Download FINAL review test

Math 107
Final Exam, Fall 2000
Name__________________________________
Legibly show all of your work below each exercise. BO
your final answers.
1. Complete the following short answer problems forX2 points each:
a) Simplify: x 7 + 2 x
h) Write x 2 using only positive exponents.
b) Simplify: 4  6  2  3
i) Write 65400000 in scientific notation.
c) Reduce to lowest terms.
261
.
900
j) Give the slope and the y-intercept for the
1
graph of the equation y  x  6 .
2
slope ______ y-intercept ______
1 1 1
,
d) Find the LCD for ,
.
6 20 15
e) Simplify: 4   2 x  6  3x  5
f) Find the x-intercept for 2x  y = 8.
g) Evaluate 4  5x for x  2 .
k) Subtract: 1 
l) Simplify:
5
21
x5
x3
m) Simplify: x 3 
n) Simplify:
5
x5
x 3
[30]
2.
Perform the indicated operations. Write final answers in simplified form.
3
4

Add:
28 21
(9 points)
 3  4 
Multiply:    
 28   21 
Divide:
3
4

28 21
3. Give:
(6 pts.)
2
_____
3
2
The absolute value of
_____
3
2
The reciprocal of
_____
3
The opposite of
4.
Find the area and perimeter of this rectangle. Remember to include the units.
(4 points)
area = ______________________________
5 cm
13 cm
perimeter = __________________________
13 cm
5. Solve the formula for the variable y: 2 x  3 y  6
(4 pts.)
6. Translate from words to symbols: The sum of twice x and three is eleven.
(3 pts.)
[26]
7. Simplify the following as much as possible, write all answers with positive exponents only and without
decimals:
(9 pts.)
a)
b)
3x y 2 xy 
3 2
2
 
x 
15 x 2 x 3
3x7
 y7 
c)  2 
y 
2
3 1
8
8. Find the slope of the line connecting 2, 6 and 1, 4
9. Given the point (2,4), and slope
1
, find and graph the equation of the line.
2
(4 pts.)
(10 pts.)
equation of the line:
__________________________
[23]
10. The length of a rectangle is one inch less than three times its width. If the perimeter of the rectangle
is twenty-two inches, find the dimensions of the rectangle.
(10 pts.)
Let x = ________________________________________
Let ___________________________________________
Equation(s):
Solve.
Write your answer in a sentence.
11. Solve each system:
4x + 3y = 15
2x  5y = 1
(12 pts.)
2x  3y  6
x  1.5 y  3
12. Solve and graph the following inequality:
(6 pts.)
3  4x > 15
[28]
13. Solve and graph the following inequality:
(6 pts.)
3x + 6y < 12
14. Ethan has $8000 to invest. He invests part of the money at 6% and the rest at 8%. If his interest for
one year is $600, how much did he invest at each rate? Use the table if you’d like.
(10 pts.)
6%
8%
Total
Amount invested
Interest earned
15.
Divide.
(7 pts.)
x  3 2 x 2  3x  5
[23]
16. Find the solution for each equation.
(8 pts.)
a.  2 x  6 x  12
_________________
solution
b.  2 x  6  12
_________________
solution
17. Find the solution for each equation.
(12 pts.)
a. 2x  3  3x  4
_________________
solution
b. 0.2 x  2  0.7 x
_________________
solution
[20]