Prelim Exam

Question 1

The volume of water in a hemispherical tank is 687 cm³. If the radius of the hemispherical bowl is 15 cm, find the depth of the tank in cm.

Answer 1

4 cm

Question 2

In the given harmonic progression shown, compute the value of x.
x, 1/4, 1/7, 1/10

Answer 2

1

Question 3

To stimulate his lazy student in the pursuit of integral calculus, a math professor offered to pay him P12 for every problem correctly solved and to fine him P6 for every incorrect solution. After the student has solved 36 problems, neither of them owed any money to the other. How many did the student solve incorrectly?

Answer 3

24

Question 4

Solve for x if logx 32 - logx 2 = 2.

Answer 4

4

Question 5

Bert is 3 times as old as Charlie. Four years ago, Bert was four times as old as Charlie. How old is Bert?

Answer 5

36

Question 6

A tower is standing on a horizontal ground. To calculate the height of the tower, a surveyor at A, due east of the tower, measures the angle of elevation of the top of the tower and found it to be 30°. He then moves to point B, directly south of A, and measures the angle of elevation of the top of the tower and found it to be 24°. Point B is 84 m from A. Calculate the height of the tower.

Answer 6

58.74 m

Question 7

A tangent and a secant are drawn to a circle from the same external point. If the internal segment of the secant is 6 units and the secant is 11.44 units long, determine the length of the tangent.

Answer 7

8

Question 8

The geometric shape used for Railroad Crossing Advance warning sign and for Civil Defense Evacuation Route Marker.

Answer 8

Circle

Question 9

It is the term of the angle that the sides of a soil bank or pile naturally form with the horizontal when the excavated soil is dumped onto the pile.

Answer 9

Angle of repose

Question 10

Two trains are running in the same direction in 2 parallel rail tracks. The 1st train in front is 150 m long and running at 120 kph. The 2nd train behind the first is 120 m long and running at 200 kph. If the tail end of the first is 1 km ahead of the front end of the second, find the time required for the second train to completely pass the first train.

Answer 10

57.15 sec

Question 11

A tank in the form of a frustum of cone with end diameters 1 m and 2 m respectively, and slant height 3.6 m. Compute the volume.

Answer 11

6.53 m³

Question 12

A circle has diameter AOB with O as the center. Chord CD is parallel to AOB with C nearer to A and D nearer to B. If arc AC is 30°, what is the measure of arc CD?

Answer 12

120°

Question 13

Ship Alpha started sailing N 40°32’ E at a rate of 3 mph. At the same time ship Gamma started from the same point going S 45°18’ E at a rate of 4 mph. After how many hours after they started when they are 14.5 mi apart?

Answer 13

2.8 hours

Question 14

How many quarts of pure sulfuric acid should be added to 6 quarts of water to obtain a 40% sulfuric acid solution?

Answer 14

4

Question 15

Art and Bob complete a certain job if they work together for 6 days, or if Art works for 12 days and Bob for 3 days. How long would it take Art alone to complete the job?

Answer 15

18 days

Question 16

Find the sum to infinity of the series 4, 4/3, 4/9, …

Answer 16

6

Question 17

Thirty men could do a project in a target time of 120 days. Thirty men started the work but 10 men resigned after 30 days and were replaced at the beginning of the 46th day. How long was the project completion delayed?

Answer 17

5 days

Question 18

A single application of hot bitumen material given to the old surface to provide adhesion to the old and new road surface.

Answer 18

Tack coat

Question 19

A water container has vertical ends in the form of an isosceles right triangle with vertical axis and is 20 feet long. It contains 40 gallons of water. How deep is the water in the container? (1 gallon = 231 cu. in.).

Answer 19

6.20 in

Question 20

Which of the following are the basic traffic maneuvers?
I. Diverging
II. Merging
III. Crossing

Answer 20

All of the above

Question 21

A lot in the form of a quadrilateral is situated on the corner of 2 streets intersecting at an angle of 78°. On one street, the side is 134.28 m and on the other street, the side is 106.74 m. The other two sides are perpendicular to each side of the streets. Compute the area of the lot.

Answer 21

11, 526. 53 m²

Question 22

A conical tank has a radius of 2 m and a slant height of 5 m. Find the amount of material needed to make the conical tank if it is open at the top.

Answer 22

10π m²

Question 23

At how many minutes after 3 P.M. will the minute hand of the clock overtakes the hour hand?

Answer 23

16.364

Question 24

Find the radius of the circumscribed circle of a triangle whose sides are 10 cm, 18 cm, and 20 cm.

Answer 24

3.74 cm

Question 25

Progressive disintegration of the surface between the wheel paths caused by dripping of gasoline or oil from vehicles.

Answer 25

Flushing

Question 26

A car’s stopping distance varies directly with the speed it travels and inversely with the friction value of the road surface. If a car takes 60 ft to stop at 32 mph on a road whose friction value is 4, what would be the stopping distance of a car traveling at 48 mph on a road with a friction value of 2?

Answer 26

180 ft

Question 27

A paint mixture contains yellow, blue and red in a ratio 3:2:1. If the mixture contains 12 pints of yellow paint, how many pints are there altogether?

Answer 27

24

Question 28

A busy manager leaves his office at one afternoon. At that time, the hands of a clock in the course of normal operation describe a time somewhere between 4:00 and 5:00 on a standard clock face. Within one hour or less, he returns and noticed the hands have exactly exchanged positions. What time did the manager leave his office?

Answer 28

4:26.853 PM

Question 29

Find the area of a regular octagon inscribed in a circle of radius 5 cm.

Answer 29

85.09 cm²

Question 30

A rectangular piece of alloy 4 cm by 5 cm by 8 cm is melted and recast into a shape of a pyramid with a square base and height 15 cm. Find the measure of the edge of the base.

Answer 30

5.66 cm

Question 31

Find the term involving z⁴ in the expansion of (x - 2z^1/2)¹².

Answer 31

144, 538 x³z⁴

Question 32

Find the volume of a spherical wedge with radius 6 cm and central angle of 24°.

Answer 32

60.32 cm³

Question 33

A triangle ABC has sides AB= 12 cm, BC = 15 cm, and AC = 21 cm. Find the distance from vertex A to the incenter.

Answer 33

9.71 cm

Question 34

The altitude of a cone is 5 ft. A smaller cone is cut from this cone by a plane 2 ft from the vertex and parallel to the base. If the volume of the smaller cone is 24 ft³, what is the volume of the larger cone?

Answer 34

375 ft³

Question 35

A ball dropped from a height of 20 ft. It rebounds 3/4 the distance on each bounce. What is the total distance it travels before coming to rest?

Answer 35

80 feet

Question 36

The total surface area of a cube is 34.56 cm². Find the volume of the cube.

Answer 36

12.684 cm³

Question 37

Convert 135° to grads.

Answer 37

200 grads

Question 38

George has a job offer of P288, 000 salary in the first year, with his employer guaranteeing he will have a salary raise of P60, 000 per year in the succeeding 5 years. Find his salary in the 4th year.

Answer 38

P468, 000

Question 39

An airplane flying with the wind took 2 hours to travel 1,000 km and 2.5 hours to fly back. What was the wind velocity in kph?

Answer 39

60 kph

Question 40

The volumes of a sphere and a right circular cylinder are equal and the diameter of the sphere equals the diameter of the base of the cylinder. Determine the altitude (h) of the cylinder in terms of the diameter (D) of the sphere.

Answer 40

h = 3/2 D

Question 41

An expensive chain necklace consists of an 18K gold chain whose weight increases uniformly from a weight of 1 carat for the end chain to 89 carats for the middle chain where a pendant is attached. The clasp weighs as much (in carats) as the total number of chains. If the necklace altogether weighs 1, 198 carats, how many chains are there in the necklace?

Answer 41

31