Download Algebra Fall Semester Review

NAME ________________________________DATE___________________PERIOD________
Algebra Fall Semester Review
1. Ax + By = C, solve for x
2. P = 2L + 2W, solve for W
3. The length of a rectangle is 3 less than twice the width.
Write an expression to represent the perimeter of this rectangle.
4. If x = 4y – (y + 4), what is the value of y, when x = 8?
5. Jeremiah rents a lot of movies from Redbox. His local “movie store” has started a Movie
Club to try to compete. The club gives members 3 free movies each month, then charge
$1.75 per movie rental. If Jeremiah has budgeted $15 for movies, how many movies can
he rent each month?
6. 3(2x – 1) + 12 = 4x +1
7. 5x – 2(4 + 3x) = 11
8. Simplify 2(x + 3y) – 3(5y + 1) – 7x
9. 5 – 4m + 8 + 2m > -17
10. 12 + x < -7
11. 3x + 7 > -2
12. Find the Domain and Range and determine whether the relation is a function or not.
{(-2 , -5), (0 , -3), (2 , 5), (-6 , -6)}
Domain = ____________________________
Range = __________________________
13. For h(x) = 6x + 3
1
What is the value of h ( ) ________
2
What is the value of h (10) _________
14. For g(x) = x2 – 4x + 7
What is the value of g (-4) _________ What is the value of g (2) __________
15. Determine whether the following maps represent a function or not.
A.
B.
C.
D.
16. Determine the following for each graph
Domain and Range
Function or Not a Function
Discrete Date or Continuous Data
A.
B.
C.
D.
17. Given the following table:
x
y
What is the value of f(0)? _______________________
-2
-2
0
4
What
is the value of f(-2)? _______________________
3
13
5
19
18. Find the domain and range of the relation graphed below.
Does the graph below represent a function?
Is the data represented in the graph below discrete or continuous?
Find f(3) from the graph ________________.
Find f(2) from the graph ________________.
Find f(7) from the graph ________________.
Find f(0) from the graph ________________.
19. Find the domain and range of the relation graphed below.
Does the graph below represent a function?
Is the data represented in the graph below discrete or continuous?
Find f(3) from the graph ________________.
Find f(1) from the graph ________________.
20. Find the domain and range of the relation graphed below.
Does the graph below represent a function?
Is the data represented in the graph below discrete or continuous?
21. Simplify the following expressions:
-3(2x – 7) + 4(6x + 2) – (4x +10)
3(2x + 5) – (2x + 24) + (7x – 5)
22. The length of a rectangle is represented by 5x – 2 and the width is represented by 3x + 7. Write
an expression to represent the perimeter.
23. The length of a rectangle is represented by 10x + 4 and the width is represent by 3x – 5.
Write an expression to represent the perimeter.
24. A linear inequality in two variables is shown below.
2x – y ≥ 3
Which graph would represent the solution set of the linear inequality?
A.
B.
C.
D.
25. Given the graph of the linear inequality below, which linear inequality in two variables correctly
represents the graph?
25a. According to the graph above, which of
the following ordered pairs would be included
in the solution set?
A. (-8, 1)
B. (6, 3)
C. (2, 3)
D. (0, 6)
E. (-4, 0)
F. (8, 0)
G. (0, 4)
H. (5, 5)
25b. Using the same coordinates given in
question 25, which of the ordered pairs would
1
be included in the solution set for y >
x+4
2
?
26. Given the line -3x =81, which of the statements below are true?
I. The line is parallel to the y-axis.
II. The line is perpendicular to the x-axis.
III. The line has a slope of zero.
IV. The line has an undefined slope.
A.
B.
C.
D.
I , II, and III only
I, II, and IV only
I and IV only
I and III only
27. What is the slope of the line represented by the following table?
x
4
6
y
-2
8
10
1
1
2
3
2
28. Find the slope of the line, given the following ordered pairs: (-8, 2) and (16, 11)
29. Which of the following equations has a slope of 3?
I. y = 3x - 8
II. (y – 4) = 3 (x – 2)
III. 6x + 2y = 6
IV. 6x – 2y = 6
A I only
B I and II only
C I, II, and III only
D I, II, and IV only
30. Find the slope of the following graphs:
31. Which linear equation in two variables represents a line containing the following points:
(2, -1) and (-2, 15)
1
a. y = x + 7
4
1
b. y =
x+7
4
c. 4x + y = 7
d. 4x – y = y
32. Which linear equation in two variables represents a line containing the following points:
(2, -6) and (-2, -4)
1
a. y – 6 =
(x + 2)
2
1
b. y – 4 =
(x + 2)
2
1
c. y + 6 =
(x – 2)
2
1
d. y + 4 =
(x + 2)
2
33. Which linear equation in two variables passes through the point (6, 8) and is parallel to the line
represented by the following equation?
2
y=
x+7
3
2
a. y =
x + 12
3
3
b. y = x – 12
2
3
c. y = x + 12
2
2
d. y =
x – 12
3
34. Which linear equation in two variables passes through the point (6, -3) and is perpendicular to
the line represented by the following equation?
2
y=
x+7
3
2
e. y =
x + 12
3
3
f. y = x – 12
2
3
g. y = x + 12
2
2
h. y =
x – 12
3
35. A representation of a linear equation in two variables is graphed on the coordinate plane below.
Which linear equation in two variables can be used to represent the line?
A. y =
3
x+3
2
2
3
B. y = x + 3
C. 3x + 2y = 6
D. 3x – 2y = -6
36. Which table of values best represents the following linear equation in two variables?
1
y=
x+3
6
a.
c.
x
y
x
Y
-3
7/2
-2
8/3
0
3
1
19/6
3
0
6
2
6
2
12
1
x
Y
x
Y
-2
10/3
-6
2
-1
19/6
-3
5/2
0
3
3
-5/2
1
17/6
6
-2
b.
d.
37. Line H is graphed on the coordinate grid below. Which linear equation in two variables can be
used to represent a line parallel to line H passing through the point (–3, 2)?
F
3x + 4y = –14
G 4x + 3y = –6
H 3x + 4y = 15
J
4x – 3y = -18
38. The table below shows pairs of values that satisfy a linear function.
x
y
2
-14
3
-5
4
4
5
13
6
22
7
31
What is the y-intercept of the graph of this function?
F
9
G H
J -32
39. The table below shows pairs of values that satisfy a linear function.
x
-8
4
12
f(x)
1
5
6
What is the correlation coefficient?
What does this tell us about the date?
40. Determine the “rate of change” of the line represented by the equation 15x + 8y = 200.
Write the slope as a decimal and as a fraction.
41. Given the following two points on a line, (7, -5) and (-14, -2), determine the following:
Slope:
42. The advertisement shows the rates
for Direct TV. Which function best
represents the situation and the cost of
purchasing Direct TV for 7 months?
Slope-intercept form equation:
DIRECT TV
BLACK FRIDAY SPECIAL
Activation Fee ONLY $5
A) C(m) = 29.99m; C(7) = $209.93
Plus $29.99 per month
B) C(m) = 5m + 29.99; C(7) = $64.99
C) C(m) = 29.99m + 5; C(7) = $214.93
D) C(m) = (5 +29.99)m; C(7) = $244.93
43. The graph represents the height, in
inches, of a banana tree. Which linear
equation in two variables can be used to
represent the height, y, for a banana tree
after, x, number of days?
F) y = 4x + 4
G) y = x + 4
H) y = x + 8
J) y = 4x + 8
44. The expenses for Mrs. Flaherty’s 20th high school reunion totaled $5,250. There were 125 tickets
sold and the “profits” were donated to Amanda, a class member who is battling cancer. The Class of
1995 was able to donate $2,000 to Amanda. Which equation could be used to find x, the cost of each
ticket?
A) 125 x + 5250 = 2000
B) 2000 – 125 x = 5250
C) 2000 + 125x = 5250
D) 125x – 5250 = 2000
45. The total cost for a dinner reception, f(x), is a function of the number of people, x, attending the
event. The equation, f(x) = 625 + 19.75x, can be used to represent this situation. The catering
company requires a minimum of 20 guests. Which inequalities represent the domain & range of this
problem?
A) Domain: x < 20
Range: f(x) > 625, where f(x) is in increments of $19.75
B) Domain: 0 < x < 20
Range: 0 < f(x) < 625
C) Domain: x > 625 , where x is in increments of $19.75
Range: f(x) > 20
D) Domain: x > 20
Range: f(x) > 625 , where f(x) is in increments of $19.75
Use the table below to answer the next three questions.
Day Number (d)
Number of Cans (c)
1
18
2
25
3
32
4
39
46. Greg decided that he would collect aluminum cans in order to earn enough money to purchase a
bike. Determine the rate of change for this linear relationship.
47. What does the rate of change represent in this relationship?
a) number of days
b) number of cans
c) number of days per can
d) number of cans per day
48. Does this table represent a direct variation?
a) Yes, it is a direct variation
b) No, it is not a direct variation
c) It cannot be determined
49. Half-Price Books is having a “sidewalk sale” this weekend. The total cost varies directly with the
number of books purchased. Mr. Purtle bought 17 books for a total cost of $42.50. If Mr. Pate
spends $57.50, how many books did he purchase?
A)
B)
C)
D)
40 books
23 books
6 books
12 books
50. Ten data points are graphed on the scatterplot below.
Which statement identifies the correlation coefficient
between the two variables and the correct interpretation of
the correlation coefficient as a measure of the strength of
the linear association?
F r = .7307; The correlation coefficient indicates a weak,
positive, linear correlation.
G r = .7307; The correlation coefficient indicates a strong,
positive, linear correlation.
H r = .8548; The correlation coefficient indicates a strong,
positive, linear correlation.
J r = .8548; The correlation coefficient indicates a weak,
positive, linear correlation.
51. Several students performed an experiment by increasing the temperature of a gas and
measuring its volume. The results of the experiment are in the table below.
Which function best represents the problem situation and the temperature of the gas it will take for the
gas volume to reach 1 cL? (100 mL = 1 cL)
A f(x) = 0.25x + 55; 180 degrees Celsius
B f(x) = x + 40; 60 degrees Celsius
C f(x) = 0.25x + 40; 240 degrees Celsius
D f(x) = x + 20; 80 degrees Celsius
52. Sandra was comparing the price of electricity with two different companies. One company was
charging $49 per month and $0.10 per kilowatt used. The other company wanted only $39 per month,
but charge $0.15 per kilowatt after the first 100 kilowatts. Sandra used this system of equations to
represent this situation:
Ca = 49 + 0.10x
Cb = 39 + 0.15(x-100)
Which answer is a reasonable solution, and what does it represent?
F) When Sandra has used 775 kilowatts, the cost for Plan A and the cost for Plan B will both be $140.25.
G) When Sandra has used 50 kilowatts, the cost for Plan A and the cost for Plan B will both be $54.
H) When Sandra has used 500 kilowatts, the cost for Plan A and the cost for Plan B will both be $99.
J) When Sandra has used 1000 kilowatts, the cost for Plan A and the cost for Plan B will both be $149.
53. Given the following graph, which system of linear equations best represents this situation?
A)
B)
C)
D)
y = x + 20
y = 3x + 10
y = .5x + 20
y = 1.5x + 10
y = 20x
y = 10x
y = 20x + 20
y = 10x + 10
54. The table below shows the charges for Netflix and Blockbuster.
Number of Movies
Cost for Netflix
0
1
2
$5.00
$6.00
$7.00
Cost for
Blockbuster
$0.00
$1.50
$3.00
Write the system of equations that represents this table.
How many videos a customer would need to rent from each store for the cost to be the same?
55. What is the solution to the system of linear equations below:
7x – 4y = 10
10 + 2y = 3.5x
A) (0, 1)
B) (-4 , 0)
7
C) No Solution
D) Infinitely Many Solutions
56. What is the approximate solution to the system of equations graphed below?
A)
B)
C)
D)
(3, 4)
(4, 3)
(4, 5)
(5, 4)
57. The Fantastic Fit Gym offers two different membership plans starting in January. The graph
below shows the cost of the beginner's plan and the veteran's plan, for one year.
Based on the graph, in what month is
the total cost for both plans the same?
F January
G June
H November
J April
58. The graph below represents a system of two linear equations in two variables.
Which system of two linear equations in
two variables best represents the graph?
F x–y=2
x – y = -4
G x + y = -2
x + y = -4
H x+y=2
x–y=4
J x – y = -2
x+y=4
59. A system of linear equations is shown below. Graph this system of linear equations to
determine a reasonable estimate of the solution.
y=-- x+3
y = 2x – 3
F (2, – )
G (3, –2)
H (- , 3)
J (2, )
60. Mrs. Flaherty sold a total of 37 cakes and pies to make some extra money to buy Christmas
presents. Each pie cost $12.50 and cakes cost $10 each and she made a total $405.
Write the system of equations that you would use to represent this situation.
Find the number of pies and the number of cakes Mrs. Flaherty sold.