Applied-Algebra Übungsmaterialien, Applied-Algebra Zertifizierungsprüfung

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WGU Applied-Algebra Exam Syllabus Topics:

Section	Objectives
Foundations of Algebra	- Equations and Inequalities 1. Inequalities and interval notation 2. Linear equations in one variable - Algebraic Expressions 1. Evaluating expressions 2. Simplifying expressions 3. Order of operations
Functions and Graphs	- Graphing Functions 1. Transformations of graphs 2. Coordinate plane interpretation - Function Concepts 1. Function notation 2. Domain and range
Exponential and Logarithmic Concepts	- Exponential Functions 1. Growth and decay models 2. Exponential equations - Logarithmic Basics 1. Logarithm properties 2. Conversion between exponential and logarithmic form
Linear Functions and Systems	- Systems of Equations 1. Elimination method 2. Substitution method - Linear Equations 1. Point-slope form 2. Slope-intercept form
Polynomial and Rational Expressions	- Polynomials 1. Factoring techniques 2. Operations with polynomials - Rational Expressions 1. Restrictions on variables 2. Simplification

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Applied-Algebra Zertifizierungsprüfung - Applied-Algebra Online Tests

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WGU Applied Algebra FXO2 PFXP C957 Applied-Algebra Prüfungsfragen mit Lösungen (Q129-Q134):

129. Frage
A researcher collected data on the number of annual bear sightings in a region over time. The results are shown in the scatterplot. The graphed regression function has an r
2value of 0.41. The predicted number of annual bear sightings after 19.4 years is 88.5.

Is this prediction appropriate?

A. No. The r2value indicates a strong fit, but x=19.4 is more than 50% of the range beyond the maximum value.
B. Yes. The r2value indicates a strong fit, and x=19.4 is within 50% of the range of the maximum value.
C. Yes. The r2value indicates a moderate fit, and x=19.4 is within 25% of the range of the maximum value.
D. No. The r2value indicates a moderate fit, but x=19.4 is more than 25% of the range beyond the maximum value.

Antwort: D

Begründung:
The r2value of 0.41 indicates a moderate fit, not a strong fit. A moderate regression model may sometimes support limited extrapolation, but only if the prediction stays close to the observed data. Here, the prediction is made at x=19.4, which is beyond the maximum x-value shown in the scatterplot. For a moderate fit, extrapolation should be more conservative than for a strong fit. The value x=19.4 is more than 25% of the data range beyond the maximum observed value, so the prediction is too far outside the data. Because the fit is only moderate and the extrapolation distance is too large, the prediction is not appropriate. Therefore, the answer is B.

130. Frage
The logistic function f(x), whose graph is shown, models the number of people who have created a website account, where xrepresents the number of days since the website started and f(x)represents the number of people who have created an account.

What is one range of values for which the graph is concave down?

A. (8#16)
B. (0#8)
C. (0#16)
D. (0#12)

Antwort: A

Begründung:
For a logistic graph, concavity changes at the inflection point.
Before the inflection point, the graph is usually concave up. This means the function is increasing faster and faster.
After the inflection point, the graph is concave down. This means the function is still increasing, but it is increasing slower and slower.
From the graph, the curve changes concavity around:
x=8
After x=8, the graph begins to level off as it approaches its upper limit.
So one interval where the graph is concave down is:
(8#16)
Therefore, the correct answer is:
# ( " A " )

131. Frage
A recipe calls for a constant ratio of water and lemon juice. The graph shows the relationship between the amounts of these two ingredients, where wis the volume of water and lis the volume of lemon juice.

What is the correct interpretation of the rate of change?

A. The amount of lemon juice must be the amount of water plus 8/5.
B. The amount of lemon juice must be the amount of water plus 5/8.
C. The amount of lemon juice must be 5/8of the amount of water.
D. The amount of lemon juice must be 8/5of the amount of water.

Antwort: C

Begründung:
The graph shows a linear relationship between:
w= " water in cups "
and
l= " lemon juice in cups "
The line passes through the origin, so the relationship has the form:
l=mw
where mis the rate of change.
From the graph, a clear point on the line is approximately:
(8#5)
This means when there are 8 cups of water, there are 5 cups of lemon juice.
The rate of change is:
m= " change in lemon juice " / " change in water "
m=5/8
So the relationship is:
l=5/8 w
This means the amount of lemon juice must be:
5/8
of the amount of water.

132. Frage
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.

What does the horizontal asymptote mean?

A. Over time, the number of licensed sellers will increase back up to 1,050.
B. After 21 months, the number of licensed sellers decreased to 300.
C. The number of licensed sellers was initially 1,050.
D. In the long run, the number of licensed sellers nears 300.

Antwort: D

Begründung:
The horizontal asymptote describes the long-term behavior of the function. In this problem, the graph shows a decreasing exponential model for the number of licensed sellers. The graph begins near a higher value and then decreases, eventually leveling off near 300. This means the number of licensed sellers approaches 300 over time. It does not mean the number necessarily becomes exactly 300 at 21 months, and it does not mean the sellers increase back to the initial value. The initial value is separate from the horizontal asymptote. Since the graph levels off around 300, the correct interpretation is that in the long run, the number of licensed sellers nears 300. Therefore, the answer is C.

133. Frage
The number of property sales in a region this year is expected to be 8 times the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 360?

A. H(360)=45
B. H(2,880)=360
C. H(360)=2,880
D. H(45)=360

Antwort: C

Begründung:
We are told that the number of property sales this year is expected to be 8 times the number of property sales last year.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 8 times last year's sales, the function rule is:
H(x)=8x
The question says that last year's property sales were:
x=360
Substitute 360into the function:
H(360)=8(360)
H(360)=2,880
So the correct notation is:
H(360)=2,880
This means: if 360 properties were sold last year, then 2,880 property sales are expected this year.
Therefore, the correct answer is:
# ( " C " )

134. Frage
......

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