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Review for Unit 1 Test Pg. 62 # 2 – 9, 10ac, 11 - 18
Sept.
20 1.11
TEST- UNIT 1
MPM 2D Lesson 1.1 Representing Linear Relations
Ex. 1 Translate Words Into Algebra
a) Write each phrase as a mathematical expression:
i) the value five increased by a number ii) seven less than twice a number
b) Write the following sentence as a mathematical equation.
i) Half of a value, decreased by seven, is one.
ii) Twice a number, subtracted from five, is three more than seven times the number.
c) Translate the following sentence into an equation, using two variables.
i) Mario’s daily earnings are $80 plus 12% commission on his sales.
ii) Fitness Club CanFit charges a $150 initial fee to join the club and a $20 monthly fee.
Ex. 2 Does the point )2,3( satisfy the linear relation 01232 yx ?
Ex. 3 Brian and Catherine want to get Internet access for their home. There are two companies in the area.
IT Plus charges a flat rate of $25/month for unlimited use. Techies Inc. charges $10/month plus $1/h . If Brian and Catherine expect to use the Internet for approximately 18 h/month, which plan is the
better option for them? Determine the two equations you would use to solve the problem.
Ex. 4 Ali owns a small airplane. He pays $50/h for flying time and $300/month for hangar fees at the local
airport. If Ian rented the same type of airplane at the local flying club, it would cost him $100/h.
How many hours will Ali have to fly each month so that the cost of renting will be the same as the cost
of flying his own plane? Determine the two equations you would use to solve the problem.
Pg. 12 # 1, 4, 5, 9, 13, 15
WS 1.1
MPM 2D Lesson 1.2 Solving Systems of Equations Graphically
Ex. 1 Solve by using tables of values (ToV).
2x + y = 5 ---
y = 33
2x ---
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
Ex. 2 Solve by using x– and y–intercepts.
3x + 2y = 6 ---
x – 2y = 10 ---
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
x
x y = 3
2x – 3
Ex. 3 Find the slope and the y-intercept of each of the following linear relations.
a) 3x + 2y = 9 b) 2x – 5y = 20
Ex. 4 Solve by using the slope and the y–intercept.
3x + y = 5 ---
–x + 3y = – 15 ---
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
Ex. 5 Determine whether or not (–3, 2) is a solution to the given system.
3x + 2y = –5 ---
–x + y = 4 ---
Pg. 26 # 1, 2, 5, 10, 14, 17ab
MPM 2D Lesson 1.3 Solving Systems of Equations by Substitution
Ex. 1 Solve using the method of substitution and check your answer.
225 yx ----- 1423 yx -----
You do not always have to rearrange for a variable. Sometimes it is easier to rearrange
for a multiple of a variable the sub it in to the other equation. Always explain each step
before you do it.
Ex. 2 Marla and Nancy played in a volleyball marathon for charity. They played for 38 h and raised $412.
Marla was sponsored for $10/h and Nancy was sponsored for $12/h. How many hours did each play?
Ex. 3 Sarah is starting a business in which she will hem pants. Her start up cost, to buy a sewing machine,
is $1045. She will use about $0.50 in materials to hem each pair of pants. She plans to charge $10 for
each pair of pants she hems. How many pairs of pants does she need to hem to break even?
Pg. 38 # 1 – 5, 10, 12, 16
MPM 2D Lesson 1.4 Solving Systems of Equations by Elimination
To solve a system by elimination,
decide which variable to eliminate
to eliminate a variable, it must have the same numerical coefficient in both equations
to eliminate, either add or subtract the equations based on the signs of the variable
o if signs are the same, subtract ie: -3 – (-3) = 0
o if signs are different, add ie: -3 + (3) = 0
continue to solve for the variables as you have previously