MATHEMATICS REE APRIL 2019
1.) Listed below are functions each denoted g(x) and each involving a real number x,
constant c > 1. If f(x) = 2x, which of these functions yield the greatest value for f(g(x)),
for all x > 1?
A.) g(x) = cx
B.) g(x) = c/x
C.) g(x) = c – x
D.) g(x) = x/c
2.) Find the volume (in cubic units) generated by rotating a circle x 2 + y2 + 6x + 4y + 12 = 0
about the y-axis.
A.) 47.23
B.) 59.22
C.) 62.11
D.) 39.48
3.) The area enclosed by the ellipse 4x^2 + 9y^2= 36 is revolved about the line x = 3, what is
the volume generated?
A.) 370.3
B.) 360.1
C.) 355.3
D.) 365.1
4.) Calculate the volume of the solid formed by revolving the area bounded by the parabola
y2 = 12x and the line x = 3 about the line x = 3.
ANS: 181
5.) A conic section whose eccentricity is less than one (1) is known as:
A.) a parabola
B.) an ellipse
C.) a circle
D.) a hyperbola
6.) If Rita can run around the block 5 times in 20 minutes, how many times can she run
around the block in hour?
A.) 10
B.) 50
C.) 15
D.) 100
7.) Evaluate the double integral of 1/ (x-y) dxdy with inner bounds of 2y to 3y and outer
bounds of 0 to 2.
A.) ln 3
B.) ln 4
C.) ln 2
D.) ln 8
8.) Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.
A.) 2.5 mils
B.) 1 mil
C.) 4 mils
D.) 2.04 mils
9.) A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a
rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8cm/hr. If the icicle is
currently 4 cm in radius and 20 cm long, is the volume of the icicle increasing or
decreasing, and at what rate?
A.) decreasing at 20 cu. cm/hr
B.) increasing at 24 cu. cm/hr
C.) decreasing at 24 cu. cm/hr
D.) increasing at 20 cu. cm/hr
10.) Lisa originally brought exact amount of money to buy 10 chocolates. She then discovers
that the price of chocolate went up by 50 centavos each. She was able to buy 8 chocolates
and have an extra of 2 pesos. How much did Lisa bring originally?
ANS: C.) 30 pesos
11.) Find the area of a triangle having vertices at -4 – i 1 + 2i, 4 – 3i.
A.) 15
B.) 16
C.) 17
D.) 18
12.) There are four geometric mean between 3 and 729. Find the sum of the geometric
progression.
A.) 1092
B.) 1094
C.) 1082
D.) 1084
13.) What percentage of the volume of a cone is the maximum right circular cylinder that can
be inscribed in it?
A.) 24%
B.) 32%
C.) 44%
D.) 54%
14.) A and B can do the work in 5 hours, B and C can do the work in 4 hours, C and A can
do the work in 2.5 hours. How long will it take if all of them work together?
TROUBLESHOOT: 5→3
ANS: 2.03hrs
15.) The geometric mean and the arithmetic mean of numbers are 8 and 10 respectively.
What is the harmonic mean?
A.) 7.5
B.) 5.7
C.) 6.4
D.) 4.6
16.) The centroid of the area bounded by the parabola y2 = 4ax and the lin x = p coincides
with the focus of the parabola. Find the value of p.
A.) 3/5 a
B.) 5/3 a
C.) 2/5 a
D.) 5/2 a
17.) N engineers and N nurses, if two engineers are replaced by nurses, 51% of the engineers
and nurses are nurses. Find N
A.) 100
B.) 110
C.) 50
D.) 200
18.) Two stones are 1 mile apart and are at the same level as the foot of a hill. The angles of
depression of the two stones viewed from the top of the hill are 5 degrees and 15 degrees
respectively. Find the height of the hill.
A.) 109.01m
B.) 209.01m
C.) 309.01m
D.) 409.01m
19.) Water is running out of a conical funnel at the rate of 1 cu. in/sec. If the radius of the
base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is
dropping when it is 2 in from the top.
A.) -1/9pi in/sec
B.) -1/2pi in/sec
C.) 1/2pi in/sec
D.) 1/9pi in/sec
20.) Find the radius of curvature of the parabola y2 = 4x at point P (4,4)?
ANS: 22.4
21.) If Nannette cuts a length of ribbon that is 13.4 inches long into 4 equal pieces, how long
will each piece be?
A.) 3.35 m
B.) 3.25 m
C.) 3.15 m
D.) 3.45 m
22.) The equation y2 = cx is a general solution of
A.) y’ = 2y/x
B.) y’ = 2x/y
C.) y’ = y/2x
D.) y’ = x/2y
23.) Find the minimum distance from the point P (4,2) to the parabola y2 = 8x.
A.) 3 sqrt. of 3
B.) 2 sqrt. of 3
C.) 3 sqrt. of 2
D.) 2 sqrt. of 2
24.) Find the general solution of y” + 8y’ + 41y = 0.
A.) y = e-5x (c1cos4x + c2sin4x)
B.) y = e5x (c1cos4x + c2sin4x)
C.) y = e-4x (c1cos5x + c2sin5x)
D.) y = e-4x (c1cos5x + c2sin5x)
25.) Find the general solution of y” + 10y’ + 41y = 0.
A.) y = e-5x (c1cos4x + c2sin4x)
B.) y = e5x (c1cos4x + c2sin4x)
C.) y = e-4x (c1cos5x + c2sin5x)
D.) y = e-4x (c1cos5x + c2sin5x)
26.) A 15m transmitter is located atop a 3km hill. What is the furthest distance along the
surface of the earth that it can see assuming the earth’s radius is 6400km?
TROUBLESHOOT: not along surface (perpendicular to z axis)
ANS: 196km
27.) Find all the values for z for which e4z = i.
A.) 1/6 pi i + 1/2 k pi i
B.) -1/6 pi i + 1/2 k pi i
C.) 1/8 pi i + 1/2 k pi i
D.) -1/8 pi i + 1/2 k pi i
28.) 3 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 student’s drug test evaluation as PPP, PPN, PNP, NPP,
PNN, NPN, NNP, NNN. Assume the possible combination is equally likely and knowing
that 1 student gets a negative result, what is the probability that all 3 students get a
negative result?
A.) 1/8
B.) 1/7
C.) 7/8
D.) 1/4
29.) Find the area under one arch of the cycloid x = a (theta – sin theta) and y = a (1 – cos
theta).
A.) 2pi a2/3
B.) pi a2
C.) 3pi a2
D.) 2pi a2
30.) Newton’s law of cooling states that the rate of change of the temperature of an object is
directly proportional to its difference in temperature to the surrounding. If the air is at
30˚C and it takes 15 minutes to cool down an object from 100˚C to 70˚C, how long will it
take to cool down from 100˚C to 50˚C?
ANS: 33.59 minutes
31.) How many possible positive real roots are there in x4 – 4x3 + 7x2 – 6x – 18 = 0.
ANS: 3 or 1
32.) Peter can finish in 2 hours while John can finish in 1.5 hours. How long will it take if
they work together?
ANS: 51.43 mins
33.) One end of a 32-meter ladder resting on a horizontal plane leans on a vertical wall.
Assume the foot of the ladder to be pushed towards the wall at the rate of 2 meters per
minute. How fast is the top of the ladder rising when its foot is 10 meters from the wall?
A.) +0.568 m/min
B.) +0.658 m/min
C.) +0.896 m/min
D.) +0.986 m/min
34.) A wall “h” meters high is 2 m away from the building. The shortest ladder that can reach
the building with one end resting on the ground outside the wall is 6 m. How high is the
wall in meters?
A.) 2.34
B.) 2.24
C.) 2.44
D.) 2.14
35.) A container is in the form of a right circular cylinder with an altitude of 6 in and a radius
of 2 in. If an asbestos of 1 in thick is inserted inside the container along its lateral surface,
find the volume capacity of the container.
A.) 12.57 cu.in
B.) 12.75 cu.in
C.) 18.58 cu.in
D.) 18.85 cu.in
36.) 60% of 390?
A.) 234
B.) 190
C.) 180
D.) 134
37.) Seven people are at the beach for a clambake. They have dug 12.6 pounds of calms. They
eat the following amounts of clams: 0.34 pounds, 1.6 pounds, 0.7 pounds, 1.265 pounds,
0.83 pounds, 1.43 pounds. How many pounds of clams are left?
A.) 7.892 pounds
B.) 4.566 pounds
C.) 5.945 pounds
D.) 6.655 pounds
38.) A game in a carnival consist of a player throwing a coin onto a table about 5 feet away.
The table contains a grid of 1-inch squares and the coin is ¾ inches in diameter. If the coin
is entirely inside of a 1-inch square, the player gains wins their bet. Otherwise, the player
loses. Given that the coin hits the table, what is the probability the player loses?
ANS: 15/16
39.) The differential equation x(y-1)dx + (x+1)dy = 0 has values at x = 1, y = 2; solve for the
value of y at x = 2.
ANS: 1.55
40.) Find the differential equation whose general solution is y = C1x + C2ex.
A.) (x – 1)y” – xy’ + y = 0
B.) (x + 1)y” – xy’ + y = 0
C.) (x – 1)y” + xy’ + y = 0
D.) (x + 1)y” + xy’ +y = 0
41.) Which of the following differential equations describes a family of circles centered at the
y-axis?
ANS: xy” + (y’)3 + y’ = 0
42.) At what value of x is y = sin2x at maximum?
ANS: pi / 4
43.) Solve for the limit
|(𝑛2 + 1)(𝑛 + 𝑖 )|
lim
𝑛→∞ |𝑖𝑛3 + 3𝑛 + 4 − 𝑖 |
ANS: 1
44.) Evaluate the integral of sin(x) raised to the 5th power and the limits from 0 to pi/2.
ANS:
45.) Solve for the integral of cos(x) from pi/4 to pi/2.
ANS: 0.293
46.) Solve for the integral
∞
1
∫ 1.0001 𝑑𝑥
0 𝑥
ANS: infinity (ata, walang sagot sa paper eh)
47.) Solve for the value of |u x v| if |u| = 9, |v| = 3, and the angle between u and v is 85˚.
ANS: 26.897
48.) The suspension cable of a bridge of length 400m takes form of a parabola. If the sag is
50m, what is the equation of the parabola if the lowest part is at the origin?
A.) x2 = 800y
B.) x2 = 1600y
C.) y2 = 800x
D.) y2 = 1600x
49.) The suspension cable of a bridge of length 800m takes form of a parabola. If the sag is
100m, what is the equation of the parabola if the lowest part is at the origin?
A.) x2 = 1600y
B.) x2 = 3200y
C.) y2 = 1600x
D.) y2 = 3200x
50.) Find the number where 4 times added to 6 times added to 6 times its reciprocal is equal to
-14.
TROUBLESHOOT: 4x +6/x = -14 (remove extra “6 times added to”)
A.) -3, -1/2
B.) -3, 1/2
C.) 3, 1/2
D.) 3, -1/2
51.) A man on an observation sees a fire directly south of him. A boy on another tower 20 km
east of the first tower observes the fire at a bearing S40˚15’W. What is the distance of the
first tower from the fire?
A.) 26.20 km
B.) 15.26 km
C.) 16.93 km
D.) 23.62 km
52.) What is the simplified expression of 3x2 multiplied to (2x3y)4?
ANS: 48x14y4
53.) Using area method, solve for the integral from x = -3 to x = 3 of sqrt (9 – x2).
ANS: 4.5 pi
54.) What is b so that the points (-2, -1, -3), (-1, 0, -1) and (a, b, 3) lie on a straight line?
A.) 2
B.) 4
C.) 3
D.) 1
55.) If equal spheres are piled in the form of a complete pyramid with a square base, find the
total number of spheres in the pile if each side of the base contains 4 spheres.
A.) 18
B.) 20
C.) 30
D.) 28
56.) Joey is x years old y years from now. How is he/she now?
ANS: x – y
57.) John, Noel, and Ryan working together is 6 hours more than John working alone and 1
hour more than Noel working alone, and twice that of Ryan working alone. How long will
it take if they all work together?
TROUBLESHOOT: John = 6hrs alone, Noel = 1hr alone, Ryan = 2x faster than John? =
3hrs alone
ANS: 40 mins
58.) Solve for the limit
lim |𝑥 + 2|
𝑥→−2
ANS: 0
59.) n is directly proportional to z. If a, b, and c are constants, which of the following describe
the relationship?
ANS: n = cz
60.) What is the polar form of 1 + i
ANS: sqrt.2(cos45˚ + isin45˚)
61.) Evaluate Re{-i-i}.
ANS: e3π/2
62.) Find the area of the ellipse 4x2 + 9y2= 36?
A.) 15.71
B.) 18.85
C.) 12.57
D.) 21.99