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Algebra 2
MIDTERM REVIEW 2016
Name: ______________________________________
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. 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)
Chapter 3ish - Absolute Value Functions
a. Solving Absolute Value Equations and Inequalities
a. Graph an Absolute Value Function (vertex, x and y-intercepts, axis of symmetry)
b. Graph an Absolute Value Inequality
c. Find Domain and Range of various functions
Chapter 4 – Quadratics (part 1)
a. Graphing Quadratics (vertex form)
b. Simplifying Radicals
c. The imaginary number and complex numbers ( i   1 )
d. Factoring Quadratic Expressions (grouping, difference of squares)
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. Area of a Rectangle
Chapter 1: Solving Equations, Inequalities
1. Evaluate: [2(4  6)  1]  2 2
2. Evaluate: 5[(3  2) 2  4  2  3]
3. Evaluate:
 14
0
4. Simplify the following expression: 2 x( x  4)  3x  2(5  x)
5. Solve the following inequality: 2 x  12
Solve each equation.
6.
2 x 1 3x 1
 

3 6 10 3
7.

Solve each inequality. Graph your solutions.
8. -9  -3x + 6  24
9. 4x + 2(x – 1) < 11
1
(2x  4) 10
2
Solve each absolute value equation or inequality.
Reminder: Absolute Value RULES
x a:
xa
x  a:
a  x  a
x  a:
x  a
10.
or
or
x  a
xa
2
x  6  12
3
11. x  4
12. 2 x  6  10
Solve the equation for x.
13. 2a + 8 = 4a + 12
14.
1
2
x 8
5
3
1
3
 2 x  6  
2
4
16.
3x  1
 8  3 x
11
15.
Solve for the variable indicated.
17. P  2L  2W ; solve for W
18. A 
1
 b1  b2  h ; solve for h
2
Identify AND correct where the mistake was made in each of the problems. If there were no mistakes were
made state so.
19. 24  4  2  3
20. (5)2  25
4  2 x  12
21. 5  25
22. 2 x  8
2
x  4
23. Evaluate each function for the given values of x:
a.
f ( x) 
1 2
x 8
2
f(2)
f(-1)
f(x) = 0; solve for x.
b. g ( x)  4  3x 2
g(-2)
g(1/2)
g(x) = -8; solve for x.
c. g ( x)  x  1
g(3)
g(-10)
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.
4 x  3 y  16
28.
4
y  x2
3
29.
3 x  2 y  16
30.
y  3x  2
Solve the system by graphing.
31.
2 x  4 y  12
2x  y  2
32.
y4
2x  y  4
2x  4 y  6
x y 3
Solve the systems using substitution.
33.
y  x  3
y  6  2x
34.
 2x  y  5
y  4x  5
Solve the following systems using elimination.
35.
3 x  5 y  13
x  2y  5
36.
 3x  7 y  1
 2x  5 y  0
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.
y2
42.
y  x 1
y  3 x  1
43.
44.
1
y  x2
2
y  2x  2
y  x  4
x3
y  2x  2
Chapter 2: Functions/Linear Equations
45. Refer to the functions below to answer parts a – d
f ( x)  3x  1
g ( x)  2 x 2  x  1
a) f(-2) =
d) if f(x) = -8, what is the value of x?
b) f(0) + h(-3)
h( x ) 
4x
6
5
c) g(-4) =
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 8x  5y  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 f ( x)  3x 2 , g ( x)  5 x  1 , h( x) 
48. f (2)  h(3) = ______________
49. g (0)  f (2) = ______________
2x
. Evaluate the following.
x 1
Let f ( x)  x  2 and g ( x)  4 x  3 . Find and evaluate the following.
50.
f ( x)  g ( x)
51. g ( x)  f ( x)
52.
g ( x)
f ( x)
53. g ( x)  f ( x)
Domain:
Let f ( x) 
1 2
x and g ( x)  2 x  4 and h( x)  x  2 . Find the following.
2
54. f ( g ( x))
55. g (h( x))
56. f ( g (h(2)))
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 2 x  y  3x  3 (hint: plug in x and y)
(0, -4)
(2, 7)
(0, -8)
(-1, -10)
65. Write an equation that is parallel to y  3 x  4 , that passes through the point (4, 2)
66. Write an equation that is perpendicular to y  3 x  4 , that passes through the point (4, 2)
67. Refer to the absolute value function y  2 x  5  6 , 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
Find the domain and range of each graph. Determine whether or not the graph shows a function.
68.
69.
Domain: __________________
Domain: ____________________
Range: ___________________
Range: ______________________
Function? Yes or No
Function? Yes or No
70.
71.
Domain: __________________
Domain: ____________________
Range: ___________________
Range: ______________________
Function? Yes or No
Function? Yes or No
Chapter 4: Quadratics
Solve each quadratic equation by factoring.
72. x 2  11x  18  0
73. 6 x 2  5 x  6  0
74. x 2  3x  2
75. 10 x 2  35  65 x
76. 5 x 2  4 x  1
77. 8 x 2  3x  2  7 x 2
Solve each equation by taking the square root.
78. 3x 2  23  247
79. 6( x 2  9)  186
80. 4 x 2  100  0
81. 3x 2  48  0
Set up a quadratic equation and solve each word problem.
82. 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.
83. The length of a rectangle is 3 inches less than twice its width. The area of the rectangle is 104 square
inches. Find the dimensions of the rectangle.
Find all the indicated information. Then sketch an accurate graph of the function.
84. f ( x)  ( x  2) 2  1
85. f ( x)  2( x  1) 2  8
Vertex: ___________ min or max?
Vertex: ___________ min or max?
Axis of Symmetry: _______________
Axis of Symmetry: ________________
y-intercept: ____________________
y-intercept: ______________________
zero(s): __________________________
zero(s): ____________________________
D: ___________ R: ________________
D: ___________ R: ________________
Simplify each expression.
86. (2  4i )  (5  i )
87. (3  5i )  (4  2i)
88. 6  (8  3i )
89. (4  3i )( 2  4i )
90. (2  5i) 2
91. (3i)(5i 2 )
Solve each quadratic equation using factoring and quadratic formula.
2
92. x  6 x  16  0
Factoring:
Quad Formula:
2
93. x  4 x  12
Factoring:
Quad Formula
Find the discriminant. Determine the number and type of solutions. Do not solve.
94. 6 x 2  2 x  3  0
95.  2 x 2  x  1
96.  4 x 2  4 x  5  0
97. 5 x 2  x  2  0