Algebra II
Final Exam REVIEW 2013
Name _______________________
10 points – Completion
20 points - Accuracy
The exam review will be graded on completion (10 points) and
randomly selected problems answered correctly with accurate work shown (20 points)
In order to earn full credit,
you must show all work for each problem!!
One point will be deducted for each problem not completed or without work.
The entire exam review packet is due no later than:

Thursday, May 16, 2013 for a maximum of 35 points out of 30 points.

Friday, May 17, 2013 for a maximum of 35 points out of 30 points.

Monday, May 20, 2013 for a maximum of 32 points out of 30 points

Tuesday, May 21, 2013for a maximum of 31 points out of 30 points

Wednesday, MAY 22, 2013 for a maximum of 30 points out of 30 points
In my hand by 3:50 pm – not in the mailbox
There will be no exceptions made!!
The Final Exam will consist of material covered from Unit 5 (statistics); Unit 6
(Polynomials – Ch 5); Unit 7 (Rational Functions – Ch 8); Chapter 12 (sequence and
series) and Chapter 7 (Exponential Functions)
Algebra 2
Final Exam Review
Name _______________________
DIRECTIONS: SHOW WORK TO RECEIVE FULL CREDIT – Box or Circle all final answers.
Unit 6 (Polynomials – Ch 5)
1.
Use synthetic substitution to find the value of f (x )  5x 4  6x 2  1 , when x = -2
2.
Complete the statement regarding the end behavior of the graph of f (x )  x 3  5 ,
as x  ,
f ( x)  ___
3.
Factor completely: x 3  8
4.
Use synthetic division to find the quotient of 5x 3  4x 2  6x  2  x  3
5.
Use long division to divide f(x) = 2x3 – 9x2 + 12x – 5 by (x – 1).
6.
Find all of the possible rational zeros of f ( x)  4 x3  2 x 2  11x  12
c
7. If 
2
is a zero, what is its factor? __________
3
8. If (3 + 4i) is a zero, what is another zero? __________
hb g
1
x 3 x 2 x 6
9. Sketch the graph the function: y 
12

b gb gb g
y



How many turning points? _____

x













10. Find all the zeros of the function using factoring: f (x )  x  11x  x  11
3
2

11. Find all the REAL solutions of the function using factoring: f (x )  x 3  27
12. Write a polynomial function in standard form that has real coefficients, the given
zeros, and a leading coefficient of 1. Zeros: 2, 4, -3i
13. Given the polynomial f(x) = x3 - 9x2 + 8x + 60, find ALL zeros given (x – 6) is a factor.
14. Find ALL the solutions of the function: f (x )  x 3  2x 2  x  4
Show the synthetic division and other work for full credit.

Unit 7 (Rational Functions – Ch 8)
Identify the vertical asymptote, horizontal asymptote, domain and range for each function
below.
y
2x 1
x 3
4
15. y 
x
16.
Vertical asymptote________
Horizontal asymptote______
Domain___________
Range____________
Vertical asymptote______
Horizontal asymptote______
Domain__________
Range___________
Graph the rational functions given and identify the necessary information below.
17.
f(x) 
2x
x4
 y



Vertical asymptote_____
Horizontal asymptote______

    
18.
f(x) 







2
1
x 3
 y


Vertical asymptote_____


Horizontal asymptote______


Domain________
Range_________

x
    

Domain________

Range_________



x





19.
The variable z varies directly with y and inversely with x.
When x = 4 and y = 28, z = 56, write an equation relating x, y, and z.
20. Wind chill factor (W) varies directly with temperature (T) and inversely with the wind
velocity (v). If k is the constant of proportionality, write the formula that represents this
relationship?
x 2  3x  10
x 1
• 2
?
2
x 4
x  6x  5
21.
What is the product
22.
What is the quotient (x + 6) ÷
23.
What is the sum of
24.
4
3x

x 2  5x  6
?
x2  7x  8
x
3x  6x
2
?
4x  12
x2  9
What is the difference of
−
x 3
x 3
6 2
4
  ?
x 3
x
25.
What is the solution of the equation
26.
What are all the solutions of the equation
x2
8

?
5
x4
Unit 5 (statistics)
27. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that evaluates
college students’ motivation, study habits, and attitudes toward school. A college gives the
SSHA to a sample of 22 of its incoming first-year students. Their scores are:
153
102
108
127
137
127
114
137
152
165
140
165
154
129
178
210
101
148
112
135
128
114
Complete the following table of indicated values.
Mean
Median
Standard Deviation
Range
28. From a group of 40 people, a jury of 12 people is selected. In how many different ways
can a jury of 12 people be selected?
29. In one Austrian province, a vehicular plate number consists of 4 letters and 3 numbers.
(example: BACK_301) Using the fundamental principle of counting (one more time!), how many
plate numbers are available?
30. A random survey was conducted to determine the cost of residential gas heat. Analysis
of the survey results indicated a normal distribution with a mean monthly cost of gas of
$125, and a standard deviation of $10.
a. What percent of homes will have a monthly bill of more than $118?
b. What percent homes will have a monthly bill between $118 and $130?
c. Determine the percentile for a monthly bill of $140.
31. If the mean is 7 and the standard deviation is 4, what is the z-score of 5?
32. What is the area under the standard normal curve corresponding to Z < 1.6?
33. A study of weekly salaries at High Tech Manufacturing indicated that weekly salaries are
normally distributed with mean = $725 and standard deviation = $45. What salary represents the
80th percentile?
34. The table below shows the New York Yankees’ payroll(in millions of dollars) from 1997
to 2004. Use your calculator to find the quadratic model that best fits the data.
Years since 1997
0
1
2
3
4
5
6
7
Payroll
59
63
88
93
112
126
153
184
a) Determine the Quadratic Model for the data set above: (round to 2 decimals)
b) Using the equation, what would you estimate the payroll to be this year, 2012?
Chapter 12 (sequence and series)
35.
Evaluate:
5
 (3k
2
 k)
k 3
36.
Select the arithmetic sequence. Then, identify the common difference: ______
a) 2, 5, 9, 14, 20
b) 1, 3, 6, 10, 15
c) −5, −2, 1, 4, 7
c) −3, 0, 4, 9, 15
37.
Write the rule for the arithmetic sequence when a14 = -73 and d = -8
38.
1
Find the sum using the formula sum.  20  
2
n 1
39.
Using the formula Sn =
40.
Write a rule for the nth term of the geometric sequence -2, 8, -32, 128, …
6
n 1
a1
3 3 3
, find the sum of 6  3     ...
2 4 8
1 r
Chapter 7 (Exponential Functions) –
This will be on your final exam but is not
covered in this packet. You need to study your materials from class to review Ch 7 for the
final!