Algebra 1 ACP Countdown

Last updated about 2 years ago

80 questions

Note from the author:

ACP Review

Instructions

Warm Up Questions for 12/13

Warm Up - 12/14

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

Which statement must be true?

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?

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?

Warm - Up Questions 12/13/23

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?

Warm Up Questions 12/12/23

The graph of a linear function is shown on the grid

Which equation is best represented by this graph?

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.

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?

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)

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

Draggable item		Corresponding Item


3y + 2x = 12
6x + 2y = 1
(5, - 11) (-9, 17)
		-2

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

A line contains the points (-2, 2) and (4, -2)
What is the slope of the line?

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.

Quick Skill: Identify all the vocabulary that can represent rate of change.

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?

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

What is the rate of change for the equation 2x - 3y = 12
The rate of change is __________

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)

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?

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?

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.

If a question is asking for the zeros, which of the following is it asking for?

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?

Linear function p has a zero of 6 and a y - intercept of -2. Which graph best represents graph k

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 __________

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.

Other Answer Choices:

x - intercept (4, 0)

x - intercept (0, 3)

y - intercept (4, 0)

x - intercept (0, 4)

y - intercept (0, 3)

slope = 

slope = 

y - intercept (3, 0)

slope = 

What are the zeros, y - intercept and slope of the given graph?

zeros __________;  y - intercept __________ ; slope __________

The table represents some points on the graph of linear function f.

Which function represents f ?

Linear function t has an x-intercept of -1and a y-intercept of 5. Which graph best represents t?

A.3D: (2 Questions)Graph the solution set of linear inequalities in two variables on the coordinate plane.

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?

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?

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.

Quick Skill: Identify if the given equation has no solutions or infinitely many solutions.

No Solutions
Infinitely Many Solutions

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

What value of n makes the equation 4(0.5 - 3) = n - 0.25(12 - 8n) true?

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

What is the solution to 8x -3(2x - 4) = 3(x - 6)

A.5C (3 Questions): Solve systems of two linear equations with two variables for mathematics and real-world problems.

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. 

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?

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.

What is the value of y in the solution to this system of equations?
6y + x = −59
x = −2y + 9

What is the x-value of the solution to this system of equations?
x = 2y − 4
7x + 5y = −66

What is the value of x in the solution to this system of equations?

3x - 5y = 22
y = -5x + 32

A.2I (2 Questions): I can write systems of two linear equations given a table of values, a graph, and a verbal description.

A system of equations is graphed on the grid.

Which system of equations does the graph represent?

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?

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?

Which graph best represents this system of equations and its solution?
8x − 4y = −16
3x + 15y = −6

A.2D (2 Questions) I can write and solve equations involving direct variation.

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)

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?

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.

The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?

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?

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.

A.2E: (1 Question) Write the equation of a line that contains a given point and is parallel to a given line.

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.

QUICK SKILL: Which equations have the same slope? Match

Draggable item		Corresponding Item
		y - 4 = -2(x - 2)

4x + 2y = 7

(7, 2) and (1, -1)

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?

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

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?

A.2F: (1 Question) Write the equation of the line that contains a given point and is perpendicular to a given line.

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.

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 ______ 
      

Other Answer Choices:

What is the slope of a line that is perpendicular to the equation

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

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.

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?

Which statement best represents the equation of the line shown on the grid and its relationship to the x-axis?

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.

                                                                      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?

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?

The graph of a function is shown.


Create an inequality that represents the domain of this function.
_______  < ______  <  ______ 

Other Answer Choices:

-9

-6

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?

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?

Algebra 1 ACP Countdown

The graph of linear function k passes through the points ( -7,0 ) and (1, 8).Which statement must be true?

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?

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 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?

The graph of a linear function is shown on the gridWhich equation is best represented by this graph?

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?

Quick Skill - Identify the form of each equation

Match the representation with the slope

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

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.

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?

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?

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?

If a question is asking for the zeros, which of the following is it asking for?

Quick Skill: Identifying x - intercept vs y - intercepts

The graph of a function is shown. What are the x and y intercepts of the graph?

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

The table represents some points on the graph of linear function f.Which function represents f ?

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?

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?

Quick Skill: Identify if the given equation has no solutions or infinitely many solutions.

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

What value of n makes the equation 4(0.5 - 3) = n - 0.25(12 - 8n) true?

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

What is the solution to 8x -3(2x - 4) = 3(x - 6)

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.

What is the value of y in the solution to this system of equations?6y + x = −59 x = −2y + 9

What is the x-value of the solution to this system of equations?x = 2y − 47x + 5y = −66

What is the value of x in the solution to this system of equations? 3x - 5y = 22 y = -5x + 32

A system of equations is graphed on the grid.Which system of equations does the graph represent?

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?

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?

The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?

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?

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.

QUICK SKILL: Which equations have the same slope? Match

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?

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?

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

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?

What is the slope of a line that is perpendicular to the equation

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

What is the equation and slope of the line shown on the grid?

Which statement best represents the equation of the line shown on the grid and its relationship to the x-axis?

What is the range of the following function?

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?

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?

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

Which statement must be true?

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 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 graph of a linear function is shown on the grid

Which equation is best represented by this graph?

A line contains the points (-2, 2) and (4, -2)
What is the slope of the line?

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?

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?

The table represents some points on the graph of linear function f.

Which function represents f ?

The graph of 2x − 5y = 10 is shown on the grid.

Which ordered pair is in the solution set of 2x − 5y ≥ 10?

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.

What is the value of y in the solution to this system of equations?
6y + x = −59
x = −2y + 9

What is the x-value of the solution to this system of equations?
x = 2y − 4
7x + 5y = −66

What is the value of x in the solution to this system of equations?

3x - 5y = 22
y = -5x + 32

A system of equations is graphed on the grid.

Which system of equations does the graph represent?

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?

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?

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?

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.

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?

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?