8th Grade Pre-Algebra

Transcription

1 8th Grade Pre-Algebra Multiple Choice Identif the choice that best completes the statement or answers the question.. Kell is learning about rational and irrational numbers. What conclusion can she draw about the number ? It is rational because it repeats. It is rational because it terminates. It is irrational because it neither repeats nor terminates. It is irrational because it repeats.. What rational number has as its decimal equivalent?. Pierre worked hours toda. What is the decimal equivalent of?. Which of these expressions is true? 5. In a right triangle, the length of one leg is s. The length of the other leg is times as long as s, or. The length of the hpotenuse is twice the length of the shorter leg s, or s. Estimate the length of the hpotenuse if the longer leg is units long..7 units units 8 units. units. Which whole number is the best approximation for? Explain. because is a little more than. 7 because is between.5 and 7.

2 5 because squares and square roots are inverse operations. because the square root of 8 is a little less than. 7. What is the relationship between and? The relationship cannot be determine 8. Between which pair of decimals does fall on a number line? Between. and. Between. and.5 Between. and.7 Between.8 and.9 9. Describe and give the value of. Irrational, Irrational, Not a real number Rational, 0. Find a rational number between and..5. Evaluate.. Colin has a square garden with an area of 97 square feet. What is the length of each side of the garden? 0 ft ft ft ft. Explain how to use the properties of exponents to write an equivalent expression for.

3 Multipl powers, both with a base of. One has an exponent of, and the other. Add powers, both with a base of. One has an exponent of, and the other. Multipl times a power with a base of and exponent of. Add to square. Use properties of exponents to write an equivalent expression for. 5. What is written in scientific notation?. What is written in standard notation? 7. Which is the product of in scientific notation? 8. In 00, the population of the Dominican Republic was about. The population of Haiti was about. About how much more was the population of Haiti than the Dominican Republic? 9. Which is the product of in scientific notation? 0. The graph shows a proportional relationship. Use the graph to identif the unit rate.

4 Cost (dollars) Distance (km) d t (hours) 0 hours per kilometer 0 kilometers per hour 0 kilometers per hour kilometers per hour. The graph shows the proportional relationship between the cost and the length for two different brands of coaxial cable. What is the unit rate for each brand? Which brand is more expensive? C 0 8 Brand A Brand B 5 l Length (m) Brand A: $.75 per meter; Brand B: $.5 per meter; Brand B Brand A: $.5 per meter; Brand B: $.50 per meter; Brand A Brand A: $.00 per meter; Brand B: $.50 per meter; Brand A Brand A:.5 meters per dollar; Brand B:.5 meters per dollar; Brand B. The number of pages p that a laser printer prints is proportional to the printing time t, in minutes. Printer A prints 0 pages in minutes. The table shows the relationship between the amount of time and the number of pages printed for printer B. Which printer prints more slowl? Pages (minutes) printed 8

5 Printer A Printer B Printer A and printer B have the same unit rate. The relationship cannot be determine. The graph shows the relationship between the number of hours h Greg has been driving and the total distance d he has traveled, in miles d h Which statement is true? Greg is traveling at 90 miles per hour. Greg is traveling at 0 miles per hour. To find Greg s rate of speed, multipl the total number of hours driven b the total distance. To find Greg s rate of speed, divide the total number of hours driven b the total distance.. The graph shows the relationship between the number of hours h Bree has been hiking and the total distance d she has traveled, in kilometers d h Which statement is true? The slope of the line is 8. The slope of the line is.

6 Cost (dollars) To find the slope of the line, ou could divide the total number of hours hiked b the total distance. To find the slope of the line, ou could multipl the total number of hours hiked b the total distance. 5. The graph shows the proportional relationship between the cost and the length for two different brands of coaxial cable. What is the unit rate for each brand? Which brand is more expensive? C 0 8 Brand A Brand B 5 l Length (m) Brand A: $.75 per meter; Brand B: $.5 per meter; Brand B Brand A: $.5 per meter; Brand B: $.50 per meter; Brand A Brand A: $.00 per meter; Brand B: $.50 per meter; Brand A Brand A:.5 meters per dollar; Brand B:.5 meters per dollar; Brand B. The number of pages p that a laser printer prints is proportional to the printing time t, in minutes. Printer A prints 0 pages in minutes. The table shows the relationship between the amount of time and the number of pages printed for printer B. Which printer prints more slowl? (minutes) Pages printed Printer A Printer B Printer A and printer B have the same unit rate. The relationship cannot be determine 7. The cost C, in dollars, for advertising on a social networking website is proportional to the number n of clicks on the advertisement. Suppose a business is charged $5 for 80 clicks on its advertisements. What is the slope of the line that represents the relationship between cost and clicks? 0.5 The slope cannot be determine

7 8. Carlita goes jogging, and her GPS collects the data for her distance over time. What would the rate of change for that data represent? Carlita s distance from home Carlita s starting point Carlita s distance over time, or speed Carlita s time since she left home 9. What equation could be written for this table? 0. What is the direct variation equation for the data in the table?. Lamar starts his own painting business. He pas for some supplies to begin, and then charges a fixed amount per room. The graph shows a linear function that models Lamar s profit per room x What does the initial value represent? The number of rooms he paints The amount he charges per room The amount he spends in supplies The amount of profit he makes per room. A bathtub filled with 0 gallons of water drains at an average rate of gallons per minute. What is the rate of change and initial value of the linear function that models the amount of water in the bathtub after it starts draining? The rate of change is 0 gallons per minute, and the initial value is gallons.

8 Distance (miles) The rate of change is gallons per minute, and the initial value is 0 gallons. The rate of change is gallons per minute, and the initial value is 0 gallons. The rate of change is gallons per minute, and the initial value is gallons.. The graph shows the distance d, in miles, that Joe can drive his car using rate of change in this situation? gallons of gasoline. What is the 00 d g Gasoline (gallons) 0 miles per gallon of gasoline 5 miles per gallon of gasoline 0 miles per gallon of gasoline 5 miles per gallon of gasoline. George is selling sandwiches at a deli. The table shows the average number s of sandwiches he sells over time, in minutes. What linear function is represented b the table? (minutes) Sandwiches sold You observe that the line shown below passes through the point and has a slope of. You choose as an arbitrar point on the line other than and use the fact that the slope of a line is constant to write which equation?

9 x. Maa sketches a graph of a linear function. Which graph might she have sketched? x x

10 x x 7. Which is a linear equation? 8. Which of these functions is a linear function? 9. Which graph represents a linear function? x x

11 x x 0. Three lines are drawn to form the right triangle below. The equation for the hpotenuse is equation for the longer leg is, and the equation for the shorter leg is. Which of these equations, if an, does not represent a linear function?, the x The equation for the hpotenuse does not represent a linear function. The equation for the longer leg does not represent a linear function. The equation for the shorter leg does not represent a linear function. Each of the equations represents a linear function.. What equation could be written for this table?. Which equation represents the values in the table?

12 . Which equation describes w?. What equation could be written for this table? 5. What equation could be written for this table? x 0 0. Which equation represents the values in the table? x Which is the rule for the function table? 8. Mariana is 0 ears old and has grown 7 inches in ears. When she was 8 ears old, she was 5 inches tall. Mariana writes and graphs a function that models her height in inches over time in ears. What is the initial value for this function?

13 Height (cm) Lamar starts his own painting business. He pas for some supplies to begin, and then charges a fixed amount per room. The graph shows a linear function that models Lamar s profit per room x What does the initial value represent? The number of rooms he paints The amount he charges per room The amount he spends in supplies The amount of profit he makes per room 50. The graph shows the relationship between a candle s height h, in centimeters, and time t, in hours, as the candle burns. What function models this relationship? 0 h t (hours)

14 5. Vincent s savings over several weeks are shown in the table. If a linear function models Vincent s savings over time, how much mone did he initiall have? (weeks) Savings (dollars) Lnn is walking from her house to the grocer store. The table shows the distance she has left to walk. What is the rate of change for the linear function represented b the table? (minutes) Distance (blocks) blocks per minute block per minute block per minute blocks per minute 5. George is selling sandwiches at a deli. The table shows the average number s of sandwiches he sells over time, in minutes. What linear function is represented b the table? (minutes) Sandwiches sold One kilometer is equal to 0. miles. Which best describes the relatinship between miles and kilometers?

15 Amount Earned ($) Cost linear and proportional relationship non-linear relationship linear, non-propotional relationship 55. The formula for the area of a circle is. Which best describes the relationship between the area and radius of a circle? linear and proportional relationship non-linear relationship linear, non-propotional relationship 5. The graph shows the cost per hour of renting a powertool x Hours Which of the following best describes the relatinship between cost and the number of hours? linear and proportional relationship non-linear relationship linear, non-propotional relationship 57. The graph shows the amount earned and the hours worke x Hours Worked Which of the following best describes the relatinship between the amount earned and the number of hours worked? linear and proportional relationship non-linear relationship linear, non-propotional relationship 58. Which of the statements is true about the data displaed in the scatter plot?

16 It shows a positive correlation. It shows no correlation. It shows a negative correlation. As speed increases, cost decreases. 59. Which statement best describes the pattern of association between the variables and shown in the scatter plot? x There is a positive, linear association between the two variables. There is a negative, linear association between the two variables. There is a positive, nonlinear association between the two variables. There is no association between the two variables. 0. Which statement best describes an clusters there are in the data displaed in the scatter plot shown? x The data cluster around.

17 The data cluster around. The data cluster around and. There are no clusters.. Maa sketches a graph of a linear function. Which graph might she have sketched? x x x x. Which of the following equations is not linear?. Which equation does not represent a linear function?

18 . Three lines are drawn to form the right triangle below. The equation for the hpotenuse is equation for the longer leg is, and the equation for the shorter leg is. Which of these equations, if an, does not represent a linear function?, the x The equation for the hpotenuse does not represent a linear function. The equation for the longer leg does not represent a linear function. The equation for the shorter leg does not represent a linear function. Each of the equations represents a linear function. 5. What equation could be written for this table?. What equation could be written for this table? 7. Which equation represents the values in the table?

19 Height (cm) 8. Which equation describes w? 9. Which equation is graphed? 70. What is the direct variation equation for the data in the table? 7. The graph shows the relationship between a candle s height h, in centimeters, and time t, in hours, as the candle burns. What function models this relationship? 0 h t (hours)

20 Distance from home Distance from home Distance from home Distance from home 7. Vincent s savings over several weeks are shown in the table. If a linear function models Vincent s savings over time, how much mone did he initiall have? (weeks) Savings (dollars) Gloria drives her daughter to school in the morning and then comes back home. She stas home until she has to go to pick up her daughter from school, and then the both return home again. Which graph best shows the situation? 7. Which situation is best represented b the graph?

21 Distance from home Distance from home Distance from home Distance from home Speed A swimmer starts at a stead pace, slows down to a stop, and then starts up swimming again, but at a slower pace than when she first starte After a ball is thrown into the air, it falls back to the ground and bounces. An airplane starts slowl on the runwa, and then quickl takes off before finding a nice cruising spee A car starts on flat ground and drives quickl up a hill, and then it keeps driving. 75. Gloria drives her daughter to school in the morning and then comes back home. She stas home until she has to go to pick up her daughter from school, and then the both return home again. Which graph best shows the situation? 7. Which statement best tells the stor of the graph?

22 A car slowed down to a stop. A car maintained constant spee A car started from a stop. A car stopped and then starte 77. Which graph corresponds to the temperature in an oven that is turned on to bake a loaf of bread then turned off when the bread is done? 78. Which of the following situations corresponds to this graph? A car accelerates from a stop, travels at a constant speed, slows, and then travels at a slower spee An airplane travels at a constant speed then decelerates to a slower spee An athlete warms up b walking around the track, runs, then jogs. A bicclist accelerates, travels at a constant speed, then slows to a stop. 79. Which of the following situations corresponds to this graph?

23 An object is lifted slowl, then lowered slowl. A car accelerates from a stop, then graduall stops. An object starts falling, accelerates, and then falls slowl. An airplane climbs to 9,000 feet, then descends. 80. In the graph of the function, for what values of is increasing? x Between and Between and Between and The function is never increasing. 8. What words best describe the function whose graph is shown? x Increasing and linear Increasing and nonlinear

24 Decreasing and linear Decreasing and nonlinear 8. Which graph represents a function that is alwas decreasing between and? x x x x 8. What segment of the graph shows the function having a constant value? x

25 8. Which of these functions is not a linear function? 85. Which of these functions is not a linear function? 8. Which of these functions is not a linear function? 87. Use the graph to explain wh is or is not a function of. (, ) (, ) x (, ) (, ) is a function of because both and have the same -coordinate. is a function of because for each -coordinate, there is exactl one -coordinate. is not a function of because both and have the same -coordinate. is not a function of because for each -coordinate, there is exactl one -coordinate. 88. Does the table below represent a function? Explain wh or wh not. Input Output 0 0

26 Yes, because each input has exactl one output assigned to it. Yes, because the inputs and outputs are integers. No, because there are positive inputs that have negative outputs and there are negative inputs that have positive outputs. No, because there are inputs that have more than one output assigned to them. 89. Carlita goes jogging, and her GPS collects the data for her distance over time. What would the rate of change for that data represent? Carlita s distance from home Carlita s starting point Carlita s distance over time, or speed Carlita s time since she left home 90. What equation could be written for this table? 9. Which equation describes w? 9. What equation could be written for this table? 9. What is the direct variation equation for the data in the table?

27 9. Which equation represents the values in the table? x Choose the equation that is represented b the data in the table. 9. Mariana is 0 ears old and has grown 7 inches in ears. When she was 8 ears old, she was 5 inches tall. Mariana writes and graphs a function that models her height in inches over time in ears. What is the initial value for this function? Vincent s savings over several weeks are shown in the table. If a linear function models Vincent s savings over time, how much mone did he initiall have? (weeks) Savings (dollars) The graph shows the distance d, in miles, that Joe can drive his car using rate of change in this situation? gallons of gasoline. What is the

28 Distance (miles) 00 d g Gasoline (gallons) 0 miles per gallon of gasoline 5 miles per gallon of gasoline 0 miles per gallon of gasoline 5 miles per gallon of gasoline 99. Lnn is walking from her house to the grocer store. The table shows the distance she has left to walk. What is the rate of change for the linear function represented b the table? (minutes) Distance (blocks) blocks per minute block per minute block per minute blocks per minute 00. Mariana is 0 ears old and has grown 7 inches in ears. When she was 8 ears old, she was 5 inches tall. Mariana writes and graphs a function that models her height in inches over time in ears. What is the initial value for this function? Multiple Response Identif one or more choices that best complete the statement or answer the question.. Which of the following rational numbers fall between and on a number line?

29 e. f.. A compan can hire new emploees. There are applicants. Which of the following rational numbers represent the ratio of applicants to available positions?.5 e. f.. Which of the following numbers fall between.7 and.8 on a number line? e. f.. Suppose each irrational number below is approximated b the whole number to which it is closest. Which of the irrational numbers have whole-number approximations that are even? e. f. 5. For which values of x is the expression irrational?

30 e. 5. Which of the following expressions are equivalent to? e. f. 7. Which of the following statements are true? is times as great as. is times as great as. is times as great as. is times as great as. e. is times as great as. f. is times as great as. 8. Identif all of the following values that are equivalent to. e. f. 9. Which of the following proportional situations can be represented with this graph?

31 Cost (dollars) 00 C n Number of Items pairs of headphones cost $. carrots cost $. packs of D batteries cost $8. bags of apples cost $. e. jigsaw puzzles cost $0. 0. Which of the following sets of ordered pairs represent as a function of? e. f. Short Answer. Use the properties of exponents to write an expression using four 8s that equals 8.. Julie is making muffins for a bake sale. It takes her 0 minutes to make a dozen muffins. Tim had alread made muffins, which he adds to the amount Julie makes. Write a linear function that models the number m of muffins based on the time, in hours, that Julie spends baking. Describe what the rate of change and initial value mean in this situation.. Find the slope of the line that passes through the points and.. Find the slope-intercept form of the line that passes through the point and has a slope of. 5. Can a function assign multiple inputs to the same output? Explain wh or wh not