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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Graphical solutions - Applications of systems |
| Topic 2: Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Properties of exponents - Basic quadratic graphs - Simplifying radical expressions |
| Topic 3: Linear Equations and Inequalities | 25% | - Real-world applications - Solving single-variable equations - Solving and graphing inequalities |
| Topic 4: Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Operations with polynomials - Order of operations - Variables, constants, and coefficients |
| Topic 5: Graphing and Functions | 25% | - Linear functions and their graphs - Function notation and evaluation - Coordinate plane and plotting points - Slope and equations of lines |
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問題 #61
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?
答案：A
解題說明：
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. "
問題 #62
The graph shows the number of books, N, checked out from a library each week. The number of weeks since the beginning of the year is on the horizontal axis, and the number of books checked out per week is on the vertical axis. Point A represents 165 books checked out in the first week, or N(0)=165. Which statement represents an accurate conclusion?
Exhibit:
答案：D
解題說明：
This question asks for the correct interpretation of a labeled point on a graph. In function notation, N(x)=y means when the input is x weeks, the output is y books checked out. The exhibit shows several plotted points.
Point B is located at approximately x=2.8 and y=177, so Point B represents N(2.8)=177. To verify a graph statement, both the horizontal coordinate and vertical coordinate must match the actual point on the graph. If either coordinate is wrong, then the statement is not accurate. Since Point B matches the stated coordinates and output value, it is the valid conclusion. Therefore, the correct answer is A.
問題 #63
The number of people auditioning for a game show is expected to be 7 more than the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A(t) represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 440 people auditioned last year?
答案：A
解題說明：
In this function-notation problem, the input represents last year's number of people and the output represents this year's expected number. Because this year's number is 7 more than last year's, the rule is A(t)=t+7. The question says 440 people auditioned last year, so the correct input is 440. Substituting gives A(440)
=440+7=447. This means if 440 people auditioned last year, then 447 are expected to audition this year. The notation must place 440 inside the parentheses because that is the input value, and 447 must be written as the output value. The other options reverse the input and output or subtract instead of adding. Therefore, option C is correct.
問題 #64
The number of property sales in a region this year is expected to be 9 more than the number of property sales in the region last year. The function H(x) represents the number of property sales this year, where x represents 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 140?
答案：B
解題說明：
This question asks for correct function notation. The input x represents the number of properties sold last year, and the output H(x) represents the expected number of property sales this year. Since this year's number is expected to be 9 more than last year's number, the function rule is H(x)=x+9. The problem states that 140 properties were sold last year, so the correct input is x=140. Substituting gives H(140)=140+9=149. This means that when last year's sales were 140, this year's expected sales are 149. The input must be inside the parentheses, and the output must follow the equals sign. Therefore, the correct answer is B.
問題 #65
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 A(t)can be used to model the situation, where trepresents the number of people who auditioned last year and Arepresents 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?
答案：D
解題說明：
The function A(t)represents the number of people expected to audition this year.
The input trepresents 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:
A(t)=t-3
We are told that 280 people auditioned last year, so:
t=280
Substitute 280into the function:
A(280)=280-3
A(280)=277
So, the notation that represents the number of people expected to audition this year is:
A(280)=277
This means if 280 people auditioned last year, then 277 people are expected to audition this year.
Therefore, the correct answer is:
# ( " A " )
問題 #66
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