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WorksheetsAlgebra 1 End of Year Review
Total questions: 53
Worksheet time: 13hrs 1mins
What are the domain and range of f(x) = -37?
Domain: All real numbers greater than or equal to -37
Range: All real numbers
Domain: {-37}
Range: All real numbers
Domain: All real numbers
Range: All real numbers greater than or equal to -37.
Domain: All real numbers
Range: {-37}
The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day. For one day of work, what is the range of the function for this situation?
0 ≤ x ≤ 8
80 ≤ y ≤ 440
0 ≤ x ≤ 10
45 ≤ y ≤ 685
At a restaurant jars of tomato sauce are stored in boxes in the pantry. Each box contains 8 jars of tomato sauce. A cook used 2 jars from 1 of the boxes. Which function shows the relationship between y, the total number of jars of tomato sauce remaining in the pantry, and x, the number of boxes in the pantry?
y = 8x + 6
y = 8x
y = 8x - 2
y = 6x
The graph of a linear function is shown on the grid shown. Which equation is best represented by this graph?
y + 7 = -3(x - 4)
y + 1 = -3(x + 2)
y - 4 = 3(x + 7)
y - 2 = 3(x - 1)
The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?
⅗
1⅔
7
15
What is the equation in slope-intercept form of the line that passes through the point (2, -2) and is perpendicular to the line represented by y = ⅖x + 2?
y = 5/2x - 7
y = 5/2x + 7
y = -5/2x - 3
y = -5/2x + 3
What are the equation and slope of the line shown on the grid?
y = 6; slope is -1/6
x = 6; slope is zero
y = 6; slope is 6.
x = 6; slope is undefined
What is the slope of the line that passes through the points (5, -11) and (-9, 17)?
-2
-1/2
7
2
The graph shows the linear relationship between the maximum area in square feet that can be painted and the number of gallons of paint used. Which of these best represents the rate of change of the maximum area painted with respect to the number of gallons of paint used?
200 ft2/gal
1/200 ft2/gal
400 ft2/gal
1/400 ft2/gal
The table shows the linear relationship between the balance of a student's savings account and the number of weeks he has been saving. Based on the table, what was the rate of change of the balance of the student's savings account in dollars and cents per week?
$7
$0.14
$25
$14
The water level of a river was measured each day during a two-week period. The graph models the linear relationship between the water level of the river in feet and the number of days the water level was measured. Which statement best describes the y-intercept of the graph?
The water level increased by 0.25 ft per day.
The maximum water level was 19.5 ft.
The initial water level was 16 ft.
The water level was measured by 14 days.
A paper airplane was thrown from the top of a tall building. The height of the paper airplane above the ground can be found using the function y = -1.5x + 60, where x is the time in seconds the airplane has been in the air. How many seconds did it take the paper airplane to reach the ground?
60 sec
40 sec
20 sec
45 sec
Which line appears to have an x-intercept of -5 and a y-intercept of 3?
The graphs of linear functions f and g are shown on the grid. Which function is best represented by the graph of g?
g(x) = f(x) - 4
g(x) = 1/3f(x)
g(x) = f(x) - 2
g(x) = 3f(x)
Which situation does NOT show causation?
When the student population at a school increases, the number of teachers at the school increases.
When the amount of sugar in a quart of apple juice is reduced, there are fewer calories in each serving.
When there are more workers on a project, the project is completed in less time.
When there is more protein in an athlete's diet, the athlete scores more points in a game.
What value of n makes the equation 4(0.5n - 3) = n- 0.25(12 - 8n) true?
3
-9
0
-15
What is the solution to
34x + 95 = 3(14x + 9)?
7.5
8.5
8
7
In a sequence of numbers, a3= 0, a4 = 6, a5 = 12, a6 = 18 and a7 = 24. Based on this information, which equation can be used to find the nth term in the sequence, an?
an = -6n + 18
an = -18n + 6
an = 6n - 18
an = 18n - 6
The table of ordered pairs represent some points on the graphs of lines q and v. Which system of equations is represented by lines q and v?
21x - y = 9
5x + 6y = 40
3x - y = -27
x + 2y = 16
21x - y = 9
5x + 6y = 20
9x - y = -27
x + 2y = 8
There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches. Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?
x + y = 140
12x + 7y = 15
7x + 12y = 140
7x + 12y = 15
x + y = 15
7x + 12y = 140
x + y = 15
12x + 7y = 140
Which graph best represents the solution set of -4x ≤ 6y - 54?
The graph of 2x - 5y = 10 is shown on the grid. Which ordered pair is in the solution set of 2x - 5y ≥ 10?
(0, 5)
(5, 0)
(-2, 5)
(-5, 2)
Which graph best represents a system of equations that has no solution?
What is the solution set for -4x + 10 ≥ 5x + 55?
x ≥ 5
x ≥ 45
x ≤ -5
x ≤ -45
Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount. The first customer paid $12 for 14 postcards and 5 large envelopes. The second customer paid $24.80 for 10 postcards and 15 large envelopes. What was the cost in dollars of each large envelope?
$1.42
$0.35
$1.15
$0.63
What is the x-value of the solution to this system of equations?
x = 2y - 4
7x + 5y = -66
-2
-19/7
-8
-62/19
Which expression is equivalent to (h2 + 9h - 1)(-4h + 3)?
-4h3 - 33h2 + 31h - 3
4h3 + 39h2 - 23h - 3
-4h3 - 39h2+ 23h + 3
4h3 + 33h2 - 31h + 3
Which expression is equivalent to -28x2 + 35x?
7x(4x + 5)
-7x(4x - 5)
7x(4x - 5)
-7x(4x + 5)
Which expression is equivalent to x2 - 17x - 60?
(x - 20)(x + 3)
(x - 5)(x - 12)
(x - 20)(x - 3)
(x + 5)(x - 12)
Which expression is a factor of
21x2 + 13x - 20?
3x - 4
7x - 5
7x + 4
3x + 5
Which expression is a factor of 9r2 - 4r + 1?
3r - 1
r - 1
9r - 1
There are no real factors.
Which expression is equivalent to √96
24
8√6
48
4√6
Which expression is equivalent to (144k2r14)1/2
12kr7
72k2r14
144kr7
12k2r14
Which expression is equivalent to the expression pictured for all values of q where the the expression is defined?
q27
1/q27
q3
1/q3
Which expression is equivalent to the expression pictured for all values of q and w where the expression is defined?
32q7/ w
20q17w9
32q7w9
20qw
What is the range of y = -x2 - 2x + 3?
x ≤ 4
x ≥ -4
y ≤ 4
y ≥ -4
The graph of the quadratic function f is shown on the grid. Which of these best represents the domain of f?
-3 ≤ x ≤ 2
All real numbers
y ≥ 5.5
All real numbers less than -3 or greater than 2
Which function is equivalent to f(x) = -4(x + 7)2 - 6?
f(x) = -4x2 - 56x - 202
f(x) = -4x2 + 14x + 43
f(x) = -4x2 - 56x - 172
f(x) = -4x2 + 190
Th graph shows the height in feet of an object above the ground t seconds after it was launched from the ground. Which function is best represented by the graph of this situation?
h(t) = -16t2 - 64t
h(t) = -16t2 + 128t -256
h(t) = -16t2 + 64t
h(t) = -16t2 - 128t - 256
Which graph best represents a quadratic function that has only one zero?
A graph of a quadratic function is shown on the grid. Which coordinates best represent the vertex of the graph?
(2.4, 0)
(0, -1)
(-0.4, 0)
(1, -2)
Which statement about g(x) = x2 - 576 is true?
The zeros, -288 and 288, can be found when 0 = (x + 288)(x - 288)
The only zero, 288, can be found when 0 = (x - 288)2
The zeros, -24 and 24, can be found when 0 = (x + 24)(x - 24)
The only zero, 24, can be found when 0 = (x - 24)2
The graph of quadratic function p is shown on the grid.
If k(x) = x2 and p(x) = k(x) + n, what is the value of n?
6
-6
3
-3
The graph of g(x) = x2 was transformed to create the graph of h(x) = -(x/4)2. Which of these describes the transformation from the graph of g to the graph of h?
A reflection over the x-axis and a horizontal stretch
A reflection over the y-axis and a horizontal stretch
A reflection over the x-axis and a vertical stretch
A reflection over the y-axis and a vertical stretch
What are the solutions to (x + 7)2= 81?
-74 and 88
-2 and 16
-88 and 74
-16 and 2
The area of a rectangular trampoline is 112 ft2. The length of the trampoline is 6 ft greater than the width of the trampoline. This situation can be represented by the equation w2 + 6w - 112 = 0. What is the width of the trampoline?
7 ft
16 ft
8 ft
14 ft
Given f(x) = ⅓(4 - x)2, what is the value of f(16)?
-48
-16
48
16
What appears to be the domain of the part of the exponential function graphed on the grid?
-1 ≤ x ≤ 3
-1 ≤ y ≤ 3
5.3 ≤ x ≤ 27
5.3 ≤ y ≤ 27
Scientists are studying a bacteria sample. The function f(x) = 245(1.12)x gives the number of bacteria in the sample at the end of x days. Which statement is the best interpretation of one of the values in this function?
The initial number of bacteria is 12.
The initial number of bacteria decreases at a rate of 88% each day.
The number of bacteria increases at a rate of 12% each day.
The number of bacteria at the end of one day is 245.
There are 1,024 players in a tennis tournament. In each round, half the players are eliminated. Which function can be used to find the number of players remaining in the tournament at the end of x rounds?
f(x) = 1,024(1.50)x
f(x) = 1,024(0.50)x
f(x) = 1,024(1.05)x
f(x) = 1,024(0.05)x
In the year 1900, the total number of metric tons of copper produced in the world was 495,000. Each year since 1900, the total number of metric tons of copper produced has increased on average by about 3.25% over the amount produced the previous year. Which function models the total number of metric tons of copper produced in the year that is x years since 1900?
c(x) = 495,000(1.0325)x
c(x) = 495,000(0.9675)x
c(x) = 495,000x1.0325
c(x) = 495,000x0.9675
Which statement about the graph of y = 8(0.25)x is true?
The coordinates of the x-intercept are (0.25, 0).
The coordinates of the y-intercept are (0, 8).
The equation of the asymptote is x = 0.
The graph includes the point (2, 1).
Which graph best represents f(x) = 2(5)x?
