Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Variables

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #218 : Algebraic Concepts

Divide:

$\frac{4x^{3}+8x^{2}-12x}{4x}$

Possible Answers:

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

$x^{2}+2x-3$

The expression cannot be simplified further.

$x^{3}+2x^{2}-3x$

$4x^{2}+8x-12$

Correct answer:

$x^{2}+2x-3$

Explanation:

To divide this problem we simplify it first. In this problem we can separate the big fraction into three smaller fractions.

$\frac{4x^{3}+8x^{2}-12x}{4x}=\frac{4x^{3}}{4x}+\frac{8x^{2}}{4x}-\frac{12x}{4x}$

Then from here, we can pull out a from both the numerator and denominator of each smaller fraction.

$\frac{4x(x^2)}{4x}+\frac{4x(2x)}{4x} - \frac{4x(3)}{4x}$

Now we cancel terms and get the following result:

x^2+2x-3

Report an Error

Example Question #219 : Algebraic Concepts

Simplify:

$\frac{2x^{4}+6x^{3}+8}{2x}$

Possible Answers:

$4x^{3}+12x^{2}+16x$

$x^{3}+3x^{2}+\frac{4}{x}$

$x^{3}+3x^{2}+4x$

$x^{3}+3x^{2}+4$

$4x^{3}+6x^{2}+16x$

Correct answer:

$x^{3}+3x^{2}+\frac{4}{x}$

Explanation:

To simplify this problem we first separate the large fraction into three smaller fractions.

$\frac{2x^{4}+6x^{3}+8}{2x}$

$=\frac{2x^{4}}{2x}+\frac{6x^{3}}{2x}+\frac{8}{2x}$

From here we can factor out from the numerator and denominator of the first two fractions.

$= \frac{2x(x^3)}{2x}+\frac{2x(3x^2)}{2x}+\frac{8}{2x}$

The can be canceled out in the first two fractions. From here we can factor out a from the numerator and denominator of the third fraction.

$=x^3+3x^2+\frac{2(4)}{2(x)}$

Thus becoming:

$=x^{3}+3x^{2}+\frac{4}{x}$

Report an Error

Example Question #31 : Variables

Divide:

$\frac{-4x^{4}-6x^{3}+8x^{2}}{2x^{2}}$

Possible Answers:

$-2x^{2}-3x+8$

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

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

$-6x^{2}-8x+10$

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

Correct answer:

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

Explanation:

To divide this problem we start by simplify it. In this problem we can break the large fraction into three smaller fractions.

$\frac{-4x^{4}-6x^{3}+8x^{2}}{2x^{2}}=\frac{-4x^{4}}{2x^{2}}-\frac{6x^{3}}{2x^{2}}+\frac{8x^{2}}{2x^{2}}$

From here we can factor out a 2x^2 from the numerator and denominator of each fraction.

$\frac{2x^2(-2x^2)}{2x^2}- \frac{2x^2(3x)}{2x^2}+ \frac{2x^2(4)}{2x^2}$

Now we can cancel the 2x^2 terms and are left with the following result:

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

Report an Error

Example Question #922 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following expression:

$\frac{343w^7}{49w^3}$

Possible Answers:

$\frac{49w^7}{w^3}$

7w^4

$\frac{343w^4}{49}$

343w^4

Correct answer:

7w^4

Explanation:

Simplify the following expression:

$\frac{343w^7}{49w^3}$

Let's begin by simplifying the coefficients

$\frac{343w^7}{49w^3}=\frac{49*7w^7}{49w^3}=\frac{7w^7}{w^3}$

Next, complete the question by subtracting the exponents:

$\frac{7w^7}{w^3}=7w^{7-3}=7w^4$

So, our answer is:

7w^4

Report an Error

Example Question #32 : Variables

Simplify the following expression:

$\frac{49x^3y^5b^{12}}{7x^2y^6b^{8}}$

Possible Answers:

7xb^4y

$\frac{7xb^4}{y}$

$\frac{49xb^4}{7y}$

$\frac{7x^2b^4}{y}$

Correct answer:

$\frac{7xb^4}{y}$

Explanation:

Simplify the following expression:

$\frac{49x^3y^5b^{12}}{7x^2y^6b^{8}}$

Let's begin by simplifying the coefficients:

We have a 49 on top and a 7 on bottom. We can treat this just like a regular fraction:

$\frac{49}{7}=7$

Next, to deal with our variables, all we need to do is subtract the bottom exponent from the top exponent. If we get a negative number, we just put that number on the bottom.

$x^{3-2}=x^1=x$

$y^{5-6}=y^{-1}=\frac{1}{y}$

$b^{12-8}=b^4$

So our answer will look like this:

$\frac{7xb^4}{y}$

Report an Error

Example Question #1 : How To Subtract Variables

Simplify:

5y + 4x + 8y - 12y

Possible Answers:

9x+4y

4x-y

4x+y

9x-4y

4x-25y

Correct answer:

4x+y

Explanation:

5y + 4x + 8y - 12y

= 4x + 5y+ 8y - 12y

$= 4x + \left ( 5+ 8 - 12 \right )y$

$= 4x + \left ( 13 - 12 \right )y$

= 4x + 1y

= 4x + y

Report an Error

Example Question #33 : Variables

Simplify the expression:

18xy - 7y + 8xy + 8x

Possible Answers:

-8x - 7y +10 xy

16x+ 11y

- 16x+ 11y

8x - 7y +26 xy

27 xy

Correct answer:

8x - 7y +26 xy

Explanation:

Group and collect like terms:

18xy - 7y + 8xy + 8x

= 8x - 7y + 18xy + 8xy

$= 8x - 7y +\left ( 18 + 8 \right ) xy$

= 8x - 7y +26 xy

Report an Error

Example Question #1 : How To Subtract Variables

Simplify:

10x - 5y + 8z -7y

Possible Answers:

10x - 5y + z

5x -7y+ 8z

10x - 2y + 8z

10x - 12y + 8z

The expression cannnot be simplified further.

Correct answer:

10x - 12y + 8z

Explanation:

Group and collect like terms:

10x - 5y + 8z -7y

=10x - 5y -7y + 8z

$=10x + \left (- 5 -7 \right )y + 8z$

$=10x + \left (- 12\right )y + 8z$

=10x - 12y + 8z

Report an Error

Example Question #34 : Variables

x + y = 10

y+ z = 17

What is x - z ?

Possible Answers:

Insufficient information is given to answer this question.

Correct answer:

Explanation:

x -z = x + y - y + z = (x + y) - (y + z) = 10 - 17 = -7

Report an Error

Example Question #5 : How To Subtract Variables

Simplify:

4x+3y+2x-5y

Possible Answers:

$6x^{2}-2y^{2}$

8x-3y

6x+8y

6x-8y

6x-2y

Correct answer:

6x-2y

Explanation:

To simplify this problem we need to combine like terms.

4x+3y+2x-5y

=4x+2x+3y-5y

=6x-2y

Report an Error

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Jaleesa
Certified Tutor

Pomona College, Bachelors, Africana Studies.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Seattle, Calculus Tutors in Chicago, LSAT Tutors in New York City, Calculus Tutors in Dallas Fort Worth, Physics Tutors in New York City, Reading Tutors in New York City, Math Tutors in San Francisco-Bay Area, Computer Science Tutors in San Francisco-Bay Area, Statistics Tutors in Chicago, Physics Tutors in San Francisco-Bay Area

Popular Courses & Classes

SSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Atlanta, SSAT Courses & Classes in Atlanta, ACT Courses & Classes in San Diego, MCAT Courses & Classes in Seattle, LSAT Courses & Classes in San Diego, ISEE Courses & Classes in San Diego, GRE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, SSAT Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Chicago, GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Atlanta, SSAT Test Prep in Phoenix, LSAT Test Prep in Philadelphia, GRE Test Prep in New York City, GMAT Test Prep in Denver, MCAT Test Prep in New York City, SAT Test Prep in Washington DC

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

ISEE Upper Level Math : Variables

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #218 : Algebraic Concepts

Example Question #219 : Algebraic Concepts

Example Question #31 : Variables

Example Question #922 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #32 : Variables

Example Question #1 : How To Subtract Variables

Example Question #33 : Variables

Example Question #1 : How To Subtract Variables

Example Question #34 : Variables

Example Question #5 : How To Subtract Variables

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: