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Algebra 1 ACP Countdown

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Last updated over 2 years ago
80 questions
Note from the author:
Warm Up - 12/14
1
A1.C.3.c
1
A1.C.2.b
1
A1.C.3.d
1
A1.C.3.c
Warm - Up Questions 12/13/23
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A1.C.2.c
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A1.C.2.c
1
A1.C.3.b
Warm Up Questions 12/12/23
1
A1.C.2.c
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A1.C.3.c
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A1.C.3.c
1
A1.C.3.d
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A1.C.12.e
A.3A: I can determine the slope of a line given a table, graph, or two points or and an equation written in various forms y = mx + b, Ax + By = C and y-y1 = m(x-x1). (1 Question)
1
A1.C.3.a
1
1
A1.C.3.a
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A1.C.3.a
A.3B (3 Questions) I can calculate the rate of change of a linear function represented tabularly, graphically or algebraically in context of mathematical and real world problems.
1
A1.C.3.b
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A1.C.3.b
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A1.C.3.b
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A1.C.3.b
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A1.C.3.b
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A1.C.3.b
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A1.C.3.b
1
A1.C.3.b
A.3C (3 Questions) I can graph linear functions on the coordianate plane and identify key features, including x - intercept, y-intercept, zeros, and slope.
1
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A1.C.3.c
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A1.C.3.c
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A1.C.3.c
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A1.C.3.c
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A1.C.3.c
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A1.C.3.c
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A1.C.3.c
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A1.C.2.c
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A1.C.3.c
A.3D: (2 Questions)Graph the solution set of linear inequalities in two variables on the coordinate plane.
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A1.C.3.d
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A1.C.3.d
1
A1.C.3.d
1
A1.C.3.d
1
A1.C.3.d
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A1.C.3.d
A.5A (3 Questions): Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
10
A1.C.5.a
10
A1.C.5.a
1
A1.C.5.a
1
A1.C.5.a
1
A1.C.5.a
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A1.C.5.a
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A1.C.5.a
A.5C (3 Questions): Solve systems of two linear equations with two variables for mathematics and real-world problems.
1
A1.C.5.c
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A1.C.5.c
1
A1.C.5.c
1
A1.C.5.c
1
A1.C.5.c
A.2I (2 Questions): I can write systems of two linear equations given a table of values, a graph, and a verbal description.
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A1.C.2.i
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A1.C.2.i
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A1.C.2.i
1
A1.C.2.i
A.2D (2 Questions) I can write and solve equations involving direct variation.
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A1.C.2.d
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A1.C.2.d
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A1.C.2.d
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A1.C.2.d
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A1.C.2.d
A.2E: (1 Question) Write the equation of a line that contains a given point and is parallel to a given line.
1
A1.C.2.e
1
1
A1.C.2.e
1
A1.C.2.e
1
A1.C.2.e
1
A1.C.2.e
1
A1.C.2.e
A.2F: (1 Question) Write the equation of the line that contains a given point and is perpendicular to a given line.
1
1
A1.C.2.f
1
A1.C.2.f
1
A1.C.2.f
A.2G:(1 Question): Write an equation of a line that is parallel or perpendicular to the x or y - axis and determine whether the slope of the line is zero or undefined.
1
A1.C.2.g
1
A1.C.2.g
1
A1.C.2.g
A.2A: (3 Questions): Determine the domain and range of a linear function in mathematical and real - world problems, both discrete and continuous and represent domain and range using inequalities.
1
1
A1.C.2.a
1
1
A1.C.2.a
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A1.C.2.a
ACP Review
Warm Up Questions for 12/13
Question 1
1.

Question 2
2.

Question 3
3.

Question 4
4.

Question 5
5.

Question 6
6.

Question 7
7.

Question 8
8.

Question 9
9.

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?
Record your answer and fill in the bubbles on your answer document.

Question 10
10.

Question 11
11.

Question 12
12.

Question 13
13.

Question 14
14.

Draggable itemarrow_right_altCorresponding Item
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Question 15
15.

What is the slope of the line 50x + 25y = 5

Question 16
16.

Question 17
17.

Question 18
18.

Question 19
19.
Jonathan purchased a new car. The table below shows the value of the car over a period of time.

Complete the statement that best describes the rate of change of the car with respect to the value.
Move the correct answer to each spot.

The car ______________ in value at a rate of ___________ per year.
Other Answer Choices:
$26,750
$4,500
increases
$2,250
decreases
Question 20
20.
What is the rate of change for the equation 2x - 3y = 12
The rate of change is __________
Question 21
21.

Maria does the same number of jumping jacks each day over a period of several days. On the 5th day she completed a total of 325 jumping jacks. By the 8th day she has completed a total of 520. What value equals the rate of change of the total number of jumping jacks when graphed against the day. (only input the number)

Question 22
22.

Question 23
23.

Question 24
24.

Question 25
25.

Question 26
26.

Question 27
27.

Question 28
28.

Question 29
29.
The graph of the linear function g passes through (7, 6) and (-7, -4) as shown.


What are the slope and y - intercept of the graph?

The slope of the graph is __________ and the y - intercept is __________
Question 30
30.

Question 31
31.
Other Answer Choices:
x - intercept (4, 0)
x - intercept (0, 3)
y - intercept (4, 0)
x - intercept (0, 4)
y - intercept (0, 3)
y - intercept (3, 0)
Question 32
32.
What are the zeros, y - intercept and slope of the given graph?


zeros __________; y - intercept __________ ; slope __________
Question 33
33.

Question 34
34.

Question 35
35.

Question 36
36.

Question 37
37.

Question 38
38.

Question 39
39.

Question 40
40.

Question 41
41.

Question 42
42.

Quick Skill: Explain the error that was made when solving the following equation and what is the correct solution?

Question 43
43.

Question 44
44.

What is the solution to 4(q + 56.5) = 30q - 112?

Question 45
45.

Question 46
46.

Question 47
47.

NOTES:

Solving a system of equations requires solving for the ordered pair (x and y coordinates) that satisfies both equations.

Equations can be in any form.
Slope - Intercept; y = mx + b
Point - slope form y - y1 = m(x - x1)
or Standard form Ax + By = C

Some equations are NOT in any form and must be converted into one of the above forms. Be familiar with those. Always reference your formula chart.
Question 48
48.

Question 49
49.

A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, and each key chain cost $2.75. If the manager spent a total of $132.50, how many coffee mugs did the manager purchase?

Record your answer and fill in the bubbles on your answer document.

Question 50
50.

Question 51
51.

Question 52
52.

Question 53
53.

Question 54
54.

Question 55
55.

Question 56
56.

Direct Variation represents a proportional relationship, where the dependent varies directly with the independent. The equation will be in the form of y = kx, in which K is the slope, and the linear line will go through the origin when graphed.

When solving for direct variation problems, set up ratios (fractions) to solve for the unknown value.

(Other vocabulary which can be used is directly varies or varies directly)
Question 57
57.

Question 58
58.

In an electrical circuit, the voltage across a resistor is directly proportional to the current running through the resistor. If a current of 12 amps produces 480 volts across a resistor, how many volts would a current of 1.5 amps produce across an identical resistor?

Record your answer and fill in the bubbles on your answer document.

Question 59
59.

Question 60
60.

Question 61
61.

The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.
What is the value of y when x = 28?
Record your answer and fill in the bubbles on your answer document.

If two lines are parallel their slopes are the same but their intercepts are different

To find the parallel line
1) First - Calculate or identify the slope of the original equation.
2) Use the slope - intercept form to substitute the given point (if given) and the slope.
3) Calculate for the y - intercept.
Question 62
62.

Draggable itemarrow_right_altCorresponding Item
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Question 63
63.

Question 64
64.

Question 65
65.

Question 66
66.

Question 67
67.

Question 68
68.

When two lines are perpendicular, their slopes are opposite reciprocals of each other.

Example: In the equation y = -5x + 9, we can see that the slope of the equation is -5.


To calculate for the reciprocal change signs to the opposites, then flip the slope.
Question 69
69.
Other Answer Choices:
2
5
3
Question 70
70.

Question 71
71.

Question 72
72.

Question 73
73.

Question 74
74.

Question 75
75.

Question 76
76.

Question 77
77.

Question 78
78.
Other Answer Choices:
x
-9
y
-6
3
2
Question 79
79.

Question 80
80.

The graph of linear function k passes through the points ( -7,0 ) and (1, 8).



Which statement must be true?
The slope of the graph of k is -4/3
The graph of k passes through the point (-1, -8)
The zero of k is 7.
The x-intercept of the graph of k is -7.
What is the equation in the point-slope form of a line passing through the point (3, -2) with a slope the same as

Which ordered pair is in the solution set of 8x + 16y > 32?

(0, 2)
( − 3, 5)
( − 1, 1)
(4, 0)
The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.


Which statement describes the x-intercept of the graph?
The x-intercept is 60, which represents the initial balance in dollars of the loan.
The x-intercept is 27,000, which represents the initial balance in dollars of the loan.
The x-intercept is 60, which represents the number of monthly payments needed to repay the loan.
The x-intercept is 27,000, which represents the number of monthly payments needed to repay the loan.
The graph of a linear function is shown on the grid.


Which equation is best represented by this graph?
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.


Based on the table, which function models this situation?
The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.


What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?
14 ft/yr
3 ft/yr
7 ft/yr
10 ft/yr
The graph of a linear function is shown on the grid

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)
Which line appears to have an x-intercept of −5 and a y-intercept of 3?
Which graph best represents the solution set of -4x ≤ 6y-54?
Which of the following is equivalent to 3x -4y = 6?
y = -\frac{6}{7}x
y = -\frac{3}{4}x
y=\frac{4}{3}x+2
y=\frac{3}{4}x-\frac{3}{2}

Quick Skill - Identify the form of each equation
y + 3 = 2(x - 3)
x + y = -35
y = 10 - 12x
7y - 8x = 15
12 = 3x - 8y
c = 3a - 8
5a + 9 = b
y + 12 = -8(x - 0)
Slope - Intercept Form (y = mx + b)
Point - Slope Form y - y1 = m(x - x1)
Standard Form Ax + By = C
Match the representation with the slope
6x + 2y = 1
(5, - 11) (-9, 17)
3y + 2x = 12
-2
A line contains the points (-2, 2) and (4, -2)
What is the slope of the line?
Quick Skill: Identify all the vocabulary that can represent rate of change.
slope
y - intercept
per
initial
every
continues
already
rate
each
The values in the table represent a linear relationship between x and y.

What is the rate of change of y in relation to x?
10
17
-10
-17
A music company service charges a monthly fee plus a fixed amount for each download. One month Rhonda downloads 12 songs and pays $15.67. The next month, she downloads 15 songs and pays $18.34. At what rate does her bill change with respect to the number of downloads?
0.89
1.22
1.31
4.99
A line is graphed on a coordinate grid as shown.


Which table represents the same rate of change as the line on the graph?
The table represents several points that fall on a graph of a linear function.


What is the rate of change of y with respect to x in this function?
-26
12
2
26
If a question is asking for the zeros, which of the following is it asking for?
the slope
the origin
the x - intercept
the y - intercept
Quick Skill: Identifying x - intercept vs y - intercepts
(4, 0)
(0, - 4)
(-3, 0)
(- 21, 0)
(0, -8)
x - intercept
y - intercept
The graph of a function is shown. What are the x and y intercepts of the graph?

x - intercept (-2, 0); y - intercept (0, 4)
x - intercept (-2, 0); y - intercept (0, 8)
x - intercept (4, 0); y - intercept (0, 8)
x - intercept (4, 0); y - intercept (0, -2)
Linear function p has a zero of 6 and a y - intercept of -2. Which graph best represents graph k
Which graph best represents the equation -5y = -6x + 15
For each of the graphs, drag and drop the x-intercept(zeros), y-intercept and slope for each.
slope =
slope =
slope =
The table represents some points on the graph of linear function f.


Which function represents f ?
f (x) = 26(x − 2)
f (x) = −26(x − 1)
f (x) = 13(x − 2)
f (x) = −2(26x − 1)
Linear function t has an x-intercept of -1and a y-intercept of 5. Which graph best represents t?
Which graph best represents the solution set of ?
Which graph best represents the solution set of y ≤ 3/4x − 4?
Which inequality is best represented by the graph?

4x + 7y ≤ 49
4x + 7y < 49
7x + 4y ≤ 28
7x + 4y < 28
Which graph best represents the solution set for
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)
Quick Skill: Identify if the given equation has no solutions or infinitely many solutions.
No Solutions
Infinitely Many Solutions
What value of n makes the equation 4(0.5 - 3) = n - 0.25(12 - 8n) true?
-2.33
-9
0
-15
What is the solution to 8x -3(2x - 4) = 3(x - 6)
6
2
30
No Solution
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 value of y in the solution to this system of equations?
6y + x = −59
x = −2y + 9
8.5
-17
43
-12.5
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
What is the value of x in the solution to this system of equations?

3x - 5y = 22
y = -5x + 32
−6.5
0.5
6.5
−0.5
A system of equations is graphed on the grid.


Which system of equations does the graph represent?
y = − x − 4; y = 2x − 2
y = − x +4; y = 2x − 4
y = x − 4; y = − 2x − 2
y = x +4; y = − 2x − 4
A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?
4y = 3x + 64; 8y = x + 68
4y = 3x + 64; 8y = x + 60
3x + 4y = 64; x + 8y = 68
3x + 4y = 64; x + 8y = 60
The tables 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
Which graph best represents this system of equations and its solution?
8x − 4y = −16
3x + 15y = −6
The total distance in centimeters a toy robot moves varies directly with the time in seconds. The toy robot moves a total distance of 264 centimeters in 11 seconds (Teacher Led Example)

What is the time in seconds the toy robot moves when the total distance is 408 centimeters?
24 s
17 s
13 s
37 s
The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?
\frac{3}{5}
1\frac{2}{3}
7
15
The total distance in centimeters a toy robot moves varies directly with the time in seconds. The toy robot moves a total distance of 264 centimeters in 11 seconds.

What is the time in seconds the toy robot moves when the total distance is 408 centimeters?
24 s
17 s
13 s
37 s
QUICK SKILL: Which equations have the same slope? Match
(7, 2) and (1, -1)
y - 4 = -2(x - 2)
4x + 2y = 7
Which is the equation of the line that is parallel to the graph of y = 5x + 7 and has a y - intercept of (0, -2)? Teacher Led Example
What is the equation in slope-intercept form of the line that passes through the point (5, 0) and is parallel to the line represented by y = 1.2x + 3.8?
y = 1.2x − 6
y = −1.2x + 6
y = 1.2x + 5
y = −1.2x − 5
What is the equation in slope-intercept form of the line that passes through the point (5, 0) and is parallel to the line represented by y = 1.2x + 3.8?
y = 1.2x − 6
y = −1.2x + 6
y = 1.2x + 5
y = −1.2x − 5
What is the equation of a line that passes through the point (3, -5) and has a zero slope?
What is the slope of a line parallel to
-6
6
What is the equation in standard form of the line that passes through the point (6, −1) and is parallel to the line represented by 8x + 3y = 15?
8x + 3y = −45
8x − 3y = −51
8x + 3y = 45
8x − 3y = 51
QUICK SKILL: Match the reciprocal slopes for perpendicular lines.
1) 4x + 2y = 7. The reciprocal is ________
2) y = - 1/3x -5 The reciprocal is ______
3) points (7, 2) and (1, -1). The reciprocal is ________
4) y - 2 = -3(x + 5) The reciprocal is ________
5) y = 3x - 12 The reciprocal is ________
6) 2x + 10y = 7 The reciprocal is ______
What is the slope of a line that is perpendicular to the equation
3
-3
What is the equation in slope-intercept form of the line that crosses the x-axis at 36 and is perpendicular to the line represented by
What is the equation in slope-intercept form of the line that crosses the x-axis at 36 and is perpendicular to the line represented by
QUICK SKILL: Determine which representations are parallel to the x and y axis
x = -9
y = -9
zero slope
undefined slope
Parallel to x - axis
Parallel to y - axis
What is the equation and slope of the line shown on the grid?


x = 6; slope is zero.
y = 6; slope is 6.
x = 6; slope is undefined.
Which statement best represents the equation of the line shown on the grid and its relationship to the x-axis?

The equation of the line is x = 2.5, and the line is parallel to the x-axis.
The equation of the line is x = 2.5, and the line is perpendicular to the x-axis.
The equation of the line is y = 2.5, and the line is parallel to the x-axis.
The equation of the line is y = 2.5, and the line is perpendicular to the x-axis.
NOTES: ________________________________________________

The domain is all the x - values of the function. (input, independent variable)
The range is all the y - values of the function (output, dependent variable)

NOTATIONS:______________________________________
open circle
<. or >
solid circle

<---- arrows at the endpoints ---->
continues in the direction to infinity

Example on analyzing the domain and range.

Given a graph:
What is the domain of the following function?




1) The endpoints of the line are solid circles therefore answer choice A and C can be eliminated.
2) The domain represents all possible x - values, therefore answer choice C and D can be eliminated
3) The only possible answer is B. 1) The endpoints are solid circles representing less than or equal to (or greater than or equal to) and all the possible values of x are from
- 4 to 1.5
What is the range of the following function?


--4 ≤ y ≤ 5
-- 4 < y < 5
--2 ≤ x ≤ 1
--2 < x < 1
A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x, the time in minutes.


Which answer choice best describes the domain and range of the function for this situation?
Domain: All real numbers greater than or equal to 0 and less than or equal to 100; Range: All real numbers greater than or equal to 0 and less than or equal to 50
Domain: {−2}, Range: {100}
Domain: All real numbers greater than or equal to 0 and less than or equal to 50; Range: All real numbers greater than or equal to 0 and less than or equal to 100
Domain: {100}, Range: {−2}
The graph of a function is shown.


Create an inequality that represents the domain of this function.
_______ < ______ < ______
A student rode a bike from school to a recreation center. The graph shows the student’s distance in miles from the recreation center after riding the bike for x minutes.


What is the range of the function for this situation?
All real numbers greater than or equal to 0 and less than or equal to 28
All real numbers greater than or equal to 0 and less than or equal to 9
All real numbers less than or equal to 28
All real numbers less than or equal to 9
The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c = 34.95u + 6.25, where u is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the domain of the function for this situation?
0 < u ≤ 12
0 < c ≤ 425.65
{8, 9, 10, 11, 12}
{285.85, 320.80, 355.75, 390.70, 425.65}