We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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 #7 : Circles

What is the equation of a circle that has its center at (-4,5) and has a radius of ?

Possible Answers:

(x+4)^2+(y-5)^2=16

(x-4)^2+(y-5)^2=16

(x+4)^2+(y+5)^2=16

(x-4)^2+(y+5)^2=16

Correct answer:

(x+4)^2+(y-5)^2=16

Explanation:

The general equation of a circle with center (a,b) and radius is:

(x-a)^2+(y-b)^2=r^2

Now, plug in the values given by the question:

(x-(-4))^2+(y-5)^2=4^2

(x+4)^2+(y-5)^2=16

Report an Error

Example Question #2 : Circles

If the center of a circle with a diameter of 5 is located at (2,-3) , what is the equation of the circle?

Possible Answers:

(x-2)^2+(y+3)^2=5

(x+2)^2+(y-3)^2=6.25

(x+2)^2+(y-3)^2=5

(x-2)^2+(y+3)^2=25

(x-2)^2+(y+3)^2=6.25

Correct answer:

(x-2)^2+(y+3)^2=6.25

Explanation:

Write the formula for the equation of a circle with a given point, (h,k) .

(x-h)^2+(y-k)^2=r^2

The radius of the circle is half the diameter, or 2.5 .

Substitute all the values into the formula and simplify.

(x-2)^2+(y-(-3))^2=(2.5)^2

(x-2)^2+(y+3)^2=6.25

Report an Error

Example Question #9 : How To Find The Equation Of A Circle

Give the circumference of the circle on the coordinate plane whose equation is

$x^{2}+ y^{2}+ 4x- 6y + 2 = 0$

Possible Answers:

$2 \pi \sqrt{11}$

$2 \pi \sqrt{2}$

$\pi \sqrt{13}$

$22 \pi$

$2 \pi$

Correct answer:

$2 \pi \sqrt{11}$

Explanation:

The standard form of the equation of a circle is

$(x-h)^{2}+(y-k)^{2} = r^{2}$

where is the radius of the circle.

We can rewrite the equation we are given, which is in general form, in this standard form as follows:

$x^{2}+ y^{2}+ 4x- 6y + 2 = 0$

$x^{2}+ y^{2}+ 4x- 6y = -2$

$\left (x^{2}+ 4x \right )+\left ( y^{2}- 6y \right )= -2$

Complete the squares. Since $\left ( \frac{4}{2} \right )^{2} = 4$ and $\left ( \frac{-6}{2} \right )^{2} = 9$ , we do this as follows:

$\left (x^{2}+ 4x +4 \right )+\left ( y^{2}- 6y +9\right )= -2+4+9$

$(x+2)^{2}+(y-3)^{2} = 11$

$r^{2} = 11$ , so $r = \sqrt{11}$ , and the circumference of the circle is

$C = 2 \pi r = 2 \pi \sqrt{11}$

Report an Error

Example Question #10 : How To Find The Equation Of A Circle

A square on the coordinate plane has as its vertices the points (0,0), (0, 6), (6,0),(6,6) . Give the equation of a circle circumscribed about the square.

Possible Answers:

$(x-3)^{2}+(y-3)^{2} = 36$

$(x-6)^{2}+(y-6)^{2} = 18$

$(x-6)^{2}+(y-6)^{2} = 36$

$(x-3)^{2}+(y-3)^{2} = 18$

$(x-3)^{2}+(y-3)^{2} = 9$

Correct answer:

$(x-3)^{2}+(y-3)^{2} = 18$

Explanation:

Below is the figure with the circle and square in question:

Circle on axes

The center of the inscribed circle coincides with that of the square, which is the point (3,3) . Its diameter is the length of a diagonal of the square, which is $\sqrt{2}$ times the sidelength 6 of the square - this is $6 \sqrt{2}$ . Its radius is, consequently, half this, or $3 \sqrt{2}$ . Therefore, in the standard form of the equation,

$(x-h)^{2}+(y-k)^{2} = r^{2}$ ,

substitute h = k = 3 and $r = 3 \sqrt{2}$ .

$(x-3)^{2}+(y-3)^{2} = \left (3 \sqrt{2} \right ) ^{2}$

$(x-3)^{2}+(y-3)^{2} = 3^{2} \left ( \sqrt{2} \right ) ^{2}$

$(x-3)^{2}+(y-3)^{2} = 9 \cdot 2$

$(x-3)^{2}+(y-3)^{2} = 18$

Report an Error

Example Question #311 : Geometry

A square on the coordinate plane has as its vertices the points (0,0), (0, 8), (8,0),(8,8) . Give the equation of a circle inscribed in the square.

Possible Answers:

$(x-4)^{2}+(y-4)^{2} = 16$

$(x-8)^{2}+(y-8)^{2} = 32$

$(x-8)^{2}+(y-8)^{2} = 16$

$(x-8)^{2}+(y-8)^{2} = 64$

$(x-4)^{2}+(y-4)^{2} = 32$

Correct answer:

$(x-4)^{2}+(y-4)^{2} = 16$

Explanation:

Below is the figure with the circle and square in question:

Circle on axes

The center of the inscribed circle coincides with that of the square, which is the point (4,4) . Its diameter is equal to the sidelength of the square, which is 8, so, consequently, its radius is half this, or 4. Therefore, in the standard form of the equation,

$(x-h)^{2}+(y-k)^{2} = r^{2}$ ,

substitute h = k = 4 and r = 4 .

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

$(x-4)^{2}+(y-4)^{2} = 16$

Report an Error

Example Question #252 : Coordinate Geometry

Give the area of the circle on the coordinate plane whose equation is

$x^{2}+ y^{2}+ 4x- 8y -11 = 0$ .

Possible Answers:

$21 \pi$

$20 \pi$

$18 \pi$

$31 \pi$

$11 \pi$

Correct answer:

$31 \pi$

Explanation:

The standard form of the equation of a circle is

$(x-h)^{2}+(y-k)^{2} = r^{2}$

where is the radius of the circle.

We can rewrite the equation we are given, which is in general form, in this standard form as follows:

$x^{2}+ y^{2}+ 4x- 8y -11 = 0$

$x^{2}+ y^{2}+ 4x- 8y =11$

$\left (x^{2}+ 4x \right ) +\left ( y^{2}- 8y \right ) =11$

Complete the squares. Since $\left ( \frac{4}{2} \right )^{2} = 4$ and $\left ( \frac{-8}{2} \right )^{2} = 16$ , we do this as follows:

$\left (x^{2}+ 4x + 4 \right ) +\left ( y^{2}- 8y + 16\right ) =11 + 4 + 16$

$(x-2)^{2}+(y-4)^{2} = 31$

$r^{2}= 31$ , and the area of the circle is

$A = \pi r^{2} = 31 \pi$

Report an Error

Example Question #253 : Coordinate Geometry

Which of the following is the equation of a circle with center at the origin and area $64 \pi$ ?

Possible Answers:

$x^{2}+ y^{2} = 128$

$x^{2}+ y^{2} = 8$

$x^{2}+ y^{2} = 64$

$x^{2}+ y^{2} = 16$

$x^{2}+ y^{2} = 32$

Correct answer:

$x^{2}+ y^{2} = 64$

Explanation:

The standard form of the equation of a circle is

$(x-h)^{2}+(y-k)^{2} = r^{2}$ ,

where the center is (h,k) and the radius is .

The center of the circle is the origin, so h = k = 0 , and the equation is

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

for some .

The area of the circle is $64 \pi$ , so

$A = \pi r^{2} = 50 \pi$

$\frac{ \pi r^{2}}{\pi} = \frac{ 64 \pi}{\pi}$

$r^{2} = 64$

We need go no further; we can substitute to get the equation $x^{2}+ y^{2} = 64$ .

Report an Error

Example Question #11 : Circles

Which of the following is the equation of a circle with center at the origin and circumference $64 \pi$ ?

Possible Answers:

$x^{2}+ y^{2} = 128$

$x^{2}+ y^{2} = 64$

$x^{2}+ y^{2} = 32$

$x^{2}+ y^{2} = 16$

None of the other responses gives the correct answer.

Correct answer:

None of the other responses gives the correct answer.

Explanation:

The standard form of the equation of a circle is

$(x-h)^{2}+(y-k)^{2} = r^{2}$ ,

where the center is (h,k) and the radius is .

The center of the circle is the origin, so h = k = 0 .

The equation will be

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

for some .

The circumference of the circle is $64 \pi$ , so

$C = 2 \pi r = 64 \pi$

$\frac{2 \pi r }{2 \pi }= \frac{64 \pi}{2 \pi }$

r = 32

$r^{2}= 32^{2} = 1,024$

The equation is $x^{2}+ y^{2} = 1,024$ , which is not among the responses.

Report an Error

Example Question #3 : How To Graph An Ordered Pair

Which point best represents the coordinate (2, 6) ?

Possible Answers:

Correct answer:

Explanation:

To get to (2, 6) , move right along the x-axis by , then move up on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin (0,0) . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

Report an Error

Example Question #312 : Geometry

Which point best represents the coordinates (-2, 4) ?

Possible Answers:

Correct answer:

Explanation:

To get to (-2, 4) , move left on the x-axis by , then move up on the y-axis by .

Report an Error

View SSAT- Upper Level Tutors

Theodore
Certified Tutor

Harvard University, Bachelor in Arts, Folklore Studies. HoHoKus-Hackensack School of Business and Medical Sciences, Doctor of...

View SSAT- Upper Level Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View SSAT- Upper Level Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

All SSAT Upper Level Math Resources

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

Popular Subjects

MCAT Tutors in Philadelphia, MCAT Tutors in Dallas Fort Worth, GRE Tutors in Boston, English Tutors in Philadelphia, SSAT Tutors in Miami, Chemistry Tutors in Los Angeles, Chemistry Tutors in Philadelphia, SAT Tutors in Miami, French Tutors in San Francisco-Bay Area, Math Tutors in Denver

Popular Courses & Classes

ACT Courses & Classes in Boston, GMAT Courses & Classes in Washington DC, GRE Courses & Classes in Houston, SSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in Denver, GMAT Courses & Classes in Chicago, MCAT Courses & Classes in Boston, ACT Courses & Classes in Washington DC

Popular Test Prep

ACT Test Prep in Washington DC, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in Chicago, LSAT Test Prep in Houston, SSAT Test Prep in Seattle, GMAT Test Prep in Los Angeles, ISEE Test Prep in Washington DC, SSAT Test Prep in Philadelphia, SSAT Test Prep in New York City, MCAT 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

SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #7 : Circles

Example Question #2 : Circles

Example Question #9 : How To Find The Equation Of A Circle

Example Question #10 : How To Find The Equation Of A Circle

Example Question #311 : Geometry

Example Question #252 : Coordinate Geometry

Example Question #253 : Coordinate Geometry

Example Question #11 : Circles

Example Question #3 : How To Graph An Ordered Pair

Example Question #312 : Geometry

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: