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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: Algebraic Expressions and Operations | 20% | - Operations with polynomials - Simplifying and evaluating expressions - Order of operations - Variables, constants, and coefficients |
| Topic 3: Linear Equations and Inequalities | 25% | - Solving and graphing inequalities - Solving single-variable equations - Real-world applications |
| Topic 4: Graphing and Functions | 25% | - Function notation and evaluation - Linear functions and their graphs - Slope and equations of lines - Coordinate plane and plotting points |
| Topic 5: Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Basic quadratic graphs - Properties of exponents - Simplifying radical expressions |
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61. Frage
The number of registered voters in a district is modeled by a decreasing exponential function, where x represents the number of years since 2005 and f(x) represents the number of registered voters.
Which interval is associated with the slowest average decrease in the number of registered voters?
Antwort: A
Begründung:
A decreasing exponential function falls quickly at first and then levels off over time. The "slowest average decrease" occurs where the graph is flattest, because the output changes by the smallest amount per year.
Earlier intervals, such as 2005 to 2008, occur when the graph is steepest, so those intervals have a faster average decrease. Later intervals occur after the exponential decay has slowed. From the graph, the interval from 2015 to 2025 is farthest to the right and has the least steep downward trend. Therefore, the number of registered voters decreases most slowly during that interval. This is why the correct answer is D.
62. Frage
A researcher collected data on the number of books donated per month to a thrift store over time. The results are shown in the scatterplot. A regression function is graphed with r
2
=0.99.
Which range of x-values is appropriate for extrapolation?
Antwort: A
Begründung:
The value r
2
=0.99 indicates a very strong regression fit because it is close to 1. A strong fit means the model explains most of the variation in the data, so limited extrapolation can be appropriate. However, extrapolation should stay close to the observed data range. From the scatterplot, the data values appear to run from about x=5 to x=15. A reasonable extrapolation range extends slightly beyond those observed values, not too far outside them. The interval x=2.5 to x=17.5 stays close to the original data and is more appropriate than the wider interval x=0 to x=20. Therefore, the correct answer is B.
63. Frage
The function p(t)represents the number of active players, p, in a game thours after 11:00 a.m. The graph of p(t) is shown.
What is one example of an interval for which the number of players is decreasing faster and faster?
Antwort: A
Begründung:
The graph represents:
p(t)= " number of active players "
where:
t= " hours after 11:00 a.m. "
The phrase "decreasing faster and faster" means two things are happening:
The graph is going downward, so the number of players is decreasing.
The graph is becoming steeper downward, so the rate of decrease is increasing.
This corresponds to a graph that is decreasing and concave down.
Looking at the graph, the number of active players reaches a maximum around:
t#9
After that, the graph begins decreasing. Near the far right side of the graph, especially around:
t=11.2 " to " t=11.5
the curve is dropping more and more steeply.
That means the number of players is decreasing faster and faster on that interval.
64. Frage
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
What is the long-term trend in the number of letters processed per day, based on the equation of the horizontal asymptote?
Antwort: B
Begründung:
The graph shows a decreasing exponential function.
In Applied Algebra, a decreasing exponential function may approach a fixed value over time. This fixed value is called the horizontal asymptote.
The horizontal asymptote represents the long-term value that the function gets closer and closer to, but does not necessarily cross or reach exactly.
From the graph, the curve decreases quickly at first, then begins to level off near:
y=1,000
This means that as time continues, the number of letters processed per day approaches:
1,000
So the long-term trend is that the mail center will process about:
1,000 " letters per day "
65. Frage
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
Which value is the number of letters processed per day trending toward as time progresses, based on the equation of the horizontal asymptote?
Antwort: D
Begründung:
The graph shows a decreasing exponential function.
The vertical axis represents:
" Letters per day "
The horizontal axis represents:
" Time in years "
For an exponential decay graph, the value decreases quickly at first and then begins to level off. The value it approaches in the long run is called the horizontal asymptote.
From the graph, the curve levels off near:
y=2,500
So the number of letters processed per day is trending toward:
2,500
This does not mean the mail center immediately processes exactly 2,500 letters per day. It means that as time continues, the number gets closer and closer to 2,500.
Therefore, the correct answer is:
# ( " B " )
66. Frage
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