We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : Other Mathematical Relationships

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 : Other Mathematical Relationships

Add in modulo 9:

5 + 6 + 5 + 4 + 3

Possible Answers:

Correct answer:

Explanation:

In modulo 9 arithmetic, a number is congruent to the remainder of its division by 9.

Since

5 + 6 + 5 + 4 + 3 = 23

and

$23 \div 9 = 2\textrm{ R }5$ ,

$5 + 6 + 5 + 4 + 3 \equiv 5 \mod 9$ ,

making "5" the correct response.

Report an Error

Example Question #1 : Other Mathematical Relationships

varies directly as and inversely as .

If T = 273 and P = 100 , then V = 1,000 .

To the nearest whole number, evaluate if T = 293 and P = 110 .

Possible Answers:

$V \approx 976$

$V \approx 1,025$

Insufficient information is given to answer the question.

$V \approx 1,073$

$V \approx 909$

Correct answer:

$V \approx 976$

Explanation:

varies directly as and inversely as . This means that for some constant of variation ,

$\frac{V P }{T } = k$

Alternatively,

$\frac{V_{1}P_{1}}{T_{1}} = \frac{V_{2}P_{2}}{T_{2}}$

We can substitute the initial conditions for thevariables on the left side and the final conditions for those on the right side, then solve for $V_{2}$ :

$\frac{1,000 \cdot 100}{273} = \frac{V_{2} \cdot 110}{293}$

$\frac{V_{2} \cdot 110}{293} \cdot \frac{293}{ 110} = \frac{1,000 \cdot 100}{273} \cdot \frac{293}{ 110}$

$V_{2} = \frac{1,000 \cdot 100 \cdot 293}{273\cdot 110} \approx 976$

Report an Error

Example Question #2 : Other Mathematical Relationships

varies directly as both and the square of .

If m = 10 and v = 40 , then E= 8,000 .

Evaluate if m = 15 and v = 30 .

Possible Answers:

E = 9,000

E = 6,750

E = 9,481

E = 13,500

E = 10,125

Correct answer:

E = 6,750

Explanation:

varies directly as both and the square of . This means that for some constant of variation ,

$\frac{E}{mv^{2}} = k$ .

Alternatively stated,

$\frac{E_{1}}{m_{1}v_{1}^{2}} = \frac{E_{2}}{m_{2}v_{2}^{2}}$ .

We can substitute the initial conditions for the variables on the left side and the final conditions for those on the right side, then solve for $E_{2}$ :

$\frac{8,000}{10 \cdot 40^{2}} = \frac{E_{2}}{15 \cdot 30^{2}}$

$\frac{8,000}{10 \cdot 40^{2}} \cdot 15 \cdot 30^{2} = \frac{E_{2}}{15 \cdot 30^{2}} \cdot 15 \cdot 30^{2}$

$E_{2} = \frac{8,000 \cdot 15 \cdot 30^{2}}{10 \cdot 40^{2}} = \frac{108,000,000}{16,000}= 6,750$

Report an Error

Example Question #151 : Sat Subject Test In Math Ii

$4 \sqrt[4] {a}+ 7 \sqrt[4] {b} =18$

$3\sqrt[4] {a} -5 \sqrt[4] {b} = 34$

Evaluate .

Possible Answers:

The system has no solution.

4,096

Correct answer:

4,096

Explanation:

Rewrite the two equations by setting $x = \sqrt [4] {a}$ and $y = \sqrt [4] {b}$ and substituting:

$4 \sqrt[4] {a}+ 7 \sqrt[4] {b} =18$

4x+7y = 18

$3\sqrt[4] {a} -5 \sqrt[4] {b} = 34$

3x-5y = 34

The result is a two-by-two linear system in terms of and :

4x+7y = 18

3x-5y = 34

This can be solved, among other ways, using Gaussian elimination on an augmented matrix:

$\begin{bmatrix} 4& 7\\ 3& -5 \end{matrix} \begin{vmatrix} 18 \\ 34 \\ \end{bmatrix}$

Perform row operations until the left two columns show identity matrix $\begin{bmatrix} 1 & 0\\ 0 &1 \end{bmatrix}$ . One possible sequence:

$R1-R2 \rightarrow R1$

$\begin{bmatrix} 4 - 3 & 7- (-5 )\\ 3& -5 \end{matrix} \begin{vmatrix} 18 - 34 \\ 34 \\ \end{bmatrix}$

$\begin{bmatrix} 1 & 12 \\ 3& -5 \end{matrix} \begin{vmatrix} -16 \\ 34 \\ \end{bmatrix}$

$R2 - 3R1 \rightarrow R2$

$\begin{bmatrix} 1 & 12 \\ 3 - 3(1)& -5 - 3(12) \end{matrix} \begin{vmatrix} -16 \\ 34 - 3(-16) \\ \end{bmatrix}$

$\begin{bmatrix} 1 & 12 \\ 0& -41\end{matrix} \begin{vmatrix} -16 \\ 82\\ \end{bmatrix}$

$R2 \div (-41 )\rightarrow R2$

$\begin{bmatrix} 1 & 12 \\ 0\div (-41 )& -41\div (-41 )\end{matrix} \begin{vmatrix} -16 \\ 82\div (-41 )\\ \end{bmatrix}$

$\begin{bmatrix} 1 & 12 \\ 0& 1 \end{matrix} \begin{vmatrix} -16 \\-2\\ \end{bmatrix}$

$R1 - 12 R2 \rightarrow R1$

$\begin{bmatrix} 1 - 12(0) & 12 - 12(1) \\ 0& 1 \end{matrix} \begin{vmatrix} -16 - 12(-2) \\ 2\\ \end{bmatrix}$

$\begin{bmatrix} 1 & 0 \\ 0& 1 \end{matrix} \begin{vmatrix} 8 \\ 2\\ \end{bmatrix}$

x= 8 and y = 2 . In the former equation, substitute $\sqrt [4] {a}$ back for , and raise both sides to the power of 4:

$\sqrt [4] {a} = 8$

$(\sqrt [4] {a}) ^{4}= 8^{4}$

a = 4,096

Report an Error

View SAT Subject Test in Mathematics Level 2 Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View SAT Subject Test in Mathematics Level 2 Tutors

Lindsey
Certified Tutor

California State University-Fresno, Bachelor of Science, Ecology and Evolutionary Biology. National University, Certificate, ...

View SAT Subject Test in Mathematics Level 2 Tutors

Jaroslaw
Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

All SAT II Math II Resources

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

Popular Subjects

Algebra Tutors in New York City, Physics Tutors in Washington DC, ISEE Tutors in Washington DC, Reading Tutors in San Francisco-Bay Area, Math Tutors in Atlanta, Calculus Tutors in San Diego, French Tutors in Phoenix, Math Tutors in Houston, MCAT Tutors in Houston, Reading Tutors in Boston

Popular Courses & Classes

Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Denver, SAT Courses & Classes in Atlanta, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in Denver, ISEE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in San Diego, SAT Courses & Classes in Denver, GRE Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, GRE Test Prep in Atlanta, SSAT Test Prep in Philadelphia, GMAT Test Prep in Boston, ISEE Test Prep in Los Angeles, GRE Test Prep in Seattle, MCAT Test Prep in San Diego, ISEE Test Prep in Seattle, SAT Test Prep in Houston, LSAT Test Prep in Atlanta

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 : Other Mathematical Relationships

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

All SAT II Math II Resources

Example Questions

Example Question #1 : Other Mathematical Relationships

Example Question #1 : Other Mathematical Relationships

Example Question #2 : Other Mathematical Relationships

Example Question #151 : Sat Subject Test In Math Ii

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: