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Date_____________________________
Algebra II
Teacher_______________________
Final Exam Review Fall 2012
1. Solve using factoring: x2 – 3x – 18 = 0
2. Solve using factoring: x2 – 5x – 14 = 0
Factor.
3.
3x2 – 16x – 12
4.
5x2 – 9x – 2
5.
9x2 – 49
6.
16x2 – 64
x2 + 3x = 0
8.
x2 + 5x = 0
10.
5x2 – 13x – 6 = 0
Solve.
7.
Solve using factoring.
9.
3x2 – 2x – 8 = 0
Use quadratic formula to solve.
11.
x2 – 5x – 1 = 0
13.
Graph: y = –(x – 5)2 – 4
14.
Graph: y = –(x + 2)2 + 1
12.
x2 + 7x + 2 = 0
15.
How would you translate the graph of y = –x2 to produce the graph of y = –(x – 2)2?
16.
How would you translate the graph of y = –x2 to produce the graph of y = –(x + 4)2?
17.
Graph the function:
y = –2(x – 1)(x – 1)
Vertex:___________________________
Axis of Symmetry:__________________
x-intercepts:________________________
18.
Graph the function:
y = –3(x – 3)(x – 3)
Vertex:___________________________
Axis of Symmetry:__________________
x-intercepts:________________________
19.
Write in standard form: y = 3(x – 5)(x – 3)
then graph.
20.
Write in standard form: y = 2(x + 6)(x + 2)
then graph.
21.
Write in standard form: y = (x + 3)2 – 2
then graph.
22.
Write in standard form: y = (x – 2)2 + 1
then graph.
23.
For what value of c will the graphs of y = 5x2 + 10x + c and y = 5(x + 1)2 + 2 be the same?
24.
For what value of c will the graphs of y = 2x2 + 24x + c and y = 2(x + 6)2 – 47 be the same?
25.
Graph y = –x2 – 5
26.
Graph y = –2x2 + 1
27.
What is the effect on the graph of the equation y = 2x2 + 3 when it is changed to y = 2x2 – 6?
28.
What is the effect on the graph of the equation y = 2x2 + 1 when it is changed to y = –2x2 + 1?
Perform the matrix operations, if possible.
29.
2  3
6 5  2 4 

  3  2

1 4  
30.
1 6
 0  4 1
Given A = 
and B =  0 1  , find AB.



  5  1 0
 1  1
Solve by completing the square.
31.
x2 + 6x – 16 = 0
32.
x2 + 10x – 11 = 0
34.
x – y + z = –3
3x + 2y – z = 15
2x + 3y + z = 0
Use inverse to solve for y.
33.
x + y + z = –4
2x – y + 3z = 1
3x + 2y – z = 4
35.
Solve the system by graphing:
x+y=7
y = 2x – 5
36.
Solve the system by graphing:
x+y=3
y = 4x – 2
37.
Solve the linear system:
x – 3y = 10
x + y = –2
38.
Solve the linear system:
5x – 2y = –1
x + 2y = 7
39.
Chicken sandwiches at the cafeteria were sold for $2.50 and hamburgers were sold for $1.50.
A total of 120 chicken sandwiches and hamburgers were sold for $250.00. How many
chicken sandwiches and hamburgers were sold?
40.
Brownies at the bake sale were sold for $0.75 and cookies were sold for $0.50. A total of
350 brownies and cookies were sold for $ 245.00. How many brownies and cookies were sold?
Write a system of equations for the situation.
41.
At the bake sale a total of 540 cookies and brownies were sold for a total of $750.00. Brownies
cost $ 1.00 each and cookies cost $0.35 each. Write a system of equations for this situation.
42.
Alice bought 4 water bottles and 3 juices for a total of $8.50. Carlo bought 2 water bottles and
5 juices for a total of $9.25. Write a system of equations for this situation.
43.
Graph the system of inequalities.
x>4
y<5
44.
Graph the system of inequalities.
x<6
y>2
Solve for b in the formula A = 8a3b.
46.
Solve for x in the formula G = 2c2x.
47.
|2x – 3| = 11
48.
|n + 2| = 13
49.
|x – 2| > 11
50.
|x – 4| < 15
45.
Solve.
51.
Graph: 3x + 5y = 35
52.
Graph: 4x + 8y = 16
53.
Graph y = 1
54.
Graph x = 2
55.
Write the equation of the line, in slope-intercept form, that passes through the point (3,–4) and
has a slope of 3.
56.
Write the equation of the line, in slope-intercept form, that passes through the point (1, 3) and
has a slope of 2.
57.
Write the equation of the line that goes through the point (–3, 5) and is parallel to the line
y = 3x – 1.
58.
Write the equation of the line that goes through the point (0, –4) and is parallel to the line
y = 4x + 2.
59.
Are the graphs of the equations below parallel or perpendicular?
2y = 8x + 10
3y = 12x + 5
60.
Are the graphs of the equations below parallel or perpendicular?
3y = 9x + 1
15y = –5x – 2
61.
Graph:
–y > –2x + 6
–2y < –3x + 10
62.
Graph:
63.
Set up an inverse matrix to solve the linear system and solve.
2x + 3y = –7
5x – 4y = 17
64.
Set up an inverse matrix to solve the linear system and solve.
-x + 2y = 12
7x – 3y = –29
65.
Let f(x) = x2 + 4 and g(x) = 6x2. Find f(g(x)).
66.
Let f(x) = x2 – 4 and g(x) = 2x2. Find f(g(x)).
67.
Find the equation for the inverse of the relation y = 2x + 1.
68.
Find the equation for the inverse of the relation y = 4x – 2.
69.
Sketch the parent graph and translate it to obtain a graph of y = |x – 3| - 1
70.
Sketch the parent graph and translate it to obtain a graph of y = |x – 4| + 2.
71.
Two hockey teams submit equipment lists for the season as shown.
Women’s Team
Men’s Team
Equipment
Sticks
14
16
Pucks
30
25
Uniforms
18
20
Each stick cost $60, each puck cost $2, and each uniform cost $35. Use matrix multiplication to find the total
cost of equipment for each team.
72.
A teacher is buying supplies for two art classes. For class 1, the teacher buys 24 tubes of paint, 12
brushes, and 17 canvases. For class 2, the teacher buys 20 tubes of paint, 14 brushes, and 15 canvases. Each
tube of paint cost $3.35, each brush costs $1.75, and each canvas costs $4.50. Write an inventory matrix and
cost per item matrix. Then use matrix multiplication to write a total cost matrix.
73.
In 1994, the average monthly cost for expanded basic cable television service was $21.62. In 2004, this
cost had increased to $38.23. Write a linear equation that models the monthly cost as a function of the
number of years since 1994. Let x = 0 correspond to 1994.
74.
The official population of Baton Rouge, Louisiana, was 219,478 in 1990 and 227,818 in 2000.
Write a linear equation that models the change in population as a function of the number of years
since 1990. Let x = 0 correspond to 1990.
75.
What is the y-value of the solution to the matrix equation below.
2 3  x 
3 1  y  =

  
76.
17
15
 
What is the y-value of the solution to the matrix equation below.
3  4  x   13
1  1  y  =   3 


   
77.
The base of a triangle is 2 inches less than three times the height. If the area of the triangle is 120
square inches, write an equation that can be used to find h, the height of the triangle in inches.
78.
The base of a triangle is 4 inches more than twice the height. If the area of the triangle is 60
square inches, write an equation that can be used to find h, the height of the triangle in inches.
79.
Does the following quadratic equation y = x2 + x – 90 have zeros of – 10 and 9?
80.
Does the following quadratic equation y = x2 – 11x + 30 have zeros of 5 and 6?
81.
The graph below of the function g was obtained from the graph of the function f using a transformation
as shown below. Based on the graph, which equation can be used to describe g(x) in terms of f(x)?
f
A.
B.
C
D.
g
g(x) = f(x – 7)
g(x) = f(x) – 7
g(x) = f(x) + 7
g(x) = f(x + 7)
82.
The graph below of the function g was obtained from the graph of the function f using a
transformation as shown below. Based on the graph, which equation can be used to describe g(x) in
terms of f(x)?
f
A.
B.
C
D.
g(x) = f(x – 5)
g(x) = f(x) – 5
g(x) = f(x) + 5
g(x) = f(x + 5)
g
83.
Graph the inverse of the function shown below.
84.
What is the domain of the function shown in this graph?
85.
86.
What is the domain of the function shown in this graph.
Graph and find the range of the function y = x2 – 5.
Solve.
87.
x2 – 10x + 34 = 0
88.
x2 – 12x + 52 = 0
89.
If the graph of f is translated 4 units to the left and 3 units
up to create a new graph, write a function that best
represents this new graph.
Write the equation in the form y = a(x – h)2 + k. Then graph the equation.
90.
y = x2 – 6x – 1
91.
y = x2 – 8x + 9
92.
A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the
ground t seconds after it is thrown is given by d = –14t2 – t + 435. How long after the rock is
thrown is it 200 feet from the ground?
93.
A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the
ground t seconds after it is thrown is given by d = –12t2 – 2t + 325. How long after the rock is
thrown is it 300 feet from the ground?
Graph.
94.
y < – x2 – 2x + 3
95.
y > x2 – 8x + 6
96.
The graph of the quadratic function f is shown on the grid below. What does the solution set
for f(x) = 0 appear to be?
97.
The graph of the quadratic function f is shown on the grid below. What does the solution set
for f(x) = 0 appear to be?