Additional Practice
Additional Practice ACTIVITY 2.1 Tyson and Kelsey are planning on meeting at the bowling alley. Tyson arrived first and chose to pay $4.50 for each game, which includes his shoe rental. Kelsey came later, and she decided to pay the $3 fee for rental shoes and then pay $3 for each game bowled.
7. The family that MacKenzie babysits for gave her two options for being paid one day. They said they would pay her $4.25 an hour or just pay her $35 for the time they were gone. Explain how MacKenzie can use this graph to decide which option to choose. y
Babysitting Earnings
50
1. Make a table that shows the cost of bowling for both Tyson and Kelsey for the first five games that they bowl.
Salary
40
2. Write an expression for the cost of bowling for each person. Be sure to define your variables.
30 20 10 0
3. Give the meaning of the coefficients in the expressions you wrote for both bowlers.
2
4
6
8
10
x
Hours
4. Tell the meaning of any constant in the expressions you wrote.
8. Which option pays the greater amount for 4 hours of work?
5. Write and solve an equation that shows when the two costs are equal.
9. Is there a point where the pay would be the same? If so, tell when.
6. Describe in words a situation that could be modeled by this equation. © 2010 College Board. All rights reserved.
UNIT 2
c = 0.02x + 4
10. Which situation should you choose if you plan on working for 7 hours? Explain how you can use the graph in Item 7 to know. ACTIVITY 2.2 11. Solve and check each equation. a. b. c. d. e.
14s = 45.5 x - 13 = 10 3n + 7 = -23 -36 = -9t -20 = -2t - 4
Level 2, Unit 2 • Equations, Inequalities, and Linear Relationships
1
Additional Practice
12. Nicki Jo pays $3.50 to watch her sister’s volleyball games. She has paid a total of $31.50 to watch her sister play this year. Write an equation that will answer how many games Nicki Jo has watched. Then solve your equation. 13. Bryce is painting a neighbor’s garage. The neighbor is paying him $20 and an additional amount for each day he paints. Bryce has painted a total of 8 days and has earned $60. Write an equation that will answer how much Bryce earned for each day he painted. Then solve your equation. 14. Simplify each expression, if possible, by combining like terms. If not possible, write simplified. a. b. c. d. e. f. g.
3x + 12x 9d - 3d 3s - 9s 8t 3 + 9t 8t 2 - 4t 2 8y 2 + 12y 3 - 8y 2 12a + 7 - 2a - 3
15. Solve and check each equation. Round answers to the nearest tenth. a. b. c. d. e. f. g.
3x + 10x + 2 = 92 2t + (-6t) - 6 = 2 102 = 8a + 5a - 3a 48 = (-8s) + s + 6 7(p + 3) = 35 -45 = 5 (x - 3) 12g - 6 = 7g
16. Nolan and Tyler bought mini-footballs for their friends. Nolan bought 3 more than Tyler. Together they bought 19. Use an equation to find the number of mini-footballs that Nolan and Tyler each bought.
2
SpringBoard® Mathematics with MeaningTM Level 2
17. Meredith, Lynette, and Renee went to the amusement park. Lynette spent twice as much as Meredith. Renee spent $13 more than Meredith. If they spent $93 altogether, how much did each person spend at the amusement park? Use an equation to find your answer. 18. Reed sells DVDs of the local sprint car races. He offers his customers two options to pay. With option #1, they can pay $12 and then $6 per month to receive the entire collection of race DVDs. With option #2, they can pay $24 and then $3 per month. a. Write and solve an equation to find the number of months at which the options cost the same. b. Which option is more economical if a customer plans to buy DVDs for 11 months? Explain your answer. ACTIVITY 2.3 19. Make an input/output table for y = 5x. Use 0, 1, 2, 3, 4, and 5 as the input, or x-values. Then plot the ordered pairs on a coordinate grid and draw a line through the points. 20. Make an input/output table for this pattern and then graph the ordered pairs.
Figure 1
Figure 2
Figure 3
21. Plot (3, 1) and (5, 5) on a coordinate grid. Then determine the change in y, the change in x, and the slope of the line between the two points.
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice 22. Plot (-7, 2) and (0, -2) on a coordinate grid. Find the change in y, the change in x and the slope of the line that passes through those two points.
25. Compare and contrast the slopes and graphs of y = 3x + 2 and y = 2x + 3. Provide a graph of both equations on a coordinate plane as part of your explanation.
23. Find the change in y, the change in x, and the slope of each line graphed below.
ACTIVITY 2.4
a.
y 4 3 2 1 -4 -3 -2 -1
1
-1
2
3
4
x
-2 -3 -4
b.
y
4 3 2 1 -1
-1
1
2
3
4
26. Nate left for a basketball trip and realized that he forgot his shoes. He called his mom, and she agreed to get his shoes and meet him at the bus. The bus was 22.5 miles away from Nate’s house when his mom left to meet the bus, which was traveling at an average rate of 50 mi/h. Nate’s mom can drive at an average rate of 65 mi/h. Let t represent the number of hours since Nate’s mom left their house. a. Write an equation that represents the distance his mom drives in t hours. b. Write an equation in terms of t that represents the distance the bus has traveled since Nate’s mom leaves with his shoes. c. In how many hours will Nate’s mother catch up with the bus?
5
© 2010 College Board. All rights reserved.
UNIT 2
x
24. Copy and complete input/output tables like the one shown below for each equation. Then graph each equation. a. y = 5x - 1 Input, x
b. y = -3x + 3 Output, y
-2 0 2
Level 2, Unit 2 • Equations, Inequalities, and Linear Relationships
3
Additional Practice
27. Shandeen bought a powdered drink mix so that she could make a sports drink to take with her to her martial arts lessons. The table below shows the amount of drink mix remaining in the container after her first five games. 0
Game Amount Left
1
2
3
32 30 28 26 scoops scoops scoops scoops
a. If the pattern continues, how much drink mix will remain in the container after 10 games? b. Let n represent the number of games in which Shandeen has played. Write and solve an equation to answer the question, “When will Shandeen use all of the drink mix in the container?” 28. On a blueprint, the distance between the family room and kitchen is 3 inches. 1 inch represents 1 foot on the blueprint, If __ 4 what is the actual distance from the family room to the kitchen? 29. If the area of a triangle is 90 in.2 and its base is 18 in., what is the height of the triangle?
h
18 in.
4
SpringBoard® Mathematics with MeaningTM Level 2
30. Solve each formula for the indicated variable. 1 bh for b a. A = __ 2 b. V = πr 2h for h 1 at 2 for t c. d = __ 2 31. The school lunch program orders some of their food items only several times a month and buys many at a time. One of the items that they buy in this manner are small packages of salad dressing. One the first day of school, the high school kitchen has 2,000 packages and the elementary school kitchen 1,000 packages. a. The high school uses 200 packages a week. Let n equal the number of weeks that have passed since the first day of school. Write an equation to represent the number of packages, y, left in the school kitchen after n weeks. b. The elementary school uses 75 packages a week. Let n equal the number of weeks that have passed since the first day of school. Write an equation to represent the number of packages, y, left in the kitchen after n weeks. c. Graph your equations from parts a and b on the same coordinate plane. d. Use your graph to predict when each school will have the same number of packets in their food pantries. Check your prediction by writing and solving an equation.
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice ACTIVITY 2.5
ACTIVITY 2.6
32. Write a situation that each inequality could describe.
36. Ashleigh is hiking at a rate of 4 miles per hour.
a. b. c. d.
x 10 d. 2m + 6 ≤ -18 e. 3x + 2 ≥ -23 2 x < 11 f. __ 3
a. Complete an input/output table that represents Ashleigh’s distance for 1, 2, 3, 4, and 5 hours of hiking and graph the data on a coordinate plane. b. Write an equation that represents the relationship between the time and her distance. c. Is the equation you wrote in part b an example of direct variation? Explain your answer. 37. Which of the equations below are examples of direct variation? Explain your choices. y = 2x y = 3x + 5 1x y = __ 2 6x = y 38. Sketch a graph representing direct variation and a graph that does not represent direct variation. Compare and contrast your graphs. 39. Write an equation that is representative of each kind of change listed. Explain why you wrote the equation you did. a. direct variation b. inverse variation
Level 2, Unit 2 • Equations, Inequalities, and Linear Relationships
5
7. The family that MacKenzie babysits for gave her two options for being paid one day. They said they would pay her $4.25 an hour or just pay her $35 for the time they were gone. Explain how MacKenzie can use this graph to decide which option to choose. y
Babysitting Earnings
50
1. Make a table that shows the cost of bowling for both Tyson and Kelsey for the first five games that they bowl.
Salary
40
2. Write an expression for the cost of bowling for each person. Be sure to define your variables.
30 20 10 0
3. Give the meaning of the coefficients in the expressions you wrote for both bowlers.
2
4
6
8
10
x
Hours
4. Tell the meaning of any constant in the expressions you wrote.
8. Which option pays the greater amount for 4 hours of work?
5. Write and solve an equation that shows when the two costs are equal.
9. Is there a point where the pay would be the same? If so, tell when.
6. Describe in words a situation that could be modeled by this equation. © 2010 College Board. All rights reserved.
UNIT 2
c = 0.02x + 4
10. Which situation should you choose if you plan on working for 7 hours? Explain how you can use the graph in Item 7 to know. ACTIVITY 2.2 11. Solve and check each equation. a. b. c. d. e.
14s = 45.5 x - 13 = 10 3n + 7 = -23 -36 = -9t -20 = -2t - 4
Level 2, Unit 2 • Equations, Inequalities, and Linear Relationships
1
Additional Practice
12. Nicki Jo pays $3.50 to watch her sister’s volleyball games. She has paid a total of $31.50 to watch her sister play this year. Write an equation that will answer how many games Nicki Jo has watched. Then solve your equation. 13. Bryce is painting a neighbor’s garage. The neighbor is paying him $20 and an additional amount for each day he paints. Bryce has painted a total of 8 days and has earned $60. Write an equation that will answer how much Bryce earned for each day he painted. Then solve your equation. 14. Simplify each expression, if possible, by combining like terms. If not possible, write simplified. a. b. c. d. e. f. g.
3x + 12x 9d - 3d 3s - 9s 8t 3 + 9t 8t 2 - 4t 2 8y 2 + 12y 3 - 8y 2 12a + 7 - 2a - 3
15. Solve and check each equation. Round answers to the nearest tenth. a. b. c. d. e. f. g.
3x + 10x + 2 = 92 2t + (-6t) - 6 = 2 102 = 8a + 5a - 3a 48 = (-8s) + s + 6 7(p + 3) = 35 -45 = 5 (x - 3) 12g - 6 = 7g
16. Nolan and Tyler bought mini-footballs for their friends. Nolan bought 3 more than Tyler. Together they bought 19. Use an equation to find the number of mini-footballs that Nolan and Tyler each bought.
2
SpringBoard® Mathematics with MeaningTM Level 2
17. Meredith, Lynette, and Renee went to the amusement park. Lynette spent twice as much as Meredith. Renee spent $13 more than Meredith. If they spent $93 altogether, how much did each person spend at the amusement park? Use an equation to find your answer. 18. Reed sells DVDs of the local sprint car races. He offers his customers two options to pay. With option #1, they can pay $12 and then $6 per month to receive the entire collection of race DVDs. With option #2, they can pay $24 and then $3 per month. a. Write and solve an equation to find the number of months at which the options cost the same. b. Which option is more economical if a customer plans to buy DVDs for 11 months? Explain your answer. ACTIVITY 2.3 19. Make an input/output table for y = 5x. Use 0, 1, 2, 3, 4, and 5 as the input, or x-values. Then plot the ordered pairs on a coordinate grid and draw a line through the points. 20. Make an input/output table for this pattern and then graph the ordered pairs.
Figure 1
Figure 2
Figure 3
21. Plot (3, 1) and (5, 5) on a coordinate grid. Then determine the change in y, the change in x, and the slope of the line between the two points.
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice 22. Plot (-7, 2) and (0, -2) on a coordinate grid. Find the change in y, the change in x and the slope of the line that passes through those two points.
25. Compare and contrast the slopes and graphs of y = 3x + 2 and y = 2x + 3. Provide a graph of both equations on a coordinate plane as part of your explanation.
23. Find the change in y, the change in x, and the slope of each line graphed below.
ACTIVITY 2.4
a.
y 4 3 2 1 -4 -3 -2 -1
1
-1
2
3
4
x
-2 -3 -4
b.
y
4 3 2 1 -1
-1
1
2
3
4
26. Nate left for a basketball trip and realized that he forgot his shoes. He called his mom, and she agreed to get his shoes and meet him at the bus. The bus was 22.5 miles away from Nate’s house when his mom left to meet the bus, which was traveling at an average rate of 50 mi/h. Nate’s mom can drive at an average rate of 65 mi/h. Let t represent the number of hours since Nate’s mom left their house. a. Write an equation that represents the distance his mom drives in t hours. b. Write an equation in terms of t that represents the distance the bus has traveled since Nate’s mom leaves with his shoes. c. In how many hours will Nate’s mother catch up with the bus?
5
© 2010 College Board. All rights reserved.
UNIT 2
x
24. Copy and complete input/output tables like the one shown below for each equation. Then graph each equation. a. y = 5x - 1 Input, x
b. y = -3x + 3 Output, y
-2 0 2
Level 2, Unit 2 • Equations, Inequalities, and Linear Relationships
3
Additional Practice
27. Shandeen bought a powdered drink mix so that she could make a sports drink to take with her to her martial arts lessons. The table below shows the amount of drink mix remaining in the container after her first five games. 0
Game Amount Left
1
2
3
32 30 28 26 scoops scoops scoops scoops
a. If the pattern continues, how much drink mix will remain in the container after 10 games? b. Let n represent the number of games in which Shandeen has played. Write and solve an equation to answer the question, “When will Shandeen use all of the drink mix in the container?” 28. On a blueprint, the distance between the family room and kitchen is 3 inches. 1 inch represents 1 foot on the blueprint, If __ 4 what is the actual distance from the family room to the kitchen? 29. If the area of a triangle is 90 in.2 and its base is 18 in., what is the height of the triangle?
h
18 in.
4
SpringBoard® Mathematics with MeaningTM Level 2
30. Solve each formula for the indicated variable. 1 bh for b a. A = __ 2 b. V = πr 2h for h 1 at 2 for t c. d = __ 2 31. The school lunch program orders some of their food items only several times a month and buys many at a time. One of the items that they buy in this manner are small packages of salad dressing. One the first day of school, the high school kitchen has 2,000 packages and the elementary school kitchen 1,000 packages. a. The high school uses 200 packages a week. Let n equal the number of weeks that have passed since the first day of school. Write an equation to represent the number of packages, y, left in the school kitchen after n weeks. b. The elementary school uses 75 packages a week. Let n equal the number of weeks that have passed since the first day of school. Write an equation to represent the number of packages, y, left in the kitchen after n weeks. c. Graph your equations from parts a and b on the same coordinate plane. d. Use your graph to predict when each school will have the same number of packets in their food pantries. Check your prediction by writing and solving an equation.
© 2010 College Board. All rights reserved.
UNIT 2
Additional Practice ACTIVITY 2.5
ACTIVITY 2.6
32. Write a situation that each inequality could describe.
36. Ashleigh is hiking at a rate of 4 miles per hour.
a. b. c. d.
x 10 d. 2m + 6 ≤ -18 e. 3x + 2 ≥ -23 2 x < 11 f. __ 3
a. Complete an input/output table that represents Ashleigh’s distance for 1, 2, 3, 4, and 5 hours of hiking and graph the data on a coordinate plane. b. Write an equation that represents the relationship between the time and her distance. c. Is the equation you wrote in part b an example of direct variation? Explain your answer. 37. Which of the equations below are examples of direct variation? Explain your choices. y = 2x y = 3x + 5 1x y = __ 2 6x = y 38. Sketch a graph representing direct variation and a graph that does not represent direct variation. Compare and contrast your graphs. 39. Write an equation that is representative of each kind of change listed. Explain why you wrote the equation you did. a. direct variation b. inverse variation
Level 2, Unit 2 • Equations, Inequalities, and Linear Relationships
5
