Alliance for College-Ready Public Schools

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1 Alliance for College-Ready Public Schools Version 2 Alliance Summative IM1 CMP AND IMP Teacher Rationale

2 About the Teacher Rationale This document contains the specific definitions for the Version 2 Alliance Summative IM1 CMP AND IMP assessment. This includes: (a) (b) (c) (d) The item number as it appears on the assessment. The item. The standard, standard description, and Depth of Knowledge (DOK) level of the item. The correct answer and rationale for each incorrect response for each multiple-choice item and scoring rubric for each short constructed response or constructed response item. These specifications have been included to help you look for consistencies in student errors, and the specific cause of the student error in turn, this should help guide your intervention and reteach strategies.

3 Test Definition File Item # Correct Answer(s) Standard 1 B CCSS.Math.Content.HSA-REI.D.12 2 See Scoring Rubric CCSS.Math.Content.HSA-CED.A.3 3 C CCSS.Math.Content.HSA-REI.B.3 4 See Scoring Rubric CCSS.Math.Content.HSF-IF.B.6 5 D CCSS.Math.Content.HSF-IF.B.4 6 B CCSS.Math.Content.HSG-CO.B.7 7 See Scoring Rubric CCSS.Math.Content.HSA-REI.B.3 8 D CCSS.Math.Content.HSN-Q.A.1 9 See Scoring Rubric CCSS.Math.Content.HSA-REI.D C CCSS.Math.Content.HSN-Q.A.1 11 See Scoring Rubric CCSS.Math.Content.HSA-CED.A.2 12 A CCSS.Math.Content.HSG-CO.B.6 13 C CCSS.Math.Content.HSF-IF.A.3 14 See Scoring Rubric CCSS.Math.Content.HSF-IF.A.1 15 B CCSS.Math.Content.HSA-REI.B.3 16 See Scoring Rubric CCSS.Math.Content.HSA-CED.A.1 17 A CCSS.Math.Content.HSA-CED.A.1 18 A CCSS.Math.Content.HSA-CED.A.3 19 A CCSS.Math.Content.HSF-IF.A.1 20 A CCSS.Math.Content.HSA-SSE.A.1.a 21 A CCSS.Math.Content.HSA-SSE.A.1.a 22 A CCSS.Math.Content.HSG-CO.B.7 23 A CCSS.Math.Content.HSG-CO.B.6 24 A CCSS.Math.Content.HSN-Q.A.1 25 C CCSS.Math.Content.HSS-ID.B.6.a 26 A CCSS.Math.Content.HSS-ID.B.6.a 27 B CCSS.Math.Content.HSS-ID.C.7 28 See Scoring Rubric CCSS.Math.Content.HSS-ID.C.7 29 A CCSS.Math.Content.HSA-REI.D A CCSS.Math.Content.HSF-IF.B.4 3

4 Standards Coverage Summary: CC Standard DOK 1 DOK 2 DOK 3 DOK 4 Total CCSS.Math.Content.HSN-Q.A CCSS.Math.Content.HSA-SSE.A.1.a CCSS.Math.Content.HSA-CED.A CCSS.Math.Content.HSA-CED.A CCSS.Math.Content.HSA-CED.A CCSS.Math.Content.HSA-REI.B CCSS.Math.Content.HSA-REI.D CCSS.Math.Content.HSA-REI.D CCSS.Math.Content.HSA-REI.D CCSS.Math.Content.HSF-IF.A CCSS.Math.Content.HSF-IF.A CCSS.Math.Content.HSF-IF.B CCSS.Math.Content.HSF-IF.B CCSS.Math.Content.HSG-CO.B CCSS.Math.Content.HSG-CO.B CCSS.Math.Content.HSS-ID.B.6.a CCSS.Math.Content.HSS-ID.C Total

5 Rationale 5

6 Question #1 (E258442) Which graph shows the solution to this system? y < 2x y > 1 3 x + 1 A. CCSS.Math.Content.HSA-REI.D.12 > DOK 1 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. A. This is the result of shading with the signs reversed, using > in the first inequality and < in the second. B. Correct: The line y = 2x is graphed with a dashed line, and the graph of y = 1/3x + 1 is also graphed using a dashed line. The area that needs to be shaded is determined by testing a point in that area. C. This is the result of shading as if the signs in both inequalities are <. D. This is the result of shading as if the signs in both inequalities are >. B. 6

7 C. D. 7

8 Question #2 (E217391) A carpenter makes wooden chairs. He has enough wood to make 30 chairs. He makes $60 profit on a dining chair and $90 profit on a rocking chair. It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair. He only has 40 hours available to work on the chairs. The carpenter wants to maximize his profit given the constraints. He draws the graph below to represent this situation. CCSS.Math.Content.HSA-CED.A.3 > DOK 2 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Rationale Given the constraints, the carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs. His total profit for all the chairs will be $2,100. The graph shows the system of inequalities x + y 30 and 2x + y 40, which represents the given constraints. The profit can be found using the equation Profit = 60x + 90y where x stands for the number of dining chairs and y stands for the number of rocking chairs. We substitute the corner points (which are (0, 20), (20, 10), and (30, 0)) into this function to find which point gives the maximum profit. 60(0) + 90(20) = 1,800 60(20) + 90(10) = 2,100 60(30) + 90(0) = 1,800 The point (20, 10) gives the maximum profit, so the carpenter should make 20 dining chairs and 10 rocking chairs for a profit of $2,100. Use the drop-down menus to correctly complete the statements below. This question must be answered online. 8

9 Question #3 (E185893) The values a and b in the equation ax = 3 + bx are constants. What value of x satisfies this equation? A. 3 + b a B. 3 a 3 b C. 3 a b D. 3a 3b Question #4 (E213585) The graph below shows the height of a small tree, in feet, as a function of the number of years since it was planted. CCSS.Math.Content.HSA-REI.B.3 > DOK 1 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A. This is the result of making a mistake in the first step when dividing the constant a on both sides. B. This is the result of making a mistake when simplifying ax bx = 3. C. Correct: This is the result of solving ax bx = 3 x(a b) = 3 x = 3/(a b). D. This is the result of making a mistake when simplifying x(a b) = 3. CCSS.Math.Content.HSF-IF.B.6 > DOK 2 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Rationale The height of the tree goes from 4 feet in year 0 to 6 feet in year 4. This is a change of 2 feet in 4 years, which equals 0.5 foot per year. Choose a response from each drop-down menu to complete the sentence below. This question must be answered online. 9

10 Question #5 (E213107) A bus is traveling 500 miles at a constant speed of 55 miles per hour. Which graph represents n, the number of miles REMAINING on the trip, as a function of t, the number of hours traveled? A. CCSS.Math.Content.HSF-IF.B.4 > DOK 2 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. A. This is incorrect because it shows the miles remaining as the independent variable and the time traveled as the dependent variable. B. This is incorrect because it shows the miles traveled as the independent variable and the time traveled as the dependent variable. C. This is incorrect because it shows the miles traveled, not remaining, as the dependent variable. D. Correct: This is correct because it shows the time traveled as the independent variable and the miles remaining as the dependent variable, and the correct intercepts. B. C. 10

11 D. Question #6 (E213294) The following are true for LMN. m L = 45 ; m M = 55 ; LM = 7 inches Triangle LMN is reflected across the x -axis and then rotated about its center to form its image, L M N. Which statement is true? A. m M = 45 B. m N = 80 C. m M = 170 D. m N = 73 Question #7 (E270575) What is the value of x that makes this equation true? 5 2x 3 + 4x = 3x + 6 Use the on-screen keyboard to complete the equation below. CCSS.Math.Content.HSG-CO.B.7 > DOK 2 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. A. This answer is incorrect. Since angle M' corresponds to angle M, its measure is 55 degrees. B. Correct: This is the correct answer. A reflection and a rotation are rigid motions, so the original triangle and its image are congruent. Since the sum of the angles of a triangle is 180, angle N = 180 ( ) = 80 degrees. C. This answer is the result of finding 180 (55 45). D. This answer is the result of finding 180 ( ). CCSS.Math.Content.HSA-REI.B.3 > DOK 1 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Rationale A correct response of x = 3. This question must be answered online. 11

12 Question #8 (E178563) Tara bakes 225 cookies in 5 hours, and she uses 8 pounds of sugar. She divides 225 by 5 to get a rate of 45. Which of the following corresponds to this rate? A. pounds per hour B. hours per cookie C. cookies per pound D. cookies per hour Question #9 (E270577) The graphs of linear functions f and g are shown below. CCSS.Math.Content.HSN-Q.A.1 > DOK 1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. A. This expression uses two units that are in the problem, but the number that is used as the dividend (225) relates to cookies, not pounds. B. This is the result of using the two correct units, but reversing their positions. C. This expression uses two units that are in the problem, but the number that is used as the divisor (5) relates to hours, not pounds. D. Correct: This unit corresponds to the units for the dividend and divisor. CCSS.Math.Content.HSA-REI.D.11 > DOK 1 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Rationale Correct response of -3 or x = -3. Responses of -1/2 or 6 indicate confusion between the solution to the system and the intercepts. A response of 5 indicates the student misinterpreted the y-coordinate of the intersection point as the solution. What is the solution to f(x) = g(x)? Use the onscreen keyboard to enter the solution. This question must be answered online. 12

13 Question #10 (E258755) On a certain date, the price of silver was $30 per ounce. The graph below shows how the total cost of the silver depends on the amount purchased. CCSS.Math.Content.HSN-Q.A.1 > DOK 2 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. A. This is the result of thinking that the line should go from (0, 0) to (10, 30). B. This uses the $30 per ounce from the problem. C. Correct: The cost of 10 ounces of silver is $300, and the line on the graph goes from (0, 0) to (10, 300). Since the line goes up 6 units, each unit represents = 50 dollars. D. This is the cost of 10 ounces of silver. The scale on the vertical axis of the graph is missing. What does each unit on the vertical axis represent? A. $5 B. $30 C. $50 D. $300 13

14 Question #11 (E270578) Mr. Rokum is comparing the costs for two different electrical providers for his home. Provider A charges $0.15 per kilowatt-hour. Provider B charges a flat rate of $20 per month plus $0.10 per kilowatt-hour. On the coordinate grid below, graph a system of equations to model c, the total cost in dollars for each plan, based on h kilowatt-hours of electricity used during a one-month period. To graph a ray, make sure the Ray button is highlighted. On the coordinate grid, find the endpoint of the ray and click on that point, then find another point on the ray and click on that point. CCSS.Math.Content.HSA-CED.A.2 > DOK 2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Rationale The correct graph is given below. Note: Any 2 points on either ray is acceptable, as long as the endpoint is one of the points. This question must be answered online. 14

15 Question #12 (E184108) In the graph, ABC A B C. CCSS.Math.Content.HSG-CO.B.6 > DOK 2 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. A. Correct: These two transformations map triangle ABC onto triangle A'B'C'. B. This transformation maps triangle ABC into the correct quadrant, but it is not the correct transformation. For example, point A' after this transformation is at ( 1, 3) instead of ( 3, 1). C. This transformation maps triangle ABC into the correct quadrant, but it is not the correct transformation. For example, point A' after this transformation is at ( 1, 3) instead of ( 3, 1). D. Two reflections are required to correctly map the triangle. However, these reflections result in a transformed triangle in the incorrect quadrant. Which transformation maps ABC onto A B C? A. Reflect about x-axis and then reflect about the y- axis. B. Rotate 90 counterclockwise and then reflect about the y axis. C. Rotate 90 clockwise and then reflect about the x- axis. D. Reflect about y = x and then reflect about the y- axis. Question #13 (E270579) Consider the sequence whose first five terms are shown below. 8, 6, 4, 2, 0 Which function, with the domain of n = {1, 2, 3, 4, 5} defines this sequence? A. f (n) = n + 9 B. f (n) = 10n + 2 C. f (n) = 2n + 10 D. f (n) = n 2 CCSS.Math.Content.HSF-IF.A.3 > DOK 2 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. A. This function is correct for only the first term. B. This function switches 2 and 10 and results in 8, 18, 28, and so on. C. Correct: The sequence corresponds to f(1), f(2), f(3), f(4), and f(5). D. This function uses the arithmetic difference of the pattern. 15

16 Question #14 (E212954) Five relations are shown below. Determine which of these relations are functions. Drag and drop each relation to the correct box. This question must be answered online. CCSS.Math.Content.HSF-IF.A.1 > DOK 1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Rationale If a relation is a function, each x value (or input) is associated with one and only one y-value (or output). Relation 1 is NOT a function. Since the input 0 is mapped to two outputs, both 1 and 7, it is not a function. Relation 2 is a function. Since each input or x value has only one output or y value associated with it, it is a function. Relation 3 is NOT a function. For each value of x, there are 2 values of y that satisfy the equation. For example if x = 3, then 9 + y 2 = 25, y 2 = 16, and y = + 4, and y = 4. Since the x value 3 is associated with 2 different y values, this is not a function. Relation 4 is a function. This graph passes the vertical line test; that is, a vertical line drawn through the graph intersects it at only one point. This shows that each x value has one and only one corresponding y value. Relation 5 is NOT a function. Note that the x value 1 corresponds to y values of both 2 and 1. To be a function, each x value must have one and only one y value. 16

17 Question #15 (E200981) What values of x satisfy the inequality 2x + 3 > 11? A. x > 4 B. x < 4 C. x > 4 D. x < 4 Question #16 (E222130) A high school booster club plans to sell bags of popcorn at their basketball games. It cost the club $700 for a popcorn machine. It costs them an additional $0.25 to make each bag of popcorn the club sells. The club sells each bag of popcorn for $1.50. Write an equation that can be used to determine x, the number of bags of popcorn the booster club must sell so that the total sales equals the total costs. Solve your equation to determine the number of bags of popcorn the booster club must sell so that the total sales equals the total costs. Type your answer in the box below. This question must be answered online. CCSS.Math.Content.HSA-REI.B.3 > DOK 1 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A. This is the result of not reversing the inequality after dividing by a negative number. B. Correct: The answer is found in these steps: 2x + 3 > 11 2x > x > 8 2x 2 < 8 2 x < 4. C. This is the result of not reversing the inequality after dividing by a negative number and not making the sign negative on the right side of the inequality. D. This is the result of failing to make the sign negative on the right side of the inequality. CCSS.Math.Content.HSA-CED.A.1 > DOK 2 Create equations and inequalities in one variable and use them to solve problems. Rationale See Rubric. 2 Point Response: The response is correct and complete. A level 2 response is characterized by: A correct equation. A correct solution. Sample Correct Answer: The total sales in dollars is $1.50 times the number of bags sold. The total cost in dollars is $700 plus $0.25 times the number of bags sold. The equation is 1.5x = x or equivalent. 1.5x = x 1.25x = 700 x = 560 The booster club must sell 560 bags to break even. 1 Point Response: The response is partially correct. A level 1 response is characterized by: A correct equation with an incorrect or no solution. A correct solution based on an incorrect equation. 0 Point Response: The response is completely incorrect, there is no response, or the response is off topic. 17

18 Question #17 (E260183) What is the solution to the inequality below? CCSS.Math.Content.HSA-CED.A.1 > DOK 1 Create equations and inequalities in one variable and use them to solve problems. A. x > 9 2 B. x < 9 2 C. x > 9 D. x < 9 2x + 3 < 12 A. Correct: This correctly states the solution to the inequality: 2x + 3 < 12, then 2x < 9, so x > 9/2. B. This answer is the result of not switching the inequality when dividing by a negative number. C. This answer is the result of incorrectly dividing by 2 first to get x + 3 > 6, while remembering to switch the inequality sign. D. This answer is the result of incorrectly dividing by 2 first to get x + 3 < 6, and also neglecting to reverse the inequality sign. Question #18 (E260863) Max bought m 8-ounce jars of olives and n 12- ounce jars of olives. The total amount of olives was at least 80 ounces. Which inequality models this situation? A. 8m + 12n 80 B. 8m + 12n 80 C. 20(m + n) 80 D. 20(m + n) 80 CCSS.Math.Content.HSA-CED.A.3 > DOK 2 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. A. Correct: The amount in ounces of olives in m 8-ounce jars is represented by the expression 8m, and the amount in ounces of olives in n 12-ounce jars is represented by the expression 12n. The total amount of olives is AT LEAST 80 ounces, which means 80 ounces or more, so the inequality sign needed is the greater-than-or-equal sign. The correct inequality is 8m + 12n 80. B. This inequality uses the less-than-or-equal sign instead of the greater-than-or-equal sign. C. This inequality adds and adds m + n before multiplying. D. This inequality adds and adds m + n before multiplying, and uses the less-than-or-equal sign instead of the greater-than-or-equal sign. 18

19 Question #19 (E258739) Which table represents a function? A. B. C. CCSS.Math.Content.HSF-IF.A.1 > DOK 1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). A. Correct: Each x-value in this table is assigned to exactly one y-value, so this table represents a function. B. This table assigns two different y-values to the x- value 0, and also two different y-values to the x- value 1, so it is not a function. C. This table assigns two different y-values to the x- value 2, so it is not a function. D. This table assigns four different y-values to the x- value 0, so it is not a function. D. Question #20 (E260114) A school ordered three different types of pizzas to sell at a fundraiser. There are x cheese pizzas, y pepperoni pizzas, and z vegetarian pizzas. The total cost in dollars of the pizzas is given by the expression below. 10x + 12y + 14z What do the coefficients in the expression represent? A. the cost in dollars of each type of pizza B. the number of each type of pizza ordered C. the total amount in dollars spent on each type of pizza D. the total number of pizzas purchased CCSS.Math.Content.HSA-SSE.A.1.a > DOK 2 Interpret parts of an expression, such as terms, factors, and coefficients. A. Correct: If the total cost in dollars is represented by the expression 10x + 12y + 14z, then the coefficient of each variable must represent the cost in dollars of the corresponding type of pizza. For example, the expression 10x represents the cost of x cheese pizzas because each cheese pizza costs 10 dollars. B. This answer describes the quantities that are represented by the variables x, y, and z. C. This answer describes the quantities that are represented by the terms 10x, 12y, and 14z. D. This answer describes the quantity that would be represented by the expression x + y + z. 19

20 Question #21 (E258692) The dollar value of a computer, based on the number of years since it was purchased, can be determined using the equation below. y = x In the equation, which of the following represents the initial cost of the computer? A B. 350 C. x D. y Question #22 (E172620) In DEF, m D = 48 and m E = 101. This triangle is rotated 75 counterclockwise about its center. What is m F? A. 31 B. 26 C. 44 D. 74 CCSS.Math.Content.HSA-SSE.A.1.a > DOK 2 Interpret parts of an expression, such as terms, factors, and coefficients. A. Correct: The computer was purchased for $2,000. B. This is the yearly decrease in the value of the computer. C. This represents the number of years since the computer was purchased. D. This is the current dollar value of the computer. CCSS.Math.Content.HSG-CO.B.7 > DOK 2 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. A. Correct: Since rotation is a rigid motion, the angle measure does not change. The measure is = 31. B. This is the difference between the largest angle (101) and the angle of rotation. C. This is the difference between the angle of rotation (75) and the missing angle (31). D. This is the sum of the two given angles ( ) minus the angle of rotation. 20

21 Question #23 (E184113) In the Cartesian plane, ΔABC ΔA B C. CCSS.Math.Content.HSG-CO.B.6 > DOK 2 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. A. Correct: This transformation maps triangle ABC onto triangle A'B'C'. B. This transformation would be another way to map the triangles only if the rotation were counterclockwise. C. These transformations are similar to one possible series of transformations, but they place the new triangle A'B'C' in the third quadrant, not the fourth. D. This series of transformations would be correct if the rotation were 90. Which transformations map ΔABC to ΔA B C? A. Reflect about the y-axis and then rotate 90 clockwise. B. Reflect about the x-axis and then rotate 90 clockwise. C. Reflect about the y-axis and then rotate 180 counterclockwise. D. Reflect about the x-axis and then rotate 180 counterclockwise. 21

22 Question #24 (E258336) The graph shows how the amount Amanda earns each day depends on the number of hours she works. CCSS.Math.Content.HSN-Q.A.1 > DOK 1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. A. Correct: The x-value of the point (0, 0) gives the number of hours worked, and the y-value gives the earnings in dollars. B. This is the result of interpreting the point (10, 160). C. This results from misinterpreting either the x- or y- value of the point (0, 0). D. This results from interpreting the meaning of the slope of the line instead of the meaning of the point (0, 0). What is the meaning of the point (0, 0) on the graph? A. If Amanda works 0 hours on a certain day, she earns $0. B. If Amanda works 10 hours on a certain day, she earns $160. C. Amanda earns $0 per hour. D. Amanda earns $16 per hour. 22

23 Question #25 (E196492) The balance in Ana's savings account may be modeled by the linear function y = 50x , where x represents the number of months that have passed and y represents the account balance. Based on this function, which of these is the BEST prediction of Ana's total savings after 3 years? A. $2,650 B. $3,700 C. $4,300 D. $7,650 CCSS.Math.Content.HSS-ID.B.6.a > DOK 2 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. A. This is the result of substituting 3 for the number of months, x, rather than converting 3 years to 36 months. B. This is the result of incorrectly calculating 3 years as 24 months and then solving the equation. C. Correct: Evaluating the function for an x- value of 36 (3 years converted to months) gives 4,300. Thus, the best prediction for her cumulative savings after 3 years is $4,300. D. This is the result of summing 2500 and 50 and then multiplying by 3 (years) 23

24 Question #26 (E193471) Which line best models the data in the scatter plot? A. B. CCSS.Math.Content.HSS-ID.B.6.a > DOK 1 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. A. Correct: This model passes through the middle of the general group of points and accurately models the trend of the data. B. This model passes through two of the data points and is the correct slope, but as most of the data points are above the line, it is too low to be a good model. C. This model shows a general positive trend as do the data points, but since the line is forced through the origin it does not model a correct slope or intercept. D. This model passes through three data points, but it does not model the data set as a whole. C. D. 24

25 Question #27 (E197553) The total amount spent by a local business on utility expenses for its factory may be modeled by the function E(x) = 380x Which best describes the slope in this function? A. the initial cost for setting up the utilities B. the average cost of the utilities each month C. the number of months for which the business has paid utility bills D. the maximum cost of the utilities Question #28 (E265087) The function H(d) = 0.2d represents the height of a lawn, in inches, d days after it was mowed. Using this model, fill in the boxes to correctly complete the statements below. Use the on-screen keyboard to type your response in each box. This question must be answered online. CCSS.Math.Content.HSS-ID.C.7 > DOK 2 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. A. This amount is represented by the y-intercept of 50. B. Correct: The slope represents the rate of change or the rate of the utilities per month. This rate is $380. C. This variable, x, represents the number of months over which the cumulative expenses have been incurred. D. Since this is a linear function, there is not a maximum amount, and the total expenses are represented by the y-value, or output value, not the slope. CCSS.Math.Content.HSS-ID.C.7 > DOK 2 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Rationale This item is worth 1 point. The correct response is: The height of the lawn immediately after it is mowed is 1.5 inch(es). The lawn grows at a rate of 0.2 inch(es) per day. 25

26 Question #29 (E220468) The length in centimeters of a goldfish, L, can be determined using the equation below, based on m, the age, in months, of the fish. L = 0.8m + 3 Which graph represents the solutions to the equation? A. CCSS.Math.Content.HSA-REI.D.10 > DOK 1 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A. Correct: This answer is correct, since the line properly represents the slope and the intercept given in the equation, which is in slope-intercept form. B. This answer is the result of reversing the slope and the intercept. C. This answer is the result of thinking the slope is run over rise that a slope of 0.8 means that for every 0.8 units the line goes right, it goes up 1. D. This answer is the result of treating the intercept as an x-intercept instead of a y-intercept. B. 26

27 C. D. 27

28 Question #30 (E212737) The graph on the coordinate plane below shows that the number of bushels of corn that can be grown on an acre of land is a function of the number of seeds planted. CCSS.Math.Content.HSF-IF.B.4 > DOK 2 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. A. Correct: This answer is not supported by the graph because the value of the function decreases after its maximum of 50. B. This answer is supported by the graph because it correctly identifies 50 as the maximum value of the function. C. This answer is supported by the graph because it correctly identifies 250,000 as generating the maximum value of the graph. D. This answer is supported by the graph because it correctly identifies the value of the function as being the same for 100,000 and 400,000. Which statement CANNOT be concluded from the graph? A. The greater the number of seeds planted, the more corn will be produced per acre. B. The maximum amount of corn produced will be 50 bushels per acre. C. The number of bushels of corn produced per acre is greatest if 250,000 seeds are planted per acre. D. Planting 100,000 seeds per acre will give the same result as planting 400,000 seeds per acre. 28