Applied Algebra FX01 Exam (C957)
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Free Applied Algebra FX01 Exam (C957) Questions
The rate at which a rumor spreads through a middle school can be determined using the following graph, where R(d) is the number of people who have heard the rumor after d days of it being introduced to the student body. What can be concluded about the spread of the rumor over time based on the graph? What happens to the amount of students who have heard the rumor as each day passes?
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The number of students increases faster and faster.
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The number of students increases slower and slower and then increases faster and faster.
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The number of students increases slower and slower.
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The number of students increases faster and faster and then increases slower and slower.
Explanation
Correct answer:
The number of students increases faster and faster and then increases slower and slower.
Explanation:
From the graph the number of students tend to increase rapidly the stopes and remain constant at 2000.
Why other options are wrong:
“The number of students increases faster and faster” This is not true since the graph starts to level at some point hence slowing down.
“The number of students increases slower and slower and then increases faster and faster” This is incorrect since the correct option is the opposite of this.
“The number of students increases slower and slower” This is not true since the gradient at some point changes significantly at some point.
The number of rats infected by a disease can be modeled by the graph below, where S(1) represents the number of rats infected, S, on day 1, and d is measured in days.
When will approximately 75% of the maximum number of rats be infected?
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On day 7
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On day 6
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On day 4
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On day 9
Explanation
Correct answer:
On day 9.
Solution:
The point where the graph flattens is at 100 rats. 75% of 100 is 75, hence the day is the point that corresponds to 75 rats on the y axis.
Why others options are wrong:
“On day 7” On this day only approximately 50 rats were infected.
“On day 6” On this day only approximately 30 rats were infected.
“On day 4” On this day only approximately 10 rats were infected.
The rate of profit in the business sector of the United States from 1929 to 1962 is illustrated by the function R in the graph below. Point A represents a rate of profit of 0.31 in the year 1929, or R(1929) = 0.31.
What can be concluded about this function?
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Point B represents R(1932) = 0.2.
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Point D represents R(1941) = 0.37.
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Point I represents R(1961) = 0.3.
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Point E represents R(1945) = 0.5.
Explanation
Solution:
Rechecking the options;
Point B represents R(1932) = 0.2
Point D represents R(1941) = 0.32.
Point I represents R(1961) = 0.3.
Point E represents R(1945) = 0.49
From the graph point B is not 1932, hence it can be concluded that Point I represents R(1961) = 0.3.
Correct answer:
Point I represents R(1961) = 0.3.
Why other options are wrong:
“Point B represents R(1932) = 0.2.” From the graph point B is not 1932
“Point D represents R(1941) = 0.37.” Point D represents R(1941) = 0.32.
“Point E represents R(1945) = 0.5.” Point E represents R(1945) = 0.49
The graph below shows the number of page views (in thousands) for a website as a function of the number of employees marketing the website.
How many additional page views, on average, are expected for each additional worker when increasing from 10 to 20 employees?
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1,040 page views per worker
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9,590 page views per worker
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959 page views per worker
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366 page views per worker
Explanation
Solution:
where v(20) = 21.99, v(10) = 12.4
= 0.959
Hence on average any additional worker there will be 0.959 thousand page views
Correct answer:
959 page views per worker
Why other options are wrong:
"1,040 page views per worker": This is incorrect because the actual calculation yields 959 page views, not 1,040.
"9,590 page views per worker": This is incorrect because 9,590 page views is the total number of additional views for 10 workers, not per worker.
"366 page views per worker": This is incorrect because the average number of additional page views per worker is 959, not 366.
The function H(d) = -3d² + 24d represents the height (in tens of meters) of a projectile after d seconds (in halves of seconds). What does H(2) mean?
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The height is 24 meters after 1 second
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The height is 240 meters after 1 second
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The height is 24 meters after 2 seconds
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The height is 240 meters after 2 seconds
Explanation
Solution:
Let's substitute d = 2 into the height function:
H(2) = -3(2)² + 24(2)
H(2) = -12 + 48
H(2) = 24
Since d is in halves of seconds, d = 2 means 1 second. Since H(d) is in tens of meters, H(2) = 24 means 240 meters.
Correct Answer:
The height is 240 meters after 1 second
Why Other Options Are Wrong:
"The height is 24 meters after 1 second": This correctly interprets the time but misinterprets H(2) = 24 as 24 meters instead of 240 meters.
"The height is 240 meters after 2 seconds": This correctly interprets the height but misinterprets d = 2 as 2 seconds instead of 1 second.
"The height is 24 meters after 2 seconds": This misinterprets both the height unit and the time unit.
How should P(1) be interpreted based on the graph of P(x)?
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The profit for producing 1,000 items is about $200.
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The profit for producing 1,000 items is about $20,000,000.
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The profit for producing 200 items is about $1,000.
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The profit for producing 20,000,000 items is about $1,000.
Explanation
Correct Answer:
The profit for producing 1,000 items is about $20,000,000.
Why the Other Options Are Wrong:
"The profit for producing 1,000 items is about $200." Incorrect because the graph shows P(1) = 20, which corresponds to $20 million, not $200.
"The profit for producing 200 items is about $1,000.” Incorrect because x = 1x refers to 1,000 items, not 200 items.
"The profit for producing 20,000,000 items is about $1,000." Incorrect because x = 1x corresponds to 1,000 items, not 20,000,000 items. The graph does not represent data for millions of items directly.
A company has the following information on last quarter’s sales (month 7 refers to July)
What was the average rate of change over the entire quarter (from July to September)?
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Sales increased an average of $15,000 per month.
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Sales increased an average of $37,000 per month.
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Sales increased an average of $6,285.71 per month.
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Sales increased an average of $10,000 per month.
Explanation
Correct Answer:
Sales increased an average of $15,000 per month.
Explanation:
The average rate of change is calculated as:
Step 1: Calculate the total change in sales from July (Month 7) to September (Month 9):
Total Change in Sales=333−303=30 (in thousands of dollars).
Step 2: Calculate the number of months:
From July to September is 2 months.
Step 3: Calculate the average rate of change:
Average Rate of Change = 302=15 (in thousands of dollars per month).
Thus, the average rate of change is $15,000 per month.
Why the Other Options Are Wrong:
"Sales increased an average of $37,000 per month." This overestimates the rate of change, as the total change in sales is only 30,000, not 37,000.
"Sales increased an average of $6,285.71 per month." This significantly underestimates the rate of change. It does not correspond to the actual total change over the 2 months.
"Sales increased an average of $10,000 per month." This underestimates the rate of change. The correct average increase is $15,000 per month.
The following table shows the height (in inches) of a sunflower plant n days after being planted:
Assuming this trend continues, what will be the height of the sunflower after 33 days?
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30 inches
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36 inches
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40 inches
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44 inches
Explanation
Solution: Step 1: Find the rate of change (slope)
The height increases linearly with time, so we can calculate the rate of change (slope) using the formula:
From n = 5 to n = 12:
= 1 inch/day
From n = 12 to n = 19:
= 1 inch/day
Since the slope is constant, the relationship is linear.
Step 2: Find the linear equation for height
The general form of a linear equation is:
H(n) = mn + b, where H(n) is the height,
m = 1 inch/day, and b is the y-intercept.
At n = 5:
H(5) = 8:
8 = 1(5) + b
8 = 5 + b
b = 3
The equation for height is: H(n) = n + 3
Step 3: Calculate height at n = 33
Substitute n = 33 into the equation:
H(33) = 33 + 3 = 36 inches
Correct answer:
The height of the sunflower after 33 days will be 36 inches (Option 2).
Why the Other Options are Wrong:
"Option 1 (30 inches)" This underestimates the growth and doesn't follow the consistent rate of 1 inch per day.
"Option 3 (40 inches)" This overestimates the growth and doesn't match the linear relationship established by the data.
"Option 4 (44 inches)" This assumes a much faster growth rate and significantly overestimates the height at day 33.
The percent concentration of a certain drug, A(f), in the bloodstream hours after it's administered is given by the graph below.
At which time is the concentration of the drug in the bloodstream at a maximum, and what is the maximum percent concentration?
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After 2 hours, it is at a maximum of 0.75%.
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After 4 hours, it is at a maximum of 0.6%.
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After 0.75 hours, it is at a maximum of 2%.
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After 1 hour, it is at a maximum of 0.5%.
Explanation
Correct answer:
After 2 hours, it is at a maximum of 0.75%.
Solution:
From the graph the maximum point for the y axis showing concentration is at 0.75% while this point corresponds to 2hrs.
Why others are wrong:
“After 4 hours, it is at a maximum of 0.6%.” Although after 4 hours the concentration is at 0.6% this is not the maximum concentration.
“After 0.75 hours, it is at a maximum of 2%.” From the graph there was no point or time the concentration reached this point, that is why the option is wrong.
“After 1 hour, it is at a maximum of 0.5%.” After 1 hour the concentration was above 0.5% hence the option is wrong.
The four lines on the graph below represent the total value, y, of purchased equipment x years after purchase for four different pieces of equipment.
Which piece of equipment loses its value the most slowly?
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D
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A
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B
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C
Explanation
Correct option: D
Explanation:
This is the only line with the highest rate of change in x with respect to y as compared to the others.
Why other options are wrong:
“A” Line A seems to be having a higher gradient than line D since it slants more, hence this option is not correct.
“B” Line B seems to be having a higher gradient than line D since it slants more, hence this option is not correct.
“C” Line C seems to be having a higher gradient than line D since it slants more, hence this option is not correct.
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Frequently Asked Question
This course covers a variety of algebraic concepts, including solving linear equations and inequalities, quadratic equations, graphing functions, systems of equations, exponents, polynomials, and real-world applications of algebra.
Yes, all practice questions and study materials are meticulously updated and aligned with the 2025 standards to ensure students are prepared for current academic and professional requirements.
The course includes practical scenarios such as calculating interest, analyzing business data, optimizing resources, and modeling real-world situations with algebraic equations and graphs.
Yes, each practice question comes with step-by-step rationales to explain the correct answers and address common mistakes, helping students develop a deeper understanding of the material.
You can prepare by reviewing the practice questions, studying the provided rationales, working on real-world application problems, and using the exam-focused blueprints included in the course materials.
Yes, a graphing calculator is highly recommended, as it is essential for solving complex problems, graphing functions, and visualizing algebraic concepts.
The course offers video tutorials, interactive problem-solving exercises, concise topic summaries, and access to an online community of students and tutors for support.
Progress is tracked through quizzes, assignments, and practice exams included in the course. These tools provide detailed feedback on areas of strength and those that need improvement.