms r = asinnϴ and r = acosnϴ where n is a positive integer, greater than 1, are called _____. a. Lemniscates b. Rose Curves c. Cardioids d. Limacons
b
6. The graphs of the equations of the forms r = asinnϴ and r = acosnϴ where n is a positive integer, greater than 1, are called _____. a. Lemniscates b. Rose Curves c. Cardioids d. Limacons
d
6. The line y=5 is the directrix of a parabola whose focus is at point (4, - 3). Find the length of the latus rectum. a. 24 b. 4 c. 8 d. 16
a
7. Find the distance of the point (6,2,3) from the z-axis. a. 2sqrt(10) b. 3sqrt(5) c. Sqrt(13) d. 7
d
7. If a derivative of a function is constant, the function is: a. sinusoidal b. logarithmic c. exponential d. First degree
c
7. In any square matrix, when the elements of any two rows are exactly the same, the determinant is: a. unity b. positive integer c. zero d. negative integer
c
7. Pabs is 4 years older than Ming. Next year, Pabs will be 2 times as old as Ming. How old is Pabs? a. 10 years old b. 21 years old c. 7 years old d. 14 years old
c
7. The altitudes of the sides of a triangle intersect at the point, which is known as: a. Centroid b. Incenter c. Orthocenter d. Circumcenter
d
7. The graph of an equation of the form r = b + asinϴ or r = b + acosϴ is called a ________. a. Lemniscates b. Rose Curves c. Cardioids d. Limacons
c
7. This states that every integral rational equation has at least one root. a. Fundamental Theorem of Arithmetic b. Fundamental Theorem of Counting c. Fundamental Theorem of Algebra d. Fundamental Theorem of Equations
b
7. What is the discriminant of the equation 4×2 = 8x - 5? A. 8 B. -16 C. 16 D. -8
a
8. A/n ______ is the set of all points P in a plane such that the sum of the distances of P from two fixed points F and G of the plane is constant. a. Ellipse b. Circle c. Conic d. Parabola
b
8. Express 45° in mils A. 80 mile B. 800 mils C. 8000 mils D. 80000 mils
b
8. In complex algebra, we use a diagram to represent a complex plane commonly called: a. De Moivre's diagram b. Argand diagram c. Funicular diagram d. Venn diagram
b
8. In how many ways can the position of President, Vice-President and secretary be filled in a club of 12 members if no person is to hold more than one position? a. 1230 b. 1320 c. 1203 d. 1302
c
8. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years? A. 88.60 B. 95.32 C. 92.16 D. 90.72
a
8. Solve for the values of k in the equation 11k2 - 32k + 10 = 0. a. k = 2.55 and k = 0.36 b. k = 2 and k = 0.3 c. k = 2.8 and k = 0.45 d. k = 3 and k = 1
a
8. The probability of A's winning a game against B is 1/3. What is the probability that A will win at least two of a total of 3 games? a. 7/27 b. 8/27 c. 19/278 d. 15/27
a
8. These variables are dimensionless combinations of the physical variable and parameters of the original. a. Canonical Variables b. Dependent Variables c. X and Y Variables d. Controlled Variables
d
9. A banca traveled at an average speed of 15 kph downstream and then back at an average speed of 12 kph upstream. If the total time of travel is 3 hours. find the total distance traveled by the banca a. 10km b. 60km c. 30km d. 40km
c
9. A point in the distribution of scores at which 50% of the score fall below and 50% fall above. a. Mode b. Mean c. Median d. Range
a
9. How many different signals, each consisting of 6 flags hung in a vertical line, can be formed from 4 identical red flags and 2 identical blue flags? a. 15 b. 672 c. 720 d. 34560
a
9. Meiko King travels 100 miles at the rate of 30 mph and then on a free way travels the next 100 miles at the rate of 55 mph. What is her average speed? a. 38.8 mph b. 42.5 mph c. 45.2 mph d. 48.8 mph
a
9. Simplify the expression i1997 + i1999, where i is an imaginary. A. 0 B. -i C. 1 + i D. 1 - i
c
9. Simplify the radical expression (6√126)/√18. a. 6√49 b. 12√196 c. 6√7 d. 7√6
b
9. Terms that a differ only in numeric coefficients are known as: a. Unequal terms b. Like terms c. Unlike terms d. Equal terms
a
9. The measures of angles A, B and C of a triangle are in the ratio 3:4:5. What is the measure, in degrees, of the largest angle? a. 75o b. 15o c. 45o d. 90o
c
9. The probability of drawing a black jack and an ace is succession from a deck of 52 cards a. 0.0003 b. 0.003 c. 0.003 d. none of the above
c
9. What is the Fahrenheit equivalent of 100 degrees Celsius? A. 200 B. 180 C. 212 D. 100
b
A ______ is a collection of objects, and these objects are called the elements. a. Venn Diagram b. Set c. Subset d. Union
c
A measure of 3200 mils is equal to a. 90 deg b. 45 deg c. 180 deg d. 120 deg
b
An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a bulb burns between 778 and 834 hours. a. 5.111 b. 0.5111 c. 0.05111 d. 0.005111
a
Find the second derivative of y = x^ - 2 when x = 2. a. 0.375 b. 0.268 c. 0.148 d. 0.425
a
Find the slope of the curve y = 6(4 + x)^1/2 at point (0,12). a. 1.5 b. 2.2 c. 1.8 d. 2.8
b
Find the differential equations of the family of lines passing through the origin. a. ydx-xdy=0 b. xdy-ydx=0 c. xdx+ydy=0 d. ydx+xdy=0
d
Find the equation of the curve at every point at which the tangent line has a slope of 2x. a. x= 〖-y〗^2+C b. y= 〖-x〗^2+C c. x= y^2+C d. y= x^2+C
b
Find the equation with an Eccentricity of 3/5 ,distance between directrices is 10. a. x^2/144+(25y^2)/9=1 b. x^2/9+(25y^2)/144=1 c. x^2/9-(25y^2)/144=1 d. x^2/144-(25y^2)/9=1
c
Find the perimeter of the curve x^(2/3)+y^(2/3)=4 a. 46 b. 47 c. 48 d. 49
c
Find the probability of obtaining an ace on both the first and second draws from a deck of cards when the first is not replaced before the second is drawn. a. 1/256 b. 1/128 c. 1/221 d. 1/121
a
If f(x) = 1+ x+ x2+ x3 ......, determine ∫ ∫_2^3▒f(x)dx a. ln 0.5 b. ln 2 c. ln 3 d. ln 1.5
a
If n is a real constant and u is a positive differentiate function of x, show that 〖du/dx〗^n=nu^(n-1) du/dx a. y=nu^(n-1) du/dx b. y=u^(n-1) du/dx c. y=nu^(n+1) du/dx d. y=nu^n du/dx
c
If the first derivative of a function is a constant, then the function is a. Sinusoidal b. Logarithmic c. Linear d. Quadratic
a
If y = x3/2 what is the approximate change in y when x changes from 9 to 9.01? a. 0.045 b. 0.068 c. 0.070 d. 0.023
d
Two cars begin a trip from the same point P. If car A travels north at the rate of 30 mi/h and car B travels west at the rate of 40 mi/h, how fast is the distance between them changing 2 hours later? a. 20 mi/h b. 30 mi/h c. 40 mi/h d. 50 mi/h
b
7. Two jeepney start at the same point but are going in different directions. If jeepney A runs at the rate of 60 km/hr and jeepney B at 50 km/hr and both start at the same time, when will the two jeepney be 550 km apart? a. 4 hrs b. 5 hrs c. 6 hrs d. 7 hrs
c
10. If x3+3x2+(5+k)x+2-k is divided by x+1 and the remainder is 3, then the value of k is a. -5 b. -3 c. -2 d. -4
d
10. If you borrow money from your friend with simple interest of 12%, find the present worth of 20,000 which is due at the end of nine months. A. P18,688.20 B. P18,518.50 C. P18,691.50 D. P18,348.60
b
2. A conic section whose eccentricity is always less than 1. a. Circle b. Ellipse c. Parabola d. Hyperbola
a
2. A man left his office for a business appointment one afternoon and noticed his watch at past 2 o'clock. Between two to three hours later, the man returned and noticed that the hands of the clock have exchanged places. What time did he leave and arrive? a. 2:26.01 and 5:12.17 b. 2:15 and 5:30 c. 2:20 and 5:32 d. 2:23 and 5:40
b
2. Carry out the following multiplication and express your answer in cubic meters: 3cm×5mm×2m. A. 3 x 10-3 B. 3 x 10-4 C. 8 x 10-2 D. 8 x 102
a
7. It states that the surface area of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance traveled by the curve's geometric centroid. a. First Theorem of Pappus b. Second Theorem of Pappus c. Third Theorem of Pappus d. Fourth Theorem of Pappus
a
2. In how many ways can 7 boys be seated in a row so that 3 boys are always seated together? a. 720 b. 360 c. 144 d. 270
d
2. Radicals can be added if they have the same radicand and the same a. coefficient b. b. exponent c. power d. order
d
2. What do you call a polyhedron of which one face called the base, is a polygon of any number of sides and the other faces are triangle which have a common vertex? a. Tetrahedron b. Icosahedron c. Prism d. Pyramid
d
2. What is the internal angle of a regular septagon? a. 135 b. 147.27 c. 150 d. 128.57
b
2. What is the probability of drawing a king or a black card? a. 15/25 b. 7/13 c. 1/2 d. 6/13
c
2. _________is the locus of appoint the absolute value of the difference of whose distances from two distinct fixed points is a positive constant a. Ellipse b. Parabola c. Hyperbola d. Circle
c
7. Peter's age 13 years ago was 1/3 of his age 7 years hence. How old is Peter? A. 15 B. 21 C. 23 D. 27
d
3. Drawing a card from a deck of cards is called a. an event b. an outcome c. a trial d. an experiment
c
4. Which of the following is NOT true about significant figures? a. All non-zero digits are significant b. Any zero between non-zero digits are significant c. Any zero not needed for placing a decimal point is not significant d. Zeros used for the purpose of placing a decimal point are not significant.
c
4.If i2=-1, then i7-i6+i5= a. i b. -I c. 1 d. -1
c
9. All board reviewees are not more than 25 years old. This statement implies that they are: a. less than 25 years old b. at least 25 years old c. 25 years old or less d. 25 years old or more
d
9. The roots of the equation 2x2 - 3x + 20 = 0 are a. real and equal b. real and unequal c. complex and equal d. complex and unequal
d
9.Mr. Rice can wash his car in 15 minutes, while his son Paul takes twice as long to do the same job. If they work together, how many minutes can they do the washing? a.1 min b.3 min c.20 min d.10 min
d
4. Peggy guesses on all 10 questions on a true-false quiz. What is the probability that exactly half of the answers are correct? a. 1/2 b. 1/32 c. 1/8 d. 63/256
a
4. The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed what is the arithmetic mean of the remaining numbers? A. 42.31 B. 57.12 C. 50 D. 38.62
a
4. The perimeter of a rectangle is 22. If one of the rectangles is doubled and the other tripled, the perimeter would be 32 more than the perimeter of the original rectangle. What are the sides of the rectangle? a. 6 and 5 b. 8 and 7 c. 10 and 9 d. 12 and 11
d
4. The set of integers does not satisfy the closure property under the operation of a. addition b. subtraction c. multiplication d. division
d
4. What is the probability of obtaining at least 4 tails when a coin is tossed five times? a. 0.1857 b. 0.1758 c. 0.1785 d. 0.1875
d
6. Find 2 numbers whose sum is 12 and the sum of their squares is 74. a. 3 and 9 b. 4 and 8 c. 6 and 6 d. 7 and 5
b
6. Two times the father's age is 8 more than six times his son's age. Ten years ago, the sum of their ages was 44. The age of the son is: A. 49 B. 15 C. 20 D. 18
b
6. What expression is equivalent to log (x) - log (y + z)? A. log x + log y + log z B. log [x/(y + z)] C. log x - log y - log z D. log y + log (x +z)
d
6. What solid is generated when an ellipse is revolved about its major axis? a. Oblate Spheroid b. Ellipsoid c. Oblong d. Prolate Spheroid
c
6. When the occurrence or no occurrence of event A has no effect on the occurrence of event B, then A and B are said to be a. complementary b. dependent c. independent d. mutually exclusive
b
6.One pipe takes 30 minutes to fill a tank and after it has been running for 10 minutes, it is shut off. A second pipe is then opened and it finishes filling the tank in 15 minutes. How long will it take the second pipe alone to fill the tank? a.20 mins b.22.5 mins c.45 mins d.40 mins
b
7. Find the median of the following: 21, 43, 20, 29, 50, 36, 17, 19. a. 24 b. 26 c. 26 d. 23
b
7. Given three vertices of a triangle whose coordinates are A (1, 1), B (3, -3) and (5, -3). Find the area of the triangle. A. 3 B. 4 C. 5 D. 6
c
7. It is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment. The solid enclosed by this surface and by two planes perpendicular to the axis. a. Cone b. Cube c. Cylinder d. Rectangular Prism
d
7. The graph of an equation of the form r = b + asinϴ or r = b + acosϴ is called a ________. a. Lemniscates b. Rose Curves c. Cardioids d. Limacons
a
7. The probability that the Ginebra basketball team will win the championship is assessed as being 1/3. Find the odds that the team will win. a. 1:2 b. 2:1 c. 1:3 d. 3:1
a
7. The roots of the equation 6x2 - 61x + 143 = 0 are a. real and distinct b. real and equal c. complex and distinct d. complex and unequal
a
7.A picture of length 12 inches and width 9 inches is framed in wood. What is the uniform width of the frame if the frame has an area of 162 square inches? a. 3 in b. 4in c. 8 in d. 1in
b
8. A man travels 4 miles north, 12 miles east and then 12 miles north. How far is he in miles from the starting point? a. 17 b. 20 c. 21 d. 24
b
8. A set of elements that is taken without regard to the order in which the elements are arranged is called a: a. permutation b. combination c. progression d. probability
b
8. Find the median of trhe following: 21, 43, 20, 29, 50, 36, 17, 19. a. 24 b. 25 c. 26 d. 23
d
8. For a parabola, the point halfway between the focus and the directrix. For an ellipse, one of two points where the line that contains the foci intersects the ellipse. For a hyperbola, one of two points at which the line containing the foci intersects the hyperbola. What is it? What are those? a. Latus Rectum b. Center c. Radii d. Vertices
d
8. The sum of the parent's ages is twice the sum of their children's ages. Five years ago, the sum of the parent's ages is four times the sum of their children's ages. In fifteen years the sum of the parent's ages will be equal to the sum of their children's ages. How many children were in the family? A. 2 B. 3 C. 4 D. 5
c
8. _____ are angles whose terminal sides coincide when the angles are in standard position. a. Transverse angles b. Opposite angles c. Co-terminal angles d. Supplementary angles
b
9. A pound of alloy of lead and nickel weights 14.4 ounces in water, where lead losses 1/11 of its weight and nickel losses 1/9 of its weight. How much of each metal is in alloy? A. Lead = 7.2 ounces Nickel = 8.8 ounces B. Lead = 8.8 ounces Nickel = 7.2 ounces C. Lead = 6.5 ounces Nickel = 5.4 ounces D. Lead = 7.8 ounces Nickel = 4.2 ounces
a
9. A/n ______ is the set of all points P in a plane such that the sum of the distances of P from two fixed points F and G of the plane is constant. a. Ellipse b. Circle c. Conic d. Parabola
a
5. Who is the French mathematician who discovered matrices in the year 1860? a. Arthur Cayley b. Pierre de Fermat c. Joseph Fourier d. Blaise Pascal
d
1. What is probability of getting the number "1" thrice when a die is tossed 5 times? a. 0.0233 b. 0.0223 c. 0.0355 d. 0.0322
c
1.Which of the following quadratic equations will have two real and distinct roots? a. 6x2-5x + 4 = 0 b. 9x2-6x + 1 = 0 c. 6x2-61x +143 = 0 d. x2-22x + 121 = 0
b
10. An infinite sum giving the value of a function f(x) in terms of the derivatives of the function evaluated at zero: f(x) = f(0) + (f′(0)x)/1! + (f″(0)x2)/2! + .... a. Taylor Series b. Macluarin Series c. Fourier Series d. Harmonic Series
a
10. Find the value of k that will make x2 - 28x +k a perfect square trinomial. a. 196 b. 169 c. 144 d. 121
b
10. If sinx = cosy,then a. xy = 900 b. x+y = 900 c. x-y = 900 d. none of the above
a
5.The sum of two numbers is 11. The sum of their reciprocals is 11 28 . Find the numbers. a. 7 and 4 b. 2 and 3 c. 6 and 2 d. 5 and 4
c
1. A positive integer is called ____ if it is different from 1 and can be expressed as the product of two or more positive integers different from itself. a. Natural b. Whole number c. Composite d. Counting number
a
1. At what time between 7 and 8 o'clock are the hands of the clock, at right angles? a. 7:22 b. 7:18 c. 7:15 d. 7:24
c
1. Refers to the construction of drawing of lines and figures the possibility of which is admitted without proof. a. Corollary b. Theorem c. Postulate d. Hypothesis e. Axiom
b
1. The distance between two points P1(2, -1) and P2(6, 2) is a. 4 b. 5 c. 6 d. 3
d
10. Postal regulations require that the sum of the length and girth of a rectangular package may not exceed 108 inches (the girth is the perimeter of an end of the box). What is the maximum volume of a package with square ends that meets this criteria? a. 11,646 in3 b. 11,466 in3 c. 11,464 in3 d. 11,664 in3
c
5. Mr. Diaz can finish a job in 9hrs. After working for 5 hrs, he decided to take a rest. Mr. Torres helped Mr. Diaz finished the job in 2 hrs and 20 minutes. How long would it take Mr. Torres to do the job alone? a. 3 hrs and 5 min b. 4 hrs and 10 min c. 5 hrs and 15 min d. 6 hrs and 20 min
b
5. The general equation of the parabola whose axis is parallel to the y-axis is a. Ax2+Cy2+Dx+Ey+F=0 b. Ax2+Dx+Ey+F=0 c. Ax2+Cy2+Dx+Ey+F=0 where A=C have the same sign d. None of the above
d
5. The graph of r = a + bcosθ is a a. Lemniscate b. Lituus c. Cardioid d. Limacon
a
3. A survey is made on the smoking habit of the male population above 18 years old of a certain community. The survey was on the three cigarettes A, B and C. 55% smoke S 40% smoke B 30% smoke C 20% smoke A and B 12% smoke B and C 10%smoke A and C 5% smoke all the three brands How many % do not smoke?
a
3. Find the 100th term of the sequence 1.01, 1.00, 0.99, a. 0.02 b. 0.03 c. 0.04 d. 0.05
b
3. If a line sklants upward to the right, then its slope is a. Zero b. Positive c. Negative d. Infinity
b
3. If f(x) = 2×2 + 2x + 4, what is f(2)? A. 4x + 2 B. 16 C. x2 + x + 2 d. 8
d
3. The graph of an equation of the form r = b + asinϴ or r = b + acosϴ is called a ________. a. Lemniscates b. Rose Curves c. Cardioids d. Limacons
d
3. When (x+3)(x-4) + 4 is divided by x - k, the remainder is k. Find the value of k. A. 4 or 2 B. 2 or -4 C. 4 or -2 D. -4 or -2
a
3.Which of the following is ALWAYS true? a. Every function is a relation b. A function is not a relation c. Every relation is a function d. A relation is not a function
c
4. A number of two digits divided by the sum of the digits, the quotient is 7 and the remainder is 6. If the digits of the number are interchanged the resulting number exceeds three times the sum of the digits by 5. What is the number? a. 39 b. 48 c. 83 d. 72
a
4. If 1/3 and -3/2 are roots of a quadratic equation, then the equation is A. 6×2 + 7x - 3 = 0 B. 6×2 - 7x + 3 = 0 C. 6×2 - 7x - 3 = 0 D. 6×2 - 7x + 1 = 0
a
4. In regular polygons, what do you call the perpendicular distance from its center to a side? a. Apothem b. Radius c. Altitude d. Diameter
c
5. A pair of dice is thrown. Find the probability that their sum is greater than 7 given that the numbers are match. a. 6/36 b. 3/36 c. 1/2 d. 1/11
