We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #211 : Exponents

Remember that $i= \sqrt{-1}$ .

Simplify: (2+3i)(1-i)

Possible Answers:

-1+i

5+i

5-i

-1+5i

-1-i

Correct answer:

5+i

Explanation:

Use FOIL to multiply complex numbers as follows:

(2+3i)(1-i)

2-2i+3i-3i^2

Since $i= \sqrt{-1}$ , it follows that i^2 = -1 , so then:

$2-2i+3i-3 \cdot (-1)$

2-2i+3i+3

Combining like terms gives:

5+i

Report an Error

Example Question #211 : Exponents

Simplify: (3+2i)(3-2i)

Possible Answers:

5-12i

13-12i

Correct answer:

Explanation:

Use FOIL:

(3+2i)(3-2i)=9-6i+6i-4i^2

Combine like terms:

=9-4i^2

But since i^2=-1 , we know

$9-4i^2=9-4 \cdot (-1)=9+4=13$

Report an Error

Example Question #49 : Squaring / Square Roots / Radicals

$x = 5+ i \sqrt{7}$ ; is the complex conjugate of .

Evaluate

$x^{2} - 2xy + y^{2}$ .

Possible Answers:

100

$\textup{None of the other choices gives the correct response}$

Correct answer:

Explanation:

$x^{2} - 2xy + y^{2}$ conforms to the perfect square trinomial pattern

$x^{2} - 2xy + y^{2} = (x-y) ^{2}$ .

The easiest way to solve this problem is to subtract and , then square the difference.

The complex conjugate of a complex number a+bi is a-bi .

$x = 5+ i \sqrt{7}$ ,

so is the complex conjugate of this;

$x = 5- i \sqrt{7}$

$x-y = (5+ i \sqrt{7}) - (5- i \sqrt{7}) = 5- 5 +i \sqrt{7}+ i \sqrt{7} = 2i \sqrt{7}$

$x^{2} - 2xy + y^{2} = (x-y) ^{2}$

$=( 2i \sqrt{7} )^{2}$

Taking advantage of the Power of a Product Rule and the fact that $i^{2} = -1$ :

$= 2^{2} \cdot i ^{2}\cdot (\sqrt{7}) ^{2}$

$=4 \cdot (-1 )\cdot 7$

= -28

Report an Error

Example Question #21 : How To Multiply Complex Numbers

Raise 7+2i to the fourth power.

Possible Answers:

1,241 +2,520 i

3,593+2,968i

None of these

2,025+2,968i

2,809 +2,520 i

Correct answer:

1,241 +2,520 i

Explanation:

By the Power of a Power Rule, the fourth power of any number is equal to the square of the square of that number:

$x^{4} = x ^{2 \cdot 2} =( x^{2})^{2}$

Therefore, one way to raise 7+2i to the fourth power is to square it, then to square the result.

Using the binomial square pattern to square 7+2i :

$(7+2i)^{2} = 7^{2} + 2 \cdot 7 \cdot 2i + (2i ) ^{2}$

Applying the Power of a Product Property:

$(7+2i)^{2} = 7^{2} + 2 \cdot 7 \cdot 2i + 2^{2} \cdot i ^{2}$

Since $i^{2} = -1$ by definition:

$(7+2i)^{2} = 7^{2} + 2 \cdot 7 \cdot 2i + 2^{2} \cdot (-1)$

= 49 + 28i -4

= 45 + 28i

Square this using the same steps:

$(45 + 28i )^{2} = 45 ^{2} + 2 \cdot 45 \cdot 28 i + (28 i) ^{2}$

$= 45 ^{2} + 2 \cdot 45 \cdot 28 i + 28^{2} i ^{2}$

$= 45 ^{2} + 2 \cdot 45 \cdot 28 i + 28^{2} (-1)$

= 2,025 +2,520 i -784

= 1,241 +2,520 i

Report an Error

Example Question #51 : Squaring / Square Roots / Radicals

Raise 8 - 3i to the fourth power.

Possible Answers:

7,633 - 7,008i

None of these

721-5,280 i

3,025 - 7,008i

5,329-5,280 i

Correct answer:

721-5,280 i

Explanation:

The easiest way to find $(8 - 3i)^{4}$ is to note that

$(8 - 3i)^{4} =[ (8 - 3i)^{2} ]^{2}$ .

Therefore, we can find the fourth power of 8 - 3i by squaring 8 - 3i , then squaring the result.

Using the binomial square pattern to square 8 - 3i :

$(8 - 3i)^{2} = 8^{2} - 2 \cdot 8 \cdot 3i + (3i)^{2}$

Applying the Power of a Product Property:

$(8 - 3i)^{2} = 8^{2} - 2 \cdot 8 \cdot 3i + 3^{2} \cdot i^{2}$

Since $i^{2} = -1$ by definition:

$(8 - 3i)^{2} = 64 - 48 i + 9 (-1)$

= 64 - 48 i -9

= 55 - 48 i

Square this using the same steps:

$( 55 - 48 i )^{2} = 55^{2} - 2 \cdot 55 \cdot 48 i + (48i)^{2}$

$= 3,025-5,280 i + 48^{2} i^{2}$

= 3,025-5,280 i + 2,304(-1)

= 3,025-5,280 i - 2,304

= 721-5,280 i

Therefore, $(8 - 3i)^{4} = 721-5,280 i$

Report an Error

Example Question #42 : Complex Numbers

Raise 5+4i to the third power.

Possible Answers:

-115 + 364i

365 + 364i

None of these

-115 + 236i

365 + 236i

Correct answer:

-115 + 236i

Explanation:

To raise any expression A+B to the third power, use the pattern

$\left (A+B \right )^{3} = A^{3} + 3A^{2} B + 3 AB^{2} + B^{3}$

Setting A = 5, B = 4i :

$(5+4i)^{3} = 5^{3} + 3\cdot 5^{2} \cdot 4i + 3 \cdot 5 \cdot (4i)^{2} + (4i)^{3}$

Taking advantage of the Power of a Product Rule:

$(5+4i)^{3} = 5^{3} + 3\cdot 5^{2} \cdot 4i + 3 \cdot 5 \cdot 4^{2} \cdot i^{2} +4 ^{3} \cdot i ^{3}$

Since $i^{2} = -1$ and $i^{3} = i^{2} \cdot i = -1 \cdot i = -i$ :

$(5+4i)^{3} = 125 + 3\cdot 25 \cdot 4 i + 3 \cdot 5 \cdot 16 \cdot (-1) +64 \cdot (- i )$

$(5+4i)^{3} = 125+ 300i -240 -64i$

Collecting real and imaginary terms:

$(5+4i)^{3} = 125 -240 + 300i -64i$

$(5+4i)^{3} = -115 + 236i$

Report an Error

Example Question #52 : Squaring / Square Roots / Radicals

Evaluate:

$i^{-31}$

Possible Answers:

The expression is undefined

Correct answer:

Explanation:

$a^{-m}$ is defined to be equal to $\frac{1}{a^{m}}$ for any real or imaginary and for any real ; therefore,

$i^{-31} = \frac{1}{i^{31}}$

To evaluate a positive power of , divide the power by 4 and note the remainder:

$31 \div 4= 7 \textrm{ R }3$

Therefore,

$i ^{31} = i ^{3} = -i$

Substituting,

$i^{-31} = \frac{1}{-i}$

Rationalizing the denominator by multiplying both numerator and denominator by :

$i^{-31} = \frac{1 \cdot i}{-i \cdot i }= \frac{ i}{-i ^{2}}= \frac{ i}{-(-1)}= \frac{ i}{1}= i$

Report an Error

Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

$2^{x}= 64$

Possible Answers:

x=5

x=64

$x=64^{2}$

x=-6

x=6

Correct answer:

x=6

Explanation:

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

Hence x=6

Report an Error

Example Question #1 : Exponents And Rational Numbers

Simplify:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Report an Error

Example Question #1 : Exponents And Rational Numbers

Solve for :

$\sqrt{x} -1= 4$

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

Report an Error

View SAT Mathematics Tutors

Momeena
Certified Tutor

State University of New York at New Paltz, Bachelors, Mathematics & Elementary Education. State University of New York at New...

View SAT Mathematics Tutors

Bill
Certified Tutor

SUNY Empire State College, Bachelors, General Sciences, Theater.

View SAT Mathematics Tutors

Stephanie
Certified Tutor

Saint Louis University-Main Campus, Bachelors, Psychology. University of Southern Mississippi, Masters, Clinical Psychology.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

GRE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Denver, LSAT Courses & Classes in Chicago, ISEE Courses & Classes in Los Angeles, ACT Courses & Classes in Chicago, SAT Courses & Classes in New York City, LSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Los Angeles

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Chicago, SSAT Test Prep in Philadelphia, ISEE Test Prep in New York City, GMAT Test Prep in Chicago, ACT Test Prep in New York City, MCAT Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, SAT Test Prep in Seattle, LSAT Test Prep in Phoenix

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

SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #211 : Exponents

Example Question #211 : Exponents

Example Question #49 : Squaring / Square Roots / Radicals

Example Question #21 : How To Multiply Complex Numbers

Example Question #51 : Squaring / Square Roots / Radicals

Example Question #42 : Complex Numbers

Example Question #52 : Squaring / Square Roots / Radicals

Example Question #1 : How To Find An Exponent From A Rational Number

Example Question #1 : Exponents And Rational Numbers

Example Question #1 : Exponents And Rational Numbers

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: