Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : How To Find The Length Of An Arc

A giant clock has a minute hand that is six feet long. The time is now 3:50 PM. How far has the tip of the minute hand moved, in inches, between noon and now?

Possible Answers:

$1,104 \pi \textrm{ in}$

The correct answer is not among these choices.

$552 \pi \textrm{ in}$

$138 \pi \textrm{ in}$

$276 \pi \textrm{ in}$

Correct answer:

$552 \pi \textrm{ in}$

Explanation:

Every hour, the tip of the minute hand travels the circumference of a circle with radius six feet, which is

$C = 2 \pi r= 2 \pi \cdot 6 = 12 \pi$ feet.

Since it is now 3:50 PM, the minute hand made three complete revolutions since noon, plus $\frac{50}{60 } = \frac{5}{6}$ of a fourth, so its tip has traveled this circumference $3\frac{5}{6}$ times.

This is

$3\frac{5}{6} \times 12 \pi = \frac{23}{6} \times 12 \pi = 46 \pi$ feet. This is

$46 \pi \times 12 = 552 \pi$ inches.

Report an Error

Example Question #3 : How To Find The Length Of An Arc

A giant clock has a minute hand seven feet long. Which is the greater quantity?

(A) The distance traveled by the tip of the minute hand between 1:30 PM and 2:00 PM

(B) The circumference of a circle seven feet in diameter

Possible Answers:

(A) is greater

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Correct answer:

(A) and (B) are equal

Explanation:

The tip of a minute hand travels a circle whose radius is equal to the length of that minute hand, which, in this question, is seven feet long. The circumference of this circle is $2 \pi$ times the radius, or $2 \pi \times 7 = 14\pi$ feet; over the course of thrity minutes (or one-half of an hour) the tip of the minute hand covers half this distance, or $\frac{1}{2} \times 14 \pi = 7 \pi$ feet.

The circumference of a circle seven feet in diameter is $\pi$ times this diameter, or $7 \pi$ feet.

The quantities are equal.

Report an Error

Example Question #181 : Geometry

A giant clock has a minute hand four and one-half feet in length. Since noon, the tip of the minute hand has traveled $110 \pi$ feet. Which of the following is true of the time right now?

Possible Answers:

The time is between 11:30 PM and 12:00 midnight.

The time is between 12:00 midnight and 12:30 AM.

The time is between 11:00 PM and 11:30 PM.

The time is between 1:00 AM and 1:30 AM.

The time is between 12:30 AM and 1:00 AM.

Correct answer:

The time is between 12:00 midnight and 12:30 AM.

Explanation:

Every hour, the tip of the minute hand travels the circumference of a circle, which here is

$C = 2 \pi r = 2 \pi \times 4 \frac{1}{2} = 9 \pi$ feet.

The minute hand has traveled $110 \pi$ feet since noon, so it has traveled the circumference of the circle

$\frac{110 \pi}{9 \pi} = \frac{110 }{9 } =12 \frac{2}{9}$ times.

Since $12 \leq 12 \frac{2}{9} \leq 12 \frac{1}{2}$ , between 12 and $12 \frac{1}{2}$ hours have elapsed since noon, and the time is between 12:00 midnight and 12:30 AM.

Report an Error

Example Question #6 : How To Find The Length Of An Arc

Acute triangle $\bigtriangleup ABC$ is inscribed in a circle. Which is the greater quantity?

(a) $m \overarc {ABC} - m \overarc {ACB}$

(b) $m \overarc {A B} - m \overarc {A C}$

Possible Answers:

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

Correct answer:

(a) and (b) are equal

Explanation:

Examine the figure below, which shows $\bigtriangleup ABC$ inscribed in a circle.

Inscribed angle

By the Arc Addition Principle,

$m \overarc {ABC} = m \overarc {AB}+ m \overarc {BC}$

and

$m \overarc {ACB} = m \overarc {AC}+ m \overarc {BC}$

Consequently,

$m \overarc {ABC} - m \overarc {ACB}$

$= (m \overarc {AB}+ m \overarc {BC} ) - ( m \overarc {AC}+ m \overarc {BC})$

$= m \overarc {AB}+ m \overarc {BC} - m \overarc {AC}- m \overarc {BC}$

$= m \overarc {A B} - m \overarc {A C}$

The two quantities are equal.

Report an Error

Example Question #51 : Circles

Which is the greater quantity?

(a) The degree measure of a 10-inch-long arc on a circle with radius 8 inches.

(b) The degree measure of a 12-inch-long arc on a circle with radius 10 inches.

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(a) is greater.

Explanation:

(a) A circle with radius 8 inches has crircumference $C = 2\pi r = 2\pi \cdot 8 = 16\pi$ inches. An arc 10 inches long is $\frac{10}{16\pi } = \frac{5}{8\pi }$ of that circle. $\frac{5}{8\pi } \times 360 ^{\circ } = \frac{225}{\pi } ^{\circ }$ , the degree measure of this arc.

(b) A circle with radius 10 inches has crircumference $C = 2\pi r = 2\pi \cdot 10 = 20\pi$ inches. An arc 12 inches long is $\frac{12}{20\pi }=\frac{3}{5\pi }$ of that circle. $\frac{3}{5\pi } \times 360 ^{\circ } = \frac{216}{\pi } ^{\circ }$ , the degree measure of this arc.

(a) is the greater quantity.

Report an Error

Example Question #52 : Circles

Circle

Note: figure NOT drawn to scale

Refer to the above figure. Which is the greater quantity?

(a) $m \widehat{ACB}$

(b) $180 ^{\circ }$

Possible Answers:

(b) is greater

(a) is greater

(It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

Since

$7^{2} + 12 ^{2} = 49 + 144 = 169 = 13 ^{2}$ ,

the triangle is a right triangle with right angle $\angle ACB$ .

$\angle ACB$ is an inscribed angle on the circle, so the arc it intercepts is a semicricle. Therefore, $\widehat{ACB}$ is also a semicircle, and it measures $180 ^{\circ }$ .

Report an Error

Example Question #53 : Circles

Circle

Note: Figure NOT drawn to scale

Refer to the above figure. Which is the greater quantity?

(a)

(b) 90

Possible Answers:

It is impossible to tell from the information given

(a) is greater

(b) is greater

(a) and (b) are equal

Correct answer:

(b) is greater

Explanation:

The measure of an arc intercepted by an inscribed angle of a circle is twice that of the angle. Therefore, $y = 2 \cdot 44 = 88 < 90$

Report an Error

Example Question #184 : Geometry

$\odot A$ has twice the radius of $\odot B$ . Sector 1 is part of $\odot A$ ; Sector 2 is part of $\odot B$ ; the two sectors are equal in area.

Which is the greater quantity?

(a) Twice the degree measure of the central angle of Sector 1

(b) The degree measure of the central angle of Sector 2

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

(b) is greater

Explanation:

$\odot A$ has twice the radius of $\odot B$ , so $\odot A$ has four times the area of $\odot B$ . This means that for a sector of $\odot A$ to have the same area as a sector of $\odot B$ , the central angle of the latter sector must be four times that of the former sector. This makes (b) greater than (a), which is only twice that of the former sector.

Report an Error

Example Question #1 : How To Find The Angle Of A Sector

Circle

Refer to the above figure. Which is the greater quantity?

(a)

(b) 55

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) and (b) are equal

Explanation:

The measure of an inscribed angle of a circle is one-half that of the arc it intercepts. Therefore, $x = \frac{1}{2} \cdot 110 = 55$ .

Report an Error

Example Question #184 : Plane Geometry

Circlesectorgeneral81

The arc-length for the shaded sector is 19.4 . What is the value of , rounded to the nearest hundredth?

Possible Answers:

74.13 ˚

127.76 ˚

29.37 ˚

18.33 ˚

81.89 ˚

Correct answer:

127.76 ˚

Explanation:

Remember that the angle for a sector or arc is found as a percentage of the total 360 degrees of the circle. The proportion of to 360 is the same as 19.4 to the total circumference of the circle.

The circumference of a circle is found by:

$C = 2*\pi*r$

For our data, this means:

$C = 2*8.7*\pi=17.4\pi$

Now we can solve for using the proportions:

$\frac{x}{360} = \frac{19.4}{17.4\pi}$

Cross multiply:

$17.4x\pi=6984$

Divide both sides by $17.4\pi$ :

x=127.76300259239047

Therefore, is 127.76 ˚.

Report an Error

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

View Tutors

Pushpendra
Certified Tutor

university of allahabad, Bachelor of Science, Mathematics.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Boston, Computer Science Tutors in Phoenix, Statistics Tutors in Boston, Calculus Tutors in Denver, SAT Tutors in Houston, MCAT Tutors in Boston, ISEE Tutors in San Diego, GRE Tutors in San Diego, Calculus Tutors in Houston, Calculus Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in Boston, GRE Courses & Classes in New York City, SAT Courses & Classes in New York City, MCAT Courses & Classes in Seattle, SSAT Courses & Classes in Phoenix, ACT Courses & Classes in Seattle, GRE Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Chicago, ACT Courses & Classes in Los Angeles

Popular Test Prep

MCAT Test Prep in Boston, LSAT Test Prep in Washington DC, ACT Test Prep in Boston, GMAT Test Prep in Philadelphia, ISEE Test Prep in Los Angeles, SSAT Test Prep in Miami, GRE Test Prep in New York City, SAT Test Prep in San Diego, SAT Test Prep in New York City, MCAT Test Prep in Los Angeles

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

ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #2 : How To Find The Length Of An Arc

Example Question #3 : How To Find The Length Of An Arc

Example Question #181 : Geometry

Example Question #6 : How To Find The Length Of An Arc

Example Question #51 : Circles

Example Question #52 : Circles

Example Question #53 : Circles

Example Question #184 : Geometry

Example Question #1 : How To Find The Angle Of A Sector

Example Question #184 : Plane Geometry

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: