1.
Sport utility vehicle (SUV) sales in the computer, find how long it takes him to
Philippines have increased since 1995. assemble the five computer units?
The function f(x) 0.005x^2%+0.325x+
7. If a radioactive element has a half-life
1.54 can be used to approximate the
of 3 hours; then x grams of the element
number of SUV sales during years 1995-
dwindles to x/2 grams after 3 hours. If a
2004, where x is the number of years
nuclear reactor has 600 grams of that
after 1995 and f(x) is the SUV sales (in
radioactive element, find the amount of
millions). Approximate the number of
radioactive material after 12 hours.
SUVS sold in 2002.
8. A ball dropped from a height of 12
2.Bottled water and medical supplies feet. It rebounds one-half the distance
are to be shipped to victims of an on each bounce. What is the total
earthquake by plane. Each container of distance it travels?
bottled water will serve 15 people and
9. A flywheel coming to rest makes 270
each medical kit will aid 8 people. if x
revolutions in the first minute and in
represents the number of bottles of
each minute thereafter makes 2/5 as
water to be shipped and y represents
many revolutions as the preceding mina
the number of medical kits, write the
Find how many revolutions the wheel
objective function that models the
makes before it comes to rest.
number of people that can he helped.
10. You and a friend spot a loose P200
3. The price of a dress is reduced by
bill simultaneously and agree to an
40%. When the dress still does not sell,
auction in which you write your bids
it is reduced by 40% of the reduced
and compare them. High bidder gets
price. If the price of the dress after both
the P200 and pays you the amount of
reductions is P1,080, what is the
the higher bid. Tie bidders split the
original price?
P200. How do you bid?
4. Every year a company pays a bonus
11. A bank area manager must visit four
of P30,000 to his most industrious
of the ten branches that the bank owns.
assistant, and P7,500 each to the rest
How many sets of four banks are there
of his staff. After how many years would
from which the manager can pick one
his outlay be exactly P600,000 if ali but
set to visit?
two of his staff bad merited the P30,000
but none of them more than twice? 12. The number of defective welds in a
length of pipe is 0 through 6 with the
5. A father and his son can dig a hole if
following probabilities:
the father works 6 hours and his son
works 12 hours, or they can do it if the
father works 12 hours and the son
works 8 hours. How long will it take for
the father to dig the hole alone? Find the expected value of the number
of defective welds.
6. A trainee in a computer company
takes 0.8 times as long to assemble 13. Eight eligible bachelors and seven
each computer as he took to assemble beautiful models happen randomly to
the preceding computer. If it took him have purchased single seats in the
30 minutes to assemble the first same 15-seat row of a theatre. On the
average, how many pairs of adjacent
seats are ticketed for marriageable heights H and h respectively. The angle
couples? of elevation of A from C and D are
respectively θ and 45°. Express the
14.It is known that the probability that a
height of building AB in terms of the
bulb will last beyond 100 hours is 0.80
height of building CD.
and the probability that it will last
beyond 150 hours is 0.36. Given that a 24. Four towns are located at the
bulb lasts beyond 100 hours, determine corners of a square highway network.
the probability that it will last beyond Four motorists set out from each town,
150 hours. each driving to the next town (in
clockwise direction), and each man but
the fourth going 8 kph faster than the
15. A bolt making machine has a 0.05 car ahead Thus the first car travels 24
chance of producing a defective product km/hr faster than the fourth. At the end
each time it produces a bolt. If three of one hour
bolts are selected randomly, what is the
the first and third cars are 204 km, and
probability of finding no defective
the second and fourth 212 (beeline) km
product in the three samples?
apart. What is the rate of the first car?
16. In 1990, a subtle flaw of Pentium
25. Find the value of x- y in the
chip would affect 1 in 9 billion division
equation (x + yi)(1-2i) =7-4i.
problems. Suppose a computer
performs 20 million divisions in the 26. Find the angle between the given
course of a particular program, what is zero-based vectors: V= (-√3,1) and Va=
the probability of no error and of at (2/3,2)
least one error.\
27. In a certain network, there are 4 nodes
17. Is a common carnival game, a player and 4 regions. How many arcs are there
tosses a penny from a distance of about 5 in the network?
feet onto surface of a table ruled in 1-inch
squares. If the penny (3/4 inch in diameter) 28. The bases of a trapezoid have lengths of
falls entirely inside a square, the player 7.6 cm and 2.9 cm, and its altitude is 4
receives 5 centavos but does not get his cm. Compute the area.
penny back; otherwise he loses his penny. If 29. . The area of a parallelogram is
the penny lands on the table, what is the
represented by x² +4. If the length of a side
chance to win if the lines are 1/16 in thick?
by x +4 and the length of the altitude to that
18.Two angles whose sum is 360° are called:
side by x-3, what is the area of the
19.Find two angles such that the angles are
parallelogram?
supplementary and the larger is twice
the smaller. 30. Which one of the following is better: a
20.Compute the hypotenuse of a right large pizza with 16-inch diameter for 650.00
triangle if one leg is 20 cm and the or a medium pizza with an 8-inch diameter
hypotenuse is 10 cm longer than the other for P325.00? What is the cost per square inch
leg. of the better buy pizza?
21. A cruise ship leaves a port and sails 35
miles due west. It then changes course and 31. . Five points are located in or on the
sail 30 miles on a bearing S32° W. How far is perimeter of an equilateral triangle with 7.
it from the port at this point? inch sides. If d is the distance between the
closest pair of points, what is the maximum
22. Given a point P on side BC of triangle
possible value of d?
ABC. Given that AB= AC = BP and AP= CP,
what is the value of angle ABC? 32. The surface area of a cylindrical
23. AB and CD are two buildings of aluminum can is a measure of how much
aluminum it requires. If the can has radius r high. Water is drained from the tank at
and height h, its surface area A and its the rate of of 36π ft³/sec. Compute the
volume v are given by the equations:
rate at which the radius of the water
surface shrinking when its radius is 16
feet.
The volume. V, of a 12 oz cola can is
355 cm³. A cola can is approximately 39. An inverted conical container has a
cylindrical. Express its surface area A as diameter of 40 in and a depth of 15 in.
function of its radius r, where r is If water is flowing out of the vertex of
measured in centimeters. the container at a rate of 25 π in³/sec,
how fast is the depth of the water
33. The number of public wireless
dropping when the height is 5 inches?
Internet (WIFI) access points (in
thousands) is projected to grow from 40. Ifa force of 420 N is required to push
2015 to 2020 according to the equation a safe up a ramp that is inclined 10°,
-66x + 2y =84, where x is the number then what is the weight of the safe?
of years after 2015. Find the slope and
41. A man pulls a rope attached to a
y-intercept of the linear equation.
sled. If the rope makes an angle of 32°
with the ground, determine the force
the man must exert on the rope so that
34. Fand the itorizontal asymptote ofthe
the effective force tending to move the
curve y
sled along the ground is 150 N.
35. An earth satellite has an apogee of
42. In the design of a supermarket,
2420 and miles and perigee of 460 . If
there are to be several ramps
the earth raduis is 400 miles, what is
connecting different parts of the store.
the value of the eccentricity of the
Customers will have to push grocery
ellipse, which form with the center of
carts up the ramps. An engineer has
the earth at one focus and whose
done a survey and found that almost no
apogee and perigee satisfy the
one complains if the force is no more
conditions above.
than 50 N. With slope θ = 5°, what force
36. The parallel sides of a rectangle are mustaperson exert, assuming a 25-kg
lengthening at the rate of 2 in/sec, grocery cart (full of groceries)? Assume
while the ether two sides are shortening friction (wheels against ground, wheel
in such a way that the figure remains on the axis, and so on), can be
rectangle with a constant area A =50 accounted for by a coefficient . = 0.10.
in².What is the rate of change of the
43. It takes a force of 160 N to stretch a
perimeter when the length of an
spring 50 cm. Find the work done in
increasing side is 5 in?
stretching the spring 30 cm beyond its
37. The radius of a sphere is when the natural( unstretched) length.
time is t seconds. Find the radius when
44. A spring stretches 0.20 m when a
the rate of change of the surface area
0.300-kg mass is hung from it. The
and the rate of change of the radius are
spring is then stretched an additional
equal.
0.120 m from this equilibrium point, and
38. An inverted conical tank is 40 feet released. Determine the amplitude of
in diameter at the base and 60 feet the oscillation.
45. Determine the time of oscillation (in certificate costs P50,000, what will be its
minutes) of a pendulum having a length value at maturity?
of 15m
46 . A 100-kg block initially at rest is 52. P210,000 was invested on the project
acted upon by a constant force of 80 N that yields annual benefit of P80,000 for 8
for 5 seconds after which an opposite years with no salvage value. Calculate the
force of 52 N is applied. In what benefit-cost ratio if the cost of money is 6%.
additional time will the block come to
rest? 53.A man made a time deposit of P500,000
with BDO that pays 9% per year,
47. A centrifuge rotor is accelerated
compounded annually. Compute the
from rest to 23,000 rpm in 5.0 min.
maximum withdrawals at the end of each
What is its average angular
year for 12 years.
acceleration?
48. A geosynchronous satellite is one
that stays at the same point on the
equator of the earth. Determine the
height above the earth's surface such a
satellite must orbit.
The universal gravitational 54.GERTC Corporation invested P4 million
constant G =6.67 x 10-11 N m²/kg2 on an equipment that will save the company
The mass of the earth is 5.98 x P1.8 million annually for 9 years. If the
1024 kg minimum attractive rate of return (MARR) is
The radius of the earth is 6.38 x 12%, what is the present worth index of the
106 m.
investment?
Hint: In order for the satellite to remain
in orbit, the gravitational force ust equal
the centripetal force: F= G Me ms/r2
Centripetal force = ms v²/r
49. The moon orbits the earth in almost
circular orbit with a radius of 384,000
km and an average period of 27.32
55. The repair costs of copier machine
days. Compute the moon's acceleration
is estimated to be P1200 the first year,
of the toward the earth.
increasing by P300 per year in the
50. A mine cable weighing 70 N/m is subsequent years. Determine the
unwound from a cylindrical drim. If the amount that the office will need to
lower end of the cable is initially 12 m deposit into a bank account, paying 4%
below the drum, how much work is interest to provide for the repair cost for
done by gravity as an additional 100 m the five years.
are unwound?
51. A commercial bank offers long-term
savings certificate at 17% per year
56.
compounded continuously. If a 12-year
