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 #1 : Quadratic Equation

Solve for x: x² + 4x = 5

Possible Answers:

None of the other answers

-5

-5 or 1

-1 or 5

-1

Correct answer:

-5 or 1

Explanation:

Solve by factoring. First get everything into the form Ax² + Bx + C = 0:

x² + 4x - 5 = 0

Then factor: (x + 5) (x - 1) = 0

Solve each multiple separately for 0:

X + 5 = 0; x = -5

x - 1 = 0; x = 1

Therefore, x is either -5 or 1

Report an Error

Example Question #2 : Quadratic Equation

Solve for x: (x² – x) / (x – 1) = 1

Possible Answers:

x = -2

x = 1

No solution

x = 2

x = -1

Correct answer:

No solution

Explanation:

Begin by multiplying both sides by (x – 1):

x² – x = x – 1

Solve as a quadratic equation: x² – 2x + 1 = 0

Factor the left: (x – 1)(x – 1) = 0

Therefore, x = 1.

However, notice that in the original equation, a value of 1 for x would place a 0 in the denominator. Therefore, there is no solution.

Report an Error

Example Question #4 : Quadratic Equation

A farmer has 44 feet of fence, and wants to fence in his sheep. He wants to build a rectangular pen with an area of 120 square feet. Which of the following is a possible dimension for a side of the fence?

Possible Answers:

$10\ ft$

$5\ ft$

$7\ ft$

24 ft

$20\ ft$

Correct answer:

$10\ ft$

Explanation:

Set up two equations from the given information:

$\dpi{100} \small 120=xy$ and 44=2x+2y

Substitute $\dpi{100} \small y=\frac{120}{x}$ into the second equation:

$44=2x+2(\frac{120}{x})$

Multiply through by $\dpi{100} \small x$ .

$44x=2x^{2}+240$

Then divide by the coefficient of 2 to simplify your work:

$22x=x^{2}+120$

Then since you have a quadratic setup, move the 22x term to the other side (via subtraction from both sides) to set everything equal to 0:

$x^{2}-22x+120=0$

As you look for numbers that multiply to positive 120 and add to -22 so you can factor the quadratic, you might recognize that -12 and -10 fit the bill. This makes your factorization:

(x-10)(x-12)=0

This makes the possible solutions 10 and 12. Since 12 does not appear in the choices, $\dpi{100} \small 10\ feet$ is the only possible correct answer.

Report an Error

Example Question #2111 : Sat Mathematics

Find the roots of the following equation:

$3x^2+7x+2{}$

Possible Answers:

$-\frac{1}{3},2$

0,1

$\frac{1}{3},2$

$\frac{1}{3},-2$

$-\frac{1}{3},-2$

Correct answer:

$-\frac{1}{3},-2$

Explanation:

The equation that is given can be factor into:

(3x+1)(x+2)

The roots is the locations where this equation equals zero as seen below:

(3x+1)(x+2)=0

This occurs when the value in either parenthesis equals zero.

$(3x+1)=0 \and\ (x+2)=0$

Solving for the first expression:

3x=-1

$x=-\frac{1}{3}$

Solving for the second root:

x=-2

Therefore the roots are:

$-\frac{1}{3},-2$

Report an Error

Example Question #34 : Quadratic Equations

Give the solution set of the equation

$18x^{2} =39x + 84$

Possible Answers:

The equation has no solution.

$\left \{ -1 \frac{1}{3 }, 3\frac{1}{2} \right \}$

$\left \{ -2, 2 \frac{1}{3 } \right \}$

$\left \{ -3\frac{1}{2}, 1 \frac{1}{3 } \right \}$

$\left \{ -2 \frac{1}{3 } , 2 \right \}$

Correct answer:

$\left \{ -1 \frac{1}{3 }, 3\frac{1}{2} \right \}$

Explanation:

$18x^{2} =39x + 84$

$18x^{2} - 39x - 84 =39x + 84 - 39x - 84$

$18x^{2} - 39x - 84 =0$

$3 ( 6x^{2} - 13x - 28)=0$

The quadratic trinomial can be factored using the method by looking for two integers whose sum is and whose product is $6 \times (-28 ) = -168$ . Throught trial and error, we see that these integers are and 8, so we continue:

$3(6x^{2} -21x+8 x - 28 ) = 0$

$3 \left [ (6x^{2} -21x)+( 8x - 28 ) \right ]= 0$

$3 \left [ 3x (2x -7)+ 4 ( 2x - 7) \right ]= 0$

3(3x+4) (2x-7)= 0

One of the factors must be equal to 0, so either:

3x+4 = 0

3x = - 4

$x = - \frac{4}{3} =- 1 \frac{1}{3 }$

2x-7 = 0

2x = 7

$x = \frac{7}{2} = 3\frac{1}{2}$

The correct choice is $\left \{ -1 \frac{1}{3 }, 3\frac{1}{2} \right \}$ .

Report an Error

Example Question #37 : Quadratic Equations

Consider the equation

$6 x ^{2} = 5x+21$ .

Which of the following statements correctly describes its solution set?

Possible Answers:

Exactly two solutions, both of which are imaginary.

Exactly two solutions, both of which are irrational.

Exactly one solution, which is irrational.

Exactly one solution, which is rational.

Exactly two solutions, both of which are rational.

Correct answer:

Exactly two solutions, both of which are rational.

Explanation:

Write the quadratic equation in standard form $ax^{2} + bx+ c = 0$ by subtracting 5x+21 from both sides:

$6 x ^{2} = 5x+21$

$6 x ^{2} - (5x+21) = 5x+21 - (5x+21)$

$6 x ^{2} - 5x-21 =0$

The nature of the solution set of a quadratic equation in standard form can be determined by examining the discriminant $b^{2} - 4ac$ . Setting a = 6, b= -5, c= -21 :

$b^{2} - 4ac = (-5) ^{2} - 4 \cdot 6 \cdot (-21) = 25 - (-504) = 529$

The discriminant is positive, so there are two real solutions.

529 is a perfect square:

$529 = 23 ^{2}$ .

Therefore, the two real solutions are also rational.

Report an Error

Example Question #36 : Quadratic Equations

Consider the equation

$4 x ^{2}+ 21 = 5x$ .

Which of the following statements correctly describes its solution set?

Possible Answers:

Exactly two solutions, both of which are rational.

Exactly one solution, which is irrational.

Exactly two solutions, both of which are irrational.

Exactly two solutions, both of which are imaginary.

Exactly one solution, which is rational.

Correct answer:

Exactly two solutions, both of which are imaginary.

Explanation:

Write the quadratic equation in standard form $ax^{2} + bx+ c = 0$ by subtracting from both sides:

$4 x ^{2}+ 21 = 5x$

$4 x ^{2}+ 21 - 5x = 5x - 5x$

$4 x ^{2}- 5x + 21 = 0$

The nature of the solution set of a quadratic equation in standard form can be determined by examining the discriminant $b^{2} - 4ac$ . Setting a = 4, b= -5 , c= 21 :

$b^{2} - 4ac =(-5) ^{2} - 4 \cdot 4 \cdot 21 = 25 - 336= -311$

The discriminant is negative, so there are two imaginary solutions.

Report an Error

Example Question #27 : How To Find The Solution To A Quadratic Equation

Consider the equation

$2x ^{2} + 7x = 12$ .

Which of the following statements correctly describes its solution set?

Possible Answers:

Exactly one solution, which is rational.

Exactly two solutions, both of which are imaginary.

Exactly two solutions, both of which are irrational.

Exactly one solution, which is irrational.

Exactly two solutions, both of which are rational.

Correct answer:

Exactly two solutions, both of which are irrational.

Explanation:

Write the quadratic equation in standard form $ax^{2} + bx+ c = 0$ by subtracting 12 from both sides:

$2x ^{2} + 7x = 12$

$2x ^{2} + 7x - 12 = 12 - 12$

$2x ^{2} + 7x - 12 = 0$

The nature of the solution set of a quadratic equation in standard form can be determined by examining the discriminant $b^{2} - 4ac$ . Setting a = 2, b= 7, c= -12 :

$b^{2} - 4ac = 7 ^{2} - 4 \cdot 2 \cdot (-12) = 49 - (-96) = 145$

The discriminant is positive, so there are two real solutions. However, 145 is not a perfect square; the two solutions are therefore irrational.

Report an Error

Example Question #341 : Equations / Inequalities

Consider the equation:

$3x^{2} + 7x =$ __________

Fill in the blank with a real constant to form an equation with exactly one real solution.

Possible Answers:

$- \frac{49}{12}$

None of the other responses gives a correct answer.

$- \frac{49}{36}$

Correct answer:

$- \frac{49}{12}$

Explanation:

We will call the constant that goes in the blank . The equation becomes

$3x^{2} + 7x = N$

Write the quadratic equation in standard form $ax^{2} + bx+ c = 0$ by subtracting from both sides:

$3x^{2} + 7x - N = N - N$

$3x^{2} + 7x - N = 0$

The solution set comprises exactly one rational solution if and only if the discriminant $b^{2} - 4ac$ is equal to 0. Setting a = 3, b= 7 , c= -N . and substituting in the equation:

$b^{2} - 4ac = 0$

$7^{2} - 4(3)(-N) = 0$

Solving for :

49 - (-12N) = 0

49 + 12 N = 0

49 + 12 N- 49 = 0 - 49

12N = -49

$12N\div 12 = -49 \div 12$

$N = - \frac{49}{12}$ ,

the correct response.

Report an Error

Example Question #342 : Equations / Inequalities

Consider the equation:

__________ $x^{2} + 16 = 7x$

Fill in the blank with a real constant to form an equation with exactly one real solution.

Possible Answers:

$\frac{64}{49}$

$\frac{7}{8}$

None of the other responses gives a correct answer.

$\frac{8}{7}$

$\frac{49}{64}$

Correct answer:

$\frac{49}{64}$

Explanation:

We will call the constant that goes in the blank . The equation becomes

$N x^{2} + 16 = 7x$

Write the quadratic equation in standard form $ax^{2} + bx+ c = 0$ by subtracting from both sides:

$N x^{2} + 16 - 7x = 7x - 7x$

$N x^{2}- 7x + 16 = 0$

The solution set comprises exactly one rational solution if and only if the discriminant $b^{2} - 4ac$ is equal to 0. Setting a =N, b= -7 , c= 16 . and substituting in the equation:

$b^{2} - 4ac = 0$

$(-7)^{2} - 4 (N)(16)= 0$

49 - 64N= 0

Solving for :

49 - 64N+ 64N = 0 + 64N

49 = 64N

$49 \div 64 = 64N \div 64$

$N = \frac{49}{64}$ ,

the correct response.

Report an Error

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Stephen
Certified Tutor

Grinnell College, Bachelor in Arts, Computer Science.

View SAT Mathematics Tutors

Scott
Certified Tutor

Rutgers College, Bachelors, Political Science and Government. Florida Coastal School of Law, PHD, Law.

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

ISEE Courses & Classes in Seattle, ACT Courses & Classes in Miami, GRE Courses & Classes in Boston, LSAT Courses & Classes in New York City, Spanish Courses & Classes in Los Angeles, GMAT Courses & Classes in Phoenix, ISEE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, GMAT Courses & Classes in Boston, ISEE Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Phoenix, ISEE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Atlanta, SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Boston, LSAT Test Prep in Miami, ACT Test Prep in Miami, LSAT Test Prep in Washington DC, ACT Test Prep in Atlanta, LSAT Test Prep in New York City

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 #1 : Quadratic Equation

Example Question #2 : Quadratic Equation

Example Question #4 : Quadratic Equation

Example Question #2111 : Sat Mathematics

Example Question #34 : Quadratic Equations

Example Question #37 : Quadratic Equations

Example Question #36 : Quadratic Equations

Example Question #27 : How To Find The Solution To A Quadratic Equation

Example Question #341 : Equations / Inequalities

Example Question #342 : Equations / Inequalities

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: