Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Variables

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Variables

Mike wants to sell candy bars for a $50\%$ profit. If he sells each bar for $\$1.20$ , how much did each bar cost him?

Possible Answers:

$\$0.60$

$\$0.80$

$\$1.00$

$\$0.75$

Correct answer:

$\$0.80$

Explanation:

In order to solve this problem, set up the following equation:

$\frac{1.20}{x}=\frac{150\%}{100\%}$

Cross multiply:

150x = 120

Divide:

$\frac{150x}{150} = \frac{120}{150} = 0.80$

The original cost of the of each candy bar is $\$0.80$

Report an Error

Example Question #2 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

$\frac{12x^3y^2p}{4ab}\div\frac{3x^3y}{2ab}$

Possible Answers:

2yp

3yp

2xy

12xp

3ax

Correct answer:

2yp

Explanation:

$\frac{12x^3y^2p}{4ab}\div\frac{3x^3y}{2ab}$

To divide monomial quotients, simply invert the divisor and multiply:

$\frac{12x^3y^2p}{4ab} *\frac{2ab}{3x^3y} = \frac{24x^3y^2pab}{12abx^3y}$

Then, reduce:

$\frac{24yp}{12} = 2yp$

Report an Error

Example Question #1 : Monomials

Choose the answer that is the simplest form of the following expression of monomial quotients:

$\frac{10m^2np}{3xy}\div\frac{3p^2}{2xym}$

Possible Answers:

$\frac{9p}{20m^3n}$

$\frac{20x^3}{9y}$

$\frac{20n^3}{9m}$

$\frac{20m^3n}{9p}$

$\frac{20p^3n}{9m}$

Correct answer:

$\frac{20m^3n}{9p}$

Explanation:

$\frac{10m^2np}{3xy}\div\frac{3p^2}{2xym}$

To find your answer, you have to invert the divisor and multiply across:

$\frac{10m^2np}{3xy} * \frac{2xym}{3p^2} = \frac{20m^3npxy}{9p^2xy}$

Then, reduce:

$\frac{20m^3n}{9p}$

Report an Error

Example Question #1 : How To Multiply A Monomial By A Polynomial

Multiply: $2x\ast(4x+3)$

Possible Answers:

$8x^{2}+6x$

8x+6

$8x^{2}+6$

6x+8

$6x^{2}+8x$

Correct answer:

$8x^{2}+6x$

Explanation:

To solve you must multiply by both terms in (4x+3)

$2x\ast4x=8x^{2}$

$2x\ast3=6x$

$8x^{2}+6x$

Report an Error

Example Question #1 : Variables

Multiply:

$4x\cdot(5x+7)$

Possible Answers:

$20x^{2}+28x$

$9x^{2}+28x$

$9x^{2}+28$

20x+11

Correct answer:

$20x^{2}+28x$

Explanation:

Multiply by both terms in (5x+7)

$4x\cdot5x=20x^{2}$

$4x\cdot7=28x$

$20x^{2}+28x$

Report an Error

Example Question #2 : Variables

Multiply $\left (7x^{2}-12x+4 \right ) \cdot 3x$

Possible Answers:

$21x^{3}-36x^{2}+12x$

$7x^{3}-12x^{2}+4x$

$21x^{3}+36x^{2}+12x$

None of the other answers

$21x^{2}-36x+12$

Correct answer:

$21x^{3}-36x^{2}+12x$

Explanation:

When multiplying a polynomial by a monomial, each term in the polynomial gets multiplied by the monomial. Calculate each term one at a time, then add the results to get the final answer. In this case, we start by multiplying $7x^{2}\cdot3x$ . $7\cdot3=21$ and $x^{2}\cdot x=x^{3}$ , thus we get $21x^{3}$ . For the second term of the polynomial, we multiply $-12\cdot3=-36$ and $x\cdot x= x^{2}$ , resulting in $-36x^{2}$ . Finally, we multiply $4\cdot3 = 12$ and $1\cdot x = x$ , resulting in 12x . Adding the three terms that we just found, we come to the answer of $21x^{3}-36x^{2}+12x$ .

Report an Error

Example Question #1 : How To Multiply Monomial Quotients

Choose the answer that is the best solution to the following expression of monomial quotients:

$\frac{4x^2p^3}{3mn^2} * \frac{2mn}{12xy}$

Possible Answers:

$\frac{8xp^3}{36ny}$

$\frac{2xp}{9n^2y}$

$\frac{4xp^3}{5ny}$

$\frac{4xp}{11n^2y}$

$\frac{2xp^3}{9ny}$

Correct answer:

$\frac{2xp^3}{9ny}$

Explanation:

$\frac{4x^2p^3}{3mn^2} * \frac{2mn}{12xy}$

To multiply monomial quotients, treat them as you would any other fraction. Combine like terms wherever possible:

$\frac{8x^2p^3mn}{36mn^2xy}$

Then, you need to reduce:

$\frac{2xp^3}{9ny}$

Report an Error

Example Question #4 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

$\frac{2x^3y^4}{10z^3} * \frac{4z^2p}{10xy}$

Possible Answers:

$\frac{2p}{25z}$

$\frac{2x^2y^3p}{25z}$

$\frac{8x^2y^3p}{25z^2}$

$\frac{2xyp}{15z}$

$\frac{13x^2y^3p}{100z}$

Correct answer:

$\frac{2x^2y^3p}{25z}$

Explanation:

$\frac{2x^3y^4}{10z^3} * \frac{4z^2p}{10xy}$

To simplify, first multiply across:

$\frac{8x^3y^4z^2p}{100z^3xy}$

Then, reduce:

$\frac{2x^2y^3p}{25z}$

Report an Error

Example Question #1 : How To Use The Direct Variation Formula

The price of silver varies directly as the square of the mass. If 3.6 g of silver is worth $64.80, what is the value of 7.5 g of silver?

Possible Answers:

$178.50

$301.75

$135.00

$215.25

$281.25

Correct answer:

$281.25

Explanation:

This is a direct variation problem of the form y = kx² The first set of data 3.6 g and $64.80 is used to calculate the proportionality constant, k. So 64.80 = k(3.6)² and solving the equation gives k = 5.

Now we move to the new data, 7.5 g and we get y = 5(7.5)² to yield an answer of $218.25.

$135.00 is the answer obtained if using proportions. This is an error because it does not take into consideration the squared elements of the problem.

Report an Error

Example Question #1 : Direct And Inverse Variation

The diameter of a specific brand of candy wrapper is 6cm longer than half the volume of the candy itself. Find the expression for the diameter, , in terms of the volume, .

Possible Answers:

$d=\frac{1}{2}v-6$

$d=\frac{1}{2}v+6$

$d=\frac{4}{3}v^2$

d=2v+6

d=2v-6

Correct answer:

$d=\frac{1}{2}v+6$

Explanation:

The question asks for an equation that can relate and to each other, based on the information given. We are told that half the volume + 6cm determines the total diameter.

This gives us:

$d=\frac{1}{2}v+6$

Report an Error

View ACT Math Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View ACT Math Tutors

Rene Solo
Certified Tutor

University of the Philippines, Bachelor of Science, Mathematics. Prairie View A & M University, Master of Arts, Educational A...

View ACT Math Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

GRE Courses & Classes in Seattle, SSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Houston, MCAT Courses & Classes in New York City, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Washington DC, ACT Test Prep in Phoenix, SSAT Test Prep in Los Angeles, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Atlanta, ISEE Test Prep in Boston, ISEE Test Prep in Denver, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Phoenix, GMAT Test Prep in New York City

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ACT Math : Variables

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Variables

Example Question #2 : Variables

Example Question #1 : Monomials

Example Question #1 : How To Multiply A Monomial By A Polynomial

Example Question #1 : Variables

Example Question #2 : Variables

Example Question #1 : How To Multiply Monomial Quotients

Example Question #4 : Variables

Example Question #1 : How To Use The Direct Variation Formula

Example Question #1 : Direct And Inverse Variation

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: