6th Grade Class Play Handheld Games Total Students

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1 Mid term Exam 2: Direct Variation/Percent, Tip, and Tax Pre-Test 1. A recent survey on movies found that 1 out of 3 students like action films. a. Use the information to complete the table. Total Number of Students Students Who Like Action Films b. Graph the relationship. 2. Analyze the table, which shows the number of 6th graders from two classes who play handheld games. Determine if the relationship is proportional. 6th Grade Class Play Handheld Games Total Students Mrs. McKenna Mr. Rodriguez 26 30

2 3. Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning. 4. A restaurant bill is $ a. Estimate a 20% tip. b. Estimate a 15% tip. 5. Sneakers are normally $89.99 but are discounted to $ What percent of the original does Raymond pay? 6. Kimberly got 3 problems wrong on a test of 25 questions. What percent of the questions did she get correct? 7. One serving of pasta contains 210 calories. What percent of a 2000-calorie diet is contained in one serving of pasta? 8. Complete the table to show the interest earned for different savings principals, interest rates, and time periods. Principal Amount Saved (in dollars) Interest Rate Time (in years) Interest Earned (in dollars) 350 5% % % Post-Test 9. Analyze the table, which shows the number of students in two grades who play on two or more sports teams each year. Determine if the relationship is proportional.

3 Grade Two or More Sports Total Students The number of trees (n) that the average American uses in paper products varies directly with the time (t) in years. Assume that the constant of proportionality is 7. a. Write an equation representing the proportional relationship between n and t using the information given. b. How many trees does the average American use in 6 years? c. In how many years would an average American use 133 trees? d. What does the constant of proportionality represent in this problem? Mid-Chapter Test 11. Noah is planning a 240-mile driving trip. He wants to see how the time the trip will take him is related to his average speed. a. Complete the table. Using the relationship distance = rate time. Average Speed (miles per hour) Time (hours) b. Complete the graph by plotting the quantities from the table you completed. Connect the points on this graph.

4 c. Describe how the average speed affects the time. d. What is the ratio of the speed to the time? e. Does the time vary directly with the speed? Explain your reasoning. 12. A sweater is on sale for 75% of the original price of $44. Calculate the sale price. Solve for the unknown value using the equation for the constant of proportionality, 13. k = 0.3 and x = 65 Standardized Test Practice 14. Which of the following graphs shows a direct variation? a. c.

5 b. d.

6 erm Exam 2: Direct Variation/Percent, Tip, and Tax er Section 1. ANS: a. Total Number of Students Students Who Like Action Films b. PTS: 1 REF: 2.1 NAT: 7.RP.1 7.RP.2.a 7.RP.2.d KEY: direct variation (direct proportional) origin 2. ANS: No. The relationship is not proportional. The first ratio is, or. The second ratio is, or. PTS: 1 REF: 2.3 NAT: 7.RP.2.b 7.RP.2.c KEY: constant of proportionality 3. ANS: The graph shows a direct variation because the points fall on a straight line going through the origin. The constant of proportionality is because the ratio of the y-coordinate to the x-coordinate for each point is. PTS: 1 REF: 2.4 NAT: 7.RP.2.a 7.RP.2.b 7.RP.2.c 7.RP.3 4. ANS: a. The bill is about $85. So, a 20% tip would be about $85 divided by 5, which is $17. b. I first rounded the bill to $85. Next, I divided $85 by 10, which is $8.50. Then, I divided this amount in half, which is $4.25. Finally I added these two amounts together to calculate a reasonable 15% tip of $12.75.

7 PTS: 1 REF: 3.1 NAT: 7.RP.1 7.RP.3 5. ANS: Raymond would pay about 63% of the original price. PTS: 1 REF: 3.2 NAT: 7.RP.1 7.RP.2.c 7.RP.3 6. ANS: Kimberly got 88% of the questions correct. PTS: 1 REF: 3.2 NAT: 7.RP.1 7.RP.2.c 7.RP.3 7. ANS: One serving of pasta is 10.5% of a 2000-calorie diet. PTS: 1 REF: 3.2 NAT: 7.RP.1 7.RP.2.c 7.RP.3 8. ANS: Principal Amount Saved (in dollars) Interest Rate Time (in years) Interest Earned (in dollars)

8 350 5% % % % PTS: 1 REF: 3.4 NAT: 7.RP.2.a 7.RP.2.c 7.RP.3 KEY: interest depreciate principal simple interest percent increase percent decrease 9. ANS: Yes. The relationship is proportional because, or, of the 6th graders play two or more sports and, or, of the 7th graders play two or more sports. There is a constant of proportionality, PTS: 1 REF: 2.2 NAT: 7.RP.2.a TOP: Post Test 10. ANS: a. n = 7 t b. n = 7 t n = 7(6) n = 42 The average American uses 42 trees in 6 years. c. The average American uses 133 trees in 19 years. d. The constant of proportionality represents the number of trees that an average American uses in paper products per year, or. PTS: 1 REF: 2.6 NAT: 7.RP.2.0a 7.RP.2.b 7.RP.2.c TOP: Post Test 11. ANS: a. Average Speed (miles per hour) Time (hours)

9 b. c. As the average speed increases, the time decreases. The product of the average speed and the time is equal to 240, which represents the distance (240 miles). d. There is not one ratio because the ratio changes for each pair of values. e. No. The graph is a curve, not a straight line, and it does not go through the origin, so the two quantities do not vary directly. Also, there is no fixed ratio of time to speed. PTS: 1 REF: 2.2 NAT: 7.RP.2.a TOP: Mid Ch Test 12. ANS: The sale price is $33. PTS: 1 REF: 3.2 NAT: 7.RP.1 7.RP.2.c 7.RP.3 TOP: Mid Ch Test 13. ANS:

10 PTS: 1 REF: 2.3 NAT: 7.RP.2.b 7.RP.2.c TOP: Mid Ch Test KEY: constant of proportionality 14. ANS: D PTS: 1 REF: 2.2 NAT: 7.RP.2.a TOP: Standardized Test