Math 081 Exam 2 Review Problems

Exam 2 covers Chapters 4, Sections 5.5 – 5.7, and Chapter 6.  These are some problems that should help you review for Exam 2.  This is not a template for the exam, and you should also do the review problems suggested in the syllabus.  Calculators may NOT be used on Exam 2.

Write a fraction to represent the shaded area of the figure.
1.	

Determine whether the pair of fractions is equivalent.  Show the work necessary to justify your answer.  
2.	and 

Write the fraction in simplest form.
3.	
4.	
5.	Simplify by dividing:  
6.	Simplify by dividing:
7.	Perform the indicated operation.  Write the answer as a mixed number in simplest form:  
8.	Write the fraction in simplest form:
9.	Add or subtract as indicated.  Write the answer in simplest form.   
10.	Add or subtract as indicated.  Write the answer in simplest form:  

11.	Add or subtract as indicated.  Write the answer in simplest form:  
12.	Determine whether the proportion is true or false:  

13.	Determine whether the proportion is true or false:  
14.	Evaluate.  Write the answer in simplest form.  
15.	Evaluate.  Write the answer in simplest form.  
16.	Divide and simplify:  
17.	Divide and simplify:  
18.	Simplify the complex fraction:  
19.	Solve the proportion for the given variable:  

20.	Solve the proportion for the given variable:  

21.	Solve the proportion for the given variable:  

22.	Solve the proportion for the given variable:  

23.	Perform the indicated operation.  Write the answer in simplest form.  

24.	Perform the indicated operation.  Write the answer in simplest form.  

25.	Perform the indicated operation.  Write the answer in simplest form.  
26.	Perform the indicated operation.  Write the answer in simplest form.  

27.	Perform the indicated operation.  Write the answer in simplest form.  
28.	Perform the indicated operation.  Write the answer in simplest form.  
29.	Perform the indicated operation.  Write the answer in simplest form.  

30.	Give the prime factorization of 1536.

31.	Give the prime factorization of 405.
32.	Determine whether the pair of fractions is equivalent:  and 
33.	Determine whether the pair of fractions is equivalent:  and 

34.	Evaluate the expression for the given replacement values.  Write the answer in simplest form.   for  and 

35.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  

36.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  

37.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  

38.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  

39.	Solve the equation:  

40.	Solve the equation:  

41.	Solve the equation:  
42.	Solve the equation:  
43.	For the proportion, find the unknown number, x:  

44.	For the proportion, find the unknown number, x:  
45.	Betty has  cups of flour.  She uses  cups of flour to make a cake.  How many cups of flour does she have left?

46.	Simplify by combining like terms.  

47.	Find the exact circumference of the circle.  Then use the approximation 3.14 for .  Label your answers.

48.	It takes Bob 20 minutes to do and check 12 math problems.  Find how long it takes him to do and check 40 problems of the same difficulty level.  Round answers to the nearest whole number, if necessary.
49.	Write the ratio as a ratio of whole numbers using fractional notation.  Write the fraction in simplest form:  48 inches to 15 inches

50.	How many feet of fencing is needed to fence a circular yard with a diameter of 30 feet?  Use 3.14 for, and give your answer to the nearest tenth of a foot.

51.	Find the area of a circle with a radius of 7 miles.  Use 3.14 for , and give your answer to the nearest tenth.  Label your answer.

52.	Write the fraction as a decimal.  If necessary, use repeating decimal notation:  
53.	Write the fraction as a decimal.  If necessary, use repeating decimal notation:  
54.	Write the fraction as a decimal.  Round to the nearest hundredth:  
55.	Solve the equation:  

56.	Write a fraction to represent the shaded area.

57.	Perform the indicated operation:  

58.	Perform the indicated operation.  Write the answer as a mixed number in simplest form:  

59.	Write the rate as a unit rate:  21 garage sales in 3 blocks

60.	There are 20 mg of a compound in 1 mL of solution.  If a chemist needs 35 mg of the compound for an experiment, how many mL of solution should he use?
61.	Find which is the better buy (lower cost per ounce by finding each unit price rounded to three decimal places if necessary.  Assume that different sizes of the same brand are being compared.  
Laundry detergent:  $$3.59 for 96 ounces or $4.12 for 128 ounces.
62.	The following weights were recorded for a group of children:  67, 81, 56, 92, 107, 83.  Find the mean, median, and mode.

63.	Solve.  If necessary, round answers to the nearest hundredth.  
The grades are given for a student for a given semester.  Find the grade point average.  The point values of grades are given below:  
A:4		B:3		C:2		D:1		F:0

Grade	Credit Hours	
B	2	
C	4	
A	3	
F	3	

64.	In a model village, a triangular garden is to have the same shape as an actual triangular garden.  Use the diagram to find the length of the miniature garden’s missing side.  Round to the nearest hundredth, if necessary.

                   14 ft            17.5 ft                                 x ft
                                                                 .5 ft             

                                                                          .375 ft
                                   10.5 ft                                

65.	Determine whether the pair of triangles is congruent.  If congruent, state the reason why, such as SSS, SAS, or ASA.         

                                      6 in       7 in          7 in            
                                                                                  6 in
                                                       
                                                             4 in
                                             4 in