Algebra 1
Final Review Second Semester part 1
Mixed review
1. Find the slope of the line through the following pairs of points.
a.  4,7  & 12, 3
b.  6, 2  &  4, 8
c. 12,1 & 12,10 
2. Solve for x in the following problems.
a. 2 x  15  24
b.
3 4  x
6
5
2  4  x  1
6
7
c.
d. 14, 2  &  14, 2 
d. 6  2  x   3  3  x 
3. Rewrite each equation in intercept form.
a. y  8  3  x  4 
b. y  5 
3
 x  8
4
4. Solve the following system of equations
a.
8 x  y  20
5 x  y  8
b.
2 x  y  7
3x  y  3
c.
x  3  3y
4 y  x  11
c.
y  2x 1
y  6  3x
d.
8 x  7 y  337
5 x  11y  310
5. Graph the following system of equations
1
y  1 x
b.
2
y  3  2 x
y  2x  3
a.
y  3x  1
Exponential Equations and Exponents (chapter 6)
6. Write an equation that represents a bacteria population that started with a culture of 20 grams and grows at a rate of
4.5% a day.
7. Using your equation in 5, how many grams of the bacteria do you have after 3 days? 10 days?
8. An animal population is modeled by the equation y  32 1.08 where y is the number of animals and x is the
x
amount of time. Based on this equation, how many animals did the population start with? What is the growth rate?
How many animals would you have in 15 years?
9. Use the properties of exponents to rewrite the following expressions completely simplified

2
a. 2x y

4 3
 ab3 
b. 

 4 
2
 x3 y 5 z 
c. 
3 8 
 92 x y 
0

d. 4mn2 3m3n
10. Rewrite the following without any negative exponents
a. 86  84
b. 4x 2 y 3
c. x 4

e.
4 w2 x 5 y 6
 2w 
3 4
Functions (chapter 7)
11. Sketch a graph of a function that contains the point (4,-2)
12. Sketch a graph of a non function.
2
13. Find the indicated values given the following functions: f  x   2 x  3x  14 & g  x   3x  7
a. f  2 
b. g  6 
c. f  8 
d. x when g  x   0
e. f  0 
14. Find the domain and range of the following graphs:
a.
b.
6
6
4
4
2
2
5
5