Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : Algebra

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #124 : Properties Of Exponents

x> 0 and y > 0

$x^{2} = 8$

$y^{2} = 18$

Evaluate $(x+ y) ^{2}$ .

Possible Answers:

144

Correct answer:

Explanation:

By the perfect square trinomial pattern,

$(x+ y) ^{2}$

$=x^{2} +2xy+ y ^{2}$

$x^{2} = 8$ and $y^{2} = 18$ .

Also, by the Power of a Power Principle,

$(xy) ^{2} = x^{2} y^{2} = 8 \cdot 18 = 144$ ,

so, since and are both positive,

$xy = \sqrt{(xy) ^{2} }= \sqrt{144}= 12$ .

Therefore,

$(x+ y) ^{2}$

$=x^{2} +2xy+ y ^{2}$

= 8 +2 (12)+18

= 8 +24 +18

= 50

Report an Error

Example Question #125 : Properties Of Exponents

$y^{3} = -17$

$y^{9} = ?$

Possible Answers:

4,913

-4,913

Correct answer:

-4,913

Explanation:

By the Power of a Power Principle,

$(y ^{3} ) ^{3} = y ^{3 \cdot 3} = y ^{9}$

Therefore, we substitute, keeping in mind that an odd power of a negative number is also negative:

$y ^{9} = (y ^{3} ) ^{3}$

$= (-17) ^{3}$

$= - 17 ^{3}$

$= - (17 \cdot 17\cdot 17)$

= -4,913

Report an Error

Example Question #183 : Algebra

x> 0 and y > 0

$x^{2} = 18$

$y^{2} = 8$

Evaluate $(x- y) ^{2}$ .

Possible Answers:

Correct answer:

Explanation:

By the perfect square trinomial pattern,

$(x- y) ^{2}$

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

$x^{2} =1 8$ and $y^{2} = 8$ .

Also, by the Power of a Power Principle,

$(xy) ^{2} = x^{2} y^{2} = 18 \cdot 8 = 144$ ,

so, since and are both positive,

$xy = \sqrt{(xy) ^{2} }= \sqrt{144}= 12$ .

Therefore,

$(x- y) ^{2}$

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

And, substituting:

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

=18 -2 (12)+8

=18 -24 +8

= 2

Report an Error

Example Question #184 : Algebra

$t^{6} = 144$

$x^{6}= 81$

t > 0, x< 0

Evaluate the expression $(t-x) (t^{2}+tx+x^{2})$ .

Possible Answers:

Correct answer:

Explanation:

Multiply out the expression by using multiple distributions and collecting like terms:

$(t-x) (t^{2}+tx+x^{2})$

$= t (t^{2}+tx+x^{2}) - x (t^{2}+tx+x^{2})$

$= t \cdot t^{2}+ t \cdot tx+ t \cdot x^{2} - x \cdot t^{2}- x \cdot tx- x \cdot x^{2}$

$= t^{3}+ t^{2} x+ t x^{2} - t^{2} x- tx^{2} - x^{3}$

$= t^{3}+ t^{2} x- t^{2} x + t x^{2} - tx^{2} - x^{3}$

$= t^{3} - x^{3}$

Since $(t^{3} ) ^{2} = t ^{3 \cdot 2 } = t^{6}$ by the Power of a Power Principle,

$t^{3} = \pm \sqrt{ t^{6}} = \pm \sqrt{144} = \pm 12$ .

However, is positive, so $t^{3}$ is as well, so we choose $t^{3} = 12$ .

Similarly,

$x^{3} = \pm \sqrt{x^{6}} = \pm \sqrt{81} = \pm 9$ .

However, since is negative, as an odd power of a negative number, $x^{3}$ is as well, so we choose $x^{3} = -9$ .

Therefore, substituting:

$(t-x) (t^{2}+tx+x^{2}) = t^{3} - x^{3} = 12 - (-9) = 21$

Report an Error

Example Question #121 : Properties Of Exponents

and are both positive integers; A is odd. What can you say about the number

$(A + B + 1)^{A+B+1}$ ?

Possible Answers:

$(A + B + 1)^{A+B+1}$ is odd if is odd, and even if is even.

$(A + B + 1)^{A+B+1}$ is even if is even, and can be odd or even if is odd.

$(A + B + 1)^{A+B+1}$ is even if is odd, and odd if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is odd if is odd, and can be odd or even if is even.

Correct answer:

$(A + B + 1)^{A+B+1}$ is odd if is odd, and even if is even.

Explanation:

If is odd, then A + B +1 , the sum of three odd integers, is odd; an odd number taken to any positive integer power is odd.

If is even, then A + B +1 , the sum of two odd integers and an even integer, is even; an even number taken to any positive integer power is even.

Therefore, $(A + B + 1)^{A+B+1}$ always assumes the same odd/even parity as .

Report an Error

Example Question #1 : Equations Of Lines

Give the equation of a line that passes through the point (4,7) and has slope 1.

Possible Answers:

x = 4

x + y = 11

x-y = 3

x-y = -3

y = 7

Correct answer:

x-y = -3

Explanation:

We can use the point slope form of a line, substituting $m = 1, x_{1} = 4, y _{1} = 7$ .

$y- y_{1} = m (x-x_{1})$

y- 7 = 1 (x-4)

y- 7 = x-4

y- 7 -y +4 = x-4 -y +4

-3 = x-y

x-y = -3

Report an Error

Example Question #181 : Algebra

A line can be represented by 2x+3y=6 . What is the slope of the line that is perpendicular to it?

Possible Answers:

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

You will first solve for Y, to get the equation in y=mx+b form.

represents the slope of the line, which would be $-\frac{2}{3}$ .

A perpendicular line's slope would be the negative reciprocal of that value, which is $\frac{3}{2}$ .

Report an Error

Example Question #1 : How To Find The Equation Of A Line

Find the equation the line goes through the points (3,4) and (0,2) .

Possible Answers:

$y=\frac{3}{2}x+2$

$y=-\frac{2}{3}x+2$

$y=\frac{2}{3}x+2$

$y=-\frac{3}{2}x+2$

Correct answer:

$y=\frac{2}{3}x+2$

Explanation:

First, find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{0-3}=\frac{-2}{-3}=\frac{2}{3}$

Now, because the problem tells us that the line goes through (0,2) , our y-intercept must be .

Putting the pieces together, we get the following equation:

$y=\frac{2}{3}x+2$

Report an Error

Example Question #3 : How To Find The Equation Of A Line

A line passes through the points (-4, 6) and (-2, -2) . Find the equation of this line.

Possible Answers:

y=-4x-10

$y=\frac{1}{4}x-8$

$y=-\frac{1}{4}x+10$

y=4x+10

Correct answer:

y=-4x-10

Explanation:

To find the equation of a line, we need to first find the slope.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-6}{-2-(-4)}=\frac{-8}{2}=-4$

Now, our equation for the line looks like the following:

y=-4x+b

To find the y-intercept, plug in one of the given points and solve for . Using (-4, 6) , we get the following equation:

6=-4(-4)+b

Solve for .

6=16+b

b=-10

Now, plug the value for into the equation.

y=-4x-10

Report an Error

Example Question #4 : How To Find The Equation Of A Line

What is the equation of a line that passes through the points (8,1) and (-2, -7) ?

Possible Answers:

$y=\frac{4}{5}x-\frac{27}{5}$

$y=\frac{27}{5}x-\frac{4}{5}$

$y=\frac{5}{4}x+\frac{32}{5}$

$y=-\frac{4}{5}x+\frac{27}{5}$

Correct answer:

$y=\frac{4}{5}x-\frac{27}{5}$

Explanation:

First, we need to find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-1}{-2-8}=\frac{-8}{-10}=\frac{4}{5}$

Next, find the -intercept. To find the -intercept, plug in the values of one point into the equation y=mx+b , where is the slope that we just found and is the -intercept.

$1=8(\frac{4}{5})+b$

Solve for .

$1=\frac{32}{5}+b$

$b=-\frac{27}{5}$

Now, put the slope and -intercept together to get $y=\frac{4}{5}x-\frac{27}{5}$

Report an Error

View SSAT- Upper Level Tutors

Meredith
Certified Tutor

University of Arkansas at Little Rock, Bachelor in Arts, English. University of Arkansas at Little Rock, Masters in Education...

View SSAT- Upper Level Tutors

Myrtle
Certified Tutor

Southern University and A M College, Bachelor of Education, English. New Mexico State University-Main Campus, Doctor of Educ...

View SSAT- Upper Level Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Boston, ACT Tutors in Seattle, Math Tutors in New York City, English Tutors in San Francisco-Bay Area, GRE Tutors in Phoenix, GMAT Tutors in San Francisco-Bay Area, ISEE Tutors in Miami, French Tutors in Denver, GMAT Tutors in Seattle, Spanish Tutors in Philadelphia

Popular Courses & Classes

GMAT Courses & Classes in Atlanta, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Chicago, ACT Courses & Classes in Chicago, ACT Courses & Classes in New York City, LSAT Courses & Classes in Denver, ISEE Courses & Classes in Houston, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Los Angeles, GRE Courses & Classes in Seattle

Popular Test Prep

ISEE Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, LSAT Test Prep in Seattle, ACT Test Prep in Chicago, GMAT Test Prep in Chicago, ISEE Test Prep in Boston, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Los Angeles, SSAT 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

SSAT Upper Level Math : Algebra

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #124 : Properties Of Exponents

Example Question #125 : Properties Of Exponents

Example Question #183 : Algebra

Example Question #184 : Algebra

Example Question #121 : Properties Of Exponents

Example Question #1 : Equations Of Lines

Example Question #181 : Algebra

Example Question #1 : How To Find The Equation Of A Line

Example Question #3 : How To Find The Equation Of A Line

Example Question #4 : How To Find The Equation Of A Line

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: