8.F.2. Consider this graph of a line. 5/3/2017. Function is represented by the. Function 2 is represented by the table.

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1 Function is represented by the equation 5y 3x = 25. Function 2 is represented by the table. 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). x y Which statement about the two functions is true? A. The rate of change for Function 2 is half the rate of change for Function 1. B. The rate of change for Function 2 is twice the rate of change for Function 1. C. The rate of change for Function 2 is 5 times the rate of change for Function 1. D. The rate of change for Function 2 is the same as the rate of change for Function Rain is flowing into two containers at different rates. The figure below shows the volume of water in each container at different times. What is the difference in the rate of change between the two containers? A. 1 gallon per minute C. 5 gallon per minute 5 2 B. 3 gallon per minute D. 15 gallon per minute Consider this graph of a line. Which equation has a rate of change greater than the rate of change for the line shown? A. y = 3x 1 B. y = x C. y = 2x + 2 D. y = x Use the two functions below to answer the question. Which statement about the slopes of the functions is true? A. The slopes of both functions are negative. B. The slopes of both functions are positive. C. The slope of function A is negative and the slope of function B is positive. D. The slope of function A is positive and the slope of function B is negative. Function A is a linear function. Some values of Function A are shown in the table. Function A x 1 y Function B is a linear function with a y-intercept of 3 and an x-intercept of 5. Which statement is true? A. The slope of Function A is greater than the slope of Function B, and the y-intercept of Function A is greater than the y-intercept of Function B. B. The slope of Function A is less than the slope of Function B, and the y-intercept of Function A is greater than the y-intercept of Function B. C. The slope of Function A is greater than the slope of Function B, and the y-intercept of Function A is less than the y-intercept of Function B. D. The slope of Function A is less than the slope of Function B, and the y-intercept of Function A is less than the y-intercept of Function B

2 Consider Function 1 and Function 2. Function 1 Function 2 x y y = 2x What is the distance, in units, between the y- intercepts of the two functions? A. 6 units C. 8 units B. 7 units D. 9 units 7 Two functions are shown. Function A x 2 1 y Function B Select the box in each row to identify which function is described. Function A Function B function with the greatest rate of change function with the greatest initial value function that produces an output value of 25 when the input value is 6 8 Ryan and Taylor are both saving money to buy new video game equipment. Ryan s savings plan can be modeled by the function s = 15m + 50 where m represents the number of months since Ryan started his plan, and s represents the amount of money saved in dollars. The table shown represents Taylor s savings plan. Taylor s Savings Plan Number of Months Amount Saved ($) Select the options that correctly complete the sentences. Ryan s rate of change is Ryan s starting balance is less than greater than Taylor s rate of change. the same as less than greater than the same as Taylor s starting balance. 9 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 10 The graph shows the locations of an eagle s nest, a tree, and a pond. On the coordinate grid, each unit represents a mile. Which distance best represents the shortest distance from the pond to the tree? Round to the nearest tenth of a mile. A miles B miles C miles D miles 11 Two cars leave Jackson, Mississippi. One travels 8 miles north, and then 6 miles east. The second car travels 12 miles south and 9 miles west. The location of each car is shown on the graph. What is the distance, in miles, between the cars? A. 15 miles B. 20 miles C. 25 miles D. 35 miles 12 2

3 The points show different locations in Joe s town. Each unit represents 1 mile. Places in Joe s Town Find the shortest distance, in miles, between Joe s home and the park. Round your answer to the nearest tenth. Rectangle ABCD is shown. What is the length of side AB? A. 4 units B. 4 units C. 32 units D. 32 units Two points are shown on a coordinate plane. What is the distance between the two points? A. 2 B. 3 C. 4 D. 5 Stanley marked two points on the grid below to show the locations of the fiction section, point F, and the travel section, point T, in a bookstore. Bookstore What is the shortest distance, in units, between the fiction section and the travel section in the bookstore? A. 146 B. 242 C. 16 D The points ( 3, 1) and ( 3, 5) are adjacent vertices of a rectangle. Two of the sides of the rectangle have a length of 8 units. What is the length of a diagonal of the rectangle? A. 9 units B. 10 units C. 12 units D. 14 units Consider the figure shown. What is the approximate perimeter of the figure, in units? A units B. 27 units C units D. 54 units

4 Consider the line segment shown with coordinates A( 4, 2) and B(4, 4). What is the length of the line segment AB, in units? A. 6 units B. 8 units C. 10 units D. 14 units 8.EE.7 a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. b. Solve linear equations and inequalities with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms Beth was given the equation 2 6x + 3 = 3(4x + 3). Select the options that correctly complete the sentences. 6x + 6 8x + 5 She simplified 2 6x + 3 to and 4x + 9 7x + 6 3(4x + 3) to. 12x x x x + 6 infinite solutions no solution She determined the equation had. a solution of 1 a solution of 0 21 A student s work to solve an equation is shown. 1 40x + 16 = 9x 7 2x x + 2 = 9x 14x x + 2 = 5x = 2 Select the options that make the following statements true. The student solve the equation correctly incorrectly no solution because the original equation has one solution. infinitely many solutions 22 Andre has $44. He must save at least $120 plus 7% sales tax to buy an electronic tablet. If he saves half the $15 he makes each week, after how many weeks will he have enough money to buy the tablet? A. 5 weeks B. 6 weeks C. 11 weeks D. 12 weeks An equation is shown below. 3.2 x = 2.4x x Which of the following statements describe a step that can be used to find the value of x? Select all that apply. A. Add like terms on the right side of the equation. B. Add 3.2x to both sides of the equation. C. Use the distributive property to expand the left side of the equation. D. Subtract 3.2x from both sides of the equation. E. Divide 3.8 from both sides of the equation

5 Which equation has infinitely many solutions? A. x = 1 4 x B. 1 3 x 5 = 2 3 x 5 C x = 2x 3 D. 3 4x = x 1 2 Robin simplified a linear equation with the variable x and got 3 = 5 as a result. Which statement is true about the linear equation? A. The linear equation has infinite solutions because the simplified equation has no variable and has constants that are not equal. B. The linear equation has a solution of 0 because the simplified equation has no variable. C. The linear equation has solutions of 3 and 5 because those are the values remaining. D. The linear equation has no solution because the simplified equation has no variable and has constants that are not equal Consider the inequality shown x + 4 < 5x What is the solution to the inequality? A. x > 4 7 C. x > 7 4 What is the solution to the inequality x 8 > 2 5 A. x > 2 5 B. x < 2 5 C. x > 5 2 2x x? B. x < 4 7 D. x < 7 4 D. x < In WXY, WY is congruent to XY. The perimeter of WXY is 76 inches. 8.F.4 How many inches long is WX? Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or the two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the its graph or a table of values

6 The graph shows the relationship between the value of a car, in dollars, after t years. Which statements are true about the relationship? Select all that apply. A. After 10 years, the car is worth $0. B. The value of the car increases by $1,200 each year. C. The value of the car decreases by $1,200 each year. D. The value of the car when it was brand new was $16,000. E. The relationship can be modeled by the linear function V = 1,200t + 16, The table shows the amount of money, in dollars, Tasha has after purchasing a certain number of songs. Each song costs the same amount. Number of Songs Amount of Money Tasha Has ($) Fill in the blanks with the correct values. According to the table, Tasha initially had $ before purchasing songs, and the cost of each song was $. 32 The relationship between the number of miles for a taxi ride and the cost in dollars for the taxi ride is shown in the table below. Number of Miles (x) Cost in dollars (y) Determine whether each statement about the function is true or false. Select the correct cell in each row. Statement True False The function is linear. The rate of change is 3. The y intercept is 3.5. Match each pair of points with the equation that models their linear relationship. y = x + 3 y = 1 3 x + 4 y = 2 x , 3, (0, 4) 3, 4, ( 3, 0) 4, 3, (0, 3) What is the initial y value of the function that models the relationship between the points (3, 0) and (8, 35)? A. 21 B. 11 C. 3 7 D. 2 7 The table below shows the cost of different numbers of goldfish at a pet store. COST OF GOLDFISH Number of Goldfish Cost 5 $ $ $ $6.00 The cost is a linear function of the number of goldfish. Which statement describes the rate of change of this function? A. The cost increases $0.30 each time 1 goldfish is added. B. The cost increases $1.50 each time 1 goldfish is added. C. The cost increases $3.00 each time 5 goldfish are added. D. The cost increases $6.00 each time 5 goldfish are added

7 For a few months, Dexter recorded the amounts, in fluid ounces, of laundry detergent remaining, y, after he and his family washed x loads of laundry. The equation of the line for his data is shown below. y = 1. 6x + 50 Which statement correctly describes the slope of Dexter s equation in the context of the situation? A. The bottle Dexter s family buys holds about 50 fluid ounces of detergent. B. For each load of laundry, Dexter s family uses about 1.6 fluid ounces of detergent. C. With 50 fluid ounces of detergent, Dexter s family can wash about 1.6 loads of laundry. D. With 1.6 bottles of detergent, Dexter s family can wash about 50 loads of laundry. 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear Which table represents a linear function? Parker states that any function written without exponents must be linear. Which function proves Parker s statement is incorrect? A. y = 5x + 3 B. y = x C. y = x D. y = x A relationship between x and y is defined by the equation y = 4 x + 1, where x is the input and 3 3 y is the output. Which statements about the relationships are true? Select each correct statement. A. y is a function of x. B. The graph of the relationship is a line. C. When the input is 3, the output is 4. D. When the input is 2, the output is 3. E. The y-intercept of the relationship is (0, 1). Which equation is not a linear function? A. y = xy + 2 B. y = x + 2y C. y = x y 2 D. y = x y

8 Select the box in each row to identify if each question is Linear or Not Linear. Linear Not Linear 4 + y = 2x x = x 2x 2 + x 5 = 3x + 2x 2 y 2 = 2(x 5) Which equations represent linear functions? Select all that apply. A. y = x 2 B. x = y C. y = 1 4 x2 + 4 D. 6x 3y = 12 E. y = 2x y = 2 x Student Dillon Faye Jeff Lana The table shows the coordinates of a function. When asked if the function is linear and why, four students respond, as shown. Response It is a linear function because it has a constant rate of change. It is a nonlinear function because it does not have a constant rate of change. It is a linear function because as x increases, the value of y increases. Which student s response best describes the function in the table? A. Dillon C. Jeff B. Faye D. Lana x y It is a nonlinear function because as x increases, the value of y decreases F.5 Describe qualitatively the functional relationship between the two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 46 The graph of a function is shown on the coordinate plane. Which statements are true? Select all that apply. A. The function is linear between x = 2 and x = 4. B. The function is linear between x = 6 and x = 8. C. The function is decreasing between x = 9 and x = 6. D. The function is increasing and linear between x = 4 and x = 1. E. The function is decreasing and nonlinear between x = 1 and x = A graph is shown. Select the options that correctly complete the sentences. When x is between 4 and 1, the function is increasing. decreasing. neither increasing nor decreasing. When x is between 1 and 5, the function increasing is decreasing. neither increasing nor decreasing 48 8

9 Donna rode her bike for three miles. She traveled 18 miles per hour the first mile, 15 miles per hour the second mile, and 21 miles per hour the third mile. Which diagram shows the most likely landscape of Donna s bike ride? Curt jogged on a path that was 2 miles long, took a break, and then jogged back along the same path to where he started. He jogged at different speeds for different distances along the path as shown in the graph. Between which times did Curt jog the fastest? A. 0 minutes and 10 minutes B. 10 minutes and 25 minutes C. 25 minutes and 30 minutes D. 30 minutes and 60 minutes A weather station recorded the amount of rain that fell during an 8-hour time frame using a rain gauge. The findings are recorded in the graph below. Between which hours was the rate at which the rain fell greater than the rate at which the rain fell between hours 0 and 1? A. between hours 1 and 4 B. between hours 4 and 5 C. between hours 5 and 6 D. between hours 7 and 8 The graph shows y as a function of x. For which intervals is the function decreasing? Select all that apply. A. 7 < x < 3 B. 3 < x < 1 C. 1 < x < 1 D. 1 < x < 3 E. 3 < x < 5 F. 5 < x < At the end of last year, Andrew has saved $1,800. At the start of that year, his savings were $400. He then saved $200 every month for five months. For the next three months, he did not save any money. In the last four minutes, he saved an equal amount each month. Which graph correctly represents this situation? Mr. Jones filled his swimming pool with water. Mr. Jones began filling the pool at a constant rate. He turned off the water for a while. He then turned the water back on at a slower constant rate. Mr. Jones turned off the water again for a while. He then turned the water back on at the first rate. Which graph best represents Mr. Jones filling the pool?

10 Which set of ordered pairs can be plotted on the graph so that the graph continues to represent a function? 8.F.1 Understand that a function is a rule that assigns each input to exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. A. 3, 2, 2, 5, 4, 5 B. 0, 0, 2, 0, (8, 0) C. 1, 1, 3, 4, (6, 2) D. 1, 1, 6, 1, (7, 1) Review the table shown here. Input Output Which statement best explains why the data in the table above does not represent a function? A. Each input has only one output. B. Each output has only one input. C. One input has more than one output. D. One output has more than one input. The graph of a nonlinear function is shown on the coordinate plane. In the graph, y is a function of x. When the input of the function is 4, what is the output of the function? A. 5 B. 1 C. 1 D Which represents the ordered pairs of a function? Select ALL that apply. A. 0, 0, 1, 1, 1, 2, 2, 2 B. { 0, 3, 0, 3, 1, 4, 1, 4 } C. { 1, 3, 3, 1, 2, 4, 5, 4 } D. { 1, 0, 1, 2, 1, 1 3, 1, 1 4 } E. { 0, 3, 1, 1 3, 2, 4, 3, 1 4 } 59 A relation R exists such that for every input (x), the output is x. Which statement about the relation R is correct? A. The relation R is not a function because there is at least one output for each input. B. The relation R is not a function because there is more than one output for each input. C. The relation R is a function because the output is the opposite of the input. D. The relation R is a function because for each input there is exactly one output

11 Consider the graph of the function. Which table does not represent a function? What integer represents the output of this function for an input of 2? A. 2 B. 2 C. 4 D A. x y C B. x y D x y x y The table shows the locations of five points on the coordinate plane. Point Location E (4, 11) F ( 4, 9) G (3, 11) H (0, 9) I (4, 9) Removing which point will allow the table to represent a function? A. Point F B. Point G C. Point H D. Point I A function is a rule that assigns to each input exactly one output. In a graph, the input is the x value, and the output is the y value. Which graph does not represent a function? A. C. B. D Select the box in each row to identify the number as rational or irrational. Rational Irrational 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number, π

12 Which values are irrational? Select all that apply. A. 4π B C. 1 3 D. 2 E Which decimal is equivalent to 6 11? A B C D Which statement explains why 30 is considered an irrational number? A. When evaluated, 30 results in a repeating decimal, which is considered an irrational number. B. When evaluated, 30 results in a terminating decimal, which is considered an irrational number. C. When evaluated, 30 results in a nonterminating and nonrepeating decimal, which is considered an irrational number. D. When evaluated, 30 results in a whole number, which is considered an irrational number. Which fraction is equivalent to 0. 45? A B C. 4 9 D Is 196 rational or irrational, and why? A. The value is irrational because all square roots represent irrational numbers. B. The value is rational because all square roots represent rational numbers. C. The value is irrational because 196 can be simplified to 14, which is irrational. D. The value is rational because 196 can be simplified to 14, which is rational. Consider the values shown. 6.3, 4π, 12, 1, 3, 7. 89, Which table shows the values correctly sorted? A. C. B. D

13 The mass of Earth is kilograms, and the mass of Venus is kilograms. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. Which mass is closest to the difference between the mass of Earth and the mass of Venus? A kg B kg C kg D kg Which of the following equations are true? Select all that apply. A = B. = C = D. = E = Approximately gallons of water flow over a waterfall each second. There are seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day. A B C D The erosion rate along a section of the coast is approximately 3 feet per year. Which of these best approximates this rate of erosion? A inches per day B inches per month C feet per day D feet per month There were approximately pieces of mail processed by the United States Postal Service in This is about 75% of the number of pieces of mail processed in Approximately how many pieces of mail were processed by the United States Postal Service in 2006? A B C D

14 Clarence is finding a quotient using a calculator. Which value represents the quotient when is divided by ? A. 0.2E-5 B. 0.2E-4 C. 5E+3 D. 5E+4 The combined volume of all the tanks at an aquarium is gallons. The aquarium plans to install a new dolphin tank with a volume of 250,000 gallons. What will be the total volume of all of the tanks at the aquarium after the new dolphin tank is installed? A B C D EE.6 Use similar triangles to explain why slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Triangles ABC and CDE are shown on the coordinate plane. Select the options that correctly complete the sentence. The slope of line segment AC is equal to the slope of line segment CE because the ratio of AB to BC AB to AC BC to CE is equal to CD to AE CD to DE CE to DE Line m and triangle PQR are shown on the graph below. Greg is creating triangle JKL to be similar to triangle PQR. Each side of triangle JKL is parallel to one side of triangle PQR. Select all points that could be the location of point L. A. 2, 0 D. (2, 3) B. 1, 1.5 E. (2.5, 3.5) C. (0, 0) F. (5.5, 8) Consider the graph of the line. What is the equation of the line? A. y = 3 4 x + 6 B. y = 3 4 x 8 C. y = 4 3 x + 6 D. y = 4 3 x

15 Two triangles are shown on the coordinate plane. Which statement regarding the triangles is correct? A. The area of the small triangle is half the area of the large triangle. B. The perimeter of the small triangle is half the perimeter of the large triangle. C. The slope of one hypotenuse is equal to the opposite reciprocal of the other. D. The slopes of the two hypotenuses are equal. Which statement is true regarding the line y = 4x + 13? A. The line has a slope of 13. B. The line has a slope of 4. C. The line passes through the point (0, 13). D. The line passes through the point (0, 4) Use the graph below to answer the question. Which equation represents a line that passes through points A and B plotted on the graph? A. y = 4 3 x B. y = 3 4 x C. y = 3 4 x D. y = 4 3 x A line contains the points (4, 2) and 0, 1. What is the equation of the line? A. y = 2x 6 B. y = 3 4 x 1 C. y = 1 4 x + 1 D. y = 4 3 x A triangle PQR is formed by arranging three squares as shown. 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. If triangle PQR is a right triangle, which statement must be true? A. Area of square Z = area of square X + area of square Y B. Perimeter of square Z = perimeter of square X + perimeter of square Y C. Area of square X = area of square Y + area of square Z D. Perimeter of square X = perimeter of square Y + perimeter of square Z

16 Ranee is creating a diagram to prove that a certain triangle is a right triangle. In her diagram she uses three white quadrilaterals that are squares. Which diagram could be the one that Ranee is creating? The figure shows a square formed by joining four congruent right triangles. For the figure, Kevin calculated the area of square ABCD as k units squared, the area of square PQRS as m units squared, and the area of triangle AQP as n units squared. How should Kevin relate his calculations to prove the Pythagorean Theorem? A. k = m + n B. m = k + n C. k = m + 4n D. m = k + 4n Tonya used side lengths a, b,and c to make different triangles. When Tonya only changed the length of side c, she noticed patterns with the side lengths used and the types of triangles formed. Which statement is true from Tonya s investigation? A. If the length of side c is equal to a 2 + b 2, the triangle formed is a right triangle. B. If the length of side c is equal to 2a + 2b, the triangle formed is a right triangle. C. If the length of side c is equal to a 2 b 2, the triangle formed is a right triangle. D. If the length of side c is equal to 2a 2b, the triangle formed is a right triangle. 93 A triangle is formed with side lengths of 24 centimeters, 26 centimeters, and 10 centimeters. Is the triangle a right triangle? A. The triangle is a right triangle because = B. The triangle is a right triangle because = 2(10). C. The triangle is not a right triangle because = D. The triangle is not a right triangle because =

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