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Integers
Solving Equations
Word Problems
Direct/Partial Variation and Slope
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100
What is an integer?
A positive or a negative whole number.
100
4x + 9x + 2x = 3
15x = 3 x = 5
100
Sam has 4 tickets to the Raptors game. If each of them cost $45, how much would it cost for all 4 tickets?
$180
100
The cost of renting a banquet hall is $200. There is an additional cost of $3 for each person attending. Identify the fixed cost and the variable cost.
Fixed = $200 Variable = $3 per person
100
A set of stairs is to be built so that each step has a vertical rise of 20cm over a horizontal run of 27.5cm. Find the slope.
20/27 = 0.74
200
(-23)+(-11)
-34
200
(4g)(-9g) + (5g)(2g)
-36g^2 +10g^2 = -26g^2
200
Ms M and Ms Chau go buy cookies from the cafeteria! They have $3.50 each to spend. If Ms Wappel joins them and has $4.00, and each cookie sells for $0.50, how many cookies can they afford altogether?
22 cookies!
200
Give an example of a equation that represents a direct variation and another that represents a partial variation.
Answers may vary.
200
Matt sells T-shirts online. He earns $12.00 per hour plus $1.50 for each T-shirt he sells. How much will he earn in 4 hours if he sells 15 shirts?
He will earn $70.50
300
(-30) + 4 - (-25)
51
300
Solve for y. 9(3y + 2)= -7(1 - y)
y = 1.25
300
Mark is 8 years older than her cousin. Together, the sum of their ages is 46. How old is Mark? How old is her cousin?
Mark is 27. Her cousin is 19.
300
From looking at a graph, how can you tell if a relation is a direct or partial variation?
A direct variation when graphed always goes through point (0,0) or the origin, whereas a partial variation has an initial y-value.
300
Determine the constant of variation for this situation. Josh earned $450 in 11 hours working at Wonderland.
450/11 = $40.91/hour
400
[(-6) - (-10)] + 20 + (-9)
15
400
Write an equation for the following scenario and define your variables. It costs Ms Chau $39 for her phone plan, plus $5 for each 100 MB, if she goes over her data limit.
C=39 + 5M, where M represents the number of 100 MB and C represents the total cost of her phone plan.
400
Jenny and Amy are playing basketball. Jenny scores three times as many points as Amy. If the sum of their points is 68, how many points did they each score?
Jenny scores 51 and Amy scores 17.
400
What is the equation for slope?
slope = rise/run
400
A water tank is being filled with water at a constant rate. After 20s, the tank contains 200L of water. What is the rate of change of the water?
200L/20s = 10L/s
500
(-8) x 4 + (-10) / 5 - 90
-124
500
Roy is twice as old as Gene. In 15 years Roy will be 9 years older than Gene will be. How old Roy is now? How old is Gene now?
Roy is 18, Gene is 9.
500
Two friends are collecting Star Wars figures. Jeremy has 250 more figures than Mike. Together they have collected 880 figures. How many figures has each person collected?
Mike has 315 figures and Jeremy has 565 figures.
500
A line segment has one endpoint of A (-3,2) and a slope of -3/5. Find the coordinates of another possible endpoint.
Answers may vary. One possible solution is B (2, -1)
500
A ladder is learning against the wall of a building so that it reaches 10m up the wall. The bottom of the ladder is 1.25m from the base of the wall. What is the slope of the ladder?
The slope is 8