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MPM 1D1
FINAL EXAM REVIEW – Units 2, 5 & 6
Name:____________________
Date:_____________________
Instructions: Refer to your notes to answer the following questions properly.
Show all your work to guarantee full marks (unless otherwise stated).
Unit #2: Graphing Relationships
2.
The table shows the lengths of the tails and the shoulder heights for a group of dogs.
Shoulder Height
(cm)
66
42
33
30
41
62
65
39
Length of Tail
(cm)
32
15
5
8
14
26
34
12
a) Draw a scatter plot of the data.
b) Describe the relationship between the shoulder height of a dog and the length of its tail.
3.
The table shows the population of a city from 1935 to 2005.
Year
1935
1945
1955
1965
1975
1995
2005
Population (1000’s)
540
610
768
804
819
844
856
a) Make a labelled scatter plot of the data.
b) Describe the trend in the population.
c) Draw a line or curve of best fit.
d) Estimate the population in 1950.
4.
The table shows the population of a town.
Year
1941
1951
1961
1971
1981
1991
2001
Population
6800
6690
6505
6003
5899
5542
5307
a) Make a scatter plot of the data.
b) Describe the trend in the population.
c) Estimate the town’s population in 2011.
5.
a) Plot the following set of points on a grid.
(1, 9), (9, 6), (5, 7), (3, 8), (4, 9),
(2, 9), (6, 8), (8, 7), (7, 6), (8, 5)
b) Draw a line or curve of best fit.
c) Does the set of points have a linear
relationship?
6.
Write a story that could be represented by the graph.
7.
Mark walks to his friend’s house. Partway there, he realizes he
forgot a CD at home. He runs back home to pick up the CD, goes in
his house to get the CD, then walks back to his friend’s house.
Construct a distance-time graph to represent this situation.
Unit #5: Linear Relations
1.
Is the line y = -4x + 9 linear or non-linear?
[1]
2.
Is the line y = 5x2 – 11 linear or non-linear?
[1]
3.
What is the formula for determining the slope of a line?
[1]
4.
Calculate the slopes of the following line segments using the slope formula.
a) M(6 , 4) N(11 , 9)
[2]
[2]
b) Q(-5 , 2) R(7 , -4)
5.
For each line, state the slope, the y-intercept, and the equation.
a) m = _________
b = _________
Equation:
[3]
b) m = _________
b = _________
Equation:
[3]
6.
Graph the following equations using the slope and y-intercept method. Remember to label
the graphs.
a) y = 4x – 6
[4]
b) y = -5 x + 8
3
[4]
7.
State the slope and y-intercept for the following equations, and then graph. Remember to label
the graphs.
a) y = 3 x
4
[6]
m = _________
b = _________
b) y = -5x
[6]
m = _________
b = _________
8.
State the slope and y-intercept for the following equations, and then graph. Remember to label
the graphs.
a) x = 2
[5]
m = _________
b = _________
b) y = -7
[5]
m = _________
b = _________
Unit #6: The Line
Questions 9 - 11 are multiple choice. Circle the letter of the correct answer.
9.
Parallel lines have:
a)
b)
c)
d)
10.
Which of the following pairs of numbers are slopes of perpendicular line segments?
a)
11.
slopes which are reciprocals
slopes which are negative reciprocals
slopes which are equal
equations which are identical
3 3
,
4 4
b)
3
4
, 
4
3
c)
3 4
,
4 3
d)
3
3
, 
4
4
A line segment which is parallel to the x-axis has a slope which is:
a) positive
b) negative
c) 0
d) undefined
[3]
Full Solution
12.
Write the equation of a line that is parallel to the y-axis and passes through the point (4, 7).
[1]
13.
Write each equation in the form y = mx + b. Identify the slope and y-intercept.
a) x + y – 10 = 0
[2]
[4]
b) 10x – 5y + 30 = 0
14.
Write each equation in standard form Ax + By + C = 0.
b) y = 9x – 14
a) y = -2x + 7
[2]
[3]
15.
Determine the x and y-intercepts for the following equation. Then, graph the equation.
Show your work.
9x – 2y = 18
x-intercept
y-intercept
[10]
16.
Find the equation of the line:
a) with a slope of m = -2 and passing through the point, P(4, 2).
[5]
1
5
b) perpendicular to y   x  4 and passing through (-2, -7).
[4]
17.
Find the equation of a line passing through the points A(1, 5) and B(4, -7).
[7]
18.
Solve the following linear system by graphing.
3x – y = 3
x+y=5
[9]
19.
In order to reduce the amount of cash Stacey had in her cash register on Saturday, her manager
took a bunch of $50 and $20 bills from her register and sent it to the cash office. The total
amount of money the manager sent to the cash office was $900.
a) Write an equation to model this situation. Introduce your variables with a “Let x be”
statements.
[3]
b) Graph the equation using the intercepts.
Remember to label the graphs.
[10]
20.
The table below relates the cost of hosting a wedding banquet with the number of people
attending.
Number of
people
Total cost
40
2200
54
2704
84
3784
What would the price be if there were 140 people attending?
[5]