We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

Create An Account

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #631 : Concepts

Simplify:

(xy^2)^2+3x^2y^4

Possible Answers:

x^2y^4

4x^4y^4

2x^2y^4

3x^2y^4

4x^2y^4

Correct answer:

4x^2y^4

Explanation:

(xy^2)^2+3x^2y^4

First we should simplify the first expression. We can first apply the power of a product rule and then apply the power of a power rule. So we can write:

$(xy^2)^2=(x)^2\times (y^2)^2=x^2\times y^{(2\times 2)}=x^2y^4$

Return to the original expression:

x^2y^4+3x^2y^4

Since the variables have the same exponents we can write:

x^2y^4+3x^2y^4=4x^2y^4

Report an Error

Example Question #112 : Ssat Middle Level Quantitative (Math)

Gina's mom baked 12 cookies. 8 were cinnamon and 4 were chocolate chip. If Gina eats one of the cinnamon cookies, how many more cinnamon cookies are there than chocolate chip?

Possible Answers:

Correct answer:

Explanation:

Gina's mom baked 12 cookies; 8 were cinnamon and 4 were chocolate chip. If Gina then eats a cinnamon cookie, there will be 7 cinnamon cookies left.

After she eats the cookie, we need to find the difference between the number of cinnamon cookies and chocolate chip cookies.

$\text{Cinnamon}-\text{Chocolate chip}$

7-4=3

There are 3 more cinnamon cookies than chocolate chip cookies.

Report an Error

Example Question #1 : How To Divide Variables

$3\frac{2}{5} \div 1 \frac{1}{5}=$

Possible Answers:

$\frac{102}{25}$

$4\frac{2}{5}$

$2\frac{5}{6}$

Correct answer:

$2\frac{5}{6}$

Explanation:

First convert each mixed number into and improper fraction

$\frac{17}{5} \div \frac{6}{5}$

Then convert the operation to multiplication and flip the second fraction

$\frac{17}{5} \ast \frac{5}{6}=$

Reduce where possible and multiply to solve:

$\frac{17}{6}=2\frac{5}{6}$

The answer is $2\frac{5}{6}$

Report an Error

Example Question #2 : How To Divide Variables

Simplify:

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

Possible Answers:

4x^3+3x-x

4x^2+3x-1

4x^2-3x+1

4x^3-3x^2+x

Correct answer:

4x^2-3x+1

Explanation:

$\frac{8x^3-6x^2+2x}{2x}=\frac{8x^3}{2x}-\frac{6x^2}{2x}+\frac{2x}{2x}=4x^2-3x+1$

Report an Error

Example Question #3 : How To Divide Variables

Solve for B

AX+B(2Y)=C

Possible Answers:

$B=\frac{C-AX}{2Y}$

$\frac{C-2Y}{AX}=B$

Not enough information provided.

$2B=\frac{C-AX}{Y}$

B=4

Correct answer:

$B=\frac{C-AX}{2Y}$

Explanation:

This problem looks strange since it mostly contains variables, in particular unknown variables. Still remember the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. We still use those operations in this case. All we must do is move the variables around to solve for .

In this case we can subtract (additive inverse) to the other side first.

AX-AX+B(2Y)=C-AX

Rewrite our problem.

B(2Y)=C-AX

Stop for a moment and look at the progress. Go back to the original question, solve for . Our problem shows about to be multiplied to , but we do not necessarily have to multiply because we can divide by to both sides of the equation, which would save us a step as well as have B by itself.

$\frac{B(2Y)}{2Y}=\frac{C-AX}{2Y}$

$B=\frac{C-AX}{2Y}$

Report an Error

Example Question #4 : How To Divide Variables

Suppose you know the values of , , and , and you want to evaluate the expression below.

$A + B^{2}\div C$

Which of the following is the first step you must complete?

Possible Answers:

Evaluate $A\div C$ .

Evaluate A^2 .

Evaluate B^2 .

Evaluate A+B .

Evaluate $B\div C$ .

Correct answer:

Evaluate B^2 .

Explanation:

Use the order of operations, PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

In our expression, there are no parentheses, so square first.

Report an Error

Example Question #5 : How To Divide Variables

Divide:

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

Possible Answers:

-4x^2-3x+2

4x^2+3x-2

-4x^2+3x-2

4x^2-3x+2

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

Correct answer:

-4x^2+3x-2

Explanation:

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

Report an Error

Example Question #6 : How To Divide Variables

Simplify:

$\frac{3^{70}}{9^{35}}$

Possible Answers:

$9^{35}$

$3^{35}$

Correct answer:

Explanation:

To simplify, we want to get the same base in both the numerator and the denominator. This will allow us to easily manipulate the exponents.

$\frac{3^{70}}{9^{35}}$

$9^{35}=(3^2)^{35}=3^{(2\times 35)}=3^{70}$

Replace the denominator with this value and simplify.

$\frac{3^{70}}{9^{35}}=\frac{3^{70}}{3^{70}}=1$

Report an Error

Example Question #26 : Algebra

Simplify:

$\frac{4^{8x}}{16^{2x}}$

Possible Answers:

$2^{8x}$

$2^{4x}$

$4^{6x}$

$2^{2x}$

$4^{8x}$

Correct answer:

$2^{8x}$

Explanation:

To simplify, we want to get the same base in both the numerator and the denominator. This will allow us to easily manipulate the exponents.

$\frac{4^{8x}}{16^{2x}}$

We can write:

$4^{8x}=(2^2)^{8x}=2^{(2\times 8x)}=2^{16x}$

and

$16^{2x}=(2^4)^{2x}=2^{(4\times 2x)}=2^{8x}$

Replace the fraction with these values and simplify.

$\frac{4^{8x}}{16^{2x}}=\frac{2^{16x}}{2^{8x}}=2^{(16x-8x)}=2^{8x}$

Report an Error

Example Question #7 : How To Divide Variables

Which of the following numbers is divisible by 7?

Possible Answers:

765

756

755

757

Correct answer:

756

Explanation:

The number 756 can be segmented into 700 and 56. Given that 700 is divisble by 7 (700 divided by 7 is 100) and that 56 is divisible by 7 (56 divided by 7 is 8), 756, as the aggregate of 700 and 56, is also divisble by 7.

Report an Error

View Tutors

Usman
Certified Tutor

New York University, Bachelor in Arts, Political Science and Government.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Bagher
Certified Tutor

San Jose State University, Master's/Graduate, Physics.

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in San Diego, English Tutors in Chicago, MCAT Tutors in Denver, MCAT Tutors in Dallas Fort Worth, English Tutors in Miami, Calculus Tutors in Seattle, English Tutors in Washington DC, French Tutors in Phoenix, ACT Tutors in Denver, GMAT Tutors in Seattle

Popular Courses & Classes

ISEE Courses & Classes in Houston, GMAT Courses & Classes in Chicago, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Los Angeles, LSAT Courses & Classes in Phoenix, ACT Courses & Classes in Philadelphia, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Denver, SAT Courses & Classes in New York City

Popular Test Prep

SAT Test Prep in Houston, ISEE Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Philadelphia, SSAT Test Prep in Atlanta, SSAT Test Prep in San Diego, GMAT Test Prep in Chicago, ISEE Test Prep in San Francisco-Bay Area, MCAT Test Prep in San Diego, ISEE Test Prep in San Diego

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

HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #631 : Concepts

Example Question #112 : Ssat Middle Level Quantitative (Math)

Example Question #1 : How To Divide Variables

Example Question #2 : How To Divide Variables

Example Question #3 : How To Divide Variables

Example Question #4 : How To Divide Variables

Example Question #5 : How To Divide Variables

Example Question #6 : How To Divide Variables

Example Question #26 : Algebra

Example Question #7 : How To Divide Variables

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: