Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : Single-Variable Algebra

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

Create An Account Create Tests & Flashcards

All SAT II Math II Resources

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

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 Next →

Example Question #3 :Solving Equations

Solve the equation for y

5y+27-5z=30

Possible Answers:

y=3+5z

$y=\frac{3+5z}{5}$

5y=3+5z

5y-5z=3

$z=\frac{3-5y}{5}$

有限公司rrect answer:

$y=\frac{3+5z}{5}$

Explanation:

5y+27-5z=30

First subtract 27 from both sides of the equation

5y-5z=3

Add 5z to both sides of the equation

5y=3+5z

Lastly, divide both sides by 5 to get the y by itself

$y=\frac{3+5z}{5}$

Report an Error

Example Question #4 :Solving Equations

Solve the equation: $\frac{2}{3x}+4=\frac{1}{2x}$

Possible Answers:

$-\frac{1}{12}$

$\frac{1}{24}$

$\frac{1}{48}$

$-\frac{1}{24}$

$\frac{1}{12}$

有限公司rrect answer:

$-\frac{1}{24}$

Explanation:

To isolate the x-variable, we can multiply both sides by the least common denominator.

The least common denominator is. This will eliminate the fractions.

$6x(\frac{2}{3x}+4)=\frac{1}{2x} \cdot 6x$

4+24x = 3

Subtract 4 on both sides.

4+24x -4= 3-4

24x=-1

Divide by 24 on both sides.

$\frac{24x}{24}=\frac{-1}{24}$

The answer is: $-\frac{1}{24}$

Report an Error

Example Question #5 :Solving Equations

Solve the equation: $\frac{1}{3}x-\frac{1}{4}x = \frac{1}{5}$

Possible Answers:

$\frac{12}{5}$

$\frac{10}{3}$

$\frac{13}{60}$

$\frac{24}{5}$

$\frac{7}{60}$

有限公司rrect answer:

$\frac{12}{5}$

Explanation:

Find the least common denominator of both sides of the equation, and multiply it on both sides.

The LCD is 60.

$60(\frac{1}{3}x-\frac{1}{4}x) = \frac{1}{5}\times 60$

20x-15x = 12

有限公司mbine like-terms on the left.

5x=12

Divide by 5 on both sides.

$\frac{5x}{5}=\frac{12}{5}$

The answer is: $\frac{12}{5}$

Report an Error

Example Question #6 :Solving Equations

Solve the equation: 8(x-3) = 16-x

Possible Answers:

$\frac{40}{7}$

$\frac{8}{9}$

$\frac{40}{9}$

有限公司rrect answer:

$\frac{40}{9}$

Explanation:

Distribute the eight through both terms of the binomial.

8x-24 = 16-x

Addon both sides.

8x-24 +x= 16-x+x

9x-24 = 16

Add 24 on both sides.

9x-24+24 = 16+24

9x=40

Divide by 9 on both sides.

$\frac{9x}{9}=\frac{40}{9}$

The answer is: $\frac{40}{9}$

Report an Error

Example Question #7 :Solving Equations

Solve the equation: -2+7x = 8x-6

Possible Answers:

$-\frac{4}{15}$

$-\frac{8}{15}$

$\frac{4}{15}$

有限公司rrect answer:

Explanation:

Subtractfrom both sides.

-2+7x-7x = 8x-6-7x

-2=x-6

Add 6 on both sides.

-2+6=x-6+6

x=4

The answer is:

Report an Error

Example Question #8 :Solving Equations

Solve $\sqrt{x^2 + 8} = 2\sqrt{2x-1}$

Possible Answers:

x=3, 9

x=7

$x= \sqrt{3}, \sqrt{6}$

x=2, 6

x=-3, 6

有限公司rrect answer:

x=2, 6

Explanation:

First, we want to get everything inside the square roots, so we distribute the:

$\sqrt{x^2 + 8} = \sqrt{4}\sqrt{2x-1}$

$\sqrt{x^2 + 8} = \sqrt{4(2x-1)}$

$\sqrt{x^2 + 8} = \sqrt{8x-4}$

Now we can clear our the square roots by squaring each side:

$(\sqrt{x^2 + 8})^{2} = (\sqrt{8x-4})^2$

x^2 + 8 = 8x-4

Now we can simplify by moving everything to one side of the equation:

x^2 -8x+ 12 = 0

将会给我们:

(x-6)(x-2)= 0

So our answers are:

x=2, 6

Report an Error

Example Question #9 :Solving Equations

Solve $6-\sqrt{x}=11$

Possible Answers:

没有解决方案.

有限公司rrect answer:

没有解决方案.

Explanation:

Begin by gathering all the constants to one side of the equation:

$-\sqrt{x}=5$

Now multiply by:

$\sqrt{x}=-5$

And finally, square each side:

x=25

This might look all fine and dandy, but let's check our solution by plugging it in to the original equation:

$6-\sqrt{25}=11$

6-5=11

$1\neq 11$

So our solution is invalid, and the problem doesn't have a solution.

Report an Error

Example Question #11 :Single Variable Algebra

Solve the equation: 3x-2 = 50

Possible Answers:

$\frac{52}{3}$

有限公司rrect answer:

$\frac{52}{3}$

Explanation:

Add two on both sides.

3x-2+2 = 50+2

3x = 52

Divide by three on both sides.

$\frac{3x }{3}=\frac{ 52}{3}$

The answer is: $\frac{52}{3}$

Report an Error

Example Question #12 :Single Variable Algebra

Solve: $\frac{2}{3}x = \frac{5}{2}$

Possible Answers:

$\frac{5}{3}$

$\frac{10}{3}$

$\frac{15}{4}$

$\frac{3}{5}$

$\frac{4}{15}$

有限公司rrect answer:

$\frac{15}{4}$

Explanation:

To isolate the x-variable, multiply both sides by the coefficient of the x-variable.

$\frac{2}{3}x \cdot \frac{3}{2} = \frac{5}{2}\cdot\frac{3}{2}$

The answer is: $\frac{15}{4}$

Report an Error

Example Question #13 :Single Variable Algebra

Give the solution set of the following rational equation:

$\frac{ x^{2}-4x}{x^{2}-2x} = 2$

Possible Answers:

$\left \{ 0\right \}$

$\left \{ 2, 4 \right \}$

$\left \{ 0, 2, 4 \right \}$

没有解决方案

$\left \{ 0, 4 \right \}$

有限公司rrect answer:

没有解决方案

Explanation:

Multiply both sides of the equation by $x^{2}-2x$ to eliminate the fraction:

$\frac{ x^{2}-4x}{x^{2}-2x} = 2$

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

$x^{2}-4x = 2 x^{2}-4x$

Subtract $x^{2}-4x$ from both sides:

$x^{2}-4x- (x^{2}-4x) = 2 x^{2}-4x - (x^{2}-4x)$

$2 x^{2} - x^{2} -4x + 4x = 0$

$x^{2} = 0$

The only possible solution is x = 0 , However, if this is substituted in the original equation, the expression at left is undefined, as seen here:

$\frac{ x^{2}-4x}{x^{2}-2x} = 2$

$\frac{ 0^{2}-4 \cdot 0}{0^{2}-2 \cdot 0} = 2$

$\frac{ 0}{ 0} = 2$

An expression with a denominator of 0 has an undefined value, so this statement is false. The equation has no solution.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 Next →

有限公司pyright Notice

View SAT Subject Test in Mathematics Level 2 Tutors

Brianna
Certified Tutor

University of Richmond, Current Undergrad, Business Administration and Management.

View SAT Subject Test in Mathematics Level 2 Tutors

Cynthia Marie
Certified Tutor

Rutgers University-New Brunswick, Bachelor in Arts, English. Harvard University, Master of Arts, English.

View SAT Subject Test in Mathematics Level 2 Tutors

Nathaniel
Certified Tutor

University of California-Los Angeles, Bachelor of Science, Applied Mathematics.

All SAT II Math II Resources

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

Popular Subjects

计算机科学ence Tutors in Philadelphia,Calculus Tutors in Washington DC,MCAT Tutors in Dallas Fort Worth,Algebra Tutors in Phoenix,Reading Tutors in Dallas Fort Worth,French Tutors in Seattle,Algebra Tutors in San Francisco-Bay Area,MCAT Tutors in Los Angeles,Algebra Tutors in New York City,Reading Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in Boston,GMAT Courses & Classes in Philadelphia,LSAT Courses & Classes in Houston,MCAT Courses & Classes in Los Angeles,SSAT Courses & Classes in Dallas Fort Worth,GRE考试课程和类es in San Francisco-Bay Area,GRE考试课程和类es in Washington DC,LSAT Courses & Classes in Atlanta,GMAT Courses & Classes in San Francisco-Bay Area,MCAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Philadelphia,ISEE Test Prep in Philadelphia,GRE Test Prep in New York City,在迈阿密行动测试准备,GMAT Test Prep in Boston,SAT Test Prep in Houston,GRE Test Prep in Washington DC,ISEE Test Prep in Miami,SSAT Test Prep in San Francisco-Bay Area,MCAT Test Prep in Boston

DMCA Complaint

如果你认为可用的内容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.

请求se 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.

请求se 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

有限公司ntact Information

*Full legal name

有限公司mpany name

*Phone number

*Email address

Address

*Address1

Address2

*City

*State

*Zipcode

*有限公司untry

有限公司mplaint Details

有限公司pyright holder you represent (if other than yourself)

*URL of copyrighted work (where your original material is located)

*请求se 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 : Single-Variable Algebra

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

All SAT II Math II Resources

Example Questions

Example Question #3 :Solving Equations

Example Question #4 :Solving Equations

Example Question #5 :Solving Equations

Example Question #6 :Solving Equations

Example Question #7 :Solving Equations

Example Question #8 :Solving Equations

Example Question #9 :Solving Equations

Example Question #11 :Single Variable Algebra

Example Question #12 :Single Variable Algebra

Example Question #13 :Single Variable Algebra

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

有限公司ntact Information

Address

有限公司mplaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: