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| Section | Weight | Objectives |
|---|---|---|
| Exponents, Radicals, and Quadratic Relationships | 15% | - Properties of exponents - Simplifying radical expressions - Solving quadratic equations - Basic quadratic graphs |
| Linear Equations and Inequalities | 25% | - Solving single-variable equations - Real-world applications - Solving and graphing inequalities |
| Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Applications of systems - Graphical solutions |
| Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Variables, constants, and coefficients - Order of operations - Operations with polynomials |
| Graphing and Functions | 25% | - Coordinate plane and plotting points - Slope and equations of lines - Function notation and evaluation - Linear functions and their graphs |
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133. Frage
The value of a collectible coin can be modeled by F(t), where t represents years since the number of years since the coin was found, and the vertical axis represents the value, in thousands of dollars.
How is the value of the coin changing over time based on the graph?
Antwort: A
Begründung:
The graph shows the value of the coin increasing over time. Since the curve rises from left to right, the value is not decreasing. The graph also becomes steeper as time increases, which means the rate of increase is getting larger. In Applied Algebra, when a graph is increasing and its slope is increasing, the quantity is described as increasing faster and faster. This is typical of exponential growth, where values grow by a repeated percent or factor rather than by a constant amount. The choices involving decreasing are incorrect because the graph moves upward. The choice "increasing slower and slower" would require the graph to flatten, which it does not. Therefore, the correct answer is B.
134. Frage
A contractor charges a flat rate plus a fixed rate per hour to come and make repairs. For a job that takes 3 hours, the contractor charges $220. For a job that takes 5 hours, the contractor charges $340.
Which function correctly represents the total charge Cfor a job that takes thours?
Antwort: C
Begründung:
The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:
C(t)=mt+b
where:
m= " hourly rate "
and
b= " flat rate "
We are given two points:
(3#220)
and
(5#340)
These mean:
A 3-hour job costs $220.
A 5-hour job costs $340.
First, find the hourly rate using slope:
m=(340-220)/(5-3)
m=120/2
m=60
So the contractor charges:
$60 " per hour "
Now the function has the form:
C(t)=60t+b
Use the point (3#220)to find the flat rate:
220=60(3)+b
220=180+b
b=40
So the function is:
C(t)=60t+40
Check with t=5:
C(5)=60(5)+40
C(5)=300+40
C(5)=340
This matches the given information.
135. Frage
A vehicle is travelling away from a rest stop. The function
D(t)=48t+23
represents the distance from the vehicle to the rest stop at time t, where t is measured in hours and D is measured in miles.
What is the value of D(1.7)?
Antwort: C
Begründung:
The function is:
D(t)=48t+23
This is a linear function because it has the form:
D(t)=mt+b
where:
48
is the rate of change, and:
23
is the starting distance from the rest stop.
We need to find:
D(1.7)
That means substitute:
t=1.7
into the function.
D(1.7)=48(1.7)+23
First multiply:
48(1.7)=81.6
Now add 23:
D(1.7)=81.6+23
D(1.7)=104.6
So the vehicle is:
104.6 miles
from the rest stop after 1.7 hours.
136. Frage
A researcher collected data on the average number of product returns per month to a company over time. The results are shown in the scatterplot. The graphed regression function has an r
2
value of 0.45.
Which range of x-values is appropriate for extrapolation?
Antwort: C
Begründung:
The coefficient of determination, r
2
, measures how well a regression model fits the data. A value close to 1 indicates a strong fit, while a lower value indicates that the model does not explain the data as reliably. Here, r
2
=0.45, which is below 0.7. That means the model does not have a strong enough fit for reliable extrapolation in this question. Extrapolation means using the model to predict values outside the observed data range, which is riskier than interpolation. Because the model fit is not strong, choosing an extended range of x-values would not be appropriate. The correct reason is that extrapolation is not appropriate because r
2
< 0.7. Therefore, the answer is D.
137. Frage
The figure shows the graph of x(t), which represents the number of users, x, watching a live video thours after
9:00 a.m.
Which interpretation of the concavity between t=3.2and t=5.7is correct?
Antwort: C
Begründung:
The graph represents:
x(t)= " number of users watching a live video "
where:
t= " hours after 9:00 a.m. "
We are asked to interpret the concavity between:
t=3.2
and
t=5.7
On this interval, the graph is going downward, so the number of users is decreasing.
Also, the graph becomes steeper as it moves downward during this interval. That means the rate of decrease is becoming larger in magnitude.
In other words, the number of users is not just decreasing; it is decreasing more quickly as time passes.
So the correct interpretation is:
" The number of users is decreasing faster and faster. "
Therefore, the correct answer is:
# ( " C " )
138. Frage
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