Chapter 5:
Modeling with Graphs
MPM 1D
Name: ________________________
Unit Test
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) y  45 x
b) y  6 x 2  2
c) y  2 x
d) y  3 x  4
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) -
9
2
b)
2
9
c) -
2
9
d)
9
2
5. What equation represents this relation?
x
0
1
2
3
4
y
4
1
–2
–5
–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) C  80n  750
b) C  80n  750
c) C  750n  80
d) C  750n  80
7. Find the slope of a line that passes through the points (-9, -3) and (-7, -1).
a) -16
b)
1
2
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.
a
b) The slope of b is greater than the slope of a.
b
c) The two slopes are equal.
the
d) The relationship cannot be determined from
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.
12. a) Is this relation linear or non-linear?
b) How can you tell without graphing?
x
2
4
6
8
y
0.16
0.64
1.44
2.56
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
-1
0
1
2
3
y
6
2
-2
-6
-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
1
2
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
Category
Assessment Rubric: Name:_______________________ Date:______________
Level 4
Level 3
Demonstrates good
understanding of Linear
Relations. Able to solve
the problem with a minor
error(s)
Level 2
Level 1
Know./
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.
Communication
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.
Has good understanding of
how to use the concepts to
form a solution.
Has some understanding of
how to use the concepts to form
a solution.
Has limited understanding
of how to use the concepts
to form a solution.
Needs to show
understanding of how to use
the concepts answer
question.
Demonstrates a solid understanding of
the connection between the questions
required solution and its interpretation.
Demonstrates good
understanding of the
connection between the
questions required solution
and its interpretation.
Demonstrates a moderate
understanding of the
connection between the
questions required solution and
its interpretation.
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.
Below Level 1
Demonstrates little
understanding of the
connection between the
questions required solution
and its interpretation.
Needs to demonstrate an
understanding of Linear
Relations. No attempt made
at solving the problem, or
the attempt has little or no
validity.
Demonstrates an
insufficient connection
between the questions
required solution and its
interpretation.