Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Numbers and Operations

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 #51 : Numbers And Operations

What is the least common multiple of and ?

Possible Answers:

Correct answer:

Explanation:

Find all of the multiples of both numbers:

6: 6,12,18,24,30,36,42,48,54,60

4:4,8,12,16,20,24,28,32,36,40

Find the first number that both sets have in common.

LCM=12

Report an Error

Example Question #52 : Numbers And Operations

Find the LCM of 12xy and 48x.

Possible Answers:

x^2y

48x^2y

48xy

144xy

96xy

Correct answer:

48xy

Explanation:

LCM is the least common multiple of the pair. There are a couple of terms at play here, so first find the LCM of 12 and 48. Since 12 goes into 48, 48 is the LCM. Then, look at xy and x. XY is the LCM between those two. So, multiply those together to get 48xy as your answer.

Report an Error

Example Question #53 : Numbers And Operations

What is the least common multiple of and ?

Possible Answers:

Correct answer:

Explanation:

A multiple of x is a number that results when x is multiplied by another whole number.

The least common multiple of two numbers is the smallest number that is a multiple of both the numbers.

24 is a multiple of 8 because 8 times 3 is 24.

24 is also a multiple of 12 because 12 times 2 is 24.

There are no numbers that are smaller than 24 which are also multiples of 8 and 12. Therefore, 24 is the least common multiple.

Report an Error

Example Question #1 : Exponents

Simplify:

3a^3-a^2+4a^2-8a^3

Possible Answers:

a(-5a+3)

a^2(-5a+2)

a^2(5a-3)

a^2(-5a+3)

a^2(5a+3)

Correct answer:

a^2(-5a+3)

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

3a^3-a^2+4a^2-8a^3=(3a^3-8a^3)+(4a^2-a^2)

=-5a^3+3a^2=a^2(-5a+3)

Report an Error

Example Question #54 : Numbers And Operations

Evaluate:

5^2+5^3-7^2-3(7^2)-4(5^3)

Possible Answers:

550

546

Correct answer:

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

5^2+5^3-7^2-3(7^2)-4(5^3)=5^2+(5^3-4(5^3))-(7^2+3(7^2))

=5^2+-3(5^3)-4(7^2)

Now they must be multiplied out before they can be added:

$=5\times 5- 3\times 5\times 5\times 5-4\times 7\times 7$

$=25-3\times 125-4\times 49$

=25-375-196=-546

Report an Error

Example Question #3 : How To Subtract Exponents

Subtract and simplify:

$\left ( 11 x^{2}- 8x-7 \right )- \left (-7 x^{2}-5x+19\right )$

Possible Answers:

$18x^{2}-3x-26$

$18x^{2}-3x+12$

$4x^{2}-3x-26$

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

$18x^{2}-13x-26$

Correct answer:

$18x^{2}-3x-26$

Explanation:

Consider a vertical subtraction process:

$\begin{matrix} 11 x^{2}- 8x-7 \\\underline{ - (-7 x^{2}-5x+19)} \end{matrix}$

Rewrite as the addition of the opposite of the second expression, as follows:

$\begin{matrix} 11 x^{2}- 8x-7 \\\underline{ \; \; 7 x^{2}+5x-19 } \\ 18x^{2}-3x-26 \end{matrix}$

Report an Error

Example Question #4 : How To Subtract Exponents

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{4} - b^{3}$ .

Evaluate: $\frac{1}{2} \Upsilon \frac{1}{4}$ .

Possible Answers:

$\frac{3}{64}$

$\frac{1}{32}$

$\frac{1}{16}$

$-\frac{1}{48}$

Correct answer:

$\frac{3}{64}$

Explanation:

$a \Upsilon b = a^{4} - b^{3}$ , so

$\frac{1}{2} \Upsilon \frac{1}{4} = \left ( \frac{1}{2} \right )^{4} - \left (\frac{1}{4} \right )^{3}$

$= \frac{1}{2^{4}} - \frac{1}{4^{3}}$

$= \frac{1}{16} - \frac{1}{64}$

$= \frac{4}{64} - \frac{1}{64}$

$= \frac{3}{64}$

Report an Error

Example Question #3 : How To Subtract Exponents

Subtract and simplify:

$\left ( 4x^{2}+ 1.2x-7 \right )- \left ( 2x^{2}-3.8x+9\right )$

Possible Answers:

$2x^{2}-2.6x-16$

$2x^{2}+ 5x+2$

$2x^{2}+ 5x-16$

$2x^{2}-2.6x+2$

The correct answer is not among the other responses.

Correct answer:

$2x^{2}+ 5x-16$

Explanation:

Consider a vertical subtraction process:

$\begin{matrix} 4x^{2}+ 1.2x-7\\\underline{ - (2x^{2}-3.8x+9)} \end{matrix}$

Rewrite as the addition of the opposite of the second expression, as follows:

$\begin{matrix} \; \; 4x^{2}+ 1.2x-7\\\underline{ -2x^{2}+3.8x-9}\\ \; 2x^{2}+\; \; 5x-16\end{matrix}$

Report an Error

Example Question #6 : How To Subtract Exponents

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{4} - b^{3}$ .

Evaluate: $0.2\; \Upsilon\; 0.1$ .

Possible Answers:

-0.0084

-0.0006

-0.0015

0.0006

0.0015

Correct answer:

0.0006

Explanation:

$a \Upsilon b = a^{4} - b^{3}$

$0.2\; \Upsilon\; 0.1= 0.2^{4} - 0.1^{3}$

= 0.0016 - 0.001

=0.0006

Report an Error

Example Question #4 : How To Subtract Exponents

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{4} - b^{3}$ .

Evaluate: $(-4) \Upsilon (-3)$

Possible Answers:

229

283

Correct answer:

283

Explanation:

$a \Upsilon b = a^{4} - b^{3}$

$(-4) \Upsilon (-3) = (-4)^{4}- (-3) ^{3}$

= 256 - (-27)

=283

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

ACT Tutors in Denver, GMAT Tutors in Miami, GRE Tutors in Miami, GRE Tutors in Atlanta, SAT Tutors in Houston, SAT Tutors in Atlanta, English Tutors in Chicago, Math Tutors in Miami, English Tutors in Washington DC, Computer Science Tutors in Phoenix

Popular Courses & Classes

MCAT Courses & Classes in New York City, ISEE Courses & Classes in Los Angeles, GRE Courses & Classes in Denver, SAT Courses & Classes in New York City, GRE Courses & Classes in Washington DC, Spanish Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Boston, LSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Philadelphia, SSAT Test Prep in Philadelphia, MCAT Test Prep in Los Angeles, GRE Test Prep in Washington DC, ISEE Test Prep in Los Angeles, ISEE Test Prep in Washington DC, LSAT Test Prep in Los Angeles, ACT Test Prep in New York City, ACT Test Prep in Phoenix, ACT Test Prep in San Francisco-Bay Area

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 : Numbers and Operations

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #51 : Numbers And Operations

Example Question #52 : Numbers And Operations

Example Question #53 : Numbers And Operations

Example Question #1 : Exponents

Example Question #54 : Numbers And Operations

Example Question #3 : How To Subtract Exponents

Example Question #4 : How To Subtract Exponents

Example Question #3 : How To Subtract Exponents

Example Question #6 : How To Subtract Exponents

Example Question #4 : How To Subtract Exponents

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: