Download MATH103-FINAL-EXAM

Math 103 - Elementary Algebra
Final Exam Review
1. For the set of numbers shown, classify the natural numbers, whole numbers, integers, rational
2
12

numbers, irrational numbers and real numbers.  , 0, 3, ,  6, 10.15,  ,  8.4
3
4

a.) 2pts. Natural numbers ___________________________________________
b.) 2pts. Whole Numbers_____________________________________________________________
c.) 2pts. Integers ______________________________________________________________________
d.) 2pts. Rational Numbers ___________________________________________________________
e.) 2pts. Irrational Numbers __________________________________________________________
f.) 2pts. Real Numbers _________________________________________________________________
Perform the following operations and, if possible, simplify your answer.
2.) 3pts. 36  31
5.) 3pts.
1
0
9
8.) 3pts.
1 3
2 1
2 4
3.) 3pts.
6.) 3pts. 
0
7
4.) 3pts.
16  11 
 
22  24 
9.) 3pts.
36  6
7
 3  50 
7.) 3pts.     
 5  51 
1 2

5 7
10.) 3pts.
2
7
26
49
Evaluate the following algebraic expressions by following the order of operations. Simplify if possible.
2
11.) 3pts. 25  3  4
13.) 3pts. 5 
30
 23  27
(8  2)
12.) 3pts. 13  (2  5)  6  3
 4  3 12 
14.) 3pts. 6  2 
  3 8
8


Simplify the following algebraic expressions:
15.) 3pts. 7t  5  4t  (2t  6)
17.) 3 pts. 5 x 3x   5 x  1  2(5 x  1) 
16.) 3pts.
3
(20 x  15)  x  5(2 x  3)
5
18.) Consider the figure below:
5x 10 cm
3
x cm
5
a) 4pts. Write an expression for the perimeter of the figure and simplify your answer.
b.) 4pts. Write an expression for the area of the figure and simplify your answer.
Translate the following phrases into algebraic expressions:
19.) 3pts. Twice the difference of a 4 and a number.
20.) 3pts. Eight more than the product of a number and 6.
21.) 3pts. Two less than the sum of a number and twelve.
Write verbal descriptions of the following algebraic expressions, without using a variable.
22.) 3pts. x  2
23.) 3 pts. 2  3x  1
24.) 3 pts
(1  x)
3
Solve the following equations.
25.) 4pts. 3( x  2)  24
26.) 4 pts. 4( x  2)  4( x  4)
Solve the following equations.
27.) 4 pts. 2(5 x  4)  4(2 x  4)
28.) 4 pts.
x 2
 0
5 15
29.) 4pts. 12  7 5(2 x  3)  7  2
30.) The bill for the repair of your car was itemized into two categories - parts and labor. The total bill
was $210.00. The parts totaled $90.00. If the rate for the mechanic was $45.00/hour.
a. 3pts. Create a mathematical model (equation) to determine the number of hours the mechanic
worked on your car.
b. 2pts. Solve the equation. Give your answer in exact hours and minutes.
c. 1 pt. Give your answer in a well written complete sentence.
31.)
To get an A in a course, you must have an average of at least 90 points for four tests of 100
points each. For the first three tests, your scores are 77, 96, 89, What must you score on the
fourth test to earn a 90% average for the course?
a.) 3pts. Create a mathematical model (equation) to determine the required score.
b.) 2pts. Solve the equation.
c.) 1pts. Give your answer in a well written complete sentence.
Solve the follow ratios:
32.) 3pts.
x
3

45 10
33.) 3pts.
6 2

t 15
34.) 3pts.
5x  4 8

3
9
35.) 3pts. Find the ratio that compares the relative sizes of these quantities. Use the same units of
measure for both quantities, and simplify as much as possible. 4 days to 30 hours.
36. a.) 4pts. A 500-milliliter intravenous bag is attached to a patient with a tube and is empty after 4
hours. At what average rate does the solution flow through the tube? Please give your
b.) 1pts. Give your answer in a well-written complete sentence.
37. a.) 3pts. Use similar triangles to write and solve a proportion that will find the height of the cell
phone tower in the picture.
?
5.75 ft
2 ft
40 ft
b.) 1pts. Give your answer in a well-written complete sentence.
38.) 4pts. Use unit analysis to determine which product has the lowest price:
A gallon of milk for $2.99 or a quart of milk for $1.20.
39.) 4pts. Use unit analysis to determine which product has the lowest price: A 20-ounce bag of
sunflower seeds selling for $1.99 or a 15-ounce bag of seeds for $1.75.
40.) 3pts. Forty-five is what percent of 2,250?
41.) 3pts. What number is 115% of 60?
42.) 3pts. Twenty-eight is 35% of what number?
43.) 4pts. This year, Rennita made $24,000. This is a 5% increase over last year’s pay. How much
money did she make last year?
44.) 3pts. Solve for r : C  2 r
45.) 3pts. Solve for L : P  2L  2W
46.) How many ounces of pure alcohol must be added to 20 ounces of a solution that is 10%
alcohol to obtain a solution that is 15% alcohol?
a)
4pts
b)
1pt
Set up the problem correctly and show all steps of the calculations.
Write your answer in a well-written, complete sentence, with the proper units.