NAME:_____________________________________DATE:____________
Algebra 2
Name: ______________________________________
MIDTERM REVIEW 2014
Date: ____________
Topics Covered on Midterm:
Chapter 1 – Solving Equations and Inequalities
a. Apply Properties of Real Numbers
b. Evaluate and Simplify Algebraic Expressions
c. Solve Linear Equations
d. Rewrite Formulas and Equations
e. Solve Linear Inequalities
f. Solving Absolute Value Equations and Inequalities
g. Rate of Change
Chapter 3 – Systems of Equations
a. Solving a system by graphing
b. Solving a system by substitution or elimination
c. Solving a system of inequalities by graphing
d. Solving Systems Word Problems
Chapter 2 – Functions
a. Functions, Relations, Vertical Line Test, Domain, Range
1. Function Operations, Composition
b. Finding Slopes of Lines, Parallel lines, Perpendicular
lines
c. Graphing Equations of Lines, Parallel lines, Perpendicular
lines
d. Scatter Plots (Linear Regression)
e. Transformations (y = x2 and y = |x|)
Chapter 4 – Quadratics (part 1)
a. Graphing Quadratics (standard form, vertex form)
b. Simplifying Radicals
c. The imaginary number and complex numbers (
)
d. Factoring Quadratic Expressions (Bust the B)
Chapter 4 – Quadratics (part 2)
a. Solving Quadratic Equations
1. Taking Square Roots
2. Factoring
3. Quadratic formula (including discriminant)
b. Quadratic Equation Applications
1. Max/Min Problems
2. Pythagorean Theorem
3. Area of a Rectangle
Chapter 1: Solving Equations, Inequalities
1. Evaluate:
2
2
]
1
)
6
4
(
2
[
-
+
-
2. Evaluate:
]
3
2
4
)
2
3
[(
5
2
×
¸
+
-
3. Evaluate:
0
14
-
4. Simplify the following expression:
)
5
(
2
3
)
4
(
2
x
x
x
x
+
+
-
-
5. Solve the following inequality:
-
<
2
12
x
Solve each equation.
6.
3
1
10
3
6
1
3
2
+
=
+
x
x
7.
1
2
(
2
x
+
4
)
=
10
Solve each inequality. Graph your solutions.
1
-
=
i
8. -9
£
-3x + 6
£
24
9. 4x + 2(x – 1) < 11
Solve each absolute value equation or inequality.
Reminder: Absolute Value RULES
a
x
=
:
a
x
=
or
a
x
-
=
a
x
<
:
a
x
a
<
<
-
a
x
>
:
a
x
-
<
or
a
x
>
10.
12
6
3
2
=
-
x
11.
4
>
x
12.
10
6
2
£
+
x
Solve the equation for x.
13. 2a + 8 = 4a + 12
14.
12
8
53
x
+=
15.
(
)
13
26
24
x
--=
16.
31
83
11
x
x
+
+=-
Solve for the variable indicated.
17.
22
PLW
=+
; solve for W
18.
(
)
12
1
2
Abbh
=+
; solve for h
Identify AND correct where the mistake was made in each of the
problems. If there were no mistakes were made state so.
19.
24423
¸×=
20.
2
(5)25
-=
21.
2
525
-=
22.
4212
28
4
x
x
x
->
->
>-
23. Evaluate each function for the given values of x:
a.
8
2
1
)
(
2
-
=
x
x
f
1. f(2)
2. f(-1)
3. f(x) = 0; solve for x.
b.
2
3
4
)
(
x
x
g
-
=
1. g(-2)
2. g(1/2)
3. g(x) = -8; solve for x.
c.
1
)
(
-
=
x
x
g
1. g(3)
2. g(-10)
3. g(x) = 3; solve for x.
Rate of Change Word Problems
24. A climber is on a hike. After 2 hours he is at an altitude
of 400 feet. After 6 hours, he is at an altitude of 700 feet. What
is his average rate of change?
Independent Variable: ________________________________
Dependent Variable: __________________________________
Average rate of change: __________________
25. A scuba diver is 30 feet below the surface of the water 10
seconds after he entered the water and 100 feet below the surface
after 40 seconds. What is the scuba divers rate of change?
Independent Variable: ________________________________
Dependent Variable: __________________________________
Average rate of change: __________________
26. A rocket is 1 mile above the earth in 30 seconds and 5 miles
above the earth in 2.5 minutes. What is the rocket’s rate of change
in miles per minute?
Independent Variable: ________________________________
Dependent Variable: __________________________________
Average rate of change: __________________
27.A teacher weighed 145 lbs in 1986 and weighs 190 lbs in 2007.
What was the rate of change in weight?
Independent Variable: ________________________________
Dependent Variable: __________________________________
Average rate of change: __________________
Chapter 3: Systems of Equations
Vocab:
Consistent Dependent System
Consistent Independent System
Inconsistent System
Solve by graphing in your calculator. Be sure to rewrite your
equations in slope-intercept form.
28.
2
3
4
16
3
4
-
=
=
-
x
y
y
x
29.
2
3
16
2
3
-
=
=
+
x
y
y
x
30.
3
6
4
2
=
+
=
+
y
x
y
x
Solve the system by graphing.
31.
2
2
12
4
2
=
-
=
+
y
x
y
x
32.
4
2
4
=
+
=
y
x
y
Solve the systems using substitution.
33.
x
y
x
y
2
6
3
=
+
-
=
-
34.
5
4
5
2
+
=
=
+
-
x
y
y
x
Solve the following systems using elimination.
35.
5
2
13
5
3
=
-
=
-
y
x
y
x
36.
0
5
2
1
7
3
=
+
-
-
=
+
-
y
x
y
x
Set up a system and solve using the method of your choice.
37. There are 13 animals in the barn. Some are chickens and some
are pigs. There are 40 legs in all. How many of each animal are
there?
38. All 231 students in the Math Club went on a field trip. Some
students rode in vans which hold 7 students each and some students
rode in buses which hold 25 students each. How many of each type of
vehicle did they use if there were 15 vehicles total?
39. Dennis mowed his next door neighbor’s lawn for a handful of
dimes and nickels, 80 coins in all. Upon completing the job he
counted out the coins and it came to $6.60. How many of each coin
did he earn?
40. At a high school championship basketball game 1200 tickets
were sold. Student tickets cost $1.50 each and adult tickets cost
$5.00 each. The total revenue collected for the game was $3200. How
many student tickets were sold? How many adult tickets were
sold?
Graph each system of linear inequalities.
41.
2
1
y
yx
³
<+
42.
4
2
2
+
-
>
-
<
x
y
x
y
43.
2
2
1
1
3
+
>
+
-
£
x
y
x
y
44.
3
22
x
yx
<
£+
Chapter 2: Functions/Linear Equations
45. Refer to the functions below to answer parts a – d
()31
fxx
=+
2
()21
gxxx
=-+
4
()6
5
x
hx
=-
a) f(-2) =
b) f(0) + h(-3)
c) g(-4) =
d) if f(x) = -8, what is the value of x?
46. Refer to the points below to answer a - b
x
1
2
4
9
y
-1
-5
-11
-30
a) What is the equation for the line of best fit for this data?
(hint: LinReg in calculator)
b) What is the correlation coefficient of this data?
47. Refer the equation
8
x
-
5
y
=
-
48
a) Rewrite the equation in slope intercept form.
b) What is the y-intercept of this equation?
c) What is the slope of this line?
d) What is the x-intercept of this line?
Let
2
3
)
(
x
x
f
=
,
1
5
)
(
-
=
x
x
g
,
1
2
)
(
+
=
x
x
x
h
. Evaluate the following.
48.
)
3
(
)
2
(
h
f
-
= ______________
49.
)
2
(
)
0
(
-
×
f
g
= ______________
Let
2
)
(
-
=
x
x
f
and
3
4
)
(
+
=
x
x
g
. Find and evaluate the following.
50.
)
(
)
(
x
g
x
f
+
51.
)
(
)
(
x
f
x
g
-
52.
)
(
)
(
x
f
x
g
53.
)
(
)
(
x
f
x
g
×
Domain:
Let
2
2
1
)
(
x
x
f
=
and
4
2
)
(
-
=
x
x
g
and
2
)
(
+
=
x
x
h
. Find the following.
54.
))
(
(
x
g
f
55.
))
(
(
x
h
g
56.
)))
2
(
(
(
h
g
f
57. Answer the following using the relation: {(-7, 3), (0, 2),
(4, 1), (-3, 1), (5, 2)}
a. Is the relation a function? Why or why not?
b. What is the domain of the relation?
c. What is the range of the relation?
Write the equation of the line that satisfies each
condition.
58. m = 4, passes through (-3, 6)
59. m = undefined, passes through (1, -4)
60. passes through (0, 7) and (-3, -2)
61. passes through (4, 5) and (6, -7)
62. Refer to the linear equation y = -5x + 2 for a through d
Determine whether each statement is true or false:
a. _____ The slope is -5
b. _____ The x intercept is at 2
c. _____ The line y = -5x – 4 is parallel to y = -5x + 2
d. _____ The line y = 5x + 3 is perpendicular to y = -5x + 2
63. Determine whether each statement is true or false in regards
to functions:
a. _____ All functions pass the horizontal line test
b. _____ All functions have each x value corresponding to
exactly 1 unique y value
c. _____ An equation with an undefined slope is also a
function
d. _____ An equation with a slope of zero is also a function
64. Circle the points that satisfy the given inequality
233
xyx
->-
(hint: plug in x and y)
(0, -4)
(2, 7)
(0, -8)
(-1, -10)
65. Write an equation that is parallel to
4
3
+
-
=
x
y
, that passes through the point (4, 2)
66. Write an equation that is perpendicular to
4
3
+
-
=
x
y
, that passes through the point (4, 2)
67. Refer to the absolute value function
6
5
2
+
-
-
=
x
y
, to answer a through d.
a) Where is the vertex of the function?
b) Where is the y intercept of the function?
c) Where are the x-intercepts of the function?
d) Create a sketch of f(x) and label parts a – c
Write the coordinates of the vertex, and graph each function
transformation.
68. f(x) =
-
+
x
2
69. f(x) =
2
)
3
(
+
-
x
vertex: ___________________
vertex: ____________________
70. f(x) =
2
2
+
x
71. f(x) =
3
2
+
-
-
x
vertex: ___________________
vertex: ____________________
Chapter 4: Quadratics
Solve each quadratic equation by factoring.
72.
0
18
11
2
=
+
+
x
x
73.
0
6
5
6
2
=
-
+
x
x
74.
2
3
2
-
=
+
x
x
75.
x
x
65
35
10
2
=
-
76.
1
4
5
2
=
+
x
x
77.
2
2
7
2
3
8
x
x
x
=
+
+
Set up a quadratic equation and solve each word problem.
78. The length of a rectangle is 3 centimeters more than its
width. The area of the rectangle is 108 square centimeters. Find
the dimensions of the rectangle.
79. One leg of a right triangle is 1 more than the other leg.
The hypotenuse is 1 less than 2 times the shorter leg. Find the
lengths of all the sides.
80. An object is projected upwards with an initial velocity of
40 ft/sec starting from a height of 4 feet. The object’s path
follows the equation:
4
40
16
)
(
2
+
+
-
=
t
t
t
h
a.) When will the object be at its highest point and how high
will it be at this time? (hint: maximum)
b.) When will the object hit the ground? (hint: x-intercept in
calculator)
Find all the indicated information. Then sketch an accurate
graph of the function. You may check your answers in a
calculator.
81.
1
)
2
(
)
(
2
-
-
=
x
x
f
82.
8
)
1
(
2
)
(
2
+
+
-
=
x
x
f
Vertex: ___________ min or max?
Vertex: ___________ min or max?
Axis of Symmetry: _______________
Axis of Symmetry: ________________
Opens up or down?
Opens up or down?
y-intercept: ____________________
y-intercept: ______________________
zero(s): __________________________
zero(s): ____________________________
Simplify each expression.
83.
)
5
(
)
4
2
(
i
i
-
+
+
84.
)
2
4
(
)
5
3
(
i
i
-
+
-
-
85.
)
3
8
(
6
i
+
-
86.
)
4
2
)(
3
4
(
i
i
+
-
87.
2
)
5
2
(
i
-
88.
)
5
)(
3
(
2
i
i
-
Solve each quadratic equation using factoring and quadratic
formula.
89.
0
16
6
2
=
-
+
x
x
Factoring:
Quad Formula:
90.
12
4
2
=
-
x
x
Factoring:
Quad Formula
Convert each function into vertex form. (hint:
a
b
h
2
-
=
)
91.
5
2
)
(
2
-
+
=
x
x
x
f
92.
10
6
)
(
2
+
-
=
x
x
x
g
Find the discriminant. Determine the number and type of
solutions. Do not solve.
93.
0
3
2
6
2
=
-
-
x
x
94.
1
2
2
=
-
-
x
x
95.
0
5
4
4
2
=
+
-
-
x
x
96.
0
2
5
2
=
-
+
x
x
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