Name: Class: Date: ID: A

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1 Name: Class: Date: 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA , MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Multiple Choice Identify the choice that best completes the statement or answers the question. 1 The table below shows the relationship between the length and the width of a rectangle. If the length of the rectangle is 10 inches, what is the width of the rectangle? A. 13 inches B. 21 inches C. 22 inches D. 29 inches 1

2 Name: 2 At an amusement park, the roller coaster rides are 5 tickets each, and the ferris wheel rides are 2 tickets each. The graph below shows the combination of rides that can be paid with 50 tickets. Based on this graph, which statement is TRUE? F. The range is discrete with an upper limit of 10 rides. G. The range is continuous with an upper limit of 10 rides. H. The domain is discrete with an upper limit of 10 rides. I. The domain is continuous with an upper limit of 10 rides. 2

3 Name: 3 Ray works at a grocery store. The table shows the relationship between the number of hours Ray works and the amount of money he earns. If this pattern continues, how much will Ray earn for working 10 hours? A. $50.00 B. $56.25 C. $62.50 D. $ The graph shows the distance a train traveled over time. Which inequality BEST represents the range of this function? F. G. H. I. 3

4 Name: 5 The graph shows the rate of descent of a parachutist after his parachute opened at an altitude of 3,500 feet. Based on the graph, which BEST represents the altitude of the parachutist 2.5 minutes after his parachute opened? A. 260 feet B. 800 feet C. 1,000 feet D. 1,340 feet 4

5 Name: 6 The linear graph below shows the number of grams of protein in different amounts of peanut butter. The slope of the line is Which statement BEST describes the meaning of the slope? F. There are 25 grams of protein in 5 tablespoons of peanut butter. G. There are 5 grams of protein in 25 tablespoons of peanut butter. H. There is 1 gram of protein in 5 tablespoons of peanut butter. I. There are 5 grams of protein in 5 tablespoons of peanut butter. 5

6 Name: 7 Which BEST represents the slope of the line shown below? A. B. C. D. 8 The graphed line passes through points and What is the slope of the line? F. G. H. I. 6

7 Name: 9 The graph below shows the number of tomatoes needed to prepare batches of spaghetti sauce. Which statement is TRUE according to this graph? A. Divide the number of tomatoes by 5 to find the number of batches they will yield. B. Divide the number of tomatoes by 8 to find the number of batches they will yield. C. Multiply the number of batches by 10 to find the number of tomatoes needed. D. Multiply the number of batches by 15 to find the number of tomatoes needed. 7

8 Name: 10 Paul had saved $120 to spend during his vacation this summer. The graph below shows his expenditures every day during his vacation. What part of the graph represents the point where Paul has used up all of his money? F. the y-intercept G. the x-intercept H. the length of the line I. the slope of the line 8

9 Name: 11 Mara started working after school and plans to save enough money to visit her cousin in New York within the next two years. The graph below shows Mara s savings per month. What does the y-intercept of the line segment represent? A. Mara had no money in savings when she began working. B. Mara had $50 dollars in savings when she started working. C. Mara saves $50 each month. D. Mara saves $300 each month. 9

10 Name: 12 Rayna paid a $200 fee to join a health club and then a $50 fee per month to use the club. The total amount of money (t) paid can be represented by the equation where m represents the number of months of club use. Nora paid a $100 fee to join another health club and then a $75 fee per month to use the club, which can be represented by the equation The graph below shows the fees paid by Rayna and Nora. In what month will both Rayna and Nora have paid an equal amount of money to their health clubs? F. Month 1 G. Month 3 H. Month 4 I. Month 5 10

11 Name: 13 Students in the 8th grade plan to sell printed T-shirts to raise funds. There will be a one-time fee of $45 for the print design. Printing each T-shirt will cost an additional $7. The T-shirts will be sold for $10 each. The table below shows the expected expenses and income. After selling how many T-shirts will the students start earning a profit? A. 10 B. 15 C. 20 D

12 Name: 14 Which graph BEST represents a system of equations with no solution? F. H. G. I. 12

13 Name: 15 The soccer team sold a total of 20 sandwiches at the game on Saturday. The selling price of a cheese sandwich was $2, and the selling price of a tuna sandwich was $4. The sandwich sales totaled $64. The graph below represents this information. Based on the graph, which statement BEST describes the y-intercept of Line n? A. If no cheese sandwiches were sold, then 20 tuna sandwiches were sold. B. If no tuna sandwiches were sold, then 20 cheese sandwiches were sold. C. If no cheese sandwiches were sold, then 16 tuna sandwiches were sold for $64. D. If no tuna sandwiches were sold, then 32 cheese sandwiches were sold for $64. 13

14 Name: 16 Sophie purchased 8 candles at a total cost of $32. The red candles cost $3 each and the silver candles cost $7 each. The equations and graph below can be used to determine the number of each type of candle Sophie purchased, where x represents the number of red candles and y represents the number of silver candles. Number of candles purchased: Total cost of candles: What is the number of red candles and silver candles Sophie purchased? F. 2 red candles, 6 silver candles G. 3 red candles, 5 silver candles H. 6 red candles, 2 silver candles I. 7 red candles, 1 silver candle 14

15 Name: 17 An Economics club holds a fundraiser selling school stickers. The graph below shows the profit, p, they will make if they sell a certain number of stickers, s. Which table matches the prediction modeled by the graph? A. C. B. D. 15

16 Name: 18 A phone company offers a monthly wireless phone plan of 900 minutes for $ Additional minutes cost $0.40 each. The graph shows the relationship between the cost and minutes offered by this plan. Which equation can be used to determine y, the cost for using x minutes per month when the minutes used exceed 900? F. y = G. H. I. 16

17 Name: 19 The graph below shows the number of calories in different amounts of steak. Which equation BEST represents this relationship? A. B. C. D. 20 Which equation describes the relationship between the values of x and y in the table below? F. G. H. I. 17

18 Name: 21 The table below shows the lengths, widths, perimeters, and areas of similar rectangles. Similar Rectangles Which equation can be used to represent the difference in the perimeters (p) of Rectangle S and Rectangle Q? A. B. C. D. 18

19 Name: 22 Richard put one 20-dollar bill in a shoebox the first week of summer for his savings. He added more bills every week. By the 4th week he had two 20-dollar bills, and by the 9th week he had three 20-dollar bills. Which graph shows the number of 20-dollar bills he saved in 9 weeks? F. H. G. I. 19

20 Name: 23 The table shows the cost of a taxicab ride for several driving distances. Which graph BEST represents the relationship between the cost and the distance? A. C. B. D. 20

21 Name: 24 A school bus was stopped for 2 minutes at a red light. When the light turned green, the driver accelerated the bus at a steady rate and then continued driving at a constant speed. Next to pick up students, the driver decreased the speed of the bus until it came to a full stop. Which graph below BEST represents the speed of the bus over the time described? F. H. G. I. 21

22 Name: 25 Which scenario BEST describes the graph shown below? A. An airplane is parked at a maintenance facility. B. A person on a bicycle rides at a constant speed. C. A train gradually gains speed when leaving a station. D. A truck gradually slows down and stops for the night. 22

23 Name: 26 A ball is thrown up in the air from 5 feet above the ground level. The ball reached a height of an additional 6 feet in 5 seconds, and then came down back to ground level in 4 more seconds. Which graph BEST represents the relationship between the height of the ball and the time? F. H. G. I. 23

24 GR 8 Advanced - Topic III Assessment TEACHER ANSWER KEY

25 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA , MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Answer Section MULTIPLE CHOICE 1 ANS: B A 13 is halfway between the 9 and the 17 B C 22 is too high; it is not halfway between 17 and 25 D 29 would be correct if 10 were halfway between 12 and 16 PTS: 1 DIF: L REF: Math OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data. STA: MA.8.A.1.1 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: F F G Chose a false statement because the range is discrete H Chose a false statement because the upper limit for the domain is 25, not 10 I Chose a false statement because the domain is discrete and the upper limit is 25 PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data. STA: MA.8.A.1.1 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF

26 3 ANS: C A B C D After 8 hrs After 9 hrs After 11 hrs PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data. STA: MA.8.A.1.1 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: H F G H I Domain and used the highest value on the x-axis Domain Used the highest value on the y-axis PTS: 1 DIF: L REF: Math OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data. STA: MA.8.A.1.1 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: B A B C D Used 3 seconds Used 2.25 seconds Used 2 seconds PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data. STA: MA.8.A.1.1 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF

27 6 ANS: F F G H Reverses meaning I Slope of 1 PTS: 1 DIF: H REF: Math OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. STA: MA.8.A.1.2 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MF ANS: B A B C D The slope is negative not positive PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. STA: MA.8.A.1.2 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MF ANS: I F G H I Negative of the slope Negative reciprocal of the slope Reciprocal of the slope PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. STA: MA.8.A.1.2 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MF

28 9 ANS: B A Used (40, 5) and interpreted it as dividing by 5 B C y-axis scale is 10 D Miscalculated PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. STA: MA.8.A.1.2 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MFIBM ANS: G PTS: 1 DIF: M REF: Topic III OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. STA: MA.8.A.1.2 linear equations. KEY: Webb: Low Grade 08 MSC: Extra Problem Bank 11 ANS: B PTS: 1 DIF: M REF: TOPIC III OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. STA: MA.8.A.1.2 linear equations. KEY: Webb: Low Grade 08 MSC: Extra Problem Bank 12 ANS: H F G H I Began in the same month Month before intersection Last month in graph PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations. STA: MA.8.A.1.3 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF

29 13 ANS: B A B C D Chose number from row just before income equals expenses Chose number from row just before income equals expenses Does not understand how to identify the unique solution for a system of equations PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations. STA: MA.8.A.1.3 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: I F G H I Chose pair of lines that will intercept because their slopes are not the same Confused parallel with perpendicular Chose both negative slopes PTS: 1 DIF: L REF: Math OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations. STA: MA.8.A.1.3 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MF ANS: C A B C D y-intercept of Line m x-intercept of Line m x-intercept of Line n PTS: 1 DIF: H REF: Math OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations. STA: MA.8.A.1.3 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF

30 16 ANS: H F G H I Inverted the abscissa and the ordinate = 8 total candles purchased = 8 candles purchased PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations. STA: MA.8.A.1.3 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: D A 2s + 20 is used instead of 2s 20 B The rate of change is used without subtracting the constant term of 20 C 20 2s is used instead of 2s 20 D PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. STA: MA.8.A.1.5 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: I F G H I Chose the equation to determine the minimum monthly cost when using up to 900 minutes The entire minimum monthly bill was multiplied by minutes used Added first 900 minutes again instead of subtracting PTS: 1 DIF: H REF: Math OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. STA: MA.8.A.1.5 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF

31 19 ANS: B A Reverses variables B C Reverses variables, the line goes up by 80 D The line goes up by 80 PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. STA: MA.8.A.1.5 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: F F G Fits x = 6 H Fits x = 3 I Fits x = 9 PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. STA: MA.8.A.1.5 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MF ANS: B A B C D Calculated difference in areas Calculated difference in perimeters of Rectangle S and Rectangle R Multiplied instead of adding length and width and multiplied 2 times area of Q PTS: 1 DIF: H REF: Math OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. STA: MA.8.A.1.5 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF

32 22 ANS: F F G Chose a linear relationship: y = 1 H Chose a linear relationship: y = x I Chose a linear relationship: x = 1 PTS: 1 DIF: L REF: Math OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. STA: MA.8.A.1.6 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: B A B C D Chose an increasing function but one that would not model the data Chose a gradually decreasing function but one that would not model the data Chose an increasing function but one that would not model the data PTS: 1 DIF: L REF: Math OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. STA: MA.8.A.1.6 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: F F G H I Did not take constant speed into consideration Did not take the acceleration into consideration Did not take the stop into consideration PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. STA: MA.8.A.1.6 linear equations. KEY: Webb: Low Grade 08 MSC: ItemCode: MF

33 25 ANS: D A B C D Graph would be horizontal line Graph would be a straight line, positive slope Graph would curve up PTS: 1 DIF: H REF: Math OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. STA: MA.8.A.1.6 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF ANS: F F G H I Did not consider the 5 ft starting height Consider the heights as mentioned in stem Stopped ball height at 5 ft instead of 0 ft PTS: 1 DIF: M REF: Math OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. STA: MA.8.A.1.6 linear equations. KEY: Webb: Moderate Grade 08 MSC: ItemCode: MF