Tutor’s Qualification Exam

Directions: Select the best answer of the four or five choices, and then write the corresponding letter in your answer sheet. 

If , what is the value of ? 

The expression is equal to 0 when and when ?

A bicycle company makes five styles of bikes in seven different colors. How many different bicycles can the company make when considering both style and color?

Which of the following statements is NOT true for the function ?

The statement “Raphael runs every Sunday” is always true. Which of the following statements is also true?

The amount of pancake mix required to make pancakes is proportional to the number of pancakes that are being made. The table below shows the required amount of pancake mix and water to make 6 pancakes.
How much water is needed to make 9 pancakes?

In the diagram below AB = BC. Which of the following statements must be true?

I.

II. is the midpoint of  

III. .

For which points on the number line below is the statement true?

I.

II.  

III.

The remainder when is divided by is

There are a total of seats in a movie theater. During a certain week there were a total of viewings at the theater with an average of unsold tickets for each viewing. Which of the following equations represents the total number of tickets that were not sold during that week?

David draws a line that is 13 units long. If is one endpoint of the line, which of the following could be the other endpoint?

A jar contains blue, red, and green marbles. The ratio of blue : red : green = 3 : 5 : 4. What is the probability that a marble chosen at random is NOT red?

The complex fraction in simplified form is equal to

In the sequence 1, 3, 5, 7, 9, 1, 3, 5, 7, 9, 1,… What is the 103rd term of the sequence?

If , then ?

If then ?

If and , then ?

If 10% of is equal to 25% of and , what is the value of?

The simplest form of is

The expression

Every 3 minutes, 4 liters of water are poured into a 2,000-liter tank. After 2 hours, what percent of the tank is full?

Ben is three times as old as Samantha, who is two years older than half of Michele’s age. If Michele is 12, how old is Ben?

Two planes leave the same airport at 2:00 pm, one travelling south at 350 kph and the other travelling north at 250 kph. At what time will they be 3600 km away?

Rebecca’s test grades in her math class for the first quarter are 90, 84, 80, 92, 84, and 98. Of the 6 grades in the first quarter, if p is the mean, q is the median, and r is the mode, which of the following inequalities is true?

How many ounces of pure acid must be added to 20 ounces of a solution that is 5% acid to strengthen it to a solution that is 24% acid?

Working together, Pepe and Tony can clean their room in 2 hours. If after 30 minutes of working together, Pepe got sick and Tony had to finish the job in 3 more hours, how many hours would it take Tony to do the job had he worked alone?

In the diagram below, line is parallel to line , and line is perpendicular to line . What is the measure of angle ?

In the figure below, is an isosceles right triangle, and What is the area of the shaded region

Triangle BDC, shown above, has an area of 48 square units. If ABCD is a rectangle, what is the area of the circle in square units?

If the diagonal of a square measures what is the area of the square?