Prelim Exam Flashcards
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.
4 cm
In the given harmonic progression shown, compute the value of x.
x, 1/4, 1/7, 1/10
1
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?
24
Solve for x if logx 32 - logx 2 = 2.
4
Bert is 3 times as old as Charlie. Four years ago, Bert was four times as old as Charlie. How old is Bert?
36
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.
58.74 m
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.
8
The geometric shape used for Railroad Crossing Advance warning sign and for Civil Defense Evacuation Route Marker.
Circle
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.
Angle of repose
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.
57.15 sec
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.
6.53 m³
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?
120°
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?
2.8 hours
How many quarts of pure sulfuric acid should be added to 6 quarts of water to obtain a 40% sulfuric acid solution?
4
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?
18 days
Find the sum to infinity of the series 4, 4/3, 4/9, …
6