BCS Math 1 Foundations Final Exam

Instructions

Questions 1 - 8 are calculator inactive. Questions 9-40 are calculator active

1

Solve the following equation for x. Type your answer in the space provided.
3(5 + 2x)-4x = -5x + 1

NC.M1.A-REI.3

1

Diego is emptying two pools at the Asheville recreation park. The first pool’s remaining water in gallons can be modeled using the linear model f(x)= 2300 - 32x, where x represents the time in minutes. The second pool’s remaining water in gallons can be modeled using the function g(x) shown in the table below:

How much more water does first pool hold than the second pool?

NC.M1.F-IF.9

1

Clare shopped at the Mast General Store for a camping trip.
She spent $131 on hiking socks and dry bags.
Hiking socks cost $15 and dry bags cost $28.
She bought a total of 7 items.
How many more pairs of hiking socks did she buy than dry bags?

NC.M1.A-REI.6

NC.M3.A-CED.3

1

Solve the system of equations to find the value of x - y:
5x + 7y =1
x = -2y + 2

NC.M1.A-REI.6

1

Solve the system of equations to find the value of x + y :
5x + 2y =48
2x + 2y = 21

NC.M1.A-REI.6

1

Which graph has a shaded region that represents the solution to the system of inequalities?
4x-6y \leq 24
y < 6-3x

NC.M1.A-REI.12

1

Which of the following is the inequality for the graph shown below:

NC.M1.A-REI.12

1

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Which best describes the shape of the distribution?

NC.M1.S-ID.1

1

15 student scores were reported in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Suppose that one student’s score had been lost, but when found, it was revealed that she got 19 problems correct!

Select ALL of the statements that are true.

NC.M1.S-ID.3

1

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Which of the following statements is true?

NC.M1.S-ID.1

NC.M1.S-ID.2

1

NC.M1.S-ID.2

1

The histograms below represent the maximum temperature in Juneau, Alaska and Asheville, North Carolina recorded on days in April 2022.

Select ALL of the statements that are true.

NC.M1.S-ID.2

1

A new video streaming service charges a $15.00 monthly fee which includes streaming 5 movies. Each movie streamed after the 5th movie costs an additional $1.25. Which of the equations below relates streaming m movies if the total monthly cost is $22.50?

NC.M1.A-CED.1

1

A “friends and family” plan for a music streaming service has a base monthly cost that includes 2 users. There is an extra charge for each additional user included on the account.

The equation 11.50 + 4.50(x - 2) = 20.50 represents the Smith family’s monthly cost.

Which of the following statements is true?

NC.M1.A-CED.1

1

The area of a trapezoid can be found using the formula:

Which of the following equations is equivalent to the formula solved for B, one of the bases of the trapezoid?

NC.M1.A-CED.4

1

Priya is considering joining the Asheville PickleBall Club. A membership costs $80.00 a month and $2.00 per hour to rent a court.

Which of the following inequalities represents the constraint on the number of hours t she could rent a court if she plans to spend no more than $100.00 per month on the club?

NC.M1.A-CED.1

1

Jada is considering becoming a member of the Asheville Country Club. Dues are $450.00 every three months and there is a fee for each round of golf she plays. She plans to spend, on average, less than $200.00 per month on golf, and uses the following inequality to represent the constraint:

Choose the statement that best describes the solution to the inequality.

NC.M1.A-CED.1

1

NC.M1.A-REI.10

1

Kiran tutors math in the afternoons for extra money.
He gets paid $15.00 an hour for tutoring middle school math and $25.50 an hour for tutoring high school math.
Last month, Kiran tutored for 13 hours and made a total of $300.00.
The system below can be used to model the number of hours he tutored middle school (x) and high school (y ) math.

15x + 25.50y = 300
x + y = 13

What is the meaning of the solution to the system of linear equations?

NC.M1.A-REI.6

1

Standard Pizza company sells slices of pizza. Toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.

Which of the following statements is true?

NC.M1.F-IF.7

1

Standard Pizza company sells slices of pizza, and toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.

Which linear equation represents the cost of a slice of pizza, c, priced on the number of toppings, t ?

NC.M1.F-BF.1.a

1

The height measured in inches of candle A can be modeled using the function A(x) = -0.25x + 5 after x hours of being lit. The height of candle B was recorded in the table below:

Which of the following statements are true?

NC.M1.F-IF.9

1

Elena buys 4 hotdogs and 2 drinks for $8.00. Carol buys 3 hotdogs and 1 drink for $5.50. Which system below represents the situation if x is the cost for a hotdog and y is the cost for a drink?

NC.M1.A-CED.3

1

Which of the following residual plots represents a good linear model?

NC.M1.S-ID.6.b

NC.M1.S-ID.8

1

The table below shows the number of hours students studied for a test and the grade each student received on the test.

Which is the linear regression equation for the hours studied, x, and test grade, y?

NC.M1.S-ID.6.a

1

The table below shows the number of hours students studied for a test and the grade each student received on the test.

Using the regression equation, predict the test grade of a student that studied 2.5 hours? Round to the nearest whole number

NC.M1.S-ID.6.a

1

The table below shows the number of hours students studied for a test and the grade each student received on the test.
Using the regression equation, predict the number of hours a student should study to make a 100 on the test? Round to the nearest tenth.

NC.M1.S-ID.6.a

1

A professor at UNCA collected data on the number of students eating lunch in the cafeteria and the number of days since the school semester started. She calculated the correlation coefficient to be r = -0.87.

Which of the following statements is true?

NC.M1.S-ID.8

1

The table below shows the U.S. average life expectancy at birth in various decades.

The linear regression equation for this data set is y = 0.208x+ 62.696. What is the residual for 1990?

NC.M1.S-ID.6.b

1

Classify each as either a "Function" or "Not A Function"

NC.M1.F-IF.1

1

The function h(t) represents the height of a dog in inches when the dog is t months old. Which of the following represents the meaning of h(12) = 18 in this situation?

NC.M1.F-IF.2

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NC.M1.F-IF.2

1

NC.M1.F-IF.4

1

The function S represents the number of centimeters of snow on the ground t hours after the snow started. Which function notation below represents 15 centimeters of snow on the ground 3 hours after it started snowing?

NC.M1.F-IF.2

1

Below represents the amount of rain in two cities. Fargo is represented by f(x) (solid line) and Georgetown is represented by g(x) (dotted line).

Which of the following statements is true?

NC.M1.A-REI.11

NC.M1.F-IF.4

1

Priya is counting the number of cars in the parking lot of the Salvage Station after a concert. She uses the function C to estimate the number of cars h hours after the concert ends. There were approximately 220 cars in the parking lot when the concert ended, and the parking lot was empty after 6 hours. Which of the following describes the domain and range best?

NC.M1.F-IF.5

1

A bug travels up a tree, from the ground, over a 30-second interval. It travels fast at first and then slows down. It stops for 10 seconds, then proceeds up the tree slowly, speeding up as it goes. Which sketch best illustrates the bug’s distance (d) from the ground over the 30-second interval (t)?

NC.M1.F-IF.4

1

The table below shows the number of reported polio cases in Nigeria from 2006 to 2015.

What is the average rate of change, to the nearest hundredth, of the number of reported polio cases per year in Nigeria from 2006 to 2013?

NC.M1.F-IF.6

1

Han is hiking a popular trail in the Pisgah National Forest. He tracks how his elevation changes as he hikes. Drag and drop each of the following intervals to classify them as an interval of increase, decrease, or constant.

Interval of Increase
Interval of Decrease

NC.M1.F-IF.4

BCS Math 1 Foundations Final Exam

Solve the following equation for x. Type your answer in the space provided.3(5 + 2x)-4x = -5x + 1

Clare shopped at the Mast General Store for a camping trip.She spent $131 on hiking socks and dry bags.Hiking socks cost $15 and dry bags cost $28.She bought a total of 7 items.How many more pairs of hiking socks did she buy than dry bags?

Solve the system of equations to find the value of x - y:5x + 7y =1x = -2y + 2

Solve the system of equations to find the value of x + y :5x + 2y =482x + 2y = 21

Which graph has a shaded region that represents the solution to the system of inequalities?4x-6y \leq 24y < 6-3x

Which of the following is the inequality for the graph shown below:

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct: [12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]Which best describes the shape of the distribution?

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]Which of the following statements is true?

The histograms below represent the maximum temperature in Juneau, Alaska and Asheville, North Carolina recorded on days in April 2022.Select ALL of the statements that are true.

A new video streaming service charges a $15.00 monthly fee which includes streaming 5 movies. Each movie streamed after the 5th movie costs an additional $1.25. Which of the equations below relates streaming m movies if the total monthly cost is $22.50?

The area of a trapezoid can be found using the formula:Which of the following equations is equivalent to the formula solved for B, one of the bases of the trapezoid?

Standard Pizza company sells slices of pizza. Toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.Which of the following statements is true?

Standard Pizza company sells slices of pizza, and toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.Which linear equation represents the cost of a slice of pizza, c, priced on the number of toppings, t ?

The height measured in inches of candle A can be modeled using the function A(x) = -0.25x + 5 after x hours of being lit. The height of candle B was recorded in the table below:Which of the following statements are true?

Elena buys 4 hotdogs and 2 drinks for $8.00. Carol buys 3 hotdogs and 1 drink for $5.50. Which system below represents the situation if x is the cost for a hotdog and y is the cost for a drink?

Which of the following residual plots represents a good linear model?

The table below shows the number of hours students studied for a test and the grade each student received on the test.Which is the linear regression equation for the hours studied, x, and test grade, y?

The table below shows the number of hours students studied for a test and the grade each student received on the test.Using the regression equation, predict the test grade of a student that studied 2.5 hours? Round to the nearest whole number

The table below shows the number of hours students studied for a test and the grade each student received on the test.Using the regression equation, predict the number of hours a student should study to make a 100 on the test? Round to the nearest tenth.

A professor at UNCA collected data on the number of students eating lunch in the cafeteria and the number of days since the school semester started. She calculated the correlation coefficient to be r = -0.87. Which of the following statements is true?

The table below shows the U.S. average life expectancy at birth in various decades.The linear regression equation for this data set is y = 0.208x+ 62.696. What is the residual for 1990?

Classify each as either a "Function" or "Not A Function"

The function h(t) represents the height of a dog in inches when the dog is t months old. Which of the following represents the meaning of h(12) = 18 in this situation?

The function S represents the number of centimeters of snow on the ground t hours after the snow started. Which function notation below represents 15 centimeters of snow on the ground 3 hours after it started snowing?

Below represents the amount of rain in two cities. Fargo is represented by f(x) (solid line) and Georgetown is represented by g(x) (dotted line).Which of the following statements is true?

The table below shows the number of reported polio cases in Nigeria from 2006 to 2015.What is the average rate of change, to the nearest hundredth, of the number of reported polio cases per year in Nigeria from 2006 to 2013?

Han is hiking a popular trail in the Pisgah National Forest. He tracks how his elevation changes as he hikes. Drag and drop each of the following intervals to classify them as an interval of increase, decrease, or constant.

Solve the following equation for x. Type your answer in the space provided.3(5 + 2x)-4x = -5x + 1

Clare shopped at the Mast General Store for a camping trip.She spent $131 on hiking socks and dry bags.Hiking socks cost $15 and dry bags cost $28.She bought a total of 7 items.How many more pairs of hiking socks did she buy than dry bags?

Solve the system of equations to find the value of x - y:5x + 7y =1x = -2y + 2

Solve the system of equations to find the value of x + y :5x + 2y =482x + 2y = 21

Which graph has a shaded region that represents the solution to the system of inequalities?4x-6y \leq 24y < 6-3x

Which of the following is the inequality for the graph shown below:

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct: [12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]Which best describes the shape of the distribution?

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]Which of the following statements is true?

Two car dealerships recorded the number of cars they each sold every month for a year. The data is displayed below in the boxplots.Select ALL of the statements that are true.

The histograms below represent the maximum temperature in Juneau, Alaska and Asheville, North Carolina recorded on days in April 2022.Select ALL of the statements that are true.

A new video streaming service charges a $15.00 monthly fee which includes streaming 5 movies. Each movie streamed after the 5th movie costs an additional $1.25. Which of the equations below relates streaming m movies if the total monthly cost is $22.50?

The area of a trapezoid can be found using the formula:Which of the following equations is equivalent to the formula solved for B, one of the bases of the trapezoid?

Standard Pizza company sells slices of pizza. Toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.Which of the following statements is true?

Standard Pizza company sells slices of pizza, and toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.Which linear equation represents the cost of a slice of pizza, c, priced on the number of toppings, t ?

The height measured in inches of candle A can be modeled using the function A(x) = -0.25x + 5 after x hours of being lit. The height of candle B was recorded in the table below:Which of the following statements are true?

Elena buys 4 hotdogs and 2 drinks for $8.00. Carol buys 3 hotdogs and 1 drink for $5.50. Which system below represents the situation if x is the cost for a hotdog and y is the cost for a drink?

Which of the following residual plots represents a good linear model?

The table below shows the number of hours students studied for a test and the grade each student received on the test.Which is the linear regression equation for the hours studied, x, and test grade, y?

The table below shows the number of hours students studied for a test and the grade each student received on the test.Using the regression equation, predict the test grade of a student that studied 2.5 hours? Round to the nearest whole number

The table below shows the number of hours students studied for a test and the grade each student received on the test.Using the regression equation, predict the number of hours a student should study to make a 100 on the test? Round to the nearest tenth.

A professor at UNCA collected data on the number of students eating lunch in the cafeteria and the number of days since the school semester started. She calculated the correlation coefficient to be r = -0.87. Which of the following statements is true?

The table below shows the U.S. average life expectancy at birth in various decades.The linear regression equation for this data set is y = 0.208x+ 62.696. What is the residual for 1990?

Classify each as either a "Function" or "Not A Function"

The function h(t) represents the height of a dog in inches when the dog is t months old. Which of the following represents the meaning of h(12) = 18 in this situation?

A child is playing outside. The graph below shows the child's distance, d(t), in yards from home over a period of time, t, in seconds.Select ALL of the statements that are true.

The graph below represents a jogger's speed during her 20-minute jog around her neighborhood.Select all of the statements below that are true:

The function S represents the number of centimeters of snow on the ground t hours after the snow started. Which function notation below represents 15 centimeters of snow on the ground 3 hours after it started snowing?

Below represents the amount of rain in two cities. Fargo is represented by f(x) (solid line) and Georgetown is represented by g(x) (dotted line).Which of the following statements is true?

The table below shows the number of reported polio cases in Nigeria from 2006 to 2015.What is the average rate of change, to the nearest hundredth, of the number of reported polio cases per year in Nigeria from 2006 to 2013?

Han is hiking a popular trail in the Pisgah National Forest. He tracks how his elevation changes as he hikes. Drag and drop each of the following intervals to classify them as an interval of increase, decrease, or constant.

Solve the following equation for x. Type your answer in the space provided.
3(5 + 2x)-4x = -5x + 1

Clare shopped at the Mast General Store for a camping trip.
She spent $131 on hiking socks and dry bags.
Hiking socks cost $15 and dry bags cost $28.
She bought a total of 7 items.
How many more pairs of hiking socks did she buy than dry bags?

Solve the system of equations to find the value of x - y:
5x + 7y =1
x = -2y + 2

Solve the system of equations to find the value of x + y :
5x + 2y =48
2x + 2y = 21

Which graph has a shaded region that represents the solution to the system of inequalities?
4x-6y \leq 24
y < 6-3x

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Which best describes the shape of the distribution?

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Which of the following statements is true?

The histograms below represent the maximum temperature in Juneau, Alaska and Asheville, North Carolina recorded on days in April 2022.

Select ALL of the statements that are true.

The area of a trapezoid can be found using the formula:

Which of the following equations is equivalent to the formula solved for B, one of the bases of the trapezoid?

Standard Pizza company sells slices of pizza. Toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.

Which of the following statements is true?

Standard Pizza company sells slices of pizza, and toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.

Which linear equation represents the cost of a slice of pizza, c, priced on the number of toppings, t ?

The height measured in inches of candle A can be modeled using the function A(x) = -0.25x + 5 after x hours of being lit. The height of candle B was recorded in the table below:

Which of the following statements are true?

The table below shows the number of hours students studied for a test and the grade each student received on the test.

Which is the linear regression equation for the hours studied, x, and test grade, y?

The table below shows the number of hours students studied for a test and the grade each student received on the test.

Using the regression equation, predict the test grade of a student that studied 2.5 hours? Round to the nearest whole number

The table below shows the number of hours students studied for a test and the grade each student received on the test.
Using the regression equation, predict the number of hours a student should study to make a 100 on the test? Round to the nearest tenth.

A professor at UNCA collected data on the number of students eating lunch in the cafeteria and the number of days since the school semester started. She calculated the correlation coefficient to be r = -0.87.

Which of the following statements is true?

The table below shows the U.S. average life expectancy at birth in various decades.

The linear regression equation for this data set is y = 0.208x+ 62.696. What is the residual for 1990?

Below represents the amount of rain in two cities. Fargo is represented by f(x) (solid line) and Georgetown is represented by g(x) (dotted line).

Which of the following statements is true?

The table below shows the number of reported polio cases in Nigeria from 2006 to 2015.

What is the average rate of change, to the nearest hundredth, of the number of reported polio cases per year in Nigeria from 2006 to 2013?

Solve the following equation for x. Type your answer in the space provided.
3(5 + 2x)-4x = -5x + 1

Clare shopped at the Mast General Store for a camping trip.
She spent $131 on hiking socks and dry bags.
Hiking socks cost $15 and dry bags cost $28.
She bought a total of 7 items.
How many more pairs of hiking socks did she buy than dry bags?

Solve the system of equations to find the value of x - y:
5x + 7y =1
x = -2y + 2

Solve the system of equations to find the value of x + y :
5x + 2y =48
2x + 2y = 21

Which graph has a shaded region that represents the solution to the system of inequalities?
4x-6y \leq 24
y < 6-3x

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Which best describes the shape of the distribution?

15 students participated in the 20 problem “Elevating Elementary” math competition. Here are the number of problems that each student got correct:
[12,9,8,9,8,9,10,13,7,10,11,12,10,10,11]

Which of the following statements is true?

Two car dealerships recorded the number of cars they each sold every month for a year. The data is displayed below in the boxplots.

Select ALL of the statements that are true.

The histograms below represent the maximum temperature in Juneau, Alaska and Asheville, North Carolina recorded on days in April 2022.

Select ALL of the statements that are true.

The area of a trapezoid can be found using the formula:

Which of the following equations is equivalent to the formula solved for B, one of the bases of the trapezoid?

Standard Pizza company sells slices of pizza. Toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.

Which of the following statements is true?

Standard Pizza company sells slices of pizza, and toppings can be added for an additional cost. The graph below shows the cost of a slice of pizza based on the number of toppings.

Which linear equation represents the cost of a slice of pizza, c, priced on the number of toppings, t ?

The height measured in inches of candle A can be modeled using the function A(x) = -0.25x + 5 after x hours of being lit. The height of candle B was recorded in the table below:

Which of the following statements are true?

The table below shows the number of hours students studied for a test and the grade each student received on the test.

Which is the linear regression equation for the hours studied, x, and test grade, y?

The table below shows the number of hours students studied for a test and the grade each student received on the test.

Using the regression equation, predict the test grade of a student that studied 2.5 hours? Round to the nearest whole number

The table below shows the number of hours students studied for a test and the grade each student received on the test.
Using the regression equation, predict the number of hours a student should study to make a 100 on the test? Round to the nearest tenth.

A professor at UNCA collected data on the number of students eating lunch in the cafeteria and the number of days since the school semester started. She calculated the correlation coefficient to be r = -0.87.

Which of the following statements is true?

The table below shows the U.S. average life expectancy at birth in various decades.

The linear regression equation for this data set is y = 0.208x+ 62.696. What is the residual for 1990?

A child is playing outside. The graph below shows the child's distance, d(t), in yards from home over a period of time, t, in seconds.

Select ALL of the statements that are true.

The graph below represents a jogger's speed during her 20-minute jog around her neighborhood.

Select all of the statements below that are true:

Below represents the amount of rain in two cities. Fargo is represented by f(x) (solid line) and Georgetown is represented by g(x) (dotted line).

Which of the following statements is true?

The table below shows the number of reported polio cases in Nigeria from 2006 to 2015.

What is the average rate of change, to the nearest hundredth, of the number of reported polio cases per year in Nigeria from 2006 to 2013?