1.
The daily payroll for a work crew is directly proportional to the number of workers, and a crew of 12 workers earns a payroll of $900. Which of the following is a mathematical model expressing the daily payroll as a function of the number of workers?
2.
At exactly 6:48 am on an analog clock, what is the number of degrees formed by the hour hand and the minute hand (smaller angle)?
3.
A water tank in the shape of a sphere is 80% full of water. There is an empty tank in the form of inverted right circular cone with radius of 1.5m and height of 3m. All the water at the spherical tank was transferred at the conical tank until it's full and an amount of 4.24 cubic meters of water overflowed. Find the radius of the spherical tank.
Note: There is an overflow because the conical tank is already full.
4.
The arithmetic mean and geometric mean of two numbers are 25 and 20, respectively. Of these two numbers, find the smaller number.
5.
How many consecutive zeroes are at the end of the product of 130^{8} and 540^{30}?
6.
Find an equation of the line tangent to the curve y = 3x^{2} - 4x and parallel to the line 2x - y + 3 = 0.
7.
There are 30 girls and 50 boys in a classroom. Determine the probability of selecting a boy at random?
8.
A surveyor measured the angle of elevation to the top of a building to be 28 degrees. The surveyor moved 10m closer to the building and measured the angle of elevation to be 40 degrees. Determine the height of the building.
9.
The ratio of girls to boys in a class is 4 to 5. If there are 27 students in that class, how many are boys?
10.
There are 55 balls in a box. Some are green, blue, and yellow. The probability of picking a green ball at random is 6/11. A boy added 20 yellow balls in the box. What is the new probability of picking a green ball?
11.
A square is divided into three equal rectangles as shown. The area of one rectangle is 1200 square units. What is the perimeter of the square?
12.
A swimming pool is to be filled with water. One pipe can fill the pool in 2 hours. Another pipe can fill the pool in 45 minutes. If both pipes are used simultaneously, how many minutes will the pool be completely filled with water?
13.
A conical vessel has a diameter of 5m at the top and a height of 17m. Water flows into it at a constant rate of 2 cubic meters per minute. How fast is the water level rising when the water is 4m deep?
14.
A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 20 in. x 18 in. by cutting equal squares from the corners and turning up the sides. Find the largest possible volume of the box.
15.
If a family has 4 children, what is the probability that they have 2 boys and 2 girls?
16.
A 4-digit number is built at random from the digits 0,1,2,3,4,5,7,8 and 9. Find the probability that both ends are odd numbers and the second digit is 0. Give your answer as a fraction.
Example of a fraction: 2/3
17.
I invested an amount of 8000 pesos at a simple interest rate of 11%. What will be the amount after 8 months? Give your answer to the nearest whole number.
18.
The LCM and GCF of two numbers are 4992 and 4, respectively. If one of the number is 128, find the other number.
19.
Marvin has 5 Algebra books, 5 Geometry books, 1 Physics book and 3 Chemistry books. He wants to arrange these books on a bookshelf. The leftmost must be 3 Algebra books, followed by 4 Geometry books and the rightmost must be 2 Chemistry books. How many arrangements are possible?
20.
The time now is 1 hour and 27 minutes before 9:00 p.m. What was the time 45 minutes ago?
21.
Find the unit's digit of 387934^{39315}?
22.
The first term of a geometric progression is 3 and the 31^{st} term is 3221225472. Find the 16th term.
23.
A man walks from his house to his office at the rate of 4 mph and back to his house at the rate of 6 mph. What is his average speed?
24.
If f(x) = x^{2} + 4x + 1, then f(x) - f(x-2) is
25.
Two sides of a triangle are 119m and 120m. If the perimeter is 408m, find its area.