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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Exponents, Radicals, and Quadratic Relationships | 15% | - Properties of exponents - Basic quadratic graphs - Solving quadratic equations - Simplifying radical expressions |
| Topic 2: Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Graphical solutions - Applications of systems |
| Topic 3: Graphing and Functions | 25% | - Coordinate plane and plotting points - Slope and equations of lines - Function notation and evaluation - Linear functions and their graphs |
| Topic 4: Linear Equations and Inequalities | 25% | - Solving single-variable equations - Real-world applications - Solving and graphing inequalities |
| Topic 5: Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Order of operations - Operations with polynomials - Variables, constants, and coefficients |
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問題 #42
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 5 sacks are removed, the total weight of the wagon and remaining sacks is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. What is the weight of each sack?
答案：C
解題說明：
This situation has a constant rate of change because each sack weighs the same amount. After 5 sacks are removed, the total weight is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. From 5 to
9 sacks removed is 4 more sacks. Over the same interval, the total weight decreases by 135#87=48 pounds.
Since 4 sacks account for a 48-pound decrease, each sack must weigh 48÷4=12 pounds. This uses the linear idea that equal changes in the input produce equal changes in the output. Therefore, the weight of each sack is
12 pounds, which is answer A.
問題 #43
The function V(t)represents the number of travelers, V, in a travel depot thours after 7:00 a.m. The graph of V (t)is shown.
What does V(2)represent?
答案：D
解題說明：
The function V(t)represents the number of travelers in the travel depot.
The input trepresents:
" hours after 7:00 a.m. "
The output V(t)represents:
" number of travelers "
So V(2)means the number of travelers in the depot:
2 " hours after 7:00 a.m. "
From the graph, when:
t=2
the value of V(t)is approximately:
79.2
Since V(t)measures travelers, not hours, V(2)represents:
79.2 " travelers "
Therefore, the correct answer is:
# ( " D " )
問題 #44
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?
答案：A
解題說明：
The average rate of change tells us how much the output changes, on average, for each 1-unit increase in the input.
Here:
x= " hours after 7:00 a.m. "
and
y= " estimated wait time in minutes "
From the graph, point Ais approximately:
A=(5,88.3)
and point Bis approximately:
B=(9,65)
Now use the average rate of change formula:
" Average rate of change " =(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
The negative sign means the estimated wait time is decreasing from point Ato point B.
So the average rate of change is approximately:
-5.83 " minutes per hour "
問題 #45
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?
答案：D
解題說明：
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.
問題 #46
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?
答案：C
解題說明：
This question asks which town's population is growing at a faster rate.
Since both population graphs are straight lines, we compare their slopes.
The slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
Town A starts at about 8.0thousand people and increases at a rate of about 1.0thousand people per year.
Town B starts at about 5.5thousand people and increases at a rate of about 1.3thousand people per year.
Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.
Compare the rates:
1.3 > 1.0
So Town B is growing faster than Town A.
問題 #47
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