NAME: _________________________________________
Date: _____________________
Ms. Park
Algebra 8 CP
Algebra 8CP MIDTERM REVIEW – CH. 6 – 7
1) Graph each system of equations. Then
2) Graph each system of equations by finding the xdetermine the number of solutions the
and y- intercepts. Then determine the number of
system has. If it has one solution, name it
solutions the system has. If it has one solution,
(as an ordered pair).
name it (as an ordered pair).
𝑦 = −𝑥 + 4
2𝑥 − 𝑦 = −3
𝑦 =𝑥−4
6𝑥 − 3𝑦 = −9
3) Use substitution to solve each system of
equations. If the system does not have
exactly one solution, state whether it has
no solution or infinitely many solutions.
𝑦 = 3𝑥
𝑥+𝑦 =4
4) Use elimination to solve each system of equations.
If the system does not have exactly one solution,
state whether it has no solution or infinitely many
solutions.
𝑥 + 4𝑦 = −8
𝑥 − 4𝑦 = −8
5) Use elimination to solve each system of
equations. If the system does not have
exactly one solution, state whether it has
no solution or infinitely many solutions.
2𝑥 + 5𝑦 = 3
−𝑥 + 3𝑦 = −7
6) Determine the best method to solve the system of
equations. Then solve the system.
Best method: _____________________
5𝑥 − 𝑦 = 17
3𝑥 − 𝑦 = 13
7) The sum of two numbers is 17 and their
difference is 29. What are the two
numbers?
8) Adult tickets for the school musical sold for $3.50
and student tickets sold for $2.50. 321 tickets were
sold altogether for $937.50. How many of each
kind of ticket were sold?
9) Caleb is saving money to purchase a new
video game system. He has $94 and plans
to save $7 each week for the next several
weeks.
a) Write an equation for the total amount
S that he has saved after w weeks.
10) The French Club is selling heart-shaped lollipops
to raise money for a trip to Quebec. They paid $20
for the candy mold, and the ingredients for each
lollipop cost $0.50. They plan to sell the lollipops
for $1.00
a) Write an equation for the cost of supplies y for
the number of lollipops sold x, and an equation
for the income y for the number of lollipops
sold x.
b) Find out how much Caleb will have
saved after 8 weeks.
b) How many lollipops do they need to sell before
they begin to make a profit?
11) At a sale, Sebastian bought 24 reams of paper and 4 inkjet cartridges for $320. Julia bought 2 reams of
paper and 1 inkjet cartridge for $50. The reams of paper were all the same price and the inkjet cartridges
were all the same price. A system of equations can be used to represent this situation. Determine the best
method to sole the system of equations. Then solve the system.
1) Simplify.
2) Simplify.
𝑎(𝑎
4 )(𝑎 7 )
3) Simplify.
(3𝑛𝑡 2 )(−4𝑛3 𝑡 2 )
4) Simplify.
2
1
( 𝑤 3 ) (6𝑤 4 )2
2
3
− 𝑎(𝑎2 𝑏 3 𝑐 4 )
4
5) Find the volume.
6) Find the volume. Leave it in terms of π.
7) Simplify. Assume that no denominator is
equal to zero.
24𝑥 5 𝑎0 𝑏 −7
−8𝑥 2
8) Simplify. Assume that no denominator is equal to
zero.
2𝑥 −2
( −3 )
𝑦
9) Find the sum or difference. Write the
expression in the standard form.
(7𝑔 + 8ℎ − 9) + (−𝑔 − 3ℎ − 6𝑘)
10)
Find the sum or difference. Write the
expression in the standard form.
(9𝑥 2 − 11𝑥𝑦 − 3𝑦 2 ) − (𝑥 2 − 16𝑥𝑦 + 12𝑦 2 )
11)
Simplify.
−𝑎𝑏(3𝑏62 + 4𝑎𝑏 − 6𝑎2 )
12)
13)
Solve.
𝑤(𝑤 + 12) = 𝑤(𝑤 + 14) + 12
14)
Simplify.
𝑥(𝑥 − 6) − 𝑥(𝑥 − 2) + 2𝑥
Solve.
−3(𝑥 + 5) + 𝑥(𝑥 − 1) = 𝑥(𝑥 + 2) − 3
15)
Find the product.
(−𝑎 + 1)(−3𝑎 − 2)
16)
Find the product.
(−𝑛 + 2)(−2𝑛2 + 𝑛 − 1)
17)
Find the product.
(4𝑝 + 3)2
18)
Find the product.
(5𝑏 − 6)(5𝑏 + 6)
19)
Find the area of the swimming pool
below.
20)
The area of a rectangle is 36𝑚4 𝑛6 square
meters. The length of the rectangle is 6𝑚3 𝑛3
meters. What is the width of the rectangle?
21)
Meaghan had a square garden. She expanded this garden by 3 feet in one direction and 5 feet in
the other.
a) Write a polynomial to describe the area of the new garden if the old garden was x feet wide.
b) If the original width was 12 feet, find the area of the new garden.
22)
Find the perimeter of the rectangle
shown below.
23)
24)
A company is designing a box for
dry pasta in the shape of a rectangular
prism. The length is 2 inches more than
twice the width, and the height is 3 inches
more than the length. Write an expression
for the volume of the box.
25)
Michael’s room is x feet on each side. He
adds book shelves that are 2 feet deep to two
adjacent walls.
a) Show how the new area of the floor space can
be modeled by the square of a binomial.
Find the area of the rectangle shown below.
b) Find the square of this binomial (it is a perfect
trinomial).