Linear Models Practice EOC Practice Standard A-CED.2 6. An ice cream shop charges $1 for a cone and $2 per scoop of ice cream. Which equation models the cost of an ice cream cone, y, with x scoops of ice cream? A. 1 = 2x + y B. 2 = x + y C. y = x + 2 D. y = 2x + 1 8. Nicholas borrowed $250 from his parents to buy a video game system. He has agreed to pay them back $15 each week. Which equation represents the amount of money Nicholas still owes his parents, p, after w weeks? A. p = 250w 15 B. p = 15w 250 C. p = 15w + 250 D. p = 15(w 250) 9. Scientists measure the total population of sea turtles, y, each year in a refuge. They discovered an initial population of 65 sea turtles and an increase of 5 turtles each year. If x is the number of years after the initial observation, which equation best models the sea turtle population? A. y = 5x + 65 B. y = 5(65) x C. y = 65x + 5 D. y = 65(5) x 10. Sarah earned $1,500 this summer. She mowed lawns for $15 per lawn and babysat for $20 per hour. Which equation represents her earnings from mowing x lawns and babysitting y hours? A. 1,500 = xy(15 + 20) B. 1,500 = 5(x + y) C. 1,500 = 15x + 20y 12. Sandra s cell phone plan gives her unlimited minutes for $15.50 per month. She is charged $0.08 for each text message, t. Which equation models the total monthly cost, C, for the cell phone? A. C = 15.50t +0.08 B. C = 0.08t + 15.50 C. C = 15.58t. C = 15.42t 16. A business buys a computer for $3,000. After 4 years, the value of the computer is expected to be $250. The value, V, can be related to the time in years, t, in a linear equation. Which equation models the relationship between V and t? A. V = 250t B. V = 12t C. V = 687.50t 3,000 D. V = -687.50t + 3,000 17. A rabbit weighed 4 ounces when it was born. The rabbit gained 2 ounces each week for the next 12 weeks. Which equation models the weight of the rabbit, w, x weeks after it was born, where x 12? A. w = 6x B. w = 2x 4 C. w = 2x + 4 D. w = 4x + 2 23. Mikel has $20 to spend at the aquarium. The aquarium charges a $10 admission fee. The aquarium also has special exhibits that cost $4.00 each to view. Which equation can be used to determine the amount of money, y, that Mikel has left if he views x exhibits? A. y = 4 10x B. y = 10x 4 C. y = 10 4x D. y = 4x 10 33. A phone company charges a $45 monthly fee for 500 minutes of phone use. For each minute over 500, the phone company charges an additional $0.08. Which equation can be used to determine the total amount the company charges, t, for a phone call that is m minutes long, where m is greater than 500? A. t = 0.08m + 45 B. t = 45 0.08(m 500) C. t = 0.08(m 500) + 45 D. t = 0.08(m + 500) + 45
40. Mary has written 10 pages for her novel. She plans to write 15 additional pages per month until she is finished. Which equation represents the total number of pages Mary has written, p, after m months? A. p = 10m + 15 B. p = 10m 15 C. p = 15m + 10 D. p = 15m 10 Standard F-LE.2 Linear Models Test Item Bank 4. Miesha is saving the same amount of money each week. After 2 weeks, she saves $85. After 4 weeks, she saves $135. Which equation models the amount of money Miesha will have saved, y, after x weeks? A. y = 25x + 35 B. y = 25x + 85 C. y = 50x 15 D. y = 50x + 85 5. In 1990, a music store sold 250 CDs per day. In 1995, they sold 175 CDs per day. Assuming a linear relationship, how many CDs did the store sell per day in 2000? A. 130 B. 115 C. 100 D. 85 13. A cupcake shop had $55,000 in sales in the year 1990. In the year 2000, the shop had $105,000 in sales. Assuming a linear relationship, which function models the amount of sales the shop had x years after 1990? A. f(x) = 5,000x + 55,000 B. f(x) = 5,000x + 105,000 C. f(x) = 55,000x + 105,000 D. f(x) = 105,000x + 55,000 16. Which choice is an equation of the linear function that passes through the points (1, 3) and (- 2, 3)? A. y = 1 B. y = 3 C. y = 2x + 3 D. y = - 2x + 3 17. Maria began the school year with $200 in her school lunch account. The amount of money in the account has decreased linearly. After 3 months, she had $155 in her account. After 5 months, she had $125 in her account. Which function models the amount of money that Maria has in her account at the end of n months? A. f(n) = 200 30n B. f(n) = 200 15n C. f(n) = 30n 200 D. f(n) = 15n 200 27. A 6-pound bag of peanuts costs $7.50, and a 10-pound bag of peanuts costs $12.50. Assuming the cost of peanuts follows a linear trend, how much would a 3-pound bag of peanuts cost? A. $1.25 B. $3.75 C. $4.25 D. $5.00
Standard S-ID.7 Linear Models Test Item Bank 3. Suppose the total cost of a ride in a taxi can be modeled by the function T = 5 + 0.85x, where T is the total cost and x is the total number of miles. What does the slope of the equation represent? A. the initial cost of the taxi B. the total cost of the trip C. the charge for each mile of the trip D. the total number of miles for the trip 6. The table below shows the number of residents in a neighborhood who received new water meters over several weeks. Weeks (w) 0 1 2 3 4 # of Residents (R) 8 15 29 54 102 What is the meaning of the y-intercept of a linear model for the data? A. the initial number of residents with meters B. the initial rate at which residents received meters C. the maximum number of residents that received meters D. the rate of change in the number of residents that received meters 18. The equation, C = 0.15(x 200) + 9.95, represents a cell phone company s monthly charge, C, for a text messaging service, where x represents the number of text messages per month. What is the best interpretation of the slope? A. The company charges $9.95 for each text message over 200 per month. B. The company charges $0.15 for each text message over 200 per month. C. The initial fee for text messaging is $9.95. D. The cost for each text is $0.15. Standard F-IF.4 Linear Models Test Item Bank 22. Shane is filling a barrel with water. The table below shows the amount of water in the barrel after different amounts of time. Time ( in seconds) Amount of Water (cubic in.) 1 2 3 4 25 32 39 46 Assuming Shane filled the barrel at a constant rate, how much water was initially in the barrel? A. 18 cubic inches B. 16 cubic inches C. 14 cubic inches D. 12 cubic inches
6. The table below shows the distance Chris is located from his school at different times. Assuming a linear relationship, how long will it take Chris to get to school? Time ( in minutes) Distance (miles) 0 3 6 9 12 15 20 18 16 14 12 10 A. 20 minutes B. 24 minutes C. 27 minutes D. 30 minutes Standard F-BF.1 Linear Models Test Item Bank 13. The function f(x) = 9.75x + 62 models the amount of money that Hector earned working x hours in a week. The function g(x) = 7.5x + 84 models the amount of money that Carl earned working x hours in the same week. Which function, h(x), models the difference in Hector s and Carl s earnings? A. h(x)= 17.25x 22 B. h(x)= 17.25x + 146 C. h(x)= 2.25x 22 D. h(x)= 2.25x + 146 Standard F-IF.6 Linear ModelsTest Item Bank 10. The table below shows the number of people that visited a state park over a period of 4 days. Day # of people (thousands) 1 5 2 9 3 13 4 17 What is the meaning of the rate of change for the data? A. The park had a decrease in attendance of 4,000 people per day. B. The park had a decrease in attendance of 4 people per day. C. The park had an increase in attendance of 4,000 people per day. D. The park had an increase in attendance of 4 people per day. 16. The population of one variety of frogs in a nature preserve is listed in the table below. Year Population 1990 1,750 1995 1,900 2000 1,950 2005 2,180 2010 2,240 What was the average rate of change in the population between 1990 and 2000? A. 20 frogs per year B. 24.5 frogs per year C. 28.7 frogs per year D. 30 frogs per year
Standard F-IF.9 Linear Models Test Item Bank 4. Sarah compared the function y = 7x + 13 to the linear function that fits the values in the table below. x -3 2 5 7 y 1-9 -15-19 What is the distance between the y-intercepts of the two functions? A. 5 B. 9 C. 13 D. 18 8. Maria compared the slope of the function f(x) = ( ) to the slope of the linear function that fits the values in the table below. x -4-2 0 2 4 y 9 8 7 6 5 Which best describes the slopes of the two functions? A. Both functions have a positive slope. B. Both functions have a negative slope. C. Function f(x) has a positive slope, while function g(x) has a negative slope. D. Function f(x) has a negative slope, while function g(x) has a positive slope. 14. Angela earns $8 for every hour she works at her job. The amount of money Kelly earns at her job is modeled by the function f(x) = 15t, where t represents hours worked. Angela and Kelly both worked 38 hours last week. Which statement accurately describes the amount of money Angela and Kelly earned last week? A. Angela made $38 more than Kelly. B. Kelly made $266 more than Angela. C. Angela made $304 more than Kelly. D. Kelly made $570 more than Angela.