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2026年最新のな厳密検証された合格させるApplied-Algebra試験にはリアル問題と解答
質問 # 62
The function F(n) represents the relationship between the number of animals in two enclosures, where n is the number of animals in enclosure A and F is the number of animals in enclosure B. The number of animals in enclosure B is 20 more than the number of animals in enclosure A.
Which function represents this situation?
- A. F(n)=n/20
- B. F(n)=n#20
- C. F(n)=n+20
- D. F(n)=20n
正解：C
解説：
The function F(n) gives the number of animals in enclosure B.
The input n represents the number of animals in enclosure A.
The problem says enclosure B has 20 more animals than enclosure A. The phrase "20 more than" means we add 20:
F(n)=n+20
For example, if enclosure A had 30 animals, then enclosure B would have:
F(30)=30+20=50
So the function that represents the situation is:
F(n)=n+20
質問 # 63
The number of tasks completed by computer B is 12 more than the number of tasks completed by computer A. Let F(x)represent the relationship between the number of tasks completed by the two computers, where xis the number of tasks completed by computer A and Fis the number of tasks completed by computer B.
Which function represents this situation?
- A. F(x)=12x
- B. F(x)=x+12
- C. F(x)=x/12
- D. F(x)=x-12
正解：B
解説：
We are told that computer B completes 12 more tasks than computer A.
Let:
x= " number of tasks completed by computer A "
and
F(x)= " number of tasks completed by computer B "
The phrase "12 more than" means add 12 to the original amount:
F(x)=x+12
So, if computer A completes xtasks, computer B completes:
x+12
tasks.
For example, if computer A completed 50 tasks, then computer B completed:
F(50)=50+12=62
Therefore, the correct answer is:
# ( " B " )
質問 # 64
The graph shows the weekly profit in hundreds of dollars for a coffee shop. The horizontal axis represents the number of years since the coffee shop opened.
What is the correct interpretation of the minimum value?
- A. Approximately 13 years after opening, a minimum weekly profit of approximately $990was earned.
- B. Approximately 13 years after opening, a minimum weekly profit of approximately $4,630was earned.
- C. Approximately 6 years after opening, a minimum weekly profit of approximately $990was earned.
- D. Approximately 6 years after opening, a minimum weekly profit of approximately $4,630was earned.
正解：C
解説：
The graph shows weekly profit as a function of time.
The horizontal axis represents:
" years since opening "
The vertical axis represents:
" weekly profit in hundreds of dollars "
The graph is an upward-opening curve, so its minimum value occurs at the lowest point, called the vertex.
From the graph, the lowest point occurs at approximately:
t=6
So the minimum weekly profit happened approximately:
6 " years after opening "
The vertical value at this point is approximately:
9.9
Since the profit is measured in hundreds of dollars:
9.9×100=990
So the minimum weekly profit was approximately:
$990
Therefore, the correct answer is:
# ( " A " )
質問 # 65
The exponential function
f(t)=2900(1.13)
t
represents the size of a bacteria population, where t is the time in hours.
How many bacteria are in the population when t=18?
- A. 20,495
- B. 23,160
- C. 29,573
- D. 26,170
正解：D
解説：
This is an exponential growth problem because the base 1.13 is greater than 1. The function starts with 2,900 bacteria and grows by a factor of 1.13 each hour, which represents a 13% hourly increase. To find the population after 18 hours, substitute t=18 into the function: f(18)=2900(1.13)
18
Evaluating the exponent and multiplying by 2900 gives approximately 26,170.38. Since bacteria are counted as whole organisms, this rounds to about 26,170 bacteria. The other answer choices do not match the exponential model at t=18. Therefore, the correct answer is C.
質問 # 66
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?
- A. $47.00
- B. $17.30
- C. $14.00
- D. $3.30
正解：C
解説：
This question asks for the cost of each additional shirt, which means we need to find the rate of change of the linear function.
On a graph, the rate of change is the slope:
" slope " = " change in total cost " / " change in number of shirts "
From the graph, two labeled points are:
(0#33)
and
(10#173)
This means:
When 0shirts are ordered, the cost is $33.
When 10shirts are ordered, the cost is $173.
Now find the slope:
m=(173-33)/(10-0)
m=140/10
m=14
So the cost increases by:
$14
for each additional shirt.
The $33represents a fixed starting cost, not the cost per shirt.
質問 # 67
The values, in dollars, of two accounts over time are modeled by
A_1 (t)=6,500× # 1.05 # ^t
and
A_2 (t)=3,000× # 0.96 # ^t
The variable tis measured in years.
What is the difference between the accounts after 3 years?
- A. The value of Account 1 is about $4,870greater than the value of Account 2.
- B. The value of Account 1 is about $2,654greater than the value of Account 2.
- C. The value of Account 1 is about $4,870less than the value of Account 2.
- D. The value of Account 1 is about $2,654less than the value of Account 2.
正解：A
解説：
We need to compare the two account values after:
t=3
First, find the value of Account 1:
A_1 (3)=6,500× # 1.05 # ^3
A_1 (3)=6,500×1.157625
A_1 (3)#7,524.56
Now find the value of Account 2:
A_2 (3)=3,000× # 0.96 # ^3
A_2 (3)=3,000×0.884736
A_2 (3)#2,654.21
Now subtract:
7,524.56-2,654.21=4,870.35
So Account 1 is about:
$4,870
greater than Account 2 after 3 years.
Therefore, the correct answer is:
# ( " C " )
質問 # 68
The number of property sales in a region this year is expected to be 8 times the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 360?
- A. H(45)=360
- B. H(360)=2,880
- C. H(2,880)=360
- D. H(360)=45
正解：B
解説：
We are told that the number of property sales this year is expected to be 8 times the number of property sales last year.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 8 times last year's sales, the function rule is:
H(x)=8x
The question says that last year's property sales were:
x=360
Substitute 360into the function:
H(360)=8(360)
H(360)=2,880
So the correct notation is:
H(360)=2,880
This means: if 360 properties were sold last year, then 2,880 property sales are expected this year.
Therefore, the correct answer is:
# ( " C " )
質問 # 69
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?
- A. 79.2 hours
- B. 79.2 travelers
- C. 2 travelers
- D. 2 hours
正解：B
解説：
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 " )
質問 # 70
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?
- A. 4,250
- B. 0
- C. 2,500
- D. 8,500
正解：C
解説：
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 " )
質問 # 71
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:
- A. Minute 4
- B. Minute 0
- C. Minute 2
- D. Minute 1
正解：D
解説：
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.
質問 # 72
The graph shows the number of people waiting in a virtual queue to buy tickets for an event.
What does the horizontal asymptote mean?
- A. The number of people in the queue was initially 750.
- B. As time passes, the number of people in the queue approaches 100.
- C. Over time, the number of people in the queue will increase back up to 750.
- D. Eventually, the number of people in the queue will decrease to 0.
正解：B
解説：
The graph shows the queue size changing over time.
The horizontal axis represents:
" Time in minutes "
The vertical axis represents:
" Queue size "
The graph is a decreasing exponential curve. It starts near 750people and decreases quickly at first. Then the curve begins to flatten near:
y=100
A horizontal asymptote is the horizontal line that the graph approaches as time continues.
Here, the graph approaches the horizontal line:
y=100
This means that as time passes, the number of people in the virtual queue gets closer and closer to 100.
It does not mean the queue decreases to 0, because the graph levels off near 100, not near 0.
Therefore, the correct interpretation is:
" As time passes, the number of people in the queue approaches 100. "
質問 # 73
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?
- A. t=11.2to t=11.5
- B. t=1.2to t=5.3
- C. t=8.6to t=9.0
- D. t=8.7to t=10.7
正解：A
解説：
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.
質問 # 74
A person makes down quilts to sell.
The graph shows the functions that model the cost and revenue.
How many down quilts need to sell to break even/start making a profit?
- A. 0
- B. 1
- C. 2
- D. 3
正解：C
解説：
This question asks us to interpret a graph showing cost and revenue.
In Applied Algebra, the break-even point is where:
" Revenue " = " Cost "
On a graph, this happens where the revenue line and the cost line intersect.
From the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The break-even point occurs where these two lines cross.
Looking carefully at the graph, the two lines intersect at approximately:
x=6
The horizontal axis represents the number of units, meaning the number of down quilts sold.
So the person needs to sell about:
6 " quilts "
to break even.
After selling more than 6 quilts, the revenue line is above the cost line, meaning the person begins making a profit.
質問 # 75
The graph shows the number of customers, C(t), showing up to a store, where the number of hours since opening is along the horizontal axis and the number of customers showing up to the store each hour is along the vertical axis.
How can the concavity be described from t=6.2to t=10.1?
- A. The number of customers decreases slower and slower and then increases faster and faster.
- B. The number of customers increases faster and faster and then increases slower and slower.
- C. The number of customers increases slower and slower and then increases faster and faster.
- D. The number of customers increases slower and slower and then decreases faster and faster.
正解：D
解説：
From t=6.2to about t=8.5, the graph is increasing, but it is becoming less steep as it approaches a local maximum.
That means the number of customers is:
" increasing slower and slower "
After the local maximum, from about t=8.5to t=10.1, the graph begins to decrease and becomes steeper downward.
That means the number of customers is:
" decreasing faster and faster "
So the full description is:
" The number of customers increases slower and slower and then decreases faster and faster. " Therefore, the correct answer is:
# ( " D " )
質問 # 76
The graph shows the value, O, in dollars, of an investment account over time.
What represents the value of the account after 8 years?
- A. $1,028.81
- B. $700.19
- C. $2,221.12
- D. $476.54
正解：C
解説：
The graph shows the total value of an investment account as time increases.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Total value in dollars "
We need to find the value of the account after:
8 " years "
From the graph, when t=8, the curve is slightly above $2,200. The closest answer choice is:
$2,221.12
So the value of the account after 8 years is approximately:
$2,221.12
Therefore, the correct answer is:
# ( " D " )
質問 # 77
The scatterplot shows data on the number of shirts sold at a gift shop per week over time. The graphed regression function has an r
2
value of 0.09.
Which range of x-values is appropriate for extrapolation?
- A. x=#3 to x=21
- B. x=0 to x=18
- C. Extrapolation is not appropriate because r
2
< 0.3. - D. Extrapolation is not appropriate because r
2
< 0.7.
正解：C
解説：
The r
2
value tells how closely the regression model fits the scatterplot data. In this problem, r
2
=0.09, which is extremely low. This means the regression model explains only a very small portion of the variation in the shirt-sales data. When r
2
is this weak, the model is not reliable for predictions outside the data range. Extrapolation is already less certain than interpolation because it predicts beyond the observed data. With such a poor fit, extending the model beyond the data would not be appropriate. Since 0.09 < 0.3, the best justification is that extrapolation is not appropriate because r
2
< 0.3. Therefore, the correct answer is C.
質問 # 78
The function P(t)represents the daily profit, in hundreds of dollars, for a museum since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
- A. Approximately 20 years after opening, a maximum daily profit of approximately $299was earned.
- B. Approximately 9.5 years after opening, a maximum daily profit of approximately $1,650was earned.
- C. Approximately 20 years after opening, a maximum daily profit of approximately $1,650was earned.
- D. Approximately 9.5 years after opening, a maximum daily profit of approximately $299was earned.
正解：B
解説：
The graph shows a curved, downward-opening function. This type of graph is commonly associated with a quadratic polynomial function.
The maximum value of a downward-opening parabola occurs at its highest point, called the vertex.
From the graph, the highest point occurs at approximately:
t=9.5
This means the museum reaches its maximum daily profit approximately:
9.5 " years after opening "
The vertical axis represents daily profit in hundreds of dollars. From the graph, the maximum P(t)-value is approximately:
16.5
Since the profit is measured in hundreds of dollars:
16.5×100=1650
So the maximum daily profit is approximately:
$1,650
Therefore, the correct interpretation is:
" Approximately 9.5 years after opening, a maximum daily profit of approximately " $1,650 " was earned. "
質問 # 79
The function d(x)=14+65xrepresents the distance, in meters, from a tower to an object at time x, in seconds.
What is the value of d(1.5)?
- A. 0.19
- B. 111.5
- C. 0
- D. 1
正解：B
解説：
We are given the function:
d(x)=14+65x
This is a linear function because it has the form:
d(x)=mx+b
where 65is the rate of change and 14is the starting value.
We need to find:
d(1.5)
That means substitute x=1.5into the function:
d(1.5)=14+65(1.5)
Now multiply:
65(1.5)=97.5
Then add:
d(1.5)=14+97.5
d(1.5)=111.5
So the distance from the tower to the object at 1.5seconds is:
111.5 " meters "
質問 # 80
......
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