C957 Applied Algebra FX01 Exam
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Free C957 Applied Algebra FX01 Exam Questions
Computers frequently use algorithms to make large files smaller, a process called compression. When given the size of the file (in gigabytes), f, the amount of time in seconds, S, for the standard algorithm to compress a file is given by the equation S(f) = 0.5f3. Its graph is shown below as the solid curve. The time to use a new algorithm for this same process is given by the function N(f) = 0.5f2 +2, which is shown below in the dashed curve.
Based on this graph, which algorithm is quicker for a file that is 5 gigabytes in size?
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The new algorithm, N, is better since N(5) < S(5).
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The standard algorithm, S, is better since N(5) > S(5).
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The new algorithm, N, is better since S(5) < N(5).
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The standard algorithm, S, is better since S(5) < N(5).
Explanation
Solution
S(f) = 0.5f3
S(5) = 0.5 * 53
= 62.5 seconds
N(f) = 0.5f2 +2
N(5) = 0.5 * 52 + 2
= 14.5 seconds
Correct answer:
The new algorithm, N, is better since N(5) < S(5).
Why other options are wrong:
“The standard algorithm, S, is better since N(5) > S(5).” N(5) < S(5) hence the option is wrong
“The new algorithm, N, is better since S(5) < N(5)” S(5) > N(5) hence the option is wrong.
“The standard algorithm, S, is better since S(5) < N(5)” S(5) > N(5) hence the option is wrong.
An employee works at a large department store and gets an employee discount on any purchases made at the store. The price the employee pays can be modeled by the function D(c) = c - 0.15c, where c is the original price of the item in dollars and D is the discounted price of the item. What does this model represent in the context of the problem?
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The employee pays $c after receiving an 15% discount for an item that originally cost $D.
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The employee pays $0 after receiving a 15% discount for an item that originally cost $c.
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The employee pays $D after receiving an 85% discount for an item that originally cost $c.
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The employee pays $c after receiving a 15% discount for an item that originally cost $D.
Explanation
Correct Answer:
The employee pays D after receiving a 85% discount for an item that originally cost \(c. Explanation: The function D(c)=c − 0.15c calculates the discounted price (D) of an item. The term 0.15c represents a 15% discount off the original price (c), so the total price the employee pays is 85% of the original price: D(c) = c(1−0.15) = 0.85c This means the employee pays D, the discounted price, which is 85% of the original price c, after receiving a 15% discount. Why the other options are wrong: "The employee pays c after receiving an 85% discount for an item that originally cost D": This is incorrect because the employee pays D, not c, after the discount is applied. Additionally, the discount is 15%, not 85%. "The employee pays\)0 after receiving a 15% discount for an item that originally cost c": This is incorrect because a 15% discount does not reduce the price to $0. The price is reduced to 85% of the original price.
"The employee pays D after receiving an 85% discount for an item that originally cost c": This is incorrect because the discount is 15%, not 85%.
After a water tank starts leaking, the amount of water in the tank is modeled by the exponential function that is graphed.
Which statement is justified considering the location of the horizontal asymptote?
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The rate of change in water volume quickens over time.
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The water volume will change by a constant rate over time.
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The water volume will not decrease to 500 gallons.
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The greatest water volume occurs after 11 minutes.
Explanation
Explanation
The horizontal asymptote represents the value the water volume approaches over time. From the graph, the asymptote seems to be at 500 gallons, indicating that the water volume will eventually stabilize at 500 gallons and will not decrease further.
Correct answer
The water volume will not decrease to 500 gallons.
A machine depreciates in value according to the function: V(t) = 12,000−800t where V(t) represents the value of the machine (in dollars) after t years. After how many years will the machine's value be $4,000?
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5 years
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7 years
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10 years
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15 years
Explanation
Correct Answer:
10 years
Solution:
Substitute V(t) = 4,000 into the equation:
4,000 = 12,000 − 800t
800t = 12,000−4,000
800 t = 8,000
t = 8,000/800
= 10
The machine's value will reach \(4,000 after 10 years. Why Other Options Are Wrong: "5 years" Incorrect because the value at 5 years would be 12,000 − 800(5) = 8,000 12,000 – 800(5) = 8,000 12,000 − 800(5) = 8,000, not\)4,000.
"7 years" Incorrect because the value at 7 years would be
12,000 − 800(7) = 6,400
12,000 - 800(7) = 6,400
12,000−800(7) = 6,400.
"15 years" Incorrect because after 15 years, the value would drop below $4,000.
A company's product varies in cost depending on the number of features added to the standard features. The base cost is $10,000, and each additional feature adds $1,100 to the base cost. The company uses a cost function, C(n), to represent the cost of the product with nn additional features. For example, C(1) represents the cost of $10,000 plus $1,100 for one additional feature.
Which interpretation is accurate?
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C(4) is the base cost plus the cost of three additional features.
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C(1) is the base cost with just the standard features.
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C(5) is the base cost plus the cost of five additional features.
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C(3) is the base cost plus the cost of four additional features.
Explanation
Correct Answer:
C(5) is the base cost plus the cost of five additional features.
Explanation:
The function C(n) represents the total cost of the product, which is calculated as the base cost ($10,000) plus $1,100 for each additional feature.
For C(5), this means the total cost is the base cost plus \(1,100 multiplied by 5 additional features: C(5) = 10,000 + (1,100×5) = 10,000 + 5,500 = 15,500. Thus, C(5) represents the base cost plus the cost of five additional features. Why the other options are wrong: "C(4) is the base cost plus the cost of three additional features." This is incorrect because C(4) refers to 4 additional features, note 3. The interpretation mixes up the number of features. "C(1) is the base cost with just the standard features." This is incorrect because C(1) includes the cost of one additional feature, not just the standard features. The standard features alone would simply cost\)10,000.
"C(3) is the base cost plus the cost of four additional features." This is incorrect because C(3) refers to 3 additional features, not 4. The interpretation overestimates the number of features.
A small pond contains 12 units of dissolved oxygen in a fixed volume of water. At time t = 0, a quantity of organic waste is introduced into the pond. The oxygen concentration, y, is shown in t weeks in the graph below.
As time passes, what will be the ultimate concentration of oxygen in the pond?
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The oxygen concentration stabilizes near 5 units.
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The oxygen concentration stabilizes near 12 units.
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The oxygen concentration stabilizes near 24 units.
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The oxygen concentration stabilizes near 42 units.
Explanation
Correct answer:
The oxygen concentration stabilizes near 12 units.
Explanation
This is because the oxygen concentration graph flattens between 11 and 12 but seems to stop the increment at 12 units.
Why other options are wrong:
“The oxygen concentration stabilizes near 5 units” This is incorrect since the horizontal asymptote is between 11 and 12 units.
“The oxygen concentration stabilizes near 24 units” This is incorrect since the oxygen level does not reach this level.
“The oxygen concentration stabilizes near 42 units” This is incorrect since the oxygen level does not reach this level.
The dog population in a small town can be modeled using a logistic function. The data from the model are given below, where P(t) represents the dog population and t is measured in years. In this data, t = 0 corresponds to the year 2010.
What is the average rate of change of the dog population from 2012 to 2018?
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The dog population is increasing at a rate of 45 dogs per year during this time.
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The dog population is increasing at a rate of 40 dogs per year during this time.
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The dog population is decreasing at a rate of 45 dogs per year during this time.
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The dog population is decreasing at a rate of 40 dogs per year during this time.
Explanation
Solution:
Step 1: Identify the population values for 2012 (t=2) and 2018 (t=8):
P(2) = 30 dogs (2012)
P(8) = 300 dogs (2018)
Step 2: Calculate the total change in population:
Change = P(8) − P(2)
Change = 300 − 30 = 270 dogs
Step 3: Calculate the average rate of change:
Time period = 8 − 2 = 6 years
= 45 dogs per year
Since the population is increasing, the average rate is positive.
Correct Answer:
The dog population is increasing at a rate of 45 dogs per year during this time.
Why the other options are incorrect:
"The dog population is increasing at a rate of 40 dogs per year": This rate is too low compared to the calculated rate of 45 dogs per year.
"The dog population is decreasing at a rate of 45 dogs per year": The population is increasing, not decreasing, so this is incorrect.
"The dog population is decreasing at a rate of 40 dogs per year": The population is increasing, not decreasing, and the rate is wrong.
The following table shows the profits of a gaming company for each month of the last fiscal year.
What has happened to the profits over the course of the year?
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The profits have risen about 40%.
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The profits have risen about 10%.
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The profits have risen about 30%.
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The profits have risen about 20%.
Explanation
Solution:
Profit at the beginning of the year (January):
= 32,384 dollars
Profit at the end of the year (December):
= 42,198 dollars.
Profit increase:
Profit Increase=42,198 − 32,384=9,814 dollars.
Percentage increase:
=
= 30.29%
Hence the profit increase is 30% increase.
Correct answer:
The profits have risen about 30%.
Why the Other Options Are Wrong:
“The profits have risen about 40%.” This overestimates the actual profit increase. A 40% increase would require: 32,384 × 1.4 = 45,337.6 dollars, which exceeds the year-end profit of 42,198.
“The profits have risen about 10%.” This underestimates the profit increase. A 10% increase would require: 32,384 × 1.1 = 35,622.4 dollars far less than the actual year-end profit.
“The profits have risen about 20%.” This underestimates the increase. A 20% increase would result in: 32,384 × 1.2 = 38,860.8 dollars, still less than the actual profit of 42,198.
For a side business, an entrepreneur purchased $50 worth of equipment to produce homemade jewelry to sell. In addition to the manufacturing equipment, each piece of jewelry costs $2 in supplies to produce. The given graph shows the average cost per piece of jewelry as the entrepreneur produces more jewelry, including the initial equipment purchase and supplies for each piece of jewelry produced.
Which conclusion can be drawn from this graph?
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The average cost per piece of jewelry produced is an asymptote and tends toward $2 per piece of jewelry produced.
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The average cost per piece of jewelry produced increases towards $3.
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The average cost per piece of jewelry produced decreases toward $0.
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The average cost per piece of jewelry produced is an asymptote and tends toward two pieces of jewelry having an average cost of $1,000.
Explanation
Correct answer:
The average cost per piece of jewelry produced is an asymptote and tends toward \(2 per piece of jewelry produced. Why other options are wrong: “The average cost per piece of jewelry produced increases towards\)3” This is incorrect since the price tends to decrease rather than increase.
“The average cost per piece of jewelry produced decreases toward \(0” This is incorrect since the graph has an asymptote at\)2 and not 0.
“The average cost per piece of jewelry produced is an asymptote and tends toward two pieces of jewelry having an average cost of \(1,000” This is incorrect since the highest average price from the graph is\)3.
The IT help desk at a college logs the calls it gets during a Tuesday morning. C(t) is the number of calls at time t (measured in hours), and t = 0 corresponds to 8 a.m.
When should the help desk expect to need the fewest staff members?
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8:00 a.m.
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8:45 a.m.
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11:00 a.m.
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11:30a.m.
Explanation
Correct answer: 11:00 a.m.
Explanation:
From the function the least calls are expected three hours after opening which is three hours after 8.00 a.m
Why other option are wrong:
“8.00 a.m” At this time the IT desk expects 10 which is greater than 2 calls expected at 11.00 a.m.
“8.45 a.m” At this time the IT desk expects 21 calls which is greater than 2 calls expected at 11.00 a.m.
“11.30 a.m” At this time the IT desk expects 5 calls which is greater than 2 calls expected at 11.00 a.m.
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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.