Name: _____________________________________ Date: _______________________ Block: _______
Final Exam Review Packet
This packet will be due at the beginning of class on May 29th for a completion
grade. All work must be shown for each problem to receive completion
credit. On the day of the exam, I will select 10 questions to grade at random.
Each question will be graded for accuracy and will be worth 2 points.
15
20
(Completion)
(Accuracy)
Topics to be covered on the final exam include:

Polynomial Functions
o
o
o
o
Factoring by grouping, like quadratics, sum/difference of cubes
Synthetic division to find zeros and factors
Writing equations
graphing
 Rational Functions
o
o
o
o
o
o
Multiplying and Dividing expressions
Simplifying complex fractions
Adding and subtracting expressions
Solving equations
Graphing functions
Direct, Inverse, and Joint variation
 Statistics
o
o
o
o
o
Counting Principles
Measures of Center
Normal Standard Curve
Z-Scores
Regression
 Series and Sequences
o Arithmetic
o Geometric
o Graphing exponentials
Polynomial Functions
1. Factor completely:
3. Factor completely:
x3 – x2 + x – 1
x4 – 10x2 + 21
2. Factor completely:
4. Factor completely:
x3 + 27
5. Factor completely:
4x3 + 32
6. Use synthetic division to factor the polynomial:
x4 + 5x3 + 5x2 + x + 6
7. Use synthetic division to factor the polynomial:
2x3 – 10x2 – 4x + 48
8. Use synthetic division to find zeros:
f(x) = x3 + 5x2 + 3x – 9
9. Use synthetic division to find zeros:
g(x) = x3 + 2x2 – 16x – 32
x3 + 3x2 – 4x – 12
 y
1
10. Sketch the graph of f ( x)  ( x  4) 2 ( x  1)( x  1)
2
A) how many turning points?______




B) list zeros________________
    
C) y – intercept? __________

D)what happens at x = –4?____________

x








11. If the zeros of a function are x = 4 and x = 2i, write an equation of the function in
standard form.
12. If the zeros of a function are x = –3, x = –1, and x = 8, write the equation of the function in
factored form.
Rational Functions
Simplify the following expressions:
1.
x2  6 x  8
x 2  x  20
2.
x2  4
x3  8
3.
x2  2 x  8
2 x2  8
8 x  32 x 4  x3  2 x 2

4.
x3  x 2 4 x 2  16 x  16
5.
x 2  8 x  16 2 x  8

x 2  6 x  9 3x  9
6.
x3
x 2  25
x2  9
x5
7.
3  4n
2

n  3n  10 n  5
8.
x 3
x5
 2
2x 1 2x  9x  5
2
Solve the following equations. Check for extraneous solutions.
9.
3
1

x  4x x  4
2
10.
2x x  2 1


3
5
6
11.
x
3 5
 
x 1 x 2x
Graph the following functions.
12.
x 2  3x  2
13. g ( x) 
x2  1
4x  4
f ( x) 
x  3
 y
Hole?_______
VA?______
SA/HA?______
X – int_______
Y – int______
 y






    

x







Hole?_______
VA?______
SA/HA?______
X – int_______
Y – int______


    

x











Write an equation that relates the variables in each problem.
14. Y varies jointly as W and X
15. Y varies directly as the square of X.
16. R varies inversely as T and directly as S.
17. Y varies jointly as X and the square of Z
18. The weight, w, that a column of a bridge can support varies directly as the fourth
power of its diameter, d, and inversely as the square of its length, l.
Statistics
19. Compute 7C2
20. Compute
10P4
21. A committee must be chosen to write a new bill in Congress. Of the 15 available
members, only 4 will be chosen to the committee. How many different ways can the 4
members be chosen?
22. There are 8 people racing in the 400 yard dash. In how many different ways can
the racers finish 1st, 2nd, and 3rd?
23. You are choosing your class ring. There are 10 different stones to choose from, 3
different font styles, and 5 different images. How many different rings can be
created?
24. A password is 5 characters long and must contain 2 letters and 3 digits. How many
different passwords can be created if letters and numbers CANNOT be repeated?
25. John’s mean test score in Chemistry is 84 and his standard deviation is 4.2. Jane’s
mean test score in Chemistry is 87 and her standard deviation is 6.1. Who is more
consistent?
26. The following is a list mile times in minutes from 5th block and 7th block:
5th block
8.25
10.5
13.25
7
9.25
7th block
10.25
11
9.75
9
8.75
A) Which class is faster on average?
B) Which class is more consistent? How do you know?
27. If the mean of a data set is 12.34 and the standard deviation is 3.22, find the zscores of the following data points
A) x = 7
B) x = 15.3
C) x = 18
28. The scores of a reference population on the Wechsler Intelligence Scale for
Children (WISC) are normally distributed with   100 and   15 . What percentage of
people score more than 140?
29. Many high school students have part-time jobs after school and on weekends.
Suppose the number of hours students spend working per week is normally distributed,
with a mean of 16 hours and a standard deviation of 4 hours. What percentage of
students work less than 12 hours a week?
30. The time it takes for the fire department to arrive at the scene of a fire emergency
is normally distributed with a mean of 6 minute and standard deviation of 1 minute.
What percentage of calls have a response time between 4 minutes and 5.5 minutes?
31. Cara has been training for a 100 yard dash. Each week, she times herself and
tracks her progress. Find the quadratic curve of best fit and use it to answer the
following questions.
Week
1
2
3
5
8
Time
(second)
16
15.5
15.2
14
11.4
A) How fast will she run after 10 weeks?
B) How fast did she run after 6 weeks?
C) After how many weeks will she run the 100 yard dash in 14.5 seconds?
Arithmetic Series and Sequences
32. Write the first five terms of an arithmetic sequence with a1 = 5 and d = –3.
33. Write the first five terms of a geometric sequence with a1 = 32 and r = 4.
34. Find the arithmetic sequence that has terms a4 = 6 and a8 = 12.
35. Find the geometric sequence that has term a3 = 8 and r = 0.5
36. Find the sum of the first 8 terms in the sequence an = 4 – 5n
37. Find the sum
5
 2(3)
i1
i 1

1
38. Find the infinite sum (if possible):  5  
i  1 3
39. Find the infinite sum (if possible):

i1
3
18  

2
i 1
i1
40. An auditorium has 16 rows of seats. There are 22 seats in the first row, 25 seats in
the second row, 28 seats in the third row, and so on. How many seats are in the
auditorium?