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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Exponents, Radicals, and Quadratic Relationships | 15% | - Simplifying radical expressions - Properties of exponents - Solving quadratic equations - Basic quadratic graphs |
| Topic 2: Graphing and Functions | 25% | - Linear functions and their graphs - Slope and equations of lines - Function notation and evaluation - Coordinate plane and plotting points |
| Topic 3: Linear Equations and Inequalities | 25% | - Solving single-variable equations - Real-world applications - Solving and graphing inequalities |
| Topic 4: Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Graphical solutions - Applications of systems |
| Topic 5: Algebraic Expressions and Operations | 20% | - Variables, constants, and coefficients - Simplifying and evaluating expressions - Order of operations - Operations with polynomials |
>> Applied-Algebra Prüfungsinformationen <<
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22. Frage
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Antwort: A
Begründung:
The graph compares the populations of two towns over time.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Population in thousands "
The graph shows:
Town A as the solid blue line.
Town B as the dashed blue line.
To determine which town's population is growing faster, we compare the slopes of the two lines.
In Applied Algebra, the slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
" Town A grows at about " 0.9 " thousand people per year "
" Town B grows at about " 1.6 " thousand people per year "
Now compare the growth rates:
1.6 > 0.9
So Town B's population is growing at a faster rate.
The values 8.0and 6.5describe starting populations, not growth rates. Since the question asks about growing at a faster rate, we must compare the slopes.
23. Frage
The population of bison in a preserve can be modeled using the logistic function f(x), where x represents the number of years since the preserve was established and f(x) represents the population. The graph of f(x) is shown.
How does the bison population change as time progresses from year 7 to year 10?
Antwort: D
Begründung:
A logistic function often increases quickly in the middle and then begins to level off as it approaches a maximum carrying capacity. From year 7 to year 10, the graph is still increasing, so the bison population is going up. However, the curve is becoming flatter during this interval. A flatter curve means the slope is getting smaller, so the population is increasing at a slower rate. This behavior is described as "increases slower and slower." It is not decreasing, because the graph continues to move upward. It is also not increasing faster and faster, because the slope is not becoming steeper in this interval. Therefore, the correct interpretation is answer B.
24. Frage
In the graph showing the number of new customer accounts, the horizontal axis shows the number of weeks since the beginning of winter and the vertical axis shows the number of new customer accounts. More customer accounts are opened during snowy weeks than during weeks without snow.
When was it likely snowy?
Antwort: D
Begründung:
This question asks us to interpret unusually high values on a graph. The problem states that more customer accounts are opened during snowy weeks than during weeks without snow. Therefore, the likely snowy weeks correspond to the peaks on the graph, where the number of new customer accounts is noticeably higher than surrounding weeks. The graph shows clear spikes at approximately week 7 and week 14. These weeks have higher account openings compared with nearby weeks, making them the best evidence of snowy conditions.
Week 1 and week 5 do not match the main peaks shown in the graph. Since the snowy weeks should correspond to the highest customer-account values, the correct answer is D.
25. Frage
The value of a collectible artifact is represented by the function
f(x)=330× # 1.15 #