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Common Core: High School - Functions : High School: Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's art department spends $\$325$ on art supplies. If the department sells each art piece for $\$10$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$10t-\$325$

$A(t)=\$10t+\$325$

$A(t)=\$10t-\$350$

$A(t)=\$325t+\$10$

$A(t)=\$325t-\$10$

Correct answer:

$A(t)=\$10t-\$325$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

For the purpose of Common Core Standards, interpret parameters in a linear or exponential function in terms of a context, falls within the Cluster B of interpret expressions for functions in terms of the situation they model concept (CCSS.Math.content.HSF.LE.B).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$10 \\ \textup{Art Supply Costs}=\$325 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs} \\A(t)=\$10t-\$325$

Report an Error

Example Question #5 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$160$ to produce a certain play. If the play sells tickets for $\$4$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$160t-\$4$

$P(t)=\$4t-\$160$

$P(t)=\$4t+\$160$

$P(t)=\$160t+\$4$

$P(t)=\$4-\$160$

Correct answer:

$P(t)=\$4t-\$160$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$4 \\ \textup{Production Costs}=\$160 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$4t-\$160$

Report an Error

Example Question #2 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$240$ to produce a certain play. If the play sells tickets for $\$12$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$240t-\$12$

$P(t)=\$12t-\$240$

$P(t)=\$240t+\$12$

$P(t)=\$240-\$12$

$P(t)=\$12t+\$240$

Correct answer:

$P(t)=\$12t-\$240$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$12 \\ \textup{Production Costs}=\$240 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$12t-\$240$

Report an Error

Example Question #1 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's art department spends $\$300$ on art supplies. If the department sells each art piece for $\$5$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$300-\$5$

$A(t)=\$300t-\$5$

$A(t)=\$300t+\$5$

$A(t)=\$5t-\$300$

$A(t)=\$5t+\$300$

Correct answer:

$A(t)=\$5t-\$300$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$5 \\ \textup{Art Supply Costs}=\$300 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs} \\A(t)=\$5t-\$300$

Report an Error

Example Question #7 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$750$ to produce a certain play. If the play sells tickets for $\$15$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$15t-\$750$

$P(t)=\$750-\$15$

$P(t)=\$750t+\$15$

$P(t)=\$750t-\$15$

$P(t)=\$15t+\$750$

Correct answer:

$P(t)=\$15t-\$750$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$15 \\ \textup{Production Costs}=\$750 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$15t-\$750$

Report an Error

Example Question #8 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$190$ to produce a certain play. If the play sells tickets for $\$8.50$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$8.50-\$190t$

$P(t)=\$8.50t-\$190$

$P(t)=\$8.50-\$190$

$P(t)=\$8.50+\$190t$

$P(t)=\$8.50t+\$190$

Correct answer:

$P(t)=\$8.50t-\$190$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$8.50 \\ \textup{Production Costs}=\$190 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$8.50t-\$190$

Report an Error

Example Question #4 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's art department spends $\$380$ on art supplies. If the department sells each art piece for $\$11$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$11-\$380t$

$A(t)=\$11+\$380t$

$A(t)=\$11t+\$380$

$A(t)=\$11t-\$380$

$A(t)=\$11-\$380$

Correct answer:

$A(t)=\$11t-\$380$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$11 \\ \textup{Art Supply Costs}=\$380 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs} \\A(t)=\$11t-\$380$

Report an Error

Example Question #351 : High School: Functions

A school's art department receives $\$380$ in donation on art supplies. If the department sells each art piece for $\$11$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$11+\$380t$

$A(t)=\$11t-\$380$

$A(t)=\$11+\$380$

$A(t)=\$11-\$380t$

$A(t)=\$11t+\$380$

Correct answer:

$A(t)=\$11t+\$380$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}+\textup{Donations}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$11 \\ \textup{Donations}=\$380 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Donations} \\A(t)=\$11t+\$380$

Report an Error

Example Question #351 : High School: Functions

A school's art department receives $\$200$ in donation on art supplies. If the department sells each art piece for $\$4$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$4+\$200t$

$A(t)=\$4-\$200t$

$A(t)=\$4t+\$200$

$A(t)=\$4+\$200$

$A(t)=\$4t-\$200$

Correct answer:

$A(t)=\$4t+\$200$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}+\textup{Donations}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$4 \\ \textup{Donations}=\$200 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Donations} \\A(t)=\$4t+\$200$

Report an Error

Example Question #1 : Radians And Arc Length: Ccss.Math.Content.Hsf Tf.A.1

Convert $135^\circ$ to radians.

Possible Answers:

$\frac{\pi}{2}$

$\frac{4\pi}{6}$

$\frac{3\pi}{4}$

$\frac{\pi}{4}$

$\pi$

Correct answer:

$\frac{3\pi}{4}$

Explanation:

This question tests one's ability to understand the conversion between radians and degrees. It relies on the understanding that the measure of an angle can be described using the properties of the unit circle and arc length. Furthermore, questions involving concepts dealing with trigonometry use the foundation of corresponding identities with angles that come from the unit circle. Recall that the unit circle is a circle that has a radius of one and is centered at the origin. Each (x,y) pair that lies on the circle can be found by creating a right triangle that has a base on the -axis and a hypotenuse that is from the center of the circle to the desired point on the edge of the circle. The height of the triangle is the vertical line that connects the point on the circle's edge to the -axis.

For the purpose of Common Core Standards, understanding radian measure of an angle as the length of the arc on the unit circle subtended by the angle, falls within the Cluster A of extend the domain of trigonometric functions using the unit circle concept (CCSS.Math.content.HSF.TF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the general formula for unit conversion between radians and degrees.

$360^\circ=2\pi \textup{ radians}\Rightarrow180^\circ=\pi\textup{ radians}$

Therefore to convert from degrees to radian is,

$\frac{x^\circ}{1}\times \frac{\pi}{180^\circ}=\textup{radian measurement}$

Step 2: Identify the values given in the question.

$x=\textup{degrees}=135^\circ$

Step 3: Substitute the value from step 2 into the formula from step 1.

$\\ \frac{x^\circ}{1}\times \frac{\pi}{180^\circ} \\ \\ =\frac{135^\circ}{1}\times \frac{\pi}{180^\circ} \\ \\ =\frac{135^\circ\pi}{180^\circ}$

The degree measurement in the numerator and denominator cancel out.

$\frac{135\pi}{180}$

From here, simplify the fraction by finding common factors that exist in both the numerator and denominator.

$\\ \frac{135\pi}{180} \\ \\ =\frac{45\cdot 3\pi}{45\cdot 4} \\ \\ =\frac{3\pi}{4}$

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: High School - Functions : High School: Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #1 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #5 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #2 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #1 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #7 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #8 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #4 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #351 : High School: Functions

Example Question #351 : High School: Functions

Example Question #1 : Radians And Arc Length: Ccss.Math.Content.Hsf Tf.A.1

All Common Core: High School - Functions Resources

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