Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : Algebra

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 #201 : Algebra

Simplify the following algebraic expression:

$\frac{x^{2} -7x-8}{x^{2} +3x +1}$

Possible Answers:

$\frac{x-8}{x-2}$

$\frac{x+8}{x+2}$

$\frac{x-7}{x+1}$

$\frac{x-8}{x +2}$

Correct answer:

$\frac{x-8}{x +2}$

Explanation:

To simplify this algebraic expression, factor the numerator and the denominator using FOIL.

$\frac{(x-8)(x+1)}{(x+2) (x+1)}$

The $\frac{x+1}{x+1}$ will cancel out.

The correct answer is

$\frac{x-8}{x+2}$

Report an Error

Example Question #202 : Algebra

$\frac{x+5}{x^{2} +2x -15}$

Possible Answers:

$\frac{1}{x-3}$

$\frac{1}{x-15}$

x-3

$\frac{-1}{x+3}$

Correct answer:

$\frac{1}{x-3}$

Explanation:

To simplify this algebraic expression, factor the denominator using the FOIL method.

$x^{2} + 2x - 15 = (x+5) (x-3)$

$\frac{x+5}{(x+5) (x-3)}$

The $\frac{x+5}{x+5} = 1$

Solve:

$\frac{1}{x-3}$

Report an Error

Example Question #203 : Algebra

Simplify $\frac{9x^{2}-6x -3}{3x +1}$

Possible Answers:

3x -3

$\frac{1}{3x-3}$

3x + 1

$\frac{3x-3}{3x+1}$

Correct answer:

3x -3

Explanation:

To simplify, factor the numerator using the FOIL Method:

$9x^{2} -6x - 3 = (3x-3) (3x+1)$

Rewrite the expression:

$\frac{(3x-3) (3x+1)}{(3x+1)}$

$\frac{3x-3}{1} = 3x-3$

Report an Error

Example Question #204 : Algebra

Which is a reduced version of the following expression?

4x-6y=8

Possible Answers:

2x-3y=8

4x-6y=4

2x+3y=4

2x-3y=4

Correct answer:

2x-3y=4

Explanation:

To reduce the expression, you need a common factor to take out from each part of the equation.

All the constants can be divided by so you just divide the whole equation by that to get,

$\\4x-6y=8 \\ \\2(2x-3y)=2(4) \\ \\\frac{2(2x-3y)}{2}=\frac{2(4)}{2}$

2x-3y=4 .

Report an Error

Example Question #816 : Concepts

$6 (3+y) + 4(5y + 3) - (x^{2} )^{3}$

Possible Answers:

$x^{6} + 20y -30$

$-x^{6} +26y +30$

$x^{5} + 14y -30$

$-x^{5} +36y + 30$

Correct answer:

$-x^{6} +26y +30$

Explanation:

To solve this equation, begin by using the Order of Operations. The first operation will be the one that is contained within the parentheses. When a term with an exponent is raised to a power, multiply the exponents.

$(x^{2})^{3} = x^{6}$

Rewrite the expression:

$18 + 6y + 20y + 12 - x^{6}$

Simplify by combining like terms:

$30 + 26y -x^{6}$

There is one more step. The terms must be placed in descending order based upon the exponents. In this equation, the term $-x^{6}$ , has the largest exponent so it will go first followed by 26y which has an exponent of 1. Constants are placed last in the equation.

$-x^{6} + 26y + 30$

Report an Error

Example Question #817 : Concepts

Simplify the following algebraic expression:

$6m^{2}n^{3} - (6mn -3m^{2}n^{3}+3) - 6$

Possible Answers:

$-9m^{2}n^{3} -6mn +3$

$9m^{2}n^{3} -6mn -9$

$15m^{2}n^{3} +3$

$3m^{2}n^{3} -6mn +3$

Correct answer:

$9m^{2}n^{3} -6mn -9$

Explanation:

To simplify this algebraic expression, combine like terms. Make sure to distribute the minus sin to all terms and constants within the parentheses.

$6m^{2} n^{3} - (-3m^{2}n^{3}) = 9m^{2}n^{3}$

$9m^{2}n^{3} -6mn - (+3) -6$

$9m^{2}n^{3} -6mn -3 - 6$

$9m^{2}n^{3} - 6mn -9$ is the correct answer.

Report an Error

Example Question #205 : Algebra

Simplify the following:

-45 + 8 (x +6)

Possible Answers:

-37x - 236

8x + 3

-37x + 6

8x - 39

8x - 3

Correct answer:

8x + 3

Explanation:

-45 + 8 (x +6)

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

$=-45 + 8 \cdot x +8 \cdot6$

=-45 + 8x +48

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

Now we have -45+48=3

= 8x + 3

Report an Error

Example Question #12 : Expressions & Equations

Simplify:

30 - 5 (x + 4)

Possible Answers:

-5x + 50

25x - 20

-5x + 10

-5x + 26

25x + 100

Correct answer:

-5x + 10

Explanation:

30 - 5 (x + 4)

When solving this problem we need to remember our order of operations, or PEMDAS.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

$= 30 - 5 \cdot x + (- 5) \cdot 4$

= 30 - 5 x + (- 20)

Addition/Subtraction: Remember, we can't add a variable to a number, so the -5x is left alone.

= - 5 x + 30 - 20

= -5x + 10

Report an Error

Example Question #41 : How To Subtract Variables

Simplify:

(3x+2)-(4x-7)

Possible Answers:

-x+9

x-9

x+9

-x-5

x-5

Correct answer:

-x+9

Explanation:

When solving this problem we need to remember our order of operations, or PEMDAS.

Parentheses: We are not able to add a variable to a number, so we move on to the next step

Multiplication: We can distribute the negative sign to the and

(3x+2)-(4x-7)

=3x+2-4x-(-7)

Remember, a negative times a negative will equal a positive, so we have a

=3x+2-4x+7

Finally we can combine like terms

3x-4x=-x

2+7=9

=-x+9

Report an Error

Example Question #206 : Algebra

Solve for :

$\frac{3}{4} t = \frac{4}{3}$

Possible Answers:

$\frac{16}{3}$

$\frac{16}{9}$

$\frac{4}{3}$

$\frac{4}{9}$

Correct answer:

$\frac{16}{9}$

Explanation:

Divide both sides by $\frac{3}{4}$ :

$\frac{3}{4} t = \frac{4}{3}$

$\frac{3}{4} t \div \frac{3}{4}= \frac{4}{3} \div \frac{3}{4}$

$t = \frac{4}{3} \cdot \frac{4}{3} = \frac{4\cdot 4}{3\cdot 3} = \frac{16}{9}$

Report an Error

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Tajrin
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Computer Science.

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

All HSPT Math Resources

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

Popular Subjects

SAT Tutors in San Francisco-Bay Area, Algebra Tutors in Denver, Physics Tutors in Atlanta, Algebra Tutors in Houston, Biology Tutors in Denver, English Tutors in Seattle, ISEE Tutors in Denver, SSAT Tutors in Miami, French Tutors in Philadelphia, Computer Science Tutors in San Francisco-Bay Area

Popular Courses & Classes

ACT Courses & Classes in San Diego, ISEE Courses & Classes in San Diego, ISEE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Denver, GRE Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Washington DC, GMAT Courses & Classes in New York City, ISEE Courses & Classes in Miami, GMAT Courses & Classes in Philadelphia

Popular Test Prep

MCAT Test Prep in Washington DC, GMAT Test Prep in Denver, GMAT Test Prep in Philadelphia, GMAT Test Prep in Phoenix, MCAT Test Prep in Miami, SSAT Test Prep in Miami, ACT Test Prep in Washington DC, ACT Test Prep in New York City, ACT Test Prep in Denver, SSAT 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

HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #201 : Algebra

Example Question #202 : Algebra

Example Question #203 : Algebra

Example Question #204 : Algebra

Example Question #816 : Concepts

Example Question #817 : Concepts

Example Question #205 : Algebra

Example Question #12 : Expressions & Equations

Example Question #41 : How To Subtract Variables

Example Question #206 : Algebra

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: