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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Graphing and Functions | 25% | - Function notation and evaluation - Linear functions and their graphs - Coordinate plane and plotting points - Slope and equations of lines |
| Topic 2: Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Operations with polynomials - Variables, constants, and coefficients - Order of operations |
| Topic 3: Exponents, Radicals, and Quadratic Relationships | 15% | - Simplifying radical expressions - Basic quadratic graphs - Properties of exponents - Solving quadratic equations |
| Topic 4: Linear Equations and Inequalities | 25% | - Solving and graphing inequalities - Real-world applications - Solving single-variable equations |
| Topic 5: Systems of Equations and Inequalities | 15% | - Applications of systems - Solving by substitution and elimination - Graphical solutions |
>> Applied-Algebra Test Guide <<
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NEW QUESTION # 130
The graph shows the number of people watching a live video. The number of minutes since the video began is on the horizontal axis, and the number of viewers is on the vertical axis. When were there 432 viewers?
Exhibit:
Answer: C
Explanation:
This problem requires reading a value from a graph. The horizontal axis gives time in minutes, and the vertical axis gives the number of viewers. To solve it, find 432 on the vertical axis, locate where the graph reaches that value, and then move down to the horizontal axis. From the exhibit, the graph reaches 432 viewers at minute 1. That means the ordered pair is approximately (1, 432), so the input is 1 minute and the output is 432 viewers. The other listed minutes correspond to different viewer counts on the graph. In graphical depictions, matching the correct input-output pair is the key step. Therefore, the correct answer is B.
NEW QUESTION # 131
A coach is placing an order for team shirts. The graph shows the total cost based on the number of shirts.
What is the cost of each additional shirt?
Exhibit:
Answer: B
Explanation:
This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139#39=100 dollars.
Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.
NEW QUESTION # 132
The logistic function f(x), whose graph is shown, models the number of registrants for an academic conference, where xrepresents the number of weeks since registration opened and f(x)represents the number of registrants.
How does the number of registrants change as time progresses from week 1 to week 7?
Answer: B
Explanation:
From week 1 to week 7, the graph is increasing and becoming steeper.
In Applied Algebra, when a graph is increasing and its slope is getting larger, the quantity is said to be:
" increasing faster and faster "
This interval is on the early increasing part of the logistic curve, before the graph begins to level off.
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 133
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?
Answer: C
Explanation:
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 "
NEW QUESTION # 134
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?
Answer: A
Explanation:
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.
NEW QUESTION # 135
......
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