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WGU Applied Algebra Exam Questions
- Topic 1: Algebraic Expressions and Operations: Covers simplifying, evaluating, and solving algebraic expressions and equations using basic algebraic rules and operations.
- Topic 2: Linear Equations and Inequalities: Focuses on solving linear equations and inequalities and interpreting their meaning in real-world situations.
- Topic 3: Functions and Graphs: Explains how to analyze functions, interpret graphs, and understand relationships between variables.
- Topic 4: Exponential and Polynomial Models: Covers working with exponential and polynomial equations to model growth, decay, and other mathematical patterns.
- Topic 5: Applied Algebra Problem Solving: Focuses on applying algebra concepts to practical scenarios, including data interpretation and mathematical decision-making.
Free WGU Applied Algebra Exam Actual Questions
Note: Premium Questions for Applied Algebra were last updated On May. 23, 2026 (see below)
The graph shows the daily practice duration for a musician, where the number of days since the beginning of the month is along the horizontal axis and the number of minutes practiced per day is along the vertical axis.
What was the practice duration for day 9, based on the graph?
This question asks us to read and interpret a value from a graph.
The horizontal axis represents:
The vertical axis represents:
We need to find the practice duration for:
To do this, locate on the horizontal axis, move upward to the blue graph, and then read the corresponding value on the vertical axis.
From the graph, the point at day is approximately:
So the musician practiced for:
The number of people auditioning for a game show is expected to be 3 less than the number of people who auditioned last year. The function can be used to model the situation, where represents the number of people who auditioned last year and represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 280 people auditioned last year?
The function represents the number of people expected to audition this year.
The input represents the number of people who auditioned last year.
The problem says this year's number is expected to be 3 less than last year's number. Therefore, the function rule is:
We are told that 280 people auditioned last year, so:
Substitute into the function:
So, the notation that represents the number of people expected to audition this year is:
This means if 280 people auditioned last year, then 277 people are expected to audition this year.
Therefore, the correct answer is:
A researcher collected data on the number of large donations per year to a charitable organization. The results are shown in the scatterplot. A regression function is graphed with .
What is the appropriate range of -values for extrapolation?
The scatterplot shows data collected over time, and a regression curve is used to model the pattern.
Extrapolation means using a model to make predictions slightly outside the observed data range. In Applied Algebra, extrapolation can be appropriate when:
and the predicted -values are not too far outside the observed data.
From the scatterplot, the data points appear to run approximately from:
So the observed data range is about:
A reasonable extrapolation range extends a little beyond the data, but not too far. The interval:
extends about 3 units beyond each side of the observed data, which is reasonable.
The interval:
extends much farther beyond the data and would be less reliable.
Also, does not have to equal exactly 1 for extrapolation to be useful. A value less than 1 can still represent a strong model.
Therefore, the correct answer is:
The weight of a radioactive sample is given by the function
where is the time, in years, and is the weight of the sample, in ounces.
What is the weight of the sample when ?
The function is:
This is an exponential decay function because the base is between 0 and 1:
That means the sample's weight decreases over time.
We need to find the weight when:
Substitute into the function:
First calculate the exponent:
Now multiply by :
Rounded to two decimal places:
So the weight of the radioactive sample after 3 years is approximately:
The value of a collectible artifact is represented by the function
In this function, represents the number of years since 2005, and represents the value of the artifact, in dollars.
Which value represents the average yearly rate of change of the value of the artifact from 2006 to 2011?
The function is:
Because represents the number of years since 2005:
The average yearly rate of change from 2006 to 2011 is:
First, find :
Now find :
Now calculate the average rate of change:
Rounded to two decimal places:
So the average yearly rate of change of the artifact's value from 2006 to 2011 is approximately:
Therefore, the correct answer is:
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