We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Algebra

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 #9 : How To Multiply Complex Numbers

What is the eighth power of 1+ i $\displaystyle 1+ i$ ?

Possible Answers:

8 - 8i $\displaystyle 8 - 8i$

$\displaystyle 16$

8 + 8i $\displaystyle 8 + 8i$

The correct response is not given among the other choices.

256i $\displaystyle 256i$

Correct answer:

$\displaystyle 16$

Explanation:

First, square 1+ i $\displaystyle 1+ i$ using the square of a binomial pattern as follows:

$\left (1+ i \right )^{2}$ $\displaystyle \left (1+ i \right )^{2}$

$= 1^{2}+ 2 \cdot 1 \cdot i + i^{2}$ $\displaystyle = 1^{2}+ 2 \cdot 1 \cdot i + i^{2}$

$\displaystyle = 1 +2i -1$

= 2i $\displaystyle = 2i$

Raising this number to the fourth power yields the correct response:

$\left (1+ i \right )^{8}$ $\displaystyle \left (1+ i \right )^{8}$

$= \left [\left (1+ i \right )^{2} \right ]^{4}$ $\displaystyle = \left [\left (1+ i \right )^{2} \right ]^{4}$

$= (2i)^{4}$ $\displaystyle = (2i)^{4}$

$= (2 )^{4} \cdot i^{4}$ $\displaystyle = (2 )^{4} \cdot i^{4}$

$=16 \cdot 1 = 16$ $\displaystyle =16 \cdot 1 = 16$

Report an Error

Example Question #10 : How To Multiply Complex Numbers

What is the ninth power of -2i $\displaystyle -2i$ ?

Possible Answers:

18i $\displaystyle 18i$

-18i $\displaystyle -18i$

None of the other responses is correct.

512 i $\displaystyle 512 i$

-512 i $\displaystyle -512 i$

Correct answer:

-512 i $\displaystyle -512 i$

Explanation:

$\left ( -2i\right )^{9}$ $\displaystyle \left ( -2i\right )^{9}$

$= \left ( -2 \right )^{9} \cdot i^{9}$ $\displaystyle = \left ( -2 \right )^{9} \cdot i^{9}$

To raise a negative number to an odd power, take the absolute value of the base to that power and give its opposite:

$\left ( -2\right )^{9} = - \left ( 2^{9}\right ) = -512$ $\displaystyle \left ( -2\right )^{9} = - \left ( 2^{9}\right ) = -512$

To raise $\displaystyle i$ to a power, divide the power by 4 and raise $\displaystyle i$ to the remainder. Since

$9 \div 4 = 2 \textup{ R }1$ $\displaystyle 9 \div 4 = 2 \textup{ R }1$,

$i^{9} = i^{1}= i$ $\displaystyle i^{9} = i^{1}= i$

Therefore,

$\left ( -2i\right )^{9}= \left ( -2 \right )^{9} \cdot i^{9} = -512 i$ $\displaystyle \left ( -2i\right )^{9}= \left ( -2 \right )^{9} \cdot i^{9} = -512 i$

Report an Error

Example Question #11 : Complex Numbers

Simplify:

$\small \left ( 3 - 2i \right )\left ( 2 + i\right )$ $\displaystyle \small \left ( 3 - 2i \right )\left ( 2 + i\right )$

Possible Answers:

$\small 6 + 3i$ $\displaystyle \small 6 + 3i$

$\small 6 - i$ $\displaystyle \small 6 - i$

$\small 8 + i$ $\displaystyle \small 8 + i$

$\small 6 - 3i$ $\displaystyle \small 6 - 3i$

$\small 8 - i$ $\displaystyle \small 8 - i$

Correct answer:

$\small 8 - i$ $\displaystyle \small 8 - i$

Explanation:

Use the FOIL method that states to multiply the Firsts, Outter, Inner, Lasts. Also remember that $\small i \times i = -1$ $\displaystyle \small i \times i = -1$ :

$\small \left ( 3 - 2i \right )\left ( 2 + i\right )$ $\displaystyle \small \left ( 3 - 2i \right )\left ( 2 + i\right )$

$\small = 3 \times 2 + 3 \times i - 2i \times 2 - 2i \times i$ $\displaystyle \small = 3 \times 2 + 3 \times i - 2i \times 2 - 2i \times i$

$\small = 6 +3i -4i + 2$ $\displaystyle \small = 6 +3i -4i + 2$

$\small = 8 - i$ $\displaystyle \small = 8 - i$

Report an Error

Example Question #1 : Exponential Ratios And Rational Numbers

If $\displaystyle m$ and $\displaystyle n$ are positive integers and $\displaystyle 4^m=64^n$, then what is the value of $\frac{m}{n}$ $\displaystyle \frac{m}{n}$?

Possible Answers:

$\frac{1}{16}$ $\displaystyle \frac{1}{16}$

$\displaystyle 3$

$\displaystyle 16$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

Correct answer:

$\displaystyle 3$

Explanation:

4³= 64

Alternatively written, this is 4(4)(4) = 64 or 4³= 64^1.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

Report an Error

Example Question #2 : Exponential Ratios And Rational Numbers

Write the following logarithm in expanded form:

$\log x^{2}y$ $\displaystyle \log x^{2}y$

Possible Answers:

$2\log x+\log y$ $\displaystyle 2\log x+\log y$

$\log x^{2}+\log y$ $\displaystyle \log x^{2}+\log y$

$2\left ( \log xy \right )$ $\displaystyle 2\left ( \log xy \right )$

$2\log x-\log y$ $\displaystyle 2\log x-\log y$

$\log x+\log y$ $\displaystyle \log x+\log y$

Correct answer:

$2\log x+\log y$ $\displaystyle 2\log x+\log y$

Explanation:

$\log x^{2}y=\log x^{2}+\log y=2\log x+\log y$ $\displaystyle \log x^{2}y=\log x^{2}+\log y=2\log x+\log y$

Report an Error

Example Question #6 : How To Find An Exponent From A Rational Number

Com_exp_1

Which of the following lists the above quantities from least to greatest?

Possible Answers:

I, III, II, IV

II, III, I, IV

IV, III, II, I

I, IV, III, II

I, IV, II, III

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

Report an Error

Example Question #1 : Exponents And Rational Numbers

Solve for $\displaystyle x$.

$2^{x}= 64$ $\displaystyle 2^{x}= 64$

Possible Answers:

$x=64^{2}$ $\displaystyle x=64^{2}$

x=-6 $\displaystyle x=-6$

x=64 $\displaystyle x=64$

x=5 $\displaystyle x=5$

x=6 $\displaystyle x=6$

Correct answer:

x=6 $\displaystyle x=6$

Explanation:

Since $2^{x}= 2^{6}$ $\displaystyle 2^{x}= 2^{6}$

Hence x=6 $\displaystyle x=6$

Report an Error

Example Question #91 : Exponents

Simplify:

$\sqrt[3]{x^{10}y^{8}z^{9}}$ $\displaystyle \sqrt[3]{x^{10}y^{8}z^{9}}$

Possible Answers:

$\sqrt[3]{xy^{2}}$ $\displaystyle \sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$ $\displaystyle x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

$x^{3}y^{3}z^{3}$ $\displaystyle x^{3}y^{3}z^{3}$

$x^{3}y^{2}z^{3}$ $\displaystyle x^{3}y^{2}z^{3}$

$x^{3}y^{2}z^{3}^{\sqrt[3]{xyz}}$ $\displaystyle x^{3}y^{2}z^{3}^{\sqrt[3]{xyz}}$

Correct answer:

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$ $\displaystyle x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Explanation:

$\sqrt[3]{x^{9}xy^{6}y^{2}z^{9}}=x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$ $\displaystyle \sqrt[3]{x^{9}xy^{6}y^{2}z^{9}}=x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Report an Error

Example Question #2 : Exponential Ratios And Rational Numbers

Solve for $\displaystyle x$:

$\sqrt{x} -1= 4$ $\displaystyle \sqrt{x} -1= 4$

Possible Answers:

$\displaystyle 9$

$\displaystyle 5$

$\displaystyle 25$

$\displaystyle 5$

$\displaystyle 36$

Correct answer:

$\displaystyle 25$

Explanation:

From the equation one can see that

$\sqrt{x} = 5$ $\displaystyle \sqrt{x} = 5$

Hence $\displaystyle x$ must be equal to 25.

Report an Error

Example Question #2 : How To Find An Exponent From A Rational Number

Evaluate:

$\log 0.1=$ $\displaystyle \log 0.1=$

Possible Answers:

$\displaystyle -2$

$\displaystyle -1$

$\displaystyle 10$

$\displaystyle 1$

$\frac{1}{10}$ $\displaystyle \frac{1}{10}$

Correct answer:

$\displaystyle -1$

Explanation:

$0.1= 10^{-1}$ $\displaystyle 0.1= 10^{-1}$

$\log 0.1=-1$ $\displaystyle \log 0.1=-1$

Report an Error

View PSAT Mathematics Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

View PSAT Mathematics Tutors

David
Certified Tutor

The University of Texas at El Paso, Bachelor of Science, Computational Mathematics. Indiana State University, Master of Scien...

View PSAT Mathematics Tutors

Benjamin
Certified Tutor

Portland State University, Bachelor of Science, Computer Science.

All PSAT Math Resources

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

Popular Subjects

GRE Tutors in Atlanta, Reading Tutors in Miami, Computer Science Tutors in San Francisco-Bay Area, MCAT Tutors in New York City, Calculus Tutors in New York City, Biology Tutors in Boston, Reading Tutors in New York City, SSAT Tutors in Houston, SSAT Tutors in Phoenix, Spanish Tutors in Boston

Popular Courses & Classes

GMAT Courses & Classes in Boston, LSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Denver, ISEE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Washington DC, GRE Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Houston, MCAT Courses & Classes in Philadelphia, ACT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Washington DC, SAT Test Prep in San Diego, GMAT Test Prep in Phoenix, LSAT Test Prep in Seattle, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Seattle, GMAT Test Prep in San Diego, GRE Test Prep in Philadelphia, LSAT Test Prep in Chicago, GRE Test Prep in Houston

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 : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #9 : How To Multiply Complex Numbers

Example Question #10 : How To Multiply Complex Numbers

Example Question #11 : Complex Numbers

Example Question #1 : Exponential Ratios And Rational Numbers

Example Question #2 : Exponential Ratios And Rational Numbers

Example Question #6 : How To Find An Exponent From A Rational Number

Example Question #1 : Exponents And Rational Numbers

Example Question #91 : Exponents

Example Question #2 : Exponential Ratios And Rational Numbers

Example Question #2 : How To Find An Exponent From A Rational Number

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: