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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Graphing and Functions | 25% | - Coordinate plane and plotting points - Slope and equations of lines - Function notation and evaluation - Linear functions and their graphs |
| Topic 2: Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Basic quadratic graphs - Simplifying radical expressions - Properties of exponents |
| Topic 3: Algebraic Expressions and Operations | 20% | - Operations with polynomials - Order of operations - Simplifying and evaluating expressions - Variables, constants, and coefficients |
| Topic 4: Systems of Equations and Inequalities | 15% | - Applications of systems - Solving by substitution and elimination - Graphical solutions |
| Topic 5: Linear Equations and Inequalities | 25% | - Real-world applications - Solving single-variable equations - Solving and graphing inequalities |
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51. Frage
The graph shows the estimated wait time, in minutes, based on the number of hours after 7:00 a.m.
What is the average rate of change of the wait time from point Ato point B?
Antwort: D
Begründung:
From the graph, the horizontal axis represents:
t= " hours after 7:00 a.m. "
The vertical axis represents:
" estimated wait time in minutes "
Point Ais approximately at:
A=(5,88.3)
Point Bis approximately at:
B=(9,65)
The average rate of change from point Ato point Bis calculated using:
(y_2-y_1)/(x_2-x_1 )
Substitute the values:
(65-88.3)/(9-5)
=(-23.3)/4
=-5.825
Rounded to two decimal places:
-5.83
So, the wait time decreases by about:
5.83 " minutes per hour "
52. Frage
The function P(t) represents the yearly profit, in thousands of dollars, for a virtual store since opening. The graph of P(t) is shown.
What is the time at which the store reached the maximum yearly profit?
Antwort: B
Begründung:
The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward- opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened.
The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.
53. Frage
A researcher collected data on the number of large donations per year to a charitable organization. The results are shown in the scatterplot. A regression function is graphed with r