College Mathematics Requirement Practice Test

  1. The 200 students at a school want to go to an event 60 miles away. If each bus holds 42 students, how many buses do they need?

    2. We need to know how many times 42 goes into 200., so division is the arithmetic operation called for

    5 buses will be needed.

  2. In the figure below, the radius of the larger circle is 5 inches and the radius of the smaller circle is 2 inches. Find the area of the shaded region.

    3. Recall the basic geometry fact:

    The area of a circle of radius r is p r2,
    where p » 3.14… .

    We need to use this fact twice. We first find the area of the larger circle, which gives us p (5 in)2 = 25p in2 » 25(3.14) in2 = 78.5 in2. Of course, this answer is too large, because we need to remove the part of the larger circle corresponding to the smaller circle. The good news is that the adjustment that we need to make involves another circular region. Applying the basic fact once again with the smaller circle gives

    p (2 in)2 = 4p in2 » 4(3.14) in2 = 12.56 in2. To get the desired area we need to subtract the area just obtained for smaller circle from that for the larger circle. Thus, we have 25p in2- 4p in2 = 21p in2 as the exact answer and 78.5 in2 – 12.56 in2 = 65.94 in2 as an approximate answer.

     

     
  3. What is the perimeter of the following figure?
    4.

    Recall that the perimeter of a polygon is computed by summing the lengths of its sides. Ordinarily, the process couldn’t be simpler, but here things are a bit trickier since we don’t know the lengths of two of the sides. The side to the far right is one of the unknown sides, but it is easy to see that it has to be 10 km (= 4 km + 6 km). The other unknown side is the one connecting the sides of length 4 km and 6 km. Clearly, the length of this side is 11 km (= 14 km – 3 km). Therefore, the perimeter is

    14 km + 10 km + 3 km + 6 km + 11 km + 4 km = 48 km.

     
  4. A jar contains 20 pennies, 6 nickels, 9 dimes and 4 quarters. If one coin is drawn at random, what is the probability that the coin is
    5. Since there        20 + 6 + 9 + 4  = 39        coins, the total number of possible outcomes, 
    from the random selection of a single coin, is 39.

    a) a dime

    Since 9 of the coins are dimes that is the number of favorable outcomes. Thus, the probability
     

    b) a penny or a quarter

    There are 20 pennies and 4 quarters, so we have 24 favorable outcomes. Hence, the probability
     

    c) a dime or a nickel

    There are 9 dimes and 6 nickels, so we have 15 favorable outcomes. Hence, the probability that
    to approach the problem is to observe that getting a dime or a nickel means NOT getting a penny or a quarter. From b), we know that there is a 62% chance of getting a penny or a quarter, so it follows that there is a 38% (100% - 62%) chance of getting a dime or a nickel.

    d) a half-dollar.

  5. A class of 34 students achieved the test scores summarized by the bar graph shown below.

    6. a) How many students achieved a grade higher than 85?

    From the graph, we see that 4 got a 90, 3 got a 95 and 1 got a 100.

    Thus, 8 (= 4 + 3 +1) students got a grade higher than 85.

    b) How many students received a grade 70 or less?

    From the graph, we see that 4 students got a 70, 3 got a 65 and 2 got a 60.

    Thus, the number of students earning a grade of 70 or less is 9 (= 4 +3 + 2).

  6. Represent the total number of jelly beans if there n bags of jelly beans and the number of beans in each bag is 10 more than the number of bags.

    7. As indicated above, the number of bags of jelly beans is n. Since the number of jelly beans per bag is 10 more than the number of bags of jelly beans, each bag must contain n + 10 jelly beans. Now, the total number of jelly beans is given by

    (the number of bags of jelly beans) ´ (the number of jelly beans per bag) = n(n + 10) = n2 + 10n.

     

  7. Label the points given on the graph below:

    8. (6,5) __C__ (2,3) __A__ (7,1) __D__ (4,7) __B__

    Recall that the first coordinate represents the distance from the vertical axis and that the second coordinate gives the distance from the horizontal axis.

     

     

      

  8. Solve for x:

    9.  

     

  9. In a certain company, 3 out of every 7 employees are men. If 99 men work for the company, what is the total number of employees?

Let x represent the total number of employees. Then, we can represent the information above in the form

 firm has 231employees.

 
  1. The number  is between what two integers? For example,  is between 3 and 4.