MATHEMATICS 2019
1. Find the parametric equation for the line through the point (1,7,2) that is
parallel to the plane x + y + z = 10 and perpendicular to the line x = 3 +
t, y = - 18 – t, z = 5t
a. x = 6t – 1, y = 4t – 7, z = -2t – 2
b. x = 4t + 1, y = -6t + 7, z = 2t + 2
c. x = 6t + 1, y = -4t + 7, z = -2t + 2
d. x = 4t + 1, y = -6t, z = 2t + 2
2. It represents the distance of a point from the y-axis.
a. ordinate
c. coordinate
b. abscissa
d. polar distance
3. The locus of a point which moves so that its distance from a fixed point and
a fixed line is always equal is
.
a. ellipse
c. circle
b. parabola
d. hyperbola
4. Jerome ate 3 oz. of a 16-oz ice cream pack. What percentage of the pack did
he eat?
a. 18.75 %
c. 17.25 %
b. 19.50 %
d. 16.25 %
5. Determine the equation that expresses the statement.
F is directly proportional to y.
Symbols a, b, c and d are constants.
a. F = a
c. F = b
b. F = a • y
d. F = cy^3 + a
6. If a quiz consists of four true-false questions, and a student guesses at
each answer, what is the probability that the student answers exactly half
of the questions correctly?
a. 0.5000
c. 0.1536 ans. 0.375
b. 0.2500
d. 0.7521
7. Evaluate lim
|(n2+3i)(n-i)|
n --> ∞ |in^3 – 3n + 4 – 1|
a. 1
c. i/2
b. 0
d. -i/2
8. Find the equation of the circle with center at the origin and passes through
(-3,4).
a. x2 + y2 = 36
c. x2 + y2 = 9
2
2
b. x + y = 25
d. x2 + y2 = 16
9. Find the area bounded by r = 2/(1 + cos θ) and cos θ = 0.
a. 1/3
c. 5/3
b. 2/3
d. 8/3
10.
The value of 5! is equal to
.
a. 120
c. 25
b. 1
d. 5
11.
If sinθ = a and cos2θ = b then what is the value of sin2θ – 2cosθ?
I.
a2 + 2 square root of b
II. a2 - 2 square root of b
III. b2 + 2 square root of a
IV. b2 - 2 square root of a
a. I only
c. III and IV only
b. I and II only
d. III only
12.
Find an equation of the parabola with vertex (-1,-2) latus rectum 12,
opens downward.
a. x2 + 12x + 12y – 25 = 0
c. x2 - 2x + y – 23 = 0
2
b. x + 12x + 2y + 22 = 0
d. x2 + 2x + 12y + 25 = 0
13.
A man is driving a car at the rate of 30km/hour towards the foot of a
monument 6m high. At what rate is he approaching the top when he is 36 m
from the foot of the monument?
a. -52.80 km/hr
c. -29.59 km/hr
b. 10.55 km/hr
d. 12.52 km/hr
14.
A cross-section of a trough is a semi-ellipse with width at the top 18
in. and depth 12 in. The trough is filled with water to a depth of 8 in.
Find the width of the surface of the water.
a. 6 square root of 5 in
c. 6 in
b. square root of 5 in
d. 5 square root of 6 in
15.
A secondary school is contracting its alumni asking for donations to
help put up a new computer laboratory. Past records show that 80% of the
alumni will make a contribution of at least P50.00. A random sample of 20
alumni is selected. What is the probability that exactly 15 alumni will make
a donation of at least P50.00?
a. 0.576
c. 0.174
b. 0.167
d. 0.204
16.
Find the two complex numbers whose sum is 4 and whose product is 8?
a. 1 ± 2i
c. 1 ± i
b. 2 ± i
d. 2 ± 2i
17.
Determine the differential equation of the family of lines passing
through (h,k).
a. (y-h) + (y-k) = dy/dx
c. (x+h)dx – (y-k)dy = 0
b. (x-h)dx – (y-k)dy = 0
d. (y-k)dx – (x-h)dy = 0
2
18.
If 3x is multiplied by the quantity 2x^3y raised to the 4th power,
what would this expression simplify to?
a. 6x^9y to the 4th power
c. 6x^14y to the 4th power
b. 48x^14y to the 4th power
d. 1296x^16y to the 4th power
19.
A point is chosen at random inside a circle having a diameter of 8
inches. What is the probability that the point is at least 1.5 inches away
from the center of the circle?
a. 55/64
c. 5/64
b. 5/8
d. 12/45
20.
In an ellipse, a chord which contains a focus and is in a line
perpendicular to the major axis is a
.
a. conjugate axis
c. focal width
b. latus rectum
d. minor axis
21.
Find the position value of c such that the area of the region bounded
by the parabola y = x2 – c2 and y = c2 – x2 is 576.
a. 13
c. 8
b. 5
d. 6
22.
Obtain L^-1 [1/(s^2+1)^2].
a. ½ (sin t – tcos t)
c. ½ (sin t + tcos t)
b. - ½ (sin t – tcos t)
d. - ½ (sin t + tcos t)
23.
If Jim and Jerry work together, they can finish a job in 4 hours. If
working alone takes Jim 10 hours to finish the job, how many hours would it
take Jerry to do the job alone?
a. 16
c. 6.7
b. 6.0
d. 5.6
24.
A line through (0,0) intersects y = x2 at a point (a,a2). The area of
the upper region bounded above by the line and below by the curve is 27.
Find a.
a. 2 cube root of 6
c. 3 cube root of 6
b. cube root of 6
d. cube root of 3
25.
Simplify i^(39).
a. -i
c. -1
b. 1
d. i
26.
If a rock is dropped, its distance below the starting point at the end
of t sec is given by s = 16t square, where s is in ft. Find the rate of
change of distance after 1.5 minutes.
a. 288 ft/sec
c. 2880 ft/sec
b. 281 ft/sec
d. 800 ft/sec
27.
Find the equation of the line with slope 3 and y-intercept -2.
a. y = 2x + 3
c. y = -3x + 2
b. y = 2x – 3
d. y = 3x – 2
28.
Three randomly chosen senior high school students was administered a
drug test. Each student was evaluated as positive to the drug test (P) or
negative to the drug test (N). Assume the possible combinations of the three
students drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN.
Assuming each possible combination is equally likely, what is the
probability that all three students get positive result?
a. 1/3
c. 3/4
b. 1/2
d. 1/8
29.
Find the area of the first octant part of the plane x/a + y/b + z/c =
1 where a, b and c are positive.
a. ½ square root of (a2b2 + b2c2 + a2c2) c. square root of (a + b + c)
b. a + b + c
d. square root of (a2 + b2 + c2)
30.
Find the volume generated by revolving the area bounded by y2 = 12x and
x = 3 about the line x = 3.
a. 131
c. 181
b. 191
d. 151
31.
Joey will be x years old y years from now. How old is she now?
a. y – x
c. x – y
b. x
d. y
32.
A rectangle with sides parallel to the coordinate axes has one vertex
at the origin, one on the positive x-axis and its fourth vertex in the first
quadrant on the line with equation 2x + y = 100. What is the maximum
possible area of rectangle?
a. 3520
c. 1908
b. 1250
d. 2250
33.
Find the volume generated by revolving the area bounded by y2 = 12x and
x = 3 about the line x = 3.
a. 191
c. 151
b. 181
d. 131
34.
Find the equation of the line passing 3 units from the origin and
parallel to 3x + 4y – 10 = 0.
a. 3x + 4y – 5 = 0
c. x - 3y + 15 = 0
b. 4x + 3y + 1 = 0
d. 3x + 4y – 15 = 0
35.
Patrick has a rectangular patio whose length is 5 m less than the
diagonal and a with that is 7 m less than the diagonal. If the area of his
patio is 195 m2, what is the length of the diagonal?
a. 20 m
c. 16 m
b. 10 m
d. 8 m
36.
Find |u x v| correct to three decimal places where |u| = 9 and |v| =
3. Let θ = 85 deg.
a. 2.989
c. 2.353
b. 31.897
d. 26.897
37.
If 1 is added to the difference when 10x is subtracted from -18x, the
result is 57. What is the value of x?
a. 7
c. -2
b. 2
d. -7
38.
Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got
to Tim. If Tim receive 2 candies, how many candies did Joseph have
originally?
a. 20
c. 40
b. 30
d. 50
39.
From past experience, it is known 90% of one-year old children can
distinguish their mother’s voice from the voice of a similar sounding
female. A random sample of 20 one-year olds are given this voice recognition
test. Let the random variable x denote the number of children who do not
recognize their mother’s voice. Find the mean of x.
a. 20
c. 4
b. 2
d. 1
40.
What percent of 50 is 12?
a. 14 %
c. 2 %
b. 4 %
d. 24 %
41.
Find all values of z for which e^3z = 1.
a. kπi
c. 1/3 kπi
b. 2kπi/3
d. 1/8 πi + ½ kπi
42.
In the vicinity of a bonfire, the temperature T in deg C at distance
of x meters from the center of the bonfire was given by:
762,500
T =
x2 + 300
At what range of distances from the fire’s center was the temperature
less than 500 deg C?
a. more than 45 meters
c. more than 35 meters
b. more than 30 meters
d. more than 20 meters
43.
During a major league career, Hank Aaron hit 38 more home runs that
Babe Ruth hit during his career. Together they hit 1,524 home runs. How much
home runs did Babe Ruth hit?
a. 781 home runs
c. 743 home runs
b. 800 home runs
d. 762 home runs
44.
If sinA = 4/5 and sinB = 7/25, what is sin (A + B) if A is in the 3rd
quadrant and B is in the 2nd quadrant?
a. -3/5
c. 2/5
b. 3/5
d. 4/5
45.
Three randomly chosen senior high school students was administered a
drug test. Each student was evaluated as positive to the drug test (P) or
negative to the drug test (N). Assume the possible combinations of the three
students drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN.
Assuming each possible combination is equally likely, what is the
probability at least one student gets negative result?
a. 4/8
c. 7/8
b. 2/7
d. 3/7
46.
A bag contains 3 red, 6 blue, 5 purple and 2 orange marbles. One
marble is selected at random. What is the probability that the marble is
blue?
a. 3/8
c. 3/5
b. 3/16
d. 3/7
47.
z varies directly as x and inversely as y2. If x = 1 and y = 2 then z
= 2. Find z when x = 3 and y = 4.
a. 1.5
c. 2.5
b. 3.5
d. 3
48.
Which of these is equal to 6 (x – 3)?
a. x^6 – 3^6
c. 6x – 18
b. 6x + 3
d. 6x + 3
49.
If z = 6e^πi/3 , evaluate e^iz.
a. e^3isq root of 3
c. e^sq root of 3
b. e^-3sq root of 3
d. e^-sq root of 3
50.
After paying commission of 7 % of the sale price to his broker, Tess
receives P103,000 for his car. How much was the car sold?
a. P110,753
c. P110,420
b. P110,000
d. P95,790
51.
What is the maximum rectangular area that can be fenced in 20 m using
two perpendicular corner sides of an existing wall?
a. 310 m2
c. 100 m2
2
b. 250 m
d. 120 m2
52.
Find the area enclosed by the lemniscate of Bernoulli r2 = a2cos 2θ.
2
a. a /2
c. a2
b. a2/4
d. a2/3
53.
A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the
success of the new product. The survey showed 40% of the consumer had seen
the advertisement for the new soap, 20% had tried the new soap, and 15% had
both seen an advertisement and tried the new soap. If a randomly selected
costumer has seen an advertisement for the new soap, what is the probability
that this costumer has tried the new soap?
a. 72 %
c. 40 %
b. 25 %
d. 37.5 %
54.
Which of the following is equal to n-4•n4?
a. 1
c. -16
b. n
d. 0
55.
Jason made 10 two-point baskets and 2 three-point baskets in Friday’s
basketball game. He did not score any other points. How many points did he
score?
a. 22
c. 26
b. 12
d. 24
56.
Evaluate
∫√(1 – cos x)dx
a. 2√2 cos x + C
c. -2√2 cos x + C
b. -2√2 cos x/2 + C
d. 2√2 cos x/2 + C
57.
If the graph of y = f(x) is transformed into graph of 2y – 6 = -4 f(x 3), point (a, b) on the graph of y = f(x) become a point (A,B) where A and B
are expressed as:
a. A = a + 4, B = 2b + 3
c. A = a + 3, B = -2b + 3
b. A = a + 6, B = 2b + 6
d. A = a + 2, B = 2b – 3
58.
From past experience, it is known 90% of one-year old children can
distinguish their mother’s voice from the voice of a similar sounding female.
A random sample of 20 one-year olds are given this voice recognition test.
Find the probability that all 20 children recognize their mother’s voices.
a. 0.222
c. 1.000
b. 0.500
d. 0.122
59.
Find the radius of curvature of the parabola y2 – 4x = 0 at the point
(4,4).
a. 22.36
c. 25.36
b. 20.36
d. 27.36
60.
Find the differential equation of the family of lines passing through
the origin.
a. xdx – ydy = 0
c. ydx + xdy = 0
b. xdy - ydx = 0
d. ydx – xdy = 0
61.
Find the point on the line 3x + y + 4 = 0 that is equidistant from the
points (-5,6) and (3,2).
a. (-2,2)
c. (-2,-2)
b. (-2,3)
d. (2,2)
62.
Find all real solutions to the logarithmic equation
ln(x2 – 1) – ln(x – 1) = ln 4
a. 0
c. 5
b. 3
d. 4
63.
Gabby cuts a piece of rope into three pieces. One piece in 5 inches
long, one piece is 4 inches long, and one piece is 3 inches long. The longest
piece of rope is approximately what percent of the original length before the
rope was cut?
a. 55 %
c. 33 %
b. 42 %
d. 50 %
64.
What is the result when 6ab + 3b is subtracted from -6ab – 3b?
a. 12ab + 6b
c. 18ab
b. -12ab – 6b
d. 0
65. Find 60 % of 390.
a. 134
c. 180
b. 190
d. 243
66.
Find the area bounded by y = x^3, the x-axis and the lines x = -2 and x
= 1.
a. 0.43
c. 1.25
b. 2.45
d. 4.25
67.
The table shows the number CD players sold in a small electronics store
in the years 1989-1999 as follows.
YEAR
CD PLAYERS SOLD
1989
545
1990
675
1991
665
1992
665
1993
600
1994
550
1995
680
1996
560
1997
545
1998
560
1999
695
What was the average rate of change of sales between 1989 and 1999?
a. 15 CD players/year
c. 70 CD players/year
b. 150 CD players/year
d. 695 CD players/year
68.
A man is driving a car at the rate of 30km/hr towards the foot of a
monument 6m high. At what rate is he approaching the top when he is 36 m
from the foot of the monument?
a. 12.52 km/hr
c. 10.55 km/hr
b. -52.80 km/hr
d. -29.59 km/hr
69.
Find the vertex of the parabola x2 = 8y
a. (2,4)
c. (0,0)
b. (0,8)
d. (-2,0)
70.
A and B working together can do a job in 5 days, B and C together can
do the same in 4 days and A and C in 2.5 days. In how many days can all of
them finish the job working together?
a. 1.07
c. 2.03
ans.2.35 days
b. 2.80
d. 3.10
71.
Which of the following is a disadvantage of using the sample range to
measures of spread or dispersion?
a. It produces very small spreads.
b. The largest of the smallest observation (or both) may be a mistake or an
outlier.
c. The sample range is not measured in the same units as the data.
d. It produces spreads that are too large.
72.
Obtain L(t^n).
a. n!/s^n-1
c. (n+1)!/s^(n+1)
b. n!/s^n
d. n!/s^(n+1)
73.
Jenny flipped a coin three times and got heads each time. What is the
probability that she gets heads on the fourth flip?
a. 1
c. 1/16
b. 0
d. 1/2
74.
Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10
glasses of milk, how many sodas dis he sell?
a. 45
c. 25
b. 20
d. 10
75.
How many positive real roots are there in the polynomial
x^4 – 4x^3 + 7x^2 – 6x - 18 = 0.
a. 1 or 2
c. 3 or 0
b. 3 or 1
d. 1 or 0
76.
The square of a number added to 25 equals 10 times the number. What is
the number?
a. -5
c. 5
b. -10
d. 10
77.
Evaluate
lim (1 + 2x)^(1 + 2x)/x
x ---> 0
a. 1
c. 0
b. e
d. e2
78.
A man on a wharf 3.60 m above sea level is pulling a rope tied to a
raft at the rate of 0.6 m/sec. How fast is the raft approaching the wharf
when there are 6 m of rope out?
a. -0.22 m/sec
c. -0.12 m/sec
b. -1.75 m/sec
d. -0.75 m/sec
79.
From a stationary point directly in front of the center of the bull’s
eye, Kim aims two arrows at the bull’s eye. The first arrow nicks one point
on the edge of the bull’s eye; the second strikes the center of the bull’s
eye. Kim knows that the second arrow traveled 20 meters since she knows how
far she is from the target. If the bull’s eye is 4 meters wide, how far did
the first arrow travel? Assume the arrows traveled in straight-line path and
the bull’s eye is circular.
a. 19.9 m
c. 20.1 m
b. 24.0 m
d. 22.5 m
80.
A voltage v = 150 + j180 is applied across an impedance and the
current flowing is found to be I = 5 – j4. Determine the resistance.
a. 0.75 ohms
c. 0.78 ohms ans. 0.73ohms
b. 0.77 ohms
d. 0.76 ohms
81.
Determine the equation that expresses that G is proportional to k and
inversely proportional to C and z. Symbols a, b and c are constants.
a.
ck
c.
a
G = ---G = ---ans. A
zC
bc
b.
bc
d.
Ck
G = ---G = ---zk
CG
82.
Determine the equation of the line passing through the points (1,17)
and (13,4).
a. 13x – 12y – 217 = 0
c. 13x + 12y – 217 = 0
b. 13x – 12y + 217 = 0
d. 13x + 12y + 217 = 0
83.
Two hundred single-sport athletes were cross-classified according to
gender as follows:
Swimmer
Runner
Cyclist
Male
25
60
25
Female
20
50
20
What is the probability that the athlete is male or a swimmer or both?
a. 0.550
c. 0.230 ans. 0.65
b. 0.450
d. 0.005
84.
Describe the locus represented by |z – i| = 2.
a. hyperbola
c. parabola
b. circle
d. ellipse
85.
Solve the equation (x2y – 2) + (x + 2xy - 5)i = 0.
a. x = 1, y = 2
c. x = 1/2, y = 3
b. x = 3, y = 4
d. x = 4, y = -1/2
86.
Find two numbers whose sum is 50 and with the largest possible
product.
a. 25, 25
c. 22, 23
b. 23, 25
d. 20, 30
87.
If dy = x2dx, what is the equation of y in terms of x if the curve
passes through (1, 1)?
a. x^(3) + 3y2 + 2 = 0
c. x2 – 3y + 3 = 0
b. x^(3) – 3y + 2 = 0
d. 2y + x3 + 2 = 0
88.
A car rental company offers two plans for renting a car:
Plan A: $ 30 / day and $ 0.20 / mile
Plan B: $ 55 / day and with free unlimited mileage
For what range of miles will plan B save a costumer’s money?
a. more than 125 miles
c. more than 170 miles
b. less than 250 miles
d. less than 170 miles
89.
Find the value of x for which f(x) = x2 + 5x + 2 is maximum.
a. 5/2
c. -2
b. 2
d. -5/2
90.
In order to pass a certain exam, candidates must answer correctly 70
%of the test questions. If there are 70 questions on the exam, how many
questions must be answered correctly in order to pass?
a. 52
c. 56
b. 60
d. 49
91.
A group consists of n engineers and n nurses. If two engineers are
replaced by two other nurses, then 51% of the group member will be nurses.
Find the value of n.
a. 100
c. 80
b. 110
d. 55
92.
While bowling in a tournament, Jake and his friends had the following
scores:
Jake
189
Charles and Max each scored 120
Terry
95
What was the total score for Jake and his friends at the tournament?
a. 524
c. 404
b. 526
d. 504
93.
Find the height of a tree if the angle of elevation of its top changes
from 20° to 40° as the observer advances 23 meters towards the base.
a. 16.78 m
c. 13.78 m
b. 14.78 m
d. 15.78 m
94.
A normal to a given plane is
.
a. oblique to the plane
c. perpendicular to the plane
b. parallel to the plane
d. lying in the plane
95.
Find the equation of the normal to x2 + y2 = 1 at the point (2,1).
a. x + y = 1
c. y = 2x
b. x = 2y
d. x – y = 0
96.
Evaluate
∫
xdx/ square root (x2 – 8x).
a. square root of (x2 – 4x + 4) ln (x – 4 + sq. root (x2 + 8x)) + C
b. square root of (x2 – 4x + 2) ln (x – 4 + sq. root (x2 - 8x)) + C
c. square root of (x2 – 8x + 4) ln (x – 4 + sq. root (x2 - 8x)) + C
d. square root of (x2 – 2x - 4) ln (x – 4 + sq. root (x2 - 2x)) + C
97.
The plane rectangular coordinate system is divided into four parts
which are known as
.
a. octants
c. coordinates
b. quadrants
d. axis
98.
What curve is described by the equation 4x2 – y2 + 8x + 4y = 15
a. hyperbola
c. parabola
b. circle
d. ellipse
99.
From a recent study, 90% of one-year old children can distinguish
their mother’s voice from the voice of a similar sounding female. A random
sample of 20 one-year-olds are given this voice recognition test. Find the
probability that all 20 children recognize their mother’s voices.
a. 0.122
c. 0.522
b. 0.001
d. 1.000
100.
What is the length of the latus rectum of the parabola y = 4px2?
a. p
c. 2p
b. -4p
d. 4p
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