Lincoln Public Schools Math 8 McDougall Littell Middle School Math Course 3 – Chapter 11 Items marked A, B, C are increasing in difficulty. Group “A” questions are the most basic while Group “C” are the most difficult and require higher levels of thinking skills. The level of difficulty is only relative to the same section. Most problems include random number generation within individual problems. [n] indicates n problems types are available in the topic. Note: Some problems require rounding. Round when finding each value which is an answer to the problem. For example, if has triangle sides a and b, round c after finding its value and before continuing any further calculations. If there is only one answer to the problem, only round the final answer. Use 3.14 for p in all equations. Section 11.1 Objective: Students will be able to use tables to represent functions. 11_1 Functions in Tables – [4] – Determine if the relation in the form of a table is a function. 11_1 Functions in Ordered Pairs – [4] – Determine if the relation in the form of ordered pairs is a function. 11_1 Complete Function Table – [4] – Complete a table of values for a function. 11_1 Write Function Rule A – [4] – Find a linear function for a table of values. X values increase by 1. 11_1 Write Function Rule B – [4] – Find a linear function for a table of values. X values increase by more than 1. Section 11.2 Objective: Students will be able to interpret scatter plots. 11_2 Relationship – [3] – Determine if the scatter plot is increasing, decreasing or has no relationship. 11_2 Identify Next Ordered Pair A –[17] – Identify the next ordered pair in a scatter plot if the function is increasing. 11_2 Identify Next Ordered Pair B – [17] – Identify the next ordered pair in a scatter plot if the function is decreasing. Section 11.3 Objective: Students will be able to finds solution of equations in two variables. 11_3 Identify Solutions – [6] – Multiple selection problem. Check each value which is a solution of the linear function. 11_3 Complete 5 Ordered Pairs – [4] – Find the y­value of an ordered pair given a function.
Section 11.4 Objective: Students will be able to graph a linear equation. 11_4 Complete Ordered Pairs­Graph A – [6] – Make a table of values and match the table to its graph. Function is in the form of x + y = c. 11_4 Complete Ordered Pairs­Graph B – [4] – Make a table of values and match the table to its graph. Function is in the form of ax + y = c. 11_4 Complete Ordered Pairs­Graph C – [4} – Make a table of values and match the table to its graph. Function is in the form of x + y = b. 11_4 Complete Ordered Pairs­Graph D – [8] – Make a table of values and match the table to its graph. Function is in the form of x + y = b. Graph is a line with no marked points. 11_4 Horizontal and Vertical Lines – [12] – Multiple choice. Select graphs of two vertical or horizontal lines which match the appropriate equation.
Lincoln Public Schools – Math 8 – McDougal Littell Middle School Math Course 3 Please note: This demo is a one problem sample from each topic. Most problems are random number problems and consist of multiple types for each topic. Some images are sliced to insert measurements and are not properly formatted in this demo due to the conversion to Word form. They will appear properly formatted when used in EDU. 11_1 Functions in Tables – [4] – Determine if the relation in the form of a table is a function. Place a check mark beside each relation which is a function. Choice Input Selected 1 4 7 4 No Output 5 17 29 9 Input ­4 ­2 0 2 Output 7 3 1 5 Input 4 7 8 3 Output ­15 ­27 ­31 ­11 7 12 16 22 Output 8 12 14 19 Input Points Yes +1 Yes +1 Yes +1 Total correct answers: 3 Partial Grading Explained Comment: Input 1 4 7 4 Output 5 17 29 9 In the relation above, 4 has two different output values of 17 and 9. The relation is not a function. All other relations are functions.
11_1 Functions in Ordered Pairs – [4] – Determine if the relation in the form of ordered pairs is a function. Place a check mark beside each relation which is a function. Choice Selected Points T = {(­4, 7), (­2, 3), (0, 1), (2, 5)} Yes +1 S = {(7, ­27), (8, ­31), (2, ­7), (7, ­19)} No R = {(4, 17), (7, 29), (6, 25), (7, 21)} No V = {(7, 5), (9, 11), (13, 14), (22, 20)} Yes +1 Total correct answers: 2 Partial Grading Explained Comment: R = {(4, 17), (7, 29), (6, 25), (7, 21)} In the relation above, 7 has two different output values of 29 and 21. The relation is not a function. S = {(7, ­27), (8, ­31), (2, ­7), (7, ­19)} In the relation above, 7 has two different output values of ­27 and ­19. The relation is not a function. All other two relations are functions. 11_1 Complete Function Table – [4] – Complete a table of values for a function. Your response Correct response Construct a table of values for the function Construct a table of values for the 2x + y = 2 function 2x + y = 2 Input ­4 ­2 0 2 4 Output 10 (20%) 6 (20%) 2 (20%) ­2 (20%) ­6 (20%) Input ­4 ­2 0 2 4 Output 10 6 2 ­2 ­6
Comment: 2x + y = 2 Solve for y. y = ­2x + 2 Input ­4 ­2 0 2 4 Output y = (­2)(­4) + 2 = 10 y = (­2)(­2) + 2 = 6 y = (­2)(0) + 2 = 2 y = (­2)(2) + 2 = ­2 y = (­2)(4) + 2 = ­6 11_1 Write Function Rule A – [4] – Find a linear function for a table of values. X values increase by 1. Write a function rule that relates x and y. Input x 1 2 3 4 Output y 3 ­2 ­7 ­12 Your Answer: y=­5x+8 Correct Answer: y=­5x + 8 Comment: Write a function rule that relates x and y. Input x 1 2 3 4 Output y 3 ­2 ­7 ­12 The change in the output is constant. Write a rule in the form of y = ax + b. change in output a = ­2 ­ 3 = change in input 2 ­ 1 y = ­5x + b Choose the pair (1, 3) to solve for b. 3 = ­5(1) + b b = 8 The function rule is y = ­5x + 8
­5 = = ­5 1 11_1 Write Function Rule B – [4] – Find a linear function for a table of values. X values increase by more than 1. Write a function rule that relates x and y. ­1 1 3 5 Input x Output y ­11 ­3 5 13 Your Answer: y=4x­7 Correct Answer: y=4x ­ 7 Comment: Write a function rule that relates x and y. Input x ­1 1 3 5 Output y ­11 ­3 5 13 The change in the output is constant. Write a rule in the form of y = ax + b. change in output a = ­3 ­ ­11 = 8 = = 4 change in input 1 ­ ­1 2 y = 4x + b Choose the pair (­1, ­11) to solve for b. ­11 = 4(­1) + b b = ­7 The function rule is y = 4x ­ 7 11_2 Relationship – [3] – Determine if the scatter plot is increasing, decreasing or has no relationship. Determine the relationship between x and y in the scatter plot shown below. Your Answer: No Relationship Correct No Relationship
Answer: Comment: The graph does not have a pattern of increasing or decreasing. There is no relationship between x and y. 11_2 Identify Next Ordered Pair A –[17] – Identify the next ordered pair in a scatter plot if the function is increasing. Determine the next ordered pair in the scatter plot shown below. Your Answer: (5,12) Correct (5, 12) Answer: Comment: The graph is increasing by 2 units in the y direction for every unit in the x direction. The next point will be (5, 12).
11_2 Identify Next Ordered Pair B – [17] – Identify the next ordered pair in a scatter plot if the function is decreasing. Determine the next ordered pair in the scatter plot shown below. Your Answer: (4,1) Correct (4, 1) Answer: Comment: The graph is decreasing by 4 units in the y direction for every unit in the x direction. The next point will be (4, 1). 11_3 Identify Solutions – [6] – Multiple selection problem. Check each value which is a solution of the linear function. Check each ordered pair which is a solution of the equation: y = 5x ­ 9 Choice Selected (­2, ­21) No (1, ­3) No (9, 35) No (6, 21) Yes Points +1 Total correct answers: 1 Partial Grading Explained Comment: x = ­2 y = (5)(­2) ­ 9 = ­10 ­ 9 = ­19 The value (­2, ­21) is not a solution. x = 1 y = (5)(1) ­ 9 = 5 ­ 9 = ­4 The value (1, ­3) is not a solution. x = 6 y = (5)(6) ­ 9 = 30 ­ 9 = 21 The value (6, 21) is a solution.
x = 9 y = (5)(9) ­ 9 = 45 ­ 9 = 36 The value (9, 35) is not a solution. 11_3 Complete 5 Ordered Pairs – [4] – Find the y­value of an ordered pair given a function. Your response Correct response Complete the ordered pairs for for the function y = 2x 2 Complete the ordered pairs for for the function y = 2x 2 (­4, 32 (20%)) (­2, 8 (20%)) (0, 0 (20%)) (2, 8 (20%)) (4, 32 (20%)) (­4, 32) (­2, 8) (0, 0) (2, 8) (4, 32) Comment: Input ­4 ­2 0 2 4 Output Ordered Pair 2 y = (2)(­4) = 32 (­4, 32) y = (2)(­2) 2 = 8 (­2, 8) 2 y = (2)(0) = 0 (0, 0) 2 y = (2)(2) = 8 (2, 8) 2 y = (2)(4) = 32 (4, 32) 11_4 Complete Ordered Pairs­Graph A – [6] – Make a table of values and match the table to its graph. Function is in the form of x + y = c. Each question has 4 possible choices for graphs. Your response Correct response Make a table of values for y = x + 3 Make a table of values for y = x + 3 (­2, 1 (17%)) (­2, 1) (­1, 2 (17%)) (­1, 2) (0, 3 (17%)) (0, 3) (1, 4 (17%)) (1, 4) (2, 5 (17%)) (2, 5) Match the ordered pairs to the graph. Match the ordered pairs to the graph.
(17%) Comment: Input Output Ordered Pair ­2 y = (1)(­2) + 3 = 1 (­2, 1) ­1 y = (1)(­1) + 3 = 2 (­1, 2) 0 y = (1)(0) + 3 = 3 (0, 3) 1 y = (1)(1) + 3 = 4 (1, 4) 2 y = (1)(2) + 3 = 5 (2, 5) The correct graph is:
11_4 Complete Ordered Pairs­Graph B – [4] – Make a table of values and match the table to its graph. Function is in the form of ax + y = c. Each question has 4 possible choices for graphs. Your response Correct response Make a table of values for 2x ­ y = ­4 Make a table of values for 2x ­ y = ­4 (­2, 0 (17%)) (­2, 0) (­1, 2 (17%)) (­1, 2) (0, 4 (17%)) (0, 4) (1, 6 (17%)) (1, 6) (2, 8 (17%)) (2, 8) Match the ordered pairs to the graph. Match the ordered pairs to the graph. (17%) Comment: 2x ­ y = ­4 ­y = ­2x ­ 4 y = 2x + 4 Input Output Ordered Pair ­2 y = (2)(­2) + 4 = 0 (­2, 0) ­1 y = (2)(­1) + 4 = 2 (­1, 2) 0 y = (2)(0) + 4 = 4 (0, 4) 1 y = (2)(1) + 4 = 6 (1, 6) 2 y = (2)(2) + 4 = 8 (2, 8) The correct graph is:
11_4 Complete Ordered Pairs­Graph C – [4] – Make a table of values and match the table to its graph. Function is in the form of x + y = b. Each question has 4 possible choices for graphs. Your response Correct response Make a table of values for 3x ­ 2y = 6 Make a table of values for 3x ­ 2y = 6 (­4, ­9 (17%)) (­4, ­9) (­2, ­6 (17%)) (­2, ­6) (0, ­3 (17%)) (0, ­3) (2, 0 (17%)) (2, 0) (4, 3 (17%)) (4, 3) Match the ordered pairs to the graph. Match the ordered pairs to the graph. (17%) Comment:
Input Output Ordered Pair ­4 y = ­6 ­ 3 = ­9 (­4, ­9) ­2 y = ­3 ­ 3 = ­6 (­2, ­6) 0 y = ­0 ­ 3 = ­3 (0, ­3) 2 y = 3 ­ 3 = 0 (2, 0) 4 y = 6 ­ 3 = 3 (4, 3) The correct graph is: 11_4 Complete Ordered Pairs­Graph D – [8] – Make a table of values and match the table to its graph. Function is in the form of x + y = b. Graph is a line with no marked points. Each question has 4 possible choices for graphs. Your response Correct response Make a table of values for 3x ­ 4y = 12 Make a table of values for 3x ­ 4y = 12 (­4, ­6 (17%)) (­4, ­6) (0, ­3 (17%)) (0, ­3) (4, 0 (17%)) (4, 0) Match the ordered pairs to the graph. Match the ordered pairs to the graph.
(17%) Comment: Input Output Ordered Pair ­4 y = ­3 ­ 3 = ­6 (­4, ­6) 0 y = ­0 ­ 3 = ­3 (0, ­3) 4 y = 3 ­ 3 = 0 (4, 0) The correct graph is:
11_4 Horizontal and Vertical Lines – [12] – Multiple choice. Select graphs of two vertical or horizontal lines which match the appropriate equation. Your response A. B. C. D. Which graph is: x = 3 x = ­3 A (50%) B (50%) Comment: x = 3 is a vertical line where x is always 3. (3, 0), (3, 1), (3, 2) ..... x = ­3 is a vertical line where x is always ­3. (­3, 0), (­3, 1), (­3, 2) .....