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BCS Math 1 Foundations Final Exam

Last updated over 2 years ago

40 questions

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

Question 1

1.

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

Question 2

2.

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?

Question 3

3.

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?

Question 4

4.

Other Answer Choices:

150

30

Question 5

5.

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

Question 6

6.

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

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Question 40

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Noah sells hotdogs and nachos at the Asheville Tourists baseball game as a walking vendor. 
Each hotdog costs $2.00 and each plate of nachos costs $3.50.
Noah’s goal is to make at least $150.00 each time he walks through the crowd.
He can carry a maximum of 30 items at a time.
Write a system of linear inequalities that models these constraints where x represents the number of hotdogs sold and y represents the number of plates of nachos sold:

________  + ________ \leq _______ 
________   + ________  \geq ________ 

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

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

2x + 3y < 12

2x + 3y \leq 12

2x+3y > 12

2x+3y \geq 12

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?

Approximately Normal

Skewed Left

Skewed Right

Bimodal

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.

The median would increase more than the mean

The mean would increase more than the median

The standard deviation would increase

The standard deviation would decrease

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 most appropriate measure of the center would be mean, and the most appropriate measure of the variability would be IQR.

The most appropriate measure of the center would be mean, and the most appropriate measure of the variability would be standard deviation.

The most appropriate measure of the center would be median, and the most appropriate measure of the variability would be IQR.

The most appropriate measure of the center would be median, and the most appropriate measure of the variability would be standard deviation.

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.

Dealership A’s IQR is higher than Dealership B’s IQR

Dealership B’s IQR is higher than  Dealership A’s IQR

Dealership A and B have a similar IQR.

Dealership A and B typically sold about the same amount of cars

Dealership A typically sold more cars than Dealership B

Dealership B typically sold more cars than Dealership A.

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.

Asheville, NC had a higher typical temperature than Juneau, Alaska

Juneau, Alaska is significantly more variable than Asheville, NC

Both histograms have shapes that are symmetric.

15 temperatures were recorded in Asheville, NC. 

Juneau, Alaska had the lowest recorded temperature between the two cities

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?

15 + 1.25m = 22.50

15 + 1.25(m-5) = 22.50

15 + 5+1.25m = 22.50

15 + 1.25(m+5) = 22.50

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?

The Smith family has 4 users on their plan. 

The Smith family receives a discount of $2.00 per month.

The Smith family pays $16.00 per month for streaming services.

The Smith family pays $6.50 per person for streaming services.

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?

B= \frac{2A-h}{C}

B= \frac{h(A+C)}{2}

B= \frac{2A-C}{h}

B= \frac{2A}{h}-C

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?

100  < 80 +2t

100 \leq 80 + 2t

100 > 80 + 2t

100 \geq 80 + 2t

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.

x < 7.5, it costs $7.50 to play golf

x < 7.5, Jada cannot play more than 7 rounds of golf over a 3 month period

x < 52.5, Jada cannot spend more than $52.50 per round of golf

x < 52.5, Jada cannot play more than 52 rounds over a 3 month period. 

Movie theater tickets cost $14.00 for adults and $8.00 for children. The theater's income from one movie showing on Monday afternoon was $224.00. The equation to represent the income based on the number of adult tickets sold, x, and children tickets sold, y, is 14x + 8y=224, and is graphed below.

Select ALL of the statements that are true.

If no adults attended the movie, 28 children went to the movie. 

If 10 adults attended, 5 children were at the movie.

If 25 people were at the movies, 4 were adults and 21 were children.

If 8 adults attended, 20 total tickets were sold.

If no children were at the movie, 16 adults attended. 

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?

Kiran tutored 13 different students

Kiran tutored 10 hours of middle school math and 3 hours of high school math

Kiran tutored 3 hours of middle school math and 10 hours of high school math

Kiran made $40.50 an hour for tutoring math, for a total of $300.00

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?

Four slices of pizza costs $5.00

A slice of pizza with four toppings costs $2.00

A slice of pizza with no toppings costs $3.00

Every topping costs an additional $1.00

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 ?

c = 3.5t

c = 3 + 0.5t

c = 0.5 + 3t

c = 3 + 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?

Candle B burns slower than Candle A.

Candle B was taller than Candle A after burning for 6 hours.

Candle A was 9 inches taller than Candle B before either were lit.

Candle B was taller than Candle A before either were lit. 

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?

y = 2x+84

y= 8x + 68

y=5.34x+76.13

y = 0.94x + 5.34

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

88

89

91

94

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.

4 hours

4.5 hours

4.7 hours

5 hours

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 variables have a weak, negative correlation. This means that the number of days since the school semester started does not correlate with the number of students eating in the cafeteria.

The variables have a strong, negative correlation. This means that as the number of days since the school semester started increases, the number of students eating in the cafeteria tends to decrease.

The variables have a strong, positive correlation. This means that as the number of days since the school semester started increases, the number of students eating in the cafeteria tends to increase.

The variables have a strong, negative correlation. This means that as the number of days since the school semester started increases, the number of students eating in the cafeteria tends to increase.

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?

75.4

75.176

-0.224

0.224

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

Function 

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 dog is 12 inches tall at 18 months old.

The dog is 18 inches tall at 12 months old.

The dog has been 18 inches tall for 12 months.

The dog is 18 inches tall when it is 12 years old.

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.

d(2) = d(3)

d(1) > d(4)

d(0) > d(1)

d(t) = 8 when t = 5

d(0) = 10

d(10) = 0 

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 jogger stood still during the 9-12 minute interval.

The jogger decreases her speed twice.

The jogger is running faster at 1 minute than at 15 minutes.

The horizontal intercept(s) are when the jogger is standing still.

The jogger is jogging at a constant rate.

The jogger hits a maximum speed at 18 minutes into her run. 

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?

S(15) = 3

S(3) = 15

S(t) = 5t + 3

S(t) = 3t + 15

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? 

f(1) > g(1)

f(4) = g(4)

f(7) > g(7)

f(10) < g(10)

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?

The domain is all real numbers from 0 and 6. The range is whole numbers only from 0 to 220.

The domain is all real numbers from 0 and 6. The range is all real numbers from 0 to 220.

The domain is whole numbers only from 0 and 6. The range is whole numbers only from 0 to 220.

The domain is whole numbers only from 0 and 6. The range is all real numbers from 0 to 220.

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)?

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?

-0.01

-134.50

-125.44

-153.71

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

Constant