Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Exponents And The Distributive Property

Simplify: $(2x+3)^{2}$

Possible Answers:

$4x^{2}+9$

$4x^{2}-9$

$4x^{2}+12x+9$

$5x^{2}$

$4x^{2}+6x+9$

Correct answer:

$4x^{2}+12x+9$

Explanation:

In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this: (2x+3)(2x+3)

Next, multiply your first terms together: $2x\times2x =4x^{2}$

Then, multiply your outside terms together: $2x\times3=6x$

Then, multiply your inside terms together: $3\times2x=6x$

Lastly, multiply your last terms together: $3\times3=9$

Together, you have $4x^{2}+6x+6x+9$

You can combine your like terms, 6x+6x , to give you the final answer: $4x^{2}+12x+9$

Report an Error

Example Question #5 : Exponents And The Distributive Property

Use FOIL to simplify the following product:

(x+9)(x-7)

Possible Answers:

x^2+7x+54

x^2+2x-63

x^2-63

x^2+11x+63

7x^2-9x

Correct answer:

x^2+2x-63

Explanation:

Use the FOIL method (first, outside, inside, last) to find the product of:

(x+9)(x-7)

First: $x\cdot x=x^2$

Outside: $-7\cdot x=-7x$

Inside: $9\cdot x=9x$

Last: $-7\cdot 9=-63$

Sum the products to find the polynomial:

x^2-7x+9x-63

x^2+2x-63

Report an Error

Example Question #1 : How To Use Foil

Simplify:

$2(x^{2}+x)(x-1)$

Possible Answers:

$2x^{3} -2x$

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

$2x^{3} -x$

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

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

Correct answer:

$2x^{3} -2x$

Explanation:

To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses: $x^{2} \cdot x =x^{3}$

Then multiply the outside terms: $x^{2}\cdot (-1) =-x^{2}$

Next, multiply the inside terms: $x \cdot x= x^{2}$

Finally, multiply the last terms: $x\cdot (-1) = -x$

When you put the pieces together, you have $2(x^{3} -x^{2} +x^{2}-x)$ . Notice that the middle terms cancel each other out, and you are left with $2(x^{3} -x)$ . When you distribute the two, you reach the answer: $2x^{3} -2x$

Report an Error

Example Question #281 : Exponents

If (x-3)^2=25 , which of the following could be the value of ?

Possible Answers:

Correct answer:

Explanation:

(x-3)^2=25

Take the square root of both sides.

$x-3=\pm 5$

$x-3=5\ \text{or}\ x-3=-5$

Add 3 to both sides of each equation.

$x=5+3\ \text{or}\ x=-5+3$

$x=8\ \text{or}\ x=-2$

Report an Error

Example Question #282 : Exponents

Simplify:

$\left ( xyz \right )^{3}+x^{2}y+\left ( xy \right )^{0}+\left ( xy^{\frac{1}{2}} \right )^{2}$

Possible Answers:

$2x^{5}y^{3}z$

$x^{3}y^{3}z^{3}+x^{2}y$

$x^{3}y^{3}z^{3}+2x^{2}y+1$

$x^{3}y^{3}z^{3}+x^{2}y+1$

$x^{3}y^{3}z^{3}+2x^{2}y$

Correct answer:

$x^{3}y^{3}z^{3}+2x^{2}y+1$

Explanation:

$\left ( xyz \right )^{3}+x^{2}y+\left ( xy \right )^{0}+\left ( xy^{\frac{1}{2}} \right )^{2}$

= x³y³z³ + x²y + x⁰y⁰ + x²y

= x³y³z³ + x²y + 1 + x²y

= x³y³z³ + 2x²y + 1

Report an Error

Example Question #5 : Exponents And The Distributive Property

(6x^4+2x^2)(3x^4+6x^2)

Possible Answers:

42x^8

18x^8+42x^6+12x^4

18x^8+36x^6+12x^4

18x^8+12x^4

$18x^{16}+42x^8+12x^4$

Correct answer:

18x^8+42x^6+12x^4

Explanation:

Use the FOIL method to find the product. Remember to add the exponents when multiplying.

First: $6x^4\cdot3x^4 = 18x^8$

Outside: $6x^4\cdot6x^2=36x^6$

Inside: $2x^2\cdot 3x^4=6x^6$

Last: $2x^2\cdot6x^2=12x^4$

Add all the terms:

18x^8+36x^6+6x^6+12x^4

18x^8+42x^6+12x^4

Report an Error

Example Question #283 : Exponents

Square the binomial.

$(x^{2}y^{4}+xy^{6})^{2}$

Possible Answers:

$x^4y^{16}+2x^2y^{24}+xy^{36}$

$2x^{8}y^{20}$

$x^8y^8+x^2y^{12}$

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

$x^4y^8+2x^3y^{10}+x^2y^{12}$

Correct answer:

$x^4y^8+2x^3y^{10}+x^2y^{12}$

Explanation:

$(x^{2}y^{4}+xy^{6})^{2}$

$(x^{2}y^{4}+xy^{6})(x^{2}y^{4}+xy^{6})$

We will need to FOIL.

First: x^2y^4*x^2y^4=x^4y^8

Inside: $xy^6*x^2y^4=x^3y^{10}$

Outside: $x^2y^4*xy^6=x^3y^{10}$

Last: $xy^6*xy^6=x^2y^{12}$

Sum all of the terms and simplify.

$x^4y^8+x^3y^{10}+x^3y^{10}+x^2y^{12}$

$x^4y^8+2x^3y^{10}+x^2y^{12}$

Report an Error

Example Question #1 : How To Use Foil With Exponents

Which of the following is equivalent to 4c(3d)³– 8c³d + 2(cd)⁴?

Possible Answers:

2cd(54d² – 4c²+ c³* d³)

2(54d²– 4c²+ 2c³* d³)

None of the other answers

cd(54c * d³– 4c³+ c²* d²)

Correct answer:

2cd(54d² – 4c²+ c³* d³)

Explanation:

First calculate each section to yield 4c(27d³) – 8c³d + 2c⁴d⁴= 108cd³– 8c³d + 2c⁴d⁴. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get: 2cd(54d²– 4c²+ c³d³).

Report an Error

Example Question #1211 : Psat Mathematics

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Possible Answers:

$\$15,007.02$

$\$14,062.50$

$\$ 14,991.24$

$\$15,011.78$

$\$14,778.51$

Correct answer:

$\$ 14,991.24$

Explanation:

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and t = 5 , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Report an Error

Example Question #2 : How To Find Compound Interest

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Possible Answers:

$90 \%$

$100 \%$

$85 \%$

$105 \%$

$95 \%$

Correct answer:

$95 \%$

Explanation:

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

In the given scenario, t = 10 , r = 0.06735 , and N = 12 (monthly); substitute:

$A = A_{0}\left ( 1+ \frac{0.06735}{12} \right )^{12 \cdot 10}$

$A \approx A_{0}\left ( 1+0.0056125 \right )^{12 0}$

$A \approx A_{0}\left ( 1 .0056125 \right )^{12 0}$

$A \approx A_{0} \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Report an Error

View PSAT Mathematics Tutors

Kaitlyn
Certified Tutor

University of South Carolina, Bachelor in Arts, English.

View PSAT Mathematics Tutors

Shivansh
Certified Tutor

University of British Columbia, Bachelor, Math major and data science minor .

View PSAT Mathematics Tutors

Nico
Certified Tutor

New York University, Bachelors, Philosophy.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Dallas Fort Worth, SAT Tutors in Miami, ACT Tutors in Atlanta, Math Tutors in Los Angeles, Calculus Tutors in Phoenix, Reading Tutors in San Diego, ISEE Tutors in Los Angeles, Reading Tutors in New York City, LSAT Tutors in Seattle, English Tutors in Los Angeles

Popular Courses & Classes

LSAT Courses & Classes in Houston, SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Phoenix, GMAT Courses & Classes in Boston, SAT Courses & Classes in San Diego, ISEE Courses & Classes in Philadelphia, MCAT Courses & Classes in Houston, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Atlanta, SAT Courses & Classes in Atlanta

Popular Test Prep

LSAT Test Prep in Washington DC, MCAT Test Prep in Washington DC, GRE Test Prep in Miami, GMAT Test Prep in Washington DC, SSAT Test Prep in Boston, GRE Test Prep in Washington DC, ACT Test Prep in Atlanta, MCAT Test Prep in Seattle, SAT Test Prep in Seattle, ISEE Test Prep in Chicago

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

PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Exponents And The Distributive Property

Example Question #5 : Exponents And The Distributive Property

Example Question #1 : How To Use Foil

Example Question #281 : Exponents

Example Question #282 : Exponents

Example Question #5 : Exponents And The Distributive Property

Example Question #283 : Exponents

Example Question #1 : How To Use Foil With Exponents

Example Question #1211 : Psat Mathematics

Example Question #2 : How To Find Compound Interest

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: