Unit 5 Practice Test
Name: ___________________________________
Date: ________________________
Part A: Multiple Choice
Circle the answer that best completes the statement or answers the question.
1. Lisa looks at the equation x + 5 = 9 and, without writing anything down, realized that the
final answer is x = 4. What method did Lisa use to come up with the answer?
A) Inspection
B) Guess and Check
C) Balance Method with Alge-Tiles
D) Balance Method with Opposite Operations
2. What is the opposite operation of squaring a number?
A) Addition
B) Subtraction
C) Square Root
D) Division
Part B: Short Answer
Show all your work Use full sentences where required. Mathematical terminology must be spelt
correctly.
1. Solve the following equations. Show your work. Solving by inspection will only get you
one out of two marks.
a) 𝑥 + 5 = 13
b) 6𝑥 = 48
𝑥
c) = 17
4
2. Solve the following equation by using the “LIDS” method.
5𝑥 + 11 = 46
3. Alexis and Austin both solved the equation 𝟑𝒙𝟐 = 𝟏𝟎𝟖.
Austin says, “the answer is x = 6.” “No! The answer is x = -6,” Alexis says.
Perform a check on both answers below. Who is right?
4. Sidney decides to start a catering company called Sidney’s Sweets. She caters desserts for
weddings and birthday parties of all sizes. She charges a base fee plus a cost per person
for her services.
The equation C = 4n + 25 represents how much it costs, C, to hire Sidney for a party with
n people attending.
a) Determine how much it would cost to hire Sidney to prepare desserts for a party with
75 people attending?
b) Mrs. Rivet is planning a party, and has $400 to spend on desserts. What is the
maximum number of people she can invite to the party? Show your work. Include a
therefore statement.
5. Choice Question - For this question, choose A or B. Do NOT answer both questions.
A – Circle the mistake that was made in the following solution. Explain what the student did
wrong. Make the necessary corrections.
3𝑥 + 1 = 7
3𝑥 + 1 − 1 = 7 – 1
3𝑥 = 6
3𝑥
=6
3
𝑥= 6
Check:
LS = 3x + 1
= 3(6) + 1
= 18 + 1
= 19
RS = 7
𝐿𝑆 ≠ 𝑅𝑆 ∴ 𝑥 = 6 is not the solution.
B – Circle the mistake that was made in the following solution. Explain what the student did
wrong. Make the necessary corrections.
4𝑥 − 3 = 29
4𝑥 − 3 + 3 = 29 + 3
4𝑥 = 32
4𝑥 32
=
4
4
𝑥= 8
Check:
LS = 4x – 3
= 4(8) -3
= 12 -3
=9
RS = 29
𝐿𝑆 ≠ 𝑅𝑆 ∴ 𝑥 = 8 is not the solution.
Part C: Open Question
1. Write down a binomial with an ‘x term’ and a constant term (for example, 2x – 3). Do
NOT use 2x – 3 as your binomial.
Write your binomial in the blank below.
__________ = 2x – 3
2. Solve the equation created in question 1.
Part D: Thinking Question


You are allowed to use your calculator for this question. However, write down the
numbers you use and the operations you carry out.
Try to give a clear, well-organized solution to illustrate your complete understanding and
ability to communicate. Give as much information as you can.
There are two bowling alleys in town.
The total cost of bowling at Briggs Bowling is represented by the graph below. Briggs
Bowling offers its customers free shoe rentals.
Briggs Bowling
Hint: Shoe rental
is the initial
value.
The total cost of bowling at Beam Bowling is $4 for shoe rental plus $3 per game.
Michaela and Meagan want to bowl 4 games each. Which bowling alley should they go to if
they want to pay the least amount of money for those games? Explain your answer. Show
your work.
**BONUS MARK: Which company is a partial variation?