Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : Number Theory

Study concepts, example questions & explanations for SAT II Math II

Create An Account

All SAT II Math II Resources

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

Example Questions

Example Question #1 : Real And Complex Numbers

Which of the following is equal to $i^{37}$ ?

Possible Answers:

-37i

37i

Correct answer:

Explanation:

To raise to a power, divide the exponent by 4 and note the remainder.

$37 \div 4 = 9 \textrm{ R }1$

Raise to the power of that remainder:

$i^{37} = i^{1} = i$

Report an Error

Example Question #2 : Real And Complex Numbers

Evaluate:

$(6 +5i)^{2}$

Possible Answers:

61+60i

11+60i

61-60i

Correct answer:

11+60i

Explanation:

Use the square of a sum pattern

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

where A = 6, B = 5i :

$(6 +5i)^{2} = 6^{2} + 2 \cdot 6i \cdot 5 + (5i)^{2}$

$= 6^{2} + 2 \cdot 6 \cdot 5i + 5^{2}i^{2}$

= 36+ 60i + 25 (-1)

= 36+ 60i -25

= 11+60i

Report an Error

Example Question #3 : Real And Complex Numbers

Multiply:

7i (5 + 9i)

Possible Answers:

35 - 63i

-63- 35i

-63+ 35i

63- 35i

-35 + 63i

Correct answer:

-63+ 35i

Explanation:

Apply the distributive property:

7i (5 + 9i)

$= 7i \cdot 5 + 7i \cdot 9i$

$= 35i + 63 i^{2}$

= 35i + 63 (-1)

= -63+ 35i

Report an Error

Example Question #11 : Number Theory

Which of the following is equal to $\left ( 4i\right )^{4}$ ?

Possible Answers:

256i

16i

256

Correct answer:

256

Explanation:

By the power of a product property,

$\left ( 4i\right )^{4} = 4^{4} \cdot i^{4} = 256 \cdot 1 = 256$

Report an Error

Example Question #5 : Real And Complex Numbers

Multiply:

(6 - 7i)(7+6i)

Possible Answers:

-84 + 13i

84 - 13i

-13i

84 +13i

Correct answer:

84 - 13i

Explanation:

Use the FOIL method:

(6 - 7i)(7+6i)

$= 6 \cdot 7 +6 \cdot 6i - 7 \cdot 7i - 7i \cdot 6i$

$=42 +36i - 49i - 42i ^{2}$

=42 +36i - 49i - 42 (-1)

=42 +36i - 49i + 42

=84 - 13i

Report an Error

Example Question #6 : Real And Complex Numbers

Which of the following is equal to $i^{77}$ ?

Possible Answers:

-77i

77i

Correct answer:

Explanation:

To raise to a power, divide the exponent by 4 and note the remainder.

$77 \div 4 = 19\textrm{ R }1$

Raise to the power of that remainder:

$i^{77} = i^{1} = i$

Report an Error

Example Question #7 : Real And Complex Numbers

Multiply:

8i (5-7i)

Possible Answers:

56+ 40i

40 + 56i

-56+ 40i

-40 + 56i

56- 40i

Correct answer:

56+ 40i

Explanation:

Apply the distributive property:

8i (5-7i)

$= 8i \cdot 5- 8i \cdot 7i$

$= 40i- 56i^{2}$

= 40i- 56 (-1)

= 40i- (-56)

= 56+ 40i

Report an Error

Example Question #12 : Number Theory

Multiply:

$\left ( -4i\right ) (-6i)(-7i)$

Possible Answers:

168

168i

-168i

None of the other responses is correct.

Correct answer:

168i

Explanation:

$\left ( -4i\right ) (-6i)(-7i)$

$= \left ( -4\right ) (-6)(-7) \cdot i \cdot i \cdot i$

$= -168 \cdot i ^{3} = -168 (-i) = 168i$

Report an Error

Example Question #13 : Number Theory

Evaluate:

$\left ( 7+3i\right )^{2}$

Possible Answers:

40 + 42i

40 - 42i

58 + 42i

Correct answer:

40 + 42i

Explanation:

Use the square of a sum pattern

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

where A = 7, B = 3i :

$\left ( 7+3i\right )^{2} = 7^{2}+ 2 \cdot 7 \cdot 3i + (3i)^{2}$

$= 7^{2}+ 2 \cdot 7 \cdot 3i + 3^{2}i^{2}$

= 49 + 42i + 9 (-1)

= 49 + 42i -9

= 40 + 42i

Report an Error

Example Question #14 : Number Theory

is a complex number; $\overline{x}$ denotes the complex conjugate of .

$x \cdot \overline{x} = 84$

Which of the following could be the value of ?

Possible Answers:

$6 - 4 i \sqrt{3}$

$7 + i \sqrt{35}$

$8 + 2 i \sqrt{5}$

Any of the numbers in the other four choices could be equal to .

$9 - i \sqrt{3}$

Correct answer:

Any of the numbers in the other four choices could be equal to .

Explanation:

The product of a complex number x = a+ bi and its complex conjugate $\overline{x} = a- bi$ is

$x \cdot \overline{x} = (a+ bi)(a-bi) = a^{2} + b^{2}$

Setting and accordingly for each of the four choices, we want to find the choice for which $x \cdot \overline{x} = a^{2} + b^{2} = 84$ :

$6 - 4 i \sqrt{3}$

$a = 6, b = - 4 \sqrt{3}$

$x \cdot \overline{x} = a^{2} + b^{2} = 6^{2}+ (-4 \sqrt{3})^{2} = 36 + 4 ^{2} (\sqrt{3} )^{2} = 36 + 16 \cdot 3 = 36 + 48 = 84$

$7 + i \sqrt{35}$

$a = 7, b = \sqrt{35}$

$x \cdot \overline{x} = a^{2} + b^{2} = 7^{2} + (\sqrt{35})^{2} = 49 + 35 = 84$

$8 + 2 i \sqrt{5}$

$a = 8 , b = 2 \sqrt{5}$

$x \cdot \overline{x} = a^{2} + b^{2} = 8^{2} + (2 \sqrt{5})^{2} = 64 + 2^{2} \cdot (\sqrt{5})^{2} = 64 + 4 \cdot 5 = 64 + 20 = 84$

$9 - i \sqrt{3}$

$a = 9 , b = - \sqrt{3}$

$x \cdot \overline{x} = a^{2} + b^{2} = 9^{2} + (- \sqrt{3})^{2} = 81 + 3 = 84$

For each given value of , $x \cdot \overline{x} = 84$ .

Report an Error

View SAT Subject Test in Mathematics Level 2 Tutors

Harriet
Certified Tutor

St. Olaf College, Bachelors, Math and Physics.

View SAT Subject Test in Mathematics Level 2 Tutors

Brooke
Certified Tutor

New York University, Bachelor in Arts, Drama and Dance Teacher Education. Georgia State University, Master of Arts, Communica...

View SAT Subject Test in Mathematics Level 2 Tutors

Shivansh
Certified Tutor

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

All SAT II Math II Resources

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

Popular Subjects

French Tutors in New York City, LSAT Tutors in New York City, SSAT Tutors in San Francisco-Bay Area, GRE Tutors in Washington DC, ACT Tutors in Philadelphia, MCAT Tutors in Houston, Reading Tutors in Denver, ACT Tutors in Seattle, Reading Tutors in Dallas Fort Worth, GMAT Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Boston, SAT Courses & Classes in Chicago, LSAT Courses & Classes in Seattle, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Atlanta, Spanish Courses & Classes in New York City, SSAT Courses & Classes in Seattle, LSAT Courses & Classes in Miami, ISEE Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC, GMAT Test Prep in Houston, GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Boston, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Houston, GMAT Test Prep in Phoenix, MCAT Test Prep in Boston, SAT 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 II Math II : Number Theory

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #1 : Real And Complex Numbers

Example Question #2 : Real And Complex Numbers

Example Question #3 : Real And Complex Numbers

Example Question #11 : Number Theory

Example Question #5 : Real And Complex Numbers

Example Question #6 : Real And Complex Numbers

Example Question #7 : Real And Complex Numbers

Example Question #12 : Number Theory

Example Question #13 : Number Theory

Example Question #14 : Number Theory

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: