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WGU C957 Applied Algebra OA (2026) exam -
Comprehensive Study Guide (100+ Q&A with rationales)
Topic 1: Variables - Qualitative vs. Quantitative
Question 1: Which choice is a variable?
A) The number of states in the United States of America
B) The cost of your daily newspaper
C) The amount a teenager makes babysitting
D) Your shoe size
Answer: C) The amount a teenager makes babysitting
Rationale: A variable is something that can change or vary. The amount a teenager makes babysitting
changes from week to week depending on hours worked and hourly rate. The number of US states is
fixed (50), a newspaper's cost is generally constant, and adult shoe size typically remains stable .
Question 2: Which choice is a qualitative variable?
A) Your bank account number
B) Your shirt color
C) Your salary
D) Your weight
Answer: B) Your shirt color
Rationale: Qualitative (categorical) variables describe non-numerical qualities or characteristics. Shirt
color (e.g., "red," "blue") fits this definition. Bank account numbers, salary, and weight are all
quantitative variables because they represent numerical values .
Question 3: Which choice is a quantitative variable?
A) S, representing the number of regular weekly shipping deliveries
B) P, representing the monthly profit based on customer numbers
C) R, representing the monthly rent for your office building
D) M, representing the federal minimum wage
Answer: B) P, representing the monthly profit based on customer numbers
Rationale: A quantitative variable measures a numerical quantity or amount. Monthly profit is a
numerical value that can be calculated and changes based on business activity .
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Question 4: In a lawn-mowing business, which choice represents a qualitative variable?
A) G, representing the amount of gas needed
B) W, representing the number of hours worked each day
C) H, representing the hilliness of the lawn
D) M, representing the maximum amount of lawn mowed per hour
Answer: C) H, representing the hilliness of the lawn
Rationale: "Hilliness" is a descriptive, non-numerical category (e.g., "flat," "slightly hilly," "very steep").
The other options represent measurable quantities .
Topic 2: Independent vs. Dependent Variables
Question 5: The amount of food prepared for a catered event depends on the number of people
attending. Which variable is the independent variable?
A) The amount of food prepared
B) The number of people attending
Answer: B) The number of people attending
Rationale: The independent variable is the input or cause. The number of people attending determines
how much food is prepared, so attendance is independent and food amount is dependent .
Question 6: The output of toy cars in a factory is affected by the number of employees per shift. Which
variable is the dependent variable? A) The number of toy cars produced
B) The number of employees working each shift
Answer: A) The number of toy cars produced
Rationale: The dependent variable is the output or outcome. The number of toy cars produced depends
on the number of employees working. If more employees work, more cars are produced .
Question 7: When you first started your job, you earned two weeks of vacation. After five years, you
earn three weeks. After ten years, you earn four weeks. What is the dependent variable?
A) The number of weeks of vacation
B) The number of years employed
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Answer: A) The number of weeks of vacation
Rationale: The number of vacation weeks depends on how many years you have been employed. Years
employed determines vacation time, making vacation weeks the dependent variable .
Question 8: Which pair would most likely be an independent and dependent variable pair?
A) Finishing times for a marathon and the price of milk
B) Number of package deliveries and number of people with blonde hair
C) Amount of rainfall and crop yield
D) House sales and food sales
Answer: C) Amount of rainfall and crop yield
Rationale: The amount of rainfall (independent) most likely affects the amount of crops produced
(dependent). More rainfall generally leads to higher crop yield, representing a logical cause-and-effect
relationship .
Topic 3: Functions and Function Notation
Question 9: A local business wants to predict the number of franchises, F, given a certain number of
years, Y, modeled by the function F(Y). What can be concluded by F(5) = 10? A) In 5 years, there will
be 10 open stores.
B) In 10 years, there will be 5 open stores.
C) There are currently 5 stores, and they will grow to 10.
D) The business opened 5 stores 10 years ago.
Answer: A) In 5 years, there will be 10 open stores.
Rationale: In function notation F(Y), Y is the input (years) and F(Y) is the output (number of franchises).
F(5) = 10 means when the input is 5 (years), the output is 10 (stores) .
Question 10: The volume of calls, V(h), at a customer service center can be written as a function of the
number of hours after opening, h. What would the ordered pair (6, 8) represent? A) There were 6 calls
8 hours after opening.
B) There were 8 calls 6 hours after opening.
C) The center received 14 calls total.
D) The call volume doubled after 6 hours.Answer: B) There were 8 calls 6 hours after opening.
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Rationale: Ordered pairs are written as (input, output) or (h, V(h)). So (6, 8) means when h = 6 (6 hours
after opening), V(h) = 8 (8 calls) .
Question 11: A company has two functions: L(t) and M(t), determining the least and most revenue in
any given month (t=1 is January). What can they conclude if L(2) = 3,000 and M(2) = 5,000? A) In
February, revenue will be exactly $4,000.
B) In February, revenue will be between $3,000 and $5,000.
C) In March, revenue will be between $3,000 and $5,000.
D) The company lost money in February.
Answer: B) In February, revenue will be between $3,000 and $5,000.
Rationale: L(t) represents the minimum expected revenue, and M(t) represents the maximum. For t=2
(February), the least revenue is $3,000 and the most is $5,000, so actual revenue should fall within this
range .
Question 12: A bank gives a $50 credit to one new customer each month through a drawing. The
amount given away, G, is a function of months, M. What function notation represents the amount given
away after 5 months?
A) G(50) = 5
B) G(5) = 250
C) G(250) = 5
D) G(5) = 50
Answer: B) G(5) = 250
Rationale: Each month, $50 is given away. After 5 months, the total given away is 5 × $50 = $250. In
function notation G(M), M is the input (months), and G(M) is the output (total dollars). So G(5) = 250 .
Question 13: A server's tips, T in dollars, are related to hours worked, h, modeled by T(h) = X. How is this
interpreted?
A) If the server works X hours, tips will be
h.B)Iftheserverworkshhours,tipswillbeh.B)Iftheserverworkshhours,tipswillbeX. C)
Tips are always equal to hours worked.
D) The server makes X dollars per hour.
Answer: B) If the server works h hours, tips will be $X.
WGU C957 Applied Algebra OA (2026) exam -
Comprehensive Study Guide (100+ Q&A with rationales)
Topic 1: Variables - Qualitative vs. Quantitative
Question 1: Which choice is a variable?
A) The number of states in the United States of America
B) The cost of your daily newspaper
C) The amount a teenager makes babysitting
D) Your shoe size
Answer: C) The amount a teenager makes babysitting
Rationale: A variable is something that can change or vary. The amount a teenager makes babysitting
changes from week to week depending on hours worked and hourly rate. The number of US states is
fixed (50), a newspaper's cost is generally constant, and adult shoe size typically remains stable .
Question 2: Which choice is a qualitative variable?
A) Your bank account number
B) Your shirt color
C) Your salary
D) Your weight
Answer: B) Your shirt color
Rationale: Qualitative (categorical) variables describe non-numerical qualities or characteristics. Shirt
color (e.g., "red," "blue") fits this definition. Bank account numbers, salary, and weight are all
quantitative variables because they represent numerical values .
Question 3: Which choice is a quantitative variable?
A) S, representing the number of regular weekly shipping deliveries
B) P, representing the monthly profit based on customer numbers
C) R, representing the monthly rent for your office building
D) M, representing the federal minimum wage
Answer: B) P, representing the monthly profit based on customer numbers
Rationale: A quantitative variable measures a numerical quantity or amount. Monthly profit is a
numerical value that can be calculated and changes based on business activity .
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Question 4: In a lawn-mowing business, which choice represents a qualitative variable?
A) G, representing the amount of gas needed
B) W, representing the number of hours worked each day
C) H, representing the hilliness of the lawn
D) M, representing the maximum amount of lawn mowed per hour
Answer: C) H, representing the hilliness of the lawn
Rationale: "Hilliness" is a descriptive, non-numerical category (e.g., "flat," "slightly hilly," "very steep").
The other options represent measurable quantities .
Topic 2: Independent vs. Dependent Variables
Question 5: The amount of food prepared for a catered event depends on the number of people
attending. Which variable is the independent variable?
A) The amount of food prepared
B) The number of people attending
Answer: B) The number of people attending
Rationale: The independent variable is the input or cause. The number of people attending determines
how much food is prepared, so attendance is independent and food amount is dependent .
Question 6: The output of toy cars in a factory is affected by the number of employees per shift. Which
variable is the dependent variable? A) The number of toy cars produced
B) The number of employees working each shift
Answer: A) The number of toy cars produced
Rationale: The dependent variable is the output or outcome. The number of toy cars produced depends
on the number of employees working. If more employees work, more cars are produced .
Question 7: When you first started your job, you earned two weeks of vacation. After five years, you
earn three weeks. After ten years, you earn four weeks. What is the dependent variable?
A) The number of weeks of vacation
B) The number of years employed
,3
Answer: A) The number of weeks of vacation
Rationale: The number of vacation weeks depends on how many years you have been employed. Years
employed determines vacation time, making vacation weeks the dependent variable .
Question 8: Which pair would most likely be an independent and dependent variable pair?
A) Finishing times for a marathon and the price of milk
B) Number of package deliveries and number of people with blonde hair
C) Amount of rainfall and crop yield
D) House sales and food sales
Answer: C) Amount of rainfall and crop yield
Rationale: The amount of rainfall (independent) most likely affects the amount of crops produced
(dependent). More rainfall generally leads to higher crop yield, representing a logical cause-and-effect
relationship .
Topic 3: Functions and Function Notation
Question 9: A local business wants to predict the number of franchises, F, given a certain number of
years, Y, modeled by the function F(Y). What can be concluded by F(5) = 10? A) In 5 years, there will
be 10 open stores.
B) In 10 years, there will be 5 open stores.
C) There are currently 5 stores, and they will grow to 10.
D) The business opened 5 stores 10 years ago.
Answer: A) In 5 years, there will be 10 open stores.
Rationale: In function notation F(Y), Y is the input (years) and F(Y) is the output (number of franchises).
F(5) = 10 means when the input is 5 (years), the output is 10 (stores) .
Question 10: The volume of calls, V(h), at a customer service center can be written as a function of the
number of hours after opening, h. What would the ordered pair (6, 8) represent? A) There were 6 calls
8 hours after opening.
B) There were 8 calls 6 hours after opening.
C) The center received 14 calls total.
D) The call volume doubled after 6 hours.Answer: B) There were 8 calls 6 hours after opening.
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Rationale: Ordered pairs are written as (input, output) or (h, V(h)). So (6, 8) means when h = 6 (6 hours
after opening), V(h) = 8 (8 calls) .
Question 11: A company has two functions: L(t) and M(t), determining the least and most revenue in
any given month (t=1 is January). What can they conclude if L(2) = 3,000 and M(2) = 5,000? A) In
February, revenue will be exactly $4,000.
B) In February, revenue will be between $3,000 and $5,000.
C) In March, revenue will be between $3,000 and $5,000.
D) The company lost money in February.
Answer: B) In February, revenue will be between $3,000 and $5,000.
Rationale: L(t) represents the minimum expected revenue, and M(t) represents the maximum. For t=2
(February), the least revenue is $3,000 and the most is $5,000, so actual revenue should fall within this
range .
Question 12: A bank gives a $50 credit to one new customer each month through a drawing. The
amount given away, G, is a function of months, M. What function notation represents the amount given
away after 5 months?
A) G(50) = 5
B) G(5) = 250
C) G(250) = 5
D) G(5) = 50
Answer: B) G(5) = 250
Rationale: Each month, $50 is given away. After 5 months, the total given away is 5 × $50 = $250. In
function notation G(M), M is the input (months), and G(M) is the output (total dollars). So G(5) = 250 .
Question 13: A server's tips, T in dollars, are related to hours worked, h, modeled by T(h) = X. How is this
interpreted?
A) If the server works X hours, tips will be
h.B)Iftheserverworkshhours,tipswillbeh.B)Iftheserverworkshhours,tipswillbeX. C)
Tips are always equal to hours worked.
D) The server makes X dollars per hour.
Answer: B) If the server works h hours, tips will be $X.
