Chapter 5: MPM 1D Unit Test
Modeling with Graphs
Name: ______Date: ______
Part A: Multiple Choice
Choose the correct answer for each question.
1. Which graph represents a direct variation?
a) b) c)
2. Which relation is a partial variation?
a) b) c) d)
3. Sophie’s earnings vary directly with the number of hours she works. She earned $25 in 4 hours. What is the rate of change?
a) 0. 16 b) 6.25
c) 100 d) 21
4. What is the slope of this ramp?
a) - b) c) - d)
5. What equation represents this relation?
x / y0 / 4
1 / 1
2 / –2
3 / –5
4 / –8
a) y = -3x + 4 b) y = 4x - 3 c) y = 3x + 4 d) y = 3x - 4
6. The cost of a newspaper advertisement is $750 plus $80 for each day it runs. Which equation represents this relation?
a) b)
c) d)
7. Find the slope of a line that passes through the points (-9, -3) and (-7, -1).
a) -16 b) c) 8 d) 1
8. A line passes through the point (-6, -3) and has a slope of 2/3. Which point is on the same line?
a) (-9, -5) b) (-3, -1) c) (3, 4) d) (19, 13)
9. Compare the slope of line a to the slope of line b. Which is true?
a) The slope of a is greater than the slope of b.
b) The slope of b is greater than the slope of a.
c) The two slopes are equal.
d) The relationship cannot be determined from the information given.
10. Three points are shown. Between which two points can you draw a line with a negative slope?
a) A and B b) C and A c) B and C d) None of these
Part B: Short Answer
Show all of your work.
10. a) Calculate the slope.
b) Find the vertical intercept (y - intercept).
c) Write an equation for the relation.
11. The cost to ship goods varies directly with the mass. Paul paid $20.40 to ship a package with mass 24 kg. Write an equation for this relation.
x / y2 / 0.16
4 / 0.64
6 / 1.44
8 / 2.56
12. a) Is this relation linear or non-linear?
b) How can you tell without graphing?
13. Sheila works in a bookstore. She earns $240 per week, plus $0.15 for every bestseller she sells.
a) Write an equation for the relationship that represents Sheila’s earnings for one week.
b) Last week, Sheila sold 19 bestsellers. How much did she earn?
14. Use the rule of four to represent this relation in three other ways.
x / y-1 / 6
0 / 2
1 / -2
2 / -6
3 / -10
a) Use a graph
b) Use words.
c) Use an equation.
Part C: Problem Solving
Show all your work.
15. The graph shows the speed of the cars on a roller coaster once the brakes are applied.
a) Calculate the rate of change of the roller coaster speed.
b) How does the rate of change relate to the graph?
c) Write an equation of the relationship.
d) Suppose the rate of change changes to - 5 m/s. How long will it take the roller coaster to stop.
16. Calculate the slope of each line segment
17. Point A (2, 3) is plotted on the grid. Draw a line segment AB with slope. What are possible coordinates of B?
18.
MPM 1D Unit #6 – Linear Relations Assessment Rubric: Name:______Date:______
Category / Level 4 / Level 3 / Level 2 / Level 1 / Below Level 1Know./
Underst. / Demonstrates a solid and thorough understanding of Linear Relations (initial value(y-intercept), slope, creating equations from words, finite differences, graphing without table of values, interpreting from graphs, direct and partial variation). Able to solve problems with no errors. / Demonstrates good understanding of Linear Relations. Able to solve the problem with a minor error(s) / Demonstrates moderate understanding of Linear Relations. Able to solve the problem with some errors. / Demonstrates a limited or inaccurate understanding of Linear Relations needed to solve the problems. / Needs to demonstrate an understanding of Linear Relations. No attempt made at solving the problem, or the attempt has little or no validity.
Commun-ication / Provides a thorough, clear and insightful explanation/justification. Solutions are well formed, with completeness, accuracy and proper mathematical form and language / Provides a complete, clear, and logical explanation, missing small details. Solutions are complete but some proper form and language is missing /
Provides a partial explanation/justification that shows some clarity and logical thought. Solutions are somewhat complete, but disorganized. /
Provides a limited or inaccurate explanation/justification that lacks clarity or logical thought. Solutions are incomplete, scattered and disorganized. /
Needs to provide some explanation/justification.
Thinking /
Shows flexibility and insight when carrying out the plan, by trying and adapting one or more strategies to solve the problem. (when necessary) /
Carries out a plan effectively by using an appropriate strategy and solving the problem. /
Carries out the plan to some extent using a strategy, and develops a limited and/or incorrect solution /
Uses a strategy and attempts to solve the problem but does not arrive at a solution. /
Needs to demonstrate a strategy that could be used to solve this problem.
Application /
Has a thorough understanding of how to use the concepts (Linear Relationships) to form a solution.
Demonstrates a solid understanding of the connection between the questions required solution and its interpretation. /
Has good understanding of how to use the concepts to form a solution.
Demonstrates good understanding of the connection between the questions required solution and its interpretation. /
Has some understanding of how to use the concepts to form a solution.
Demonstrates a moderate understanding of the connection between the questions required solution and its interpretation. /
Has limited understanding of how to use the concepts to form a solution.
Demonstrates little understanding of the connection between the questions required solution and its interpretation. /
Needs to show understanding of how to use the concepts answer question.
Demonstrates an insufficient connection between the questions required solution and its interpretation.