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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Graphing and Functions | 25% | - Linear functions and their graphs - Coordinate plane and plotting points - Slope and equations of lines - Function notation and evaluation |
| Topic 2: Systems of Equations and Inequalities | 15% | - Graphical solutions - Applications of systems - Solving by substitution and elimination |
| Topic 3: Algebraic Expressions and Operations | 20% | - Order of operations - Variables, constants, and coefficients - Operations with polynomials - Simplifying and evaluating expressions |
| Topic 4: Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Properties of exponents - Simplifying radical expressions - Basic quadratic graphs |
| Topic 5: Linear Equations and Inequalities | 25% | - Solving and graphing inequalities - Solving single-variable equations - Real-world applications |
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質問 # 115
The graphed function n(t)represents the number of people, n, at a park thours after 8:00 a.m. The plotted points Aand Bhave coordinates (2#110)and (6#182).
Which statement gives the correct interpretation of the average rate of change of the number of people over the interval from point Ato point B?
正解：D
解説：
The average rate of change measures how much the output changes per one unit of input.
Here:
t= " hours after 8:00 a.m. "
and
n(t)= " number of people at the park "
The two given points are:
A=(2,110)
and
B=(6,182)
This means:
At t=2hours after 8:00 a.m., there were 110people at the park.
At t=6hours after 8:00 a.m., there were 182people at the park.
Now calculate the average rate of change:
" Average rate of change " =(182-110)/(6-2)
=72/4
=18
Because the value is positive, the number of people is increasing.
So the correct interpretation is:
" The number of people at the park increases at an average rate of 18 people per hour. "
質問 # 116
The function P(t)represents the daily profit, in hundreds of dollars, for a museum since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
正解：C
解説：
The graph shows a curved, downward-opening function. This type of graph is commonly associated with a quadratic polynomial function.
The maximum value of a downward-opening parabola occurs at its highest point, called the vertex.
From the graph, the highest point occurs at approximately:
t=9.5
This means the museum reaches its maximum daily profit approximately:
9.5 " years after opening "
The vertical axis represents daily profit in hundreds of dollars. From the graph, the maximum P(t)-value is approximately:
16.5
Since the profit is measured in hundreds of dollars:
16.5×100=1650
So the maximum daily profit is approximately:
$1,650
Therefore, the correct interpretation is:
" Approximately 9.5 years after opening, a maximum daily profit of approximately " $1,650 " was earned. "
質問 # 117
The function d(x)=14+65xrepresents the distance, in meters, from a tower to an object at time x, in seconds.
What is the value of d(1.5)?
正解：C
解説：
We are given the function:
d(x)=14+65x
This is a linear function because it has the form:
d(x)=mx+b
where 65is the rate of change and 14is the starting value.
We need to find:
d(1.5)
That means substitute x=1.5into the function:
d(1.5)=14+65(1.5)
Now multiply:
65(1.5)=97.5
Then add:
d(1.5)=14+97.5
d(1.5)=111.5
So the distance from the tower to the object at 1.5seconds is:
111.5 " meters "
質問 # 118
The scatterplot shows data on the usage of a computer ' s CPU over time. The graphed regression function has an r