ALGEBRA 1
Final Exam Review
Name: _________________________________
1. Find the missing input or output values for the following functions. If there is no value, explain why not.
a.
b.
x  __________
2.
f ( x)  __________
a. For any graph, explain how you determine whether or not the graph is a function.
__________________________________________________________________________________
__________________________________________________________________________________
b. For any table, explain how you determine whether or not the relation is a function.
__________________________________________________________________________________
__________________________________________________________________________________
3.
Write an equation for the given line. (There should be arrows on the ends of this line.)
y
a.
equation = _______________________
b.
slope = _________________________
c.
y-intercept = _____________________
d.
x-intecept = _____________________
e.
domain = _______________________
f.
range = ________________________
x
4.
Simplify each expression. Final answers should contain no parentheses or negative exponents.
a.
2xy 5x y 
d.
 2x3 y 5 


7
 x y 
3
2 4
b.
2
e.
14x 2 y12
7x 5 y 7
2x y  5x 
5 3 0
4x y 
2 3 3
c.
f.
16 
3
4
g.
 27 
1
3
5.
6.
Solve the following equations. Check your solutions.
x 6x  2   3x x 12 
a.
3  c  4   2  14
b.
1
2
c.
2x 12x  5  4x 1x 1
d.
2 x  3  10  4
2
Solve each equation for the specified variable.
a.
Solve for y:
5x  3y  15
b.
Solve for x:
4x  3y  8
7.
Solve the following systems of equations using the most efficient method. Be sure to check your
solution in BOTH equations.
a.
y  5x  4
y  4x  23
Solution: _______________
Check:
b.
x  3y
4x  y  26
Solution: _______________
Check:
c.
3x  2 y  12
5 x  3 y  37
Solution: _______________
Check:
8.
Mike spent $11.19 on a bag containing red and green candies. The bag weighed 11 pounds.
The red candies cost $1.29 per pound. The green candies cost $0.79 per pound.
a.
Define your variables:
Let __________________________________
Let __________________________________
b.
Write two equations to represent the situation then solve the system.
c.
How much of each type of candy did Mike buy? Answer in a complete sentence.
_______________________________________________________________________
_______________________________________________________________________
9.
For each of the following sequences, write an explicit equation, a recursive equation, then calculate the
25th term in the sequence. Show all work.
a.
14 , 10 , 6 , 2 , …
b.
-16 , -13 , -10 , -7 , …
explicit:
explicit:
recursive:
recursive:
25th term:
25th term:
c.
32 , 64 , 128 , 256 , …
d.
5 , -5 , 5 , -5 , …
explicit:
explicit:
recursive:
recursive:
25th term:
25th term:
10.
It seems reasonable that there would be a relationship between the amount of time a student spends
studying and their GPA. Suppose you were interested in predicting a student’s GPA based on the hours they
study per week. You were able to randomly select 12 students and have them record the number of hours they
studied in a week.
Hours
4
5
11
1
15
2
10
6
7
0
7
9
GPA
2.9
3.3
3.9
2.2
4.1
1.8
4.6
2.9
2.2
3.0
3.3
4.5
a.
Create a scatterplot and sketch it below.
b.
Create a residual plot and sketch it below.
c.
Enter the data into your calculator and calculate the LSRL. (Round to the hundredth.)
__________________________________________________
d.
Interpret the meaning of the slope of the LSRL in context. _________________________________
________________________________________________________________________________
e.
Interpret the meaning of the y-intercept of the LSRL in context. ______________________________
________________________________________________________________________________
f.
What is the value of r? (Round to the thousandth.) __________ Interpret the meaning of r: ___________
________________________________________________________________________________
g.
Describe the association between the variables.
direction: ___________________________
strength: ____________________________
form: ______________________________
outliers: _____________________________
h.
Use the LSRL to predict the GPA for a student who studies for 8 hours a week.
i.
Calculate the residual for a student who studied for 8 hours actually had a 3.9 GPA.
11.
Based on the tables below, find the equation of the exponential function
Check your equations using your calculator.
a.
y  ab x
by hand.
equation: _____________________
x
0
1
2
3
f(x)
1600
2000
2500
3125
Based on your equation, what is the percent of increase or decrease? _____________________
b.
x
1
2
3
y
40
32
25.6
equation: _____________________
Based on your equation, what is the percent of increase or decrease? _____________________
12.
In seven years, Seta’s son Stu is leaving home for college. Seta hopes to save $8000 to pay for his first year.
She has $5000 now. If her bank pays 6.75% interest annually, how much money will Seta have for Stu’s first
year of college? (Round to the nearest penny.) Will she have enough?
13.
Tungsten has many chemical and commercial uses, but some forms of it need to be combined with heavy
alloys. W-187 has a half-life of 23.9 hours. If a manufacturer has 100 g sample, but won’t be receive the
necessary heavy alloys for 3 days (72 hours), how much W-187 will remain?
14.
Calculate linear and exponential equations that pass through the two points
a.
Line: _______________________
b.
1,21 and  4,7203 .
Exponential: _______________________
15.
Factor the following expressions COMPLETELY. Do not solve for x!
a.
16.
b.
24 x3  4 x2
3x2  30 x  75
c.
Solve the following equations using the most appropriate method.
a.
17.
x2  5x  6
0  x2  7 x  2
b.
10 x2  3x  7  0
Solve each inequality and graph the solution.
a.
2  x  5  8
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
b.
1
2
3
4
5
6
7
8
9 10
12  3x  2 x  2
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9 10
18.
19.
Write an inequality for each of the given graphs:
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
Use the equation x 2  8 x  9  y to answer all of the following questions:
Use Factoring and the Zero Product Property to solve for x. Circle your answers.
Use Completing the Square to solve for x. Circle your answers.
Use the Quadratic Formula to solve for x. Circle your answers.
b  b2  4ac
x
2a
y
2
–6
–4
–2
2
–2
–4
–6
–8
–10
–12
–14
–16
Graph the equation by providing the following information:
–18
y-intercept:
( _______ , _______ )
x-intercepts:
( _______ , _______ ) and ( _______ , _______ )
–22
vertex:
( _______ , _______ )
–24
domain: ____________________________
–20
–26
–28
range: _____________________________
shape: _____________________________
–30
–32
4
6
8
10
12
x
20.
Graph the following systems. Pay attention to the signs!
a.
y   23 x  5
b.
y   x  2  1
2
y   23 x  5
y   x  2  1
2
y
y
x
x
c. Check your solutions to these systems in your calculator.
21.
Solve the following equations for x. Show all work.
a.
x
5

2
x
 4 
x
5
b.
16x  8x1
22.
A survey of 155 recent high school graduates found that 130 had driver licenses and 58 had jobs.
Twenty-one said they had neither a license nor a job.
a. Create a two way table.
Job
No Job
Total
License
No License
Total
b. What is the probability that a high school graduate has both a job and a license?
c. What is the probability that a high school graduate with a license has a job?
d. What is the probability that a high school graduate has either a job or a license?
e. Create a relative frequency table.
Job
No Job
License
No License
f. Is there an association between having a license and having a job? Explain how you know.