To prepare for your midterm exam, please follow these suggested steps. The more practice you do, the better prepared you will be for the exam. Be sure to have your
calculator ready the day of the exam with WORKING batteries, a straightedge, and more than one sharpened pencil. Do not expect to borrow materials.
1.
Review key vocabulary terms at the beginning of each chapter or use the list at the end of the chapter in the review.
2.
Read the chapter summary at the end of each chapter several times. Write down any ideas that are unclear.
3.
Review the quizzes and tests you have already taken and be sure that you would get
100% if you took the same test today.
4.
Complete the lesson-by-lesson review in the Study Guide and Review section at the end of each chapter.
5.
Complete the practice test at the end of each chapter.
6.
Use pages 949, 955-960,965-966 for extra practice problems for each section of each chapter. This is the EXTRA PRACTICE section of the back of your book.
7.
Use pages 983-984 for extra practice word problems for each section of each chapter. This is the MIXED PROBLEM SOLVING section of the back of your book.
8.
For additional practice on areas you may use previous homework assignments. Your homework should be a solution key to check your work.
9.
Use the guiding questions in the remainder of this packet for a general review. However, do not rely solely on these questions.
*REMINDER: Bring all quizzes and tests to the exam for extra credit on the midterm!!
You must have all of them or no credit.

Functions
A.
Function notation
B.
Graph absolute value functions
C.
Identify transformations of absolute value
D.
Identify domain and range
E.
Evaluate a function for a given value
F.
Identify key characteristics of graphs
G.
Compositions of functions
H.
Inverses
Graph the function.
1) y = 4 x + 2 3 2) f(x) = x +
5
6
3) In 1990 Marc earned $42,360 per year, and he now earns $61,800. What is the rate of change for Marc’s salary per year?

4) I DENTIFY THE KEY CHARACTERISTICS OF THE GRAPH domain range zeros y-intercept intervals of increase intervals of decrease intervals where the graph is positive intervals where the graph is negative
Is it a function?
5) If f(x) = x + 3 and g(x) = 4x – 1, find the following:
a) f(x) – g(x) b) f(x)  g(x) c) f(g(x)) d) g(f(x))
6) Find the inverse of the function f(x) = 4x - 2. Is the inverse a function?

7) Verify that f and g are inverses of each other. (Show f(g(x)) = g(f(x)) = x) f(x) = 6x - 5 and g(x) =
1
6
C H .
5 – Q UADRATIC F UNCTIONS AND F ACTORING x +
5
6
A.
Graph Quadratic Functions
B.
Perform Operations with Complex Numbers
C.
Solve by Factoring
D.
Solve Quadratic Equations by Finding Square Roots
E.
Complete the Square
F.
Use the Quadratic Formula and the Discriminant
Factor:
1) x 2 - 7x + 6 2) x 2 - 81
3) 4x 2 + 12x + 9
5) 15x 3 + 10x 2 + 6x + 4
4) 3x
6) k
3 - 24x
3 + 4k 2
2 + 21x
– 9k – 36

Simplify:
7) -
9) i 15
144
11) (2 + 3i) + (5 - 4i)
12) (2 + 3i)(5 - 4i)
Solve:
14) 3x 2 - 24 = 0
16) x 2 - 10x - 4 = 0
8) 28 + 63
10) (3i)(2i)
11) (2 + 3i) - (5 - 4i)
13) (4 -5i) 2
15) 5x 2
17) -2x
+ 19x = 125 + 19x
2 + 3x -7 = -9

18) x 2 + 5x + 7 = 0 19) 2x 2 - 2x = -3
For each of the following, find: the vertex, axis of symmetry, y-intercept, and xintercepts. Then graph the function.
20) y = x 2 - 4x + 3 21) y = 2x 2 - x – 6
Applications:
22) Marcus is shooting of a rocket from a 160 foot cliff at a velocity of 48 ft/sec. a) Find the time it takes the rocket to hit the ground? b) What is the maximum height the rocket reaches? c) How long does it take for it to reach the height in problem b?

23) If the discriminant of a quadratic equation is -40 what does that tell you about the roots of the equation?
24) The length of a rectangle is 16 cm longer than its width. The area of the rectangle is 65 m 2 . Find the dimensions of the rectangle, rounding to the nearest hundredth of a meter.
C HAPTER 6 – P OLYNOMIALS AND P OLYNOMIAL F UNCTIONS
 Polynomial division
 Remainder & Factor Theorems
 Rational Zero Test
 Connection between zeros/factors/solutions
 Fundamental Theorem of Algebra
 Writing polynomial equations/functions
1) Perform the operation for each of the problems given. a) (12x 4 - 4x 2 - 3)  (x – 5) b) (8x 3 + 2x 2 - 5)  (x + 1) c) (6x 3 + 11x 2 - 4x - 9) + (3x - 2) d) (3x 4 - 5x 3 + 15x 2 – 4x + 3) - (x 2 - x + 4)

2) What is the remainder when (x 3 - 2x 2 - 9)  (x + 5)?
3) Is (x + 4) a factor of (x 3 - 12x + 16)?
4) Find the missing factors for each of the following.
a)x 3 - 5x 2 - 12x + 36 = (x + 3)( )( ) b)2x 3 - 13x 2 - 13x + 42 = (x - 7)( )( )
5) List the possible rational zeros given by the Rational Zero Test for the function: f(x) = 4x 3 + 15x 2 – 8x – 3
6) How many solutions does the equation 2x 3 – 4x 2 + 6x = 7 have?
7) Two of the zeros of f(x) = x 3 + 3x 2 be what kind of a number? Why?
– 10x – 24 are 3 and – 4. The third zero must
8) Write a polynomial function that has the given zeros and a leading coefficient of 1. a) -6, 4, 2 b) 4, 3i

9) One zero of f(x) = x 3 – 2x 2 – 9x + 18 is x = 2. Find the other zeros.
10) Factor f(x) = 2x 3 + 11x 2 + 18x + 9 given that f(-3) = 0.
11) List the possible rational roots for each of the following polynomials and describe the end behaviors of the graphs. a) f(x) = 3x 4 - 6x 2 + 14 b) g(x) = -6x 3 - x + 12
12) Find all the zeros of the polynomial function f(x) = x 4 + x 3 + 2x 2 + 4x – 8.

13) State the degree, type, and leading coefficient of the polynomial function: 𝑔(𝑥) =
6𝑥 3 + 9𝑥 2 − 7
. Then use direct substitution or synthetic substitution to evaluate the polynomial function for x = 3.
14) A storage container is a rectangular prism with a volume of 392 cubic inches. The height of the container is 3 inches less than its length and its width is twice the length.
What are the dimensions of the container?
15) Graph the function 𝑓(𝑥) =
1
2
(𝑥 + 2)(𝑥 − 1) 2

C HAPTER 9 – R ATIONAL E XPRESSIONS
 Simplifying expressions and restrictions
 Multiplying and dividing expressions
 Solving equations with fractions
1) Perform the indicated operations. a)
3x 2 y
16x 3 y 4
·
24xy 5
9x 2 y 2 b) c)
2
3
2
2
2) Solve each of the following. a)
x x
+ 3
=
2 x 3 d)
5 x 2
=
3x + 1 x 1 b) e) d) x 2
2x 2
+ x 6
+ 9x + 9
·
3x 2 x 2
+ 6x
4
6𝑎+18
5 𝑎+3
10
3𝑥+6 𝑥 2 −4
= 𝑥+1 𝑥−2 c) 𝑥−4 𝑥−2
−
2𝑥−1 𝑥−2
= 2 f)
5 𝑥
+ 𝑥+1 𝑥+2
=
2𝑥+9 𝑥+2
2 𝑦+3
−
3
4−𝑦
= 𝑦 2
2𝑦−2
−𝑦−12

Graph 𝑓(𝑥) =
3𝑥−1
4𝑥+5
. Identify any asymptotes, any holes, domain, range, and intercepts
G RAPHING R EVIEW
 Graph a given function
 Identify domain and range
 Identify function shifts
 Identify equations of asymptotes
 Describe right and left end behaviors of functions
 Find vertices, axes of symmetry, end points, turning points, etc for a given function