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 #151 : Ssat Middle Level Quantitative (Math)

Simplify:

$5xy + 21x - 3y - 14xy + 2x^{2}$

Possible Answers:

$31x^{3}y$

$21x + 2x^{2} - 3y - 9xy$

$21x + 2x^{2} - 3y - 19xy$

$29xy + 2x^{2}$

$21x + 2x^{2} - 3y + 9xy$

Correct answer:

$21x + 2x^{2} - 3y - 9xy$

Explanation:

Begin by moving all like terms next to each other. Remember that you must treat every variable type separately:

$5xy - 14xy + 21x - 3y + 2x^{2}$

Combine like terms:

$-9xy + 21x - 3y + 2x^{2}$

You merely need to reorder the variables to get to the form in the answer choice.

Report an Error

Example Question #92 : Algebra

Simplify:

3x + 14y + 4(xy - 4x)

Possible Answers:

10y - 9x

$5x^{2}y^{2}$

14y - x + 4xy

5xy

14y - 13x + 4xy

Correct answer:

14y - 13x + 4xy

Explanation:

Begin by distributing the through the group:

3x + 14y + 4(xy) - (4)(4x)

Next, perform the multiplications:

3x + 14y + 4xy - 16x

Group the like terms:

3x - 16x+ 14y + 4xy

Combine like terms:

-13x+ 14y + 4xy

Rearrange the terms to get the answer as it appears in the answer choices.

Report an Error

Example Question #91 : Variables

Simplify:

$43x^{2} + 2xy - 3y - 4(7xy - 22x^{2})$

Possible Answers:

$131x^{2} - 26xy - 3y$

$65x^{2} - 26xy - 3y$

$131x^{2} - 29xy$

$-45x^{2} - 26xy - 3y$

$-45x^{2} - 45xy - 3y$

Correct answer:

$131x^{2} - 26xy - 3y$

Explanation:

Begin by multiplying through by :

$43x^{2} + 2xy - 3y + (-4)(7xy) - (-4)(22x^{2})$

Perform the multiplications:

$43x^{2} + 2xy - 3y - 28xy - (-88x^{2})$

The double negation becomes addition:

$43x^{2} + 2xy - 3y - 28xy + 88x^{2}$

Group like terms:

$43x^{2}+ 88x^{2} + 2xy - 28xy - 3y$

Combine like terms:

$131x^{2} + 26xy - 3y$

Report an Error

Example Question #1 : Expressions & Equations

Simplify:

8(x+7) - 3 (x + 10)

Possible Answers:

5x+ 46

5x+ 26

9x + 43

9x+22

Correct answer:

5x+ 26

Explanation:

8(x+7) - 3 (x + 10)

$= 8 \cdot x+ 8 \cdot 7 - 3 \cdot x - 3 \cdot 10$

= 8 x+ 56 - 3x - 30

= 5x+ 26

Report an Error

Example Question #60 : How To Multiply Variables

Simplify:

$(2a)(3r^{2})(3a^{3})(5a^{3})(2a^{3})(b^{2})$

Possible Answers:

$180a^{10}b^{2}r^{2}$

$15a^{7}b^{2}r^{5}$

$15a^{9}b^{2}r^{6}$

$45a^{4}b^{2}r^{7}$

$180a^{9}b^{2}r^{6}$

Correct answer:

$180a^{10}b^{2}r^{2}$

Explanation:

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$(2 *3 *3 *5 *2)(a *a^{3} *a^{3} * a^{3})(b^{2})(r^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(180)(a^{1+3+3+3})(b^2)(r^2)$

$(180)(a^{10})(b^{2})(r^{2})$

This is the same as:

$180a^{10}b^{2}r^{2}$

Report an Error

Example Question #174 : Ssat Middle Level Quantitative (Math)

14s - 3s=

Possible Answers:

11s

42s

21s

17s

Correct answer:

11s

Explanation:

Subtract the numbers and keep the variable:

14s-3s=11s

Answer: 11s

Report an Error

Example Question #101 : Algebra

Simplify: $\frac{9x}{(\frac{2y}{9x})}$

Possible Answers:

$\frac{x}{2y}$

$\frac{2y}{81x^2}$

$\frac{1}{2y}$

$\frac{81x^2}{2y}$

Correct answer:

$\frac{81x^2}{2y}$

Explanation:

To solve this problem, rewrite the operation using a division sign.

$\frac{9x}{(\frac{2y}{9x})}= 9x \div \frac{2y}{9x}$

When dividing fractions, we replace the division sign with a multiplication sign and take the inverse of the second term.

$9x \div \frac{2y}{9x}= 9x \times \frac{9x}{2y}$

When we simplify the problem we get $\frac{9x}{1}\times \frac{9x}{2y}=\frac{81x^{2}}{2y}$

Report an Error

Example Question #102 : Algebra

Simplify: $\frac{a^2b^6c^0}{a^{-4}b^{9}c^{-1}}$

Possible Answers:

$\frac{1}{a^6b^3c}$

$\frac{a^2c}{b^3}$

$\frac{a^6c}{b^3}$

$\frac{a^2}{b^3c}$

$\frac{b^3}{a^6c}$

Correct answer:

$\frac{a^6c}{b^3}$

Explanation:

The powers of like-terms can be subtracted top to bottom when the terms are divided. Simplify the terms.

$a^{2-(-4)}=a^6$

$b^{6-9}=b^{-3}$

$c^{0-(-1)}=c$

Combine the terms as one whole. Positive exponents go in the numerator and negative exponents go in the denominator to get rid of the negative. The correct answer is: $\frac{a^6c}{b^3}$

Report an Error

Example Question #711 : Concepts

Simplify: $a^3 \times a^{-6}\times a^{-2}$

Possible Answers:

$\frac{1}{a}$

$\frac{1}{a^5}$

a^5

$a^{36}$

$\frac{1}{a^4}$

Correct answer:

$\frac{1}{a^5}$

Explanation:

To simplify the expression, notice that the bases are all alike and are multiplied.

The powers to the bases can then be added to be combined to one term.

$a^3 \times a^{-6}\times a^{-2}=a^{3-6-2}= a^{-5} = \frac{1}{a^5}$

Report an Error

Example Question #712 : Concepts

Simplify: -x^2(2x+x^2)

Possible Answers:

-x^2+2x

-2x^3-x^4

-2x^3

-2x^3+x^4

-2x^2-x^4

Correct answer:

-2x^3-x^4

Explanation:

Distribute the negative outer term to the two inner terms inside the parenthesis.

-x^2(2x+x^2) = (-x^2)(2x)+(-x^2)(x^2) = -2x^3-x^4

Report an Error

View Tutors

Mark
Certified Tutor

Eastern Michigan University, Bachelor of Science, Education of Individuals in Secondary Special Education Programs. Eastern M...

View Tutors

Colton
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Mathematics.

View Tutors

Joseph
Certified Tutor

Brown University, Bachelor of Science, Education.

All HSPT Math Resources

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

Popular Subjects

Calculus Tutors in Dallas Fort Worth, SSAT Tutors in San Diego, GRE Tutors in Seattle, Chemistry Tutors in Washington DC, Calculus Tutors in Boston, Reading Tutors in Phoenix, ACT Tutors in Philadelphia, Chemistry Tutors in Dallas Fort Worth, Biology Tutors in Los Angeles, Spanish Tutors in Los Angeles

Popular Courses & Classes

ACT Courses & Classes in Denver, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Denver, ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in Phoenix, SAT Courses & Classes in Miami, SSAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in New York City, SAT Test Prep in Phoenix, SAT Test Prep in New York City, ACT Test Prep in Miami, LSAT Test Prep in Los Angeles, ISEE Test Prep in Philadelphia, ISEE Test Prep in Seattle, GRE Test Prep in Los Angeles, SSAT Test Prep in Chicago, GRE Test Prep in Denver

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 #151 : Ssat Middle Level Quantitative (Math)

Example Question #92 : Algebra

Example Question #91 : Variables

Example Question #1 : Expressions & Equations

Example Question #60 : How To Multiply Variables

Example Question #174 : Ssat Middle Level Quantitative (Math)

Example Question #101 : Algebra

Example Question #102 : Algebra

Example Question #711 : Concepts

Example Question #712 : Concepts

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: