Algebra 2 Honors Midterm Review Guide
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 chapter review and chapter test practice at the end of each chapter.
5. Use pages 1010-1014, 1017 for extra practice problems for each chapter.
6. For additional practice on areas you may use previous homework assignments. Your
homework should be a solution key to check your work.
*REMINDER: Bring all quizzes and tests to the exam for extra credit on the midterm!!
You must have all of them or no credit
Use the following guiding questions to also help you prepare for the midterm.
SUMMER PACKET/ALGEBRA REVIEW – CHAPTERS 1-3
EQUATIONS AND INEQUALITIES
A. Apply Properties of Real Numbers
B. Evaluate and Simplify Algebraic Expressions
C. Solve Linear Equations
D. Rewrite Formulas and Equations (Literal Equations)
E. Use Problem Solving Strategies and Models
F. Solve Linear Inequalities
G. Solve Absolute Value Equations and Inequalities
Simplify:
1)
2(-1 + 3) - 428
2)
2(3 + 189) - 7
4)
43x - 3y + 2 for x=5, y = -3
Evaluate:
3)
2t3 - 4t + 3 when t = 2
Solve:
5)
3(5 - a) = -4(a - 4)
6)
15(x - 2) = -13(x + 1) + 11
7)
A = P + Prt for t
8)
S = L - rL for L
9)
V = r2h for h
10) | 5r - 8 | = 2
11) | 3x + 2 | = 13
Solve and graph:
12) 5x - 2 < 13
13) -2x - 1  5
14) | 2x - 1 | < 3
15) | -3x -2 |  4
16) | 3x - 5 | > 9
17) | -2x - 3 | > 7
CH. 2 – LINEAR EQUATIONS
A.
B.
C.
D.
E.
F.
G.
AND
FUNCTIONS
Represent Relations and Functions
Find Slope and Rate of Change
Graph and Write Equations of Lines
Model Direction, Inverse, and Joint Variation
Draw Scatter Plots and Best-Fitting Lines
Use Absolute Value Functions and Transformations
Graph Linear Inequalities in Two Variables
PROBLEM SET
Find the x- and y-intercepts for:
1) -3x + 4y = -2
2)
2x + 3y – 12 = 0
-2
and a y-intercept of 4.
3
3)
Write the equation of the line with slope of
4)
Write the equation of the line that goes through the points (-6, -1) and (3, 2).
5)
Write the equation of the line that goes through the points (4, 3) and (0, -5).
6)
Write the equation of the horizontal line through the point (3, -7).
7)
Write the equation of the vertical line through the point (-2, -4).
Graph:
8)
2x + 3y = 6
10) 5x + 3y < 6
9)
5x - 2y = -4
11) 6x – 2y  8
Graph and analyze the following scatter plot.
The manager of a band has kept track of the price of tickets and the attendance at the
band’s recent concerts.
Price ($)
6
Attendance 213
Concert Attendance by Ticket Sales
5
8.5
8
10
5.5
256
155
194
160
267
7
258
7.5
210
8
235
16) Make a scatter plot of the data using price as the independent variable on your
calculator.
17) Find the equation of the line of best fit on your calculator.
18) Using the equation above, predict the attendance at a concert where the price of
tickets is $9. Show calculations.
Graph the function.
19) y = - 4 x + 2 - 3
20) f(x) = 2x + 2 - 6
22) 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?
CH. 3 – LINEAR SYSTEMS
A. Solve Linear Systems by Graphing
B. Solve Linear Systems Algebraically
C. Graph Systems of Linear Inequalities
PROBLEM SET
Solve the system:
1)
ì- 2x + 3y = 5
í
î 3x - 2y = 0
2)
ì2x - 5y = -4
í
î 4x + 3y = 5
3) Draw an example of a system that is inconsistent. Explain how you know that it is
inconsistent.
Graph:
4)
1
ì
ïy £ x + 4
í
2
ïî x + 2y > 4
5)
ì6x - 2y > 2
í
î x+y³3
Solve by writing a system of equations.
6)
7)
A nut wholesaler sells a mix of peanuts and cashews. The wholesaler charges $2.80
per pound for peanuts and $5.30 per pound for cashews. The mix is to sell for
$3.30 per pound. How many pounds of peanuts and how many pounds of cashews
should be used to make 100 pounds of the mix?
Graph the system of inequalities
 x0
 y0


x  4 y  4
 x  y  2
CH. 4 – QUADRATIC FUNCTIONS
A.
B.
C.
D.
E.
F.
G.
H.
AND
FACTORING
Graph Quadratic Functions in Standard Form
Graph Quadratic Functions in Vertex or Intercept Form
Perform Operations with Complex Numbers
Solve x2 + bx + c = 0 by Factoring
Solve ax2 + bx + c = 0 by Factoring
Solve Quadratic Equations by Finding Square Roots
Complete the Square
Use the Quadratic Formula and the Discriminant
PROBLEM SET
Factor:
1)
x2 - 7x + 6
2)
x3 – 8
3)
4y3 + 108
4)
3x3 - 24x2 + 21x
5)
8x3 + 27
6)
4x2 + 12x + 9
7)
x2 - 81
8)
64x3 – 27
9)
15x3 + 10x2 + 6x + 4
10) k3 + 4k2 – 9k – 36
Simplify:
22)
- 144
23)
- 28 +
- 63
24) i15
25) (3i)(2i)
26) (2 + 3i) + (5 - 4i)
27) (2 + 3i) - (5 - 4i)
28) (2 + 3i)(5 - 4i)
29)
30) (3i)5
31) (4 -5i)2
(2 + 3i)
(5 - 4i)
Solve:
11) 3x2 - 24 = 0
12) 5x2 + 19x = 125 + 19x
13) x2 - 10x - 4 = 0
14) -2x2 + 3x -7 = -9
15) x2 + 5x + 7 = 0
16) 2x2 - 2x = -3
For each of the following, find: the vertex, axis of symmetry, y-intercept, and xintercepts. Then graph the function.
17) y = x2 - 4x + 3
(Complete the square to put into
Vertex form for this one)
18) y = 2x2 - x – 6
Applications:
20) The length of a rectangle is 16 cm longer than its width. The area of the rectangle
is 65 m2. Find the dimensions of the rectangle, rounding to the nearest hundredth of a
meter.
21) 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?
22) If the discriminant of a quadratic equation is -40 what does that tell you about the
roots of the equation?
CHAPTER 5 – POLYNOMIALS
AND
POLYNOMIAL FUNCTIONS
 Polynomial division
 Remainder & Factor Theorems
 Rational Zero Test
 Connection between zeros/factors/solutions
 Fundamental Theorem of Algebra
 Writing polynomial equations/functions
1)
Perform the division for each of the problems given.
a)
(12x4 - 4x2 - 3)  (x – 5)
b)
(8x3 + 2x2 - 5)  (x + 1)
c)
(6x3 + 11x2 - 4x - 9) + (3x - 2)
d)
(3x4- 5x3 + 15x2 – 4x + 3) - (x2 - x + 4)
2)
What is the remainder when (x3 - 2x2 - 9)  (x + 5)?
3)
Is (x + 4) a factor of (x3 - 12x + 16)?
4) Find the missing factors for each of the following.
a)x3 - 5x2 - 12x + 36 = (x + 3)(
)(
)
b)2x3 - 13x2 - 13x + 42 = (x - 7)(
)(
)
5)
List the possible rational zeros given by the Rational Zero Test for the function:
f(x) = 4x3 + 15x2 – 8x – 3
6)
How many solutions does the equation 2x3 – 4x2 + 6x = 7 have?
7)
Two of the zeros of f(x) = x3 + 3x2 – 10x – 24 are 3 and – 4. The third zero must
be what kind of a number? Why?
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) = x3 – 2x2 – 9x + 18 is x = 2. Find the other zeros.
10) Factor f(x) = 2x3 + 11x2 + 18x + 9 given that f(-3) = 0.
11) Find all the real zeros of f(x) = 10x4 – 3x3 – 29x2 + 5x + 12.
12) Find all the complex zeros of the polynomial function f(x) = x4 + x3 + 2x2 + 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?
CHAPTER 8 – RATIONAL EXPRESSIONS
 Simplifying expressions and restrictions
 Adding, subtracting, multiplying, and dividing expressions
 Complex fractions
 Solving equations with fractions
1)
Perform the indicated operations.
a)
c)
3x 2y
16x 3y 4
·
x 3 - 27
4x 2 - 25
24xy 5
b)
9x 2y 2
¸
2x 3 + 6x 2 + 18x
2x 2 - x - 10
d)
x2 + x - 6
2x 2 + 9x + 9
2y 2 - y
2y 2 - y - 1
·
·
3x 2 + 6x
x2 - 4
4y 2 - 1
y - y2
¸
(2y - 1)2
2y - 2
2)
Identify the least common multiple for each of the following polynomials.
a)
x2 - 9, x - 3, 3
b)
x2, 2x(x - 2), x2 - 4
c)
4x, x3, x - 1
3)
a)
4)
Perform the indicated operation.
3𝑎+2
7
8
2𝑥−5
−
b)
−
𝑎2 −16
6𝑎+24
𝑥−3
𝑥 2 −12𝑥+27
c)
𝑥 2 +𝑦2
𝑦
𝑥 2 −𝑦
𝑥+𝑦
2 +
+
𝑥
𝑥−𝑦
Solve each of the following.
a)
d)
x
x +3
5
x -2
=
=
2
x -3
3x + 1
x -1
b)
3𝑥+6
e)
𝑥−4
𝑥 2 −4
𝑥−2
=
−
𝑥+1
c)
𝑥−2
2𝑥−1
𝑥−2
=2
f)
5
𝑥
+
2
𝑦+3
𝑥+1
𝑥+2
−
=
3
4−𝑦
2𝑥+9
𝑥+2
=
2𝑦−2
𝑦 2 −𝑦−12
5)
Simplify each of the following.
4
a)
x
1
2x
+2
-8
3
b)
x
2
2-
+
1
x
4
5x
4
c)
x +2
2
x +2
+
+
3
x +1
8
x +1
GRAPHING REVIEW
 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
1) List the possible roots for each of the following polynomials and describe the
end behaviors of the graphs.
a) f(x) = 3x4 - 6x2 + 14
b)
g(x) = -6x3 - x + 12
c)
f(x) = 9x5 + 3x4 – 10
d)
g(x) = x3 – 4x2 + 6x - 3
1
2) Graph the function 𝑓(𝑥) = (𝑥 + 2)(𝑥 − 1)2
2
3𝑥−1
3) Graph 𝑓(𝑥) = 4𝑥+5. Identify any asymptotes, domain, range, and intercepts.