January 2020

Index

College Algebra
Exponents and radicals • Logarithm and division by zero • Quadratic equation, quadratic formula, and roots of quadratic equation • Special products and factoring • Binomial expansion and Pascal's triangle • Verbal problem categories • Number problems • Digit problems • Clock problems • Age problems • Mixture problems • Work problems • Motion problems

Problem
An engineering company prepares an estimate for a job. The cost of preparing the estimate is Php10,000. The amount of profit over and above the Php10,000 is Php25,000 if their estimate is accepted. The probability that their estimate will be accepted 0.7 and the probability that their estimate will not be accepted is 0.3. What is the expected profit?

A.   Php12,500 C.   Php14,500
B.   Php13,500 D.   Php10,500

 

Problem
The following interior angles (in degree) of a triangular traverse were measured with the same precision.
 

Angle Value No. of Measurement
A 41 2
B 77 6
C 63 2

 

What is the most probable value of angle C, in degrees?
 

A.   62.423° C.   62.571°
B.   62.874° D.   62.745°

 

Problem
A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects 2 cell phones at random without replacement. What is the probability that exactly 1 is defective?

A.   0.0190 C.   0.0390
B.   0.0490 D.   0.0290

 

Number of Hours for Pipe to Fill the Tank if the Drain is Closed

Problem 1
A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Problem 2
A pipe can fill a tank in 4 hours if the drain is open. The tank is initially empty. If the pipe runs with the drain open for 1 hour and the pipe is then closed, the tank will be emptied in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Answer Key