Algebra 2 Midterm Exam REVIEW
2013-2014
Name ___________________________________________
Completion:
30
Accuracy:
50
The exam review will be graded on completion (15 points) and randomly selected problems
solved and answered correctly (25 points). In order to earn full credit, you must show all work
for each problem!!
The exam review is due no later than:
• Wednesday, January 8, 2014 for a maximum of 3 bonus points.
• Thursday, January 9, 2014 for a maximum of 2 bonus points.
• Friday, January 10, 2014 for a maximum of 1 bonus point.
• Monday, January 13, 2014 is the final due date.
The exam review is due no later than Monday January 13th by 4:00
pm for completion and accuracy. You need to turn in the packet
directly to the teacher - NOT the teacher mailboxes in the main
office.
The midterm exam will cover:
o
o
All material in Units 1 - 4
Systems of equations (not covered in this packet - you will learn in January)
*Be sure to study your old tests and quizzes from all units!
Name ____________________________________________
Cumulative Review
Date _____________
Circle your final solutions!!
UNIT 1 & 2: Number Sense; Solving equations and inequalities
Solve the following equations for the indicated variable.
1. 3(r + 5) – 2 = 17
2. 9x + 6 = 3x
3.
4. |q + 3| = 1
5.
2|5+ 2x|- 7 = 15
7. x6 = 64
6. |2x + 12| = 4x
8.
5 (x – 2)2 – 6 = 24
9. 3x5 = −729
10. -3 (x + 1)2 = 81
11.
(2x - 3)2 = 121
12.
(x – 3)2 = - 144
13.
(3x – 7)3 = 729
14.
4 (x – 1)2 – 3 = 25
Solve and graph the following inequalities.
15. 2 + 3x < 5
16.
17. 5 < 2x + 3 < 11
18.
-3x + 8 ≤ x
19.
20.
21.
22.
Exponent Rules
23.
26.
24.
27.
25.
28.
4x3y-5z
Evaluating Nth roots
29. What is
•
in exponential form? _____________
radical notation? ___________
Simplify the following. NO decimal answers!
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
Complex Numbers: Simplify the following.
42. (3 + 2i) (4 – 3i)
43. (3 + 4i) – (5 – 8i)
44. (2 + 6i) + (7 – 12i)
UNIT 3: Graphing
Graph the following functions using your knowledge of transformations. Then verify by
graphing in your calculator.
45.
46.
Function Type:
Shape:
Function Type:
Shape:
Vertex:
Standard/Stretch/Shrink:
48.
49.
50.
Function Type:
Shape:
Function Type:
Shape:
Vertex:
Standard/Stretch/Shrink:
Function Type:
Shape:
Vertex:
Standard/Stretch/Shrink:
47.
Function Type:
Shape:
Vertex:
Standard/Stretch/Shrink:
#51 & 52: Evaluate the function for the given value of x
51.
f(x) = 2x2 + 3x
52.
f (x) = 9 - 3x
f (-l) = ______
f (2) = ______
f (l) = ______
f (-2) = ______
f (x - l) = ______
f (x - 2) = ______
53.
Graph x = 4
Write the equation of each absolute value function.
54.
55.
_______________________
_______________________
Piecewise functions
56. Graph:
57. Fill in the correct domain information for the
piecewise function shown.
58. Use the function from #57.
Find f(4).
Composition and Inverse
59. f(x) =
and g(x) =
60. f(x) =
and g(x) =
Find
Find
62. f(x) = x2 + x + 4, g(x) = x + 1
63. f(x) = x2 + x + 4, g(x) = x + 1
Find f(g(-2))
Find g(f(-3))
Find f(g(x))
Find g(f(x))
Find g(f(x))
Find f(g(x))
65.
66.
Find the inverse of:
f(x) =
x3 + 1
What is the domain of:
61. f(x) = 7x2 − 3x and g(x) = −5x
Find g(x) − f(x)
64.
Find the inverse of:
f(x) = - 5x + 8
67.
State the Domain of:
UNIT 4: Quadratics
68. How do you know if an equation is quadratic? ____________________________________
69. What are the zeros of:
y = x2 – 9x + 20?
70. What are all the solutions of:
x2 = x + 6?
71.
If x2 – 10x + c is a perfect square
trinomial, what is the value of c?
Then, write the trinomial in
factored form, i.e, as a square
binomial.
72.
How many real and imaginary
solutions does the equation
5x2 – 3x + 7 = 0 have? Explain.
73.
Solve the equation by
completing the square:
x2 – 6x – 7 = 0
74.
Solve the equation using the
quadratic formula:
x2 + 2x + 7 = 0
75. Write the standard form of
y = 3 (x + 2) (x + 3)
76.
Factor completely:
x2 – 5x – 24
77.
78. Solve: x2 – 6x = 0
79.
Factor completely:
121x2 – 169y2
80. Factor completely:
2x2 - 32x + 96
Factor completely:
3x2 + 14x – 5
81. Given the quadratic equation:
x2 – 4x – 12 = 0
Solve by the Zero Product
Property (Factoring)
x2 – 4x – 12 = 0
Solve by Completing the Square:
Solutions:____________
Rewrite to Intercept Form
y = x2 – 4x – 12
Solutions:____________
Rewrite to Vertex Form
y = x2 – 4x – 12
x2 – 4x – 12 = 0
Solve Using the Quadratic
Formula
x2 – 4x – 12 = 0
Solutions:____________
Describe the Root
y = x2 – 4x – 12
Find the Discriminant:
________________________
Intercept form:_____________
Vertex Form:_______________
Identify the x-intercepts
( , ) and ( , )
Identify the Vertex: ________
Given y = x2 – 4x – 12
Graph y = x2 – 4x – 12
Identify the Number and Type of
Solutions: _________________
__________________________
You must include
5 distinct points.
Find the Vertex: ________
Axis of symmetry: _______
Direction: ______
Size (Stretch, Shrink or Normal):
_____________________
82. Draw a graph of a parabola that has:
2 real solutions
1 real solution
2 imaginary solutions