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| Section | Weight | Objectives |
|---|---|---|
| Systems of Equations and Inequalities | 15% | - Graphical solutions - Solving by substitution and elimination - Applications of systems |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Properties of exponents - Simplifying radical expressions - Solving quadratic equations |
| Linear Equations and Inequalities | 25% | - Solving single-variable equations - Real-world applications - Solving and graphing inequalities |
| Graphing and Functions | 25% | - Coordinate plane and plotting points - Linear functions and their graphs - Slope and equations of lines - Function notation and evaluation |
| Algebraic Expressions and Operations | 20% | - Variables, constants, and coefficients - Order of operations - Simplifying and evaluating expressions - Operations with polynomials |
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質問 # 98
The number of employees under supervisor B is 13 more than the number of employees under supervisor A.
Let F(n)represent the number of employees under the two supervisors, where nis the number of employees under supervisor A and Fis the number of employees under supervisor B.
Which is the correct function to represent this relationship?
正解：C
解説：
We are told that supervisor B has 13 more employees than supervisor A.
Let:
n= " number of employees under supervisor A "
and
F(n)= " number of employees under supervisor B "
The phrase "13 more than" means we add 13:
F(n)=n+13
So, if supervisor A has nemployees, supervisor B has 13 additional employees.
For example, if supervisor A had 20 employees, then supervisor B would have:
F(20)=20+13=33
Therefore, the correct answer is:
# ( " C " )
質問 # 99
A team was assembled at a manufacturing plant in order to boost productivity. The team was tasked with producing as many widgets each day as possible. The results are shown in the graph.
What is the correct interpretation of the average rate of change from day 6 to day 14?
正解：C
解説：
The graph models the number of widgets the team can produce each day.
The horizontal axis represents:
" days "
The vertical axis represents:
" widgets "
The graph gives two labeled points:
(6#3.4)
and
(14#23)
The average rate of change is:
" change in widgets " / " change in days "
Substitute the values:
(23-3.4)/(14-6)
=19.6/8
=2.45
Rounded to the nearest tenth:
2.5
This means the team increased production by an average of approximately:
2.5 " widgets each day "
Therefore, the correct answer is:
# ( " B " )
質問 # 100
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?
正解：A
解説：
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.
質問 # 101
The population of fish in a lake is changing according to the function
P(t)=24t+185
where tis the number of months since the beginning of the year and P(t)is the fish population at time t.
Which interpretation of the rate of change is correct?
正解：C
解説：
The function is:
P(t)=24t+185
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In the function:
P(t)=24t+185
the coefficient of tis:
24
So the rate of change is:
24 " fish per month "
Because 24is positive, the fish population is increasing.
The number 185is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=24(0)+185=185
Therefore, the correct interpretation is:
" The number of fish in the lake is increasing at a constant rate of 24 fish per month. " So the correct answer is:
# ( " B " )
質問 # 102
The number of people, P, in a festival audience is represented by the graph, with the number of hours since the beginning of the festival along the horizontal axis and the size of the audience along the vertical axis.
Point Arepresents an audience size of 402 for the first hour of the festival, or P(0)=402.
Which ordered pair represents a point on the graph?
正解：D
解説：
This question is about reading an ordered pair from a graph.
An ordered pair has the form:
(x#y)
where:
x= " time in hours "
and
y= " audience size "
From the graph:
Point Ais at approximately (0#402)
Point Bis at (2#401)
Point Cis at (4#403)
Point Dis at (6#406)
Point Eis at approximately (8#410)
Point Fis at (10#408)
Now compare these graph points with the answer choices.
Choice A says:
(2#401)
This matches point Bon the graph exactly.
The other choices do not match the graph:
(4#404)
is incorrect because at x=4, the graph shows about 403, not 404.
(8#409)
is incorrect because at x=8, the graph is about 410, not 409.
(10#407)
is incorrect because at x=10, the graph shows about 408, not 407.
質問 # 103
......
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