MPM2D - Review from grade 9
EQUATIONS
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1. Solve for the unknown variable and check. Show your work.
a. y  8  21
b. y 13  17
y

3

15
c.
d. 3y  36
y
e. 7y  35
f.  16
4
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y
 2
g.
h. 2y  7  33
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4
y
i. 3y 18  27
j. 12  2
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6
k. 2y  5 18
l.
3
y  4  8
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m. 3y  8  2y 12
n. 2y  7  5y  2  8
3y  2
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o. 7 
5
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2. Rachel sells bags of popcorn at the Toronto Maple
Leafs hockey games. She is paid $12.50 per hour
and 30 cents for each bag of popcorn she sells.
a. If Rachel worked four hours and sold 73 bags of popcorn, how much money would she earn?
Show your work.
b. If Rachel earned $105.00 and she worked 6 hours, how many bags of popcorn did she sell? Show
you work.
3. For each one of the following word problems you must have let statements with one variable, an
equation, solution of the variable and there statements which answer the question.
a. Allie is five years younger than Liam. If the sum of their ages is 51, how old is each one?
b. The sum of three consecutive integers is 168. What are the numbers?
c. Avery and Taylor had a bouncing contest. If Avery bounced seven less than twice the bounces of
Taylor and their combined bounces totalled 383, how many times did each one bounce?
4. Two friends are collecting pop-can tabs. Natasha has 250 more pop-tabs than Kristin. Together they
have collected 88 pop-can tabs. How many pop-can tabs has each friend collected?
5. Anoja, Amani, and Azra are three freidns who each have part-time jobs. Last week, Anoja earned
twice as much money as Azra, while Amani earned $25 more than Anoja. The total earnings of the
three friends last week was $450. How much money did each of them earn last week?
6. John has $23.65 to spend on a book and magazine. The book costs $5.95. The magazines costs $2.95
each.
a. Write an equation that models the number of magazines that John can afford.
b. Solve the equation.
7. The total of three cousins’ ages is 48. Salley is half as old as Hawkins and 4 years older than Dale.
How old are the cousins?
8. Kelly sells T-Shirts at a rock concert. She earns $8.00/h, plus $0.50 for each T-shirt she sells.
a. How much will Kelly earn in a 4 hour shift if she sells 35 T-shirts?
b. How many T-shirts must Kelly sell to earn $80 in a 6 hour shift?
Modelling with Graphs
9. Richard works at a jean outlet, he is paid $18 per hour.
a. Write an equation for her pay.
______________________________
b. Is this a direct or partial variation? ______________________________
c. What is the constant of variation (rate of change)?______________________________
d. Construct a table of values for 0, 1, 2, 3, and 4 hours of work
e. Graph the relationship on a properly labelled graph.
f. How much did Richard earn if he worked 8 hours? Show all your work!
g. How much did Richard earn if he worked 6 hours?
10. The volume of water in a barrel is 22 litres (already there) plus 15 litres a minute when Matthew is
pouring.
a. Write an equation for the volume of water in a barrel.
b. Is this a direct or partial variation? How do you know?
c. What is the constant?
d. What is the rate of change?
e. What is the volume of water n the barrel after 8 minutes?
f. How much time will it take to fill the barrel to 218 litres?
11. Determine the slope of each line given the information presented:
a.
b. A line passing through points (-9, 7) and (8, 21).
12. A ramp rises 3 m over a run of 12 m.
a. How would you change the run to make the slope steeper?
b. How would you change the rise to make the slope steeper?
13. A steel beam goes between the tops of two buildings. The first building is 32 metres high and the
second building is 59 metres high. If the two buildings are 9 metres apart, what is the slope of the
beam? Draw a diagram to illustrate & SHOW ALL YOUR WORK!
14. Using first differences, classify each relation as being linear or non-linear.
a.
x
y
0
1
2
3
20
21
23
28
b.
x
y
-3
-4
-5
-6
0
5
10
15
c.
x
y
1
2
3
4
17
28
39
50
15. Greg charges $70 plus $50/hour to repair computers.
a. Write an equation representing the relationship
b. What is the total cost of a repair that takes 4.5 hours?
c. How many hours did he work if the repair job cost $255?
16. Use the rule of 4 to represent the relation in three other ways
17. Matthew cycles 50 km to a friend’s home. The distance, d, in kilometres, varies directly with the
time, t, in hours.
a. Find an equation relating d and t, if d=24 when t = 1.5. What does the constant of variation
represent?
b. Use the equation to determine how long it will take Matthew to reach his destination.
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Linear Relations
1. For each one of the following linear equations determine the slope and the t-intercept.
Equation
Slope
y-intercept
y  3x  5
y
2
x 9
3
y 6
x  8
3x  6y 12  0
2. For each one of the graphed lines, write a linear equation in y  mx  b
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A ________________________
B ________________________
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C ________________________
D ________________________
E ________________________
3. Graph each one of the following linear equations on the graph provided. Label each line.
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A
y  x3
B
3
y  x 3
4
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4. Rewrite the linear equations. Write the ones in standard form in y-intercept form.
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a. x  y  4  0
b. x  4 y  3  0
c. 2x  5y 10  0
d. 3x  2y  6  0
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5. Determine the slope of a line passing through points (2, 7) and (4, 13).
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6. Determine the slope of a line passing through points (2, -5) and (8, -1).
7. Determine the x and y intercepts of the line 4 x  3y  24
8. Determine the x and y intercepts and graph the line 2x  4 y  12
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9. Write a linear equation in y-intercept form for each one of the following lines.
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a. A line passing through point (3, -7) with a slope of 2.
b. A line passing through points (-3, 8) and (-7, 16)
1
c. A line passing through point (-3, 8) with a slope perpendicular to line y   x  9
2
d. A line passing through point (1, 6) and parallel to line 2x  4 y  9  0
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10. Determine which one of the following is the intersection point of the lines. SHOW YOUR WORK.
xy 3
and
a. (2, 3)
b. (1, 2)
c. (-5, 8)
d. (-2, 5)
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2x  3y  19