Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : How To Find The Solution To An Equation

Solve for :

$x - 4 \sqrt {x} - 12 = 0$

Possible Answers:

$x = 4\textrm{ or }x = 36$

$x = -4\textrm{ or }x = 4$

x = 36

$x = -4\textrm{ or }x = 36$

x = -4

Correct answer:

x = 36

Explanation:

Substitute $t = \sqrt {x}$ and, subsequently, $t^{2} = x$ :

$x - 4 \sqrt {x} - 12 = 0$

$t^{2} - 4 t - 12 = 0$

Factor as (t + ?) (t + ?) , replacing the two question marks with integers whose product is and whose sum is . These integers are -6, 2 :

(t - 6) (t + 2) = 0

Break this up into two equations, replacing $\sqrt {x}$ for in each:

t - 6 = 0

t = 6

$\sqrt {x} = 6$

$(\sqrt {x})^{2} = 6^{2}$

x = 36

t + 2 = 0

t = -2

$\sqrt {x} = -2$

This has no solution, since $\sqrt {x}$ must be nonnegative.

x = 36 is the only solution.

Report an Error

Example Question #41 : Algebraic Concepts

Solve the equation:

$\frac{2}{3}-\frac{3}{x}=\frac{8}{x}$

Possible Answers:

5.5

4.5

6.5

Correct answer:

5.5

Explanation:

First multiply both sides by :

$\frac{2}{3}-\frac{3}{x}=\frac{8}{x}\Rightarrow 3x(\frac{2}{3})-3x(\frac{3}{x})=3x(\frac{8}{x})\Rightarrow 6x-9=24\Rightarrow 6x=33$

$\Rightarrow x=5.5$

Report an Error

Example Question #41 : Algebraic Concepts

For what values of is $2\left |x+5 \right |-5< 7$ ?

Possible Answers:

-11<x<4

-11<x<1

-10<x<1

-11<x<2

-11<x<10

Correct answer:

-11<x<1

Explanation:

$\left |x \right |< a\Rightarrow -a< x< a$

We have $\left |x+5 \right |< 6$ , so:

$-6<x+5<6\Rightarrow -6-5<x+5-5<6-5\Rightarrow -11<x<1$

Report an Error

Example Question #41 : Equations

Find :

$\left |2x+4 \right |-7>9$

Possible Answers:

$x>-6 \ or \ x<10$

$x>6\: or \: x<6$

-10<x<6

$x>6 \ or \ x<10$

$x>6 \: or \: x<-10$

Correct answer:

$x>6 \: or \: x<-10$

Explanation:

$\left |x \right |>a$ means that x<-a or x>a .

Then we can write:

$\left |2x+4 \right |>16\Rightarrow 2x+4>16$

2x+4<-16

$2x+4>16\Rightarrow 2x+4-4>16-4\Rightarrow 2x>12\Rightarrow x>6$

$2x+4<-16\Rightarrow 2x+4-4<-16-4\Rightarrow 2x<-20\Rightarrow x<-10$

Report an Error

Example Question #741 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve the equation for :

$7\sqrt{x}+11=5$

Possible Answers:

$\frac{6}{7}$

No solution

Correct answer:

No solution

Explanation:

$7\sqrt{x}+11=5\Rightarrow 7\sqrt{x}+11-11=5-11\Rightarrow 7\sqrt{x}=-6\Rightarrow \sqrt{x}=-\frac{6}{7}$

Since $\sqrt{x}$ cannot be negative, no real number satisfies the equation.

Report an Error

Example Question #746 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What are the roots of the equation?

3x^2-6x-45=0

Possible Answers:

$x=-5 \ or \ x=-3$

$x=3 \ or\ x=-3$

$x=5 \ or\ x=-3$

$x=5 \ or \ x=3$

$x=-5\ or \ x=3$

Correct answer:

$x=5 \ or\ x=-3$

Explanation:

First simplify the equation by dividing both sides by :

$3x^2-6x-45=0\Rightarrow x^2-2x-15=0$

If a, b, c are real numbers with $a\neq 0$ , and if ax^2+bx+c=0 , then

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

The expression b^2-4ac is called the discriminant of the quadratic equation, and we say D=b^2-4ac .

We can write $x=\frac{-b\pm \sqrt{D}}{2a}$ .

In this problem we have $a=1,\ b=-2, \ and\ c=-15.$

$D=b^2-4ac=(-2)^2-4\times 1\times (-15)=4+60=64$

$x=\frac{-b\pm \sqrt{D}}{2a}=\frac{-(-2)\pm \sqrt{64}}{2\times 1}=\frac{2\pm 8}{2}$

Therefore the roots are

$x=\frac{2+8}{2}=5$ or $x=\frac{2-8}{2}=-3$ .

Report an Error

Example Question #747 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What are the roots of the equation?

x^2=28-3x

Possible Answers:

$x=-4\ or\ x=-7$

$x=-4\ or\ x=7$

$x=4\ or \ x=-7$

$x=4 \ or\ x=7$

x=4

Correct answer:

$x=4\ or \ x=-7$

Explanation:

First rewrite the equation in the form of ax^2+bx+c=0 :

x^2+3x-28=0

If a, b, c are real numbers with $a\neq 0$ , and if ax^2+bx+c=0 , then we have:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The expression b^2-4ac is called the discriminant of the quadratic equation, and we say D=b^2-4ac . We can write

$x=\frac{-b\pm \sqrt{D}}{2a}$ .

In this problem we have $a=1, \ b=3,\ and\ c=-28.$

$D=b^2-4ac=(3)^2-4\times 1\times (-28)=9+112=121$

$x=\frac{-b\pm \sqrt{D}}{2a}=\frac{-3\pm \sqrt{121}}{2\times 1}=\frac{-3\pm 11}{2}$

Then the roots are $x=\frac{-3+11}{2}=4$ and $x=\frac{-3-11}{2}=-7$ .

Report an Error

Example Question #748 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the roots of the equation:

3x^2+6x-11=0

Possible Answers:

$x=1+\sqrt{21}$ or $x=1-\sqrt{21}$

$x=1+\sqrt{42}$ or $x=1-\sqrt{42}$

$x=3+\sqrt{21}$ or $x=3-\sqrt{21}$

$x=1+\frac{\sqrt{42}}{3}$ or $x=1-\frac{\sqrt{42}}{3}$

$x=-\sqrt{42}$ or $x=\sqrt{42}$

Correct answer:

$x=1+\frac{\sqrt{42}}{3}$ or $x=1-\frac{\sqrt{42}}{3}$

Explanation:

If a, b, c are real numbers with $a\neq 0$ , and if ax^2+bx+c=0 , then we have

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

The expression b^2-4ac is called the discriminant of the quadratic equation, and we say D=b^2-4ac . We can write

$x=\frac{-b\pm \sqrt{D}}{2a}$ .

In this problem we have $a=3,\ b=6,\ and \ c=-11.$

$D=b^2-4ac=(6)^2-4\times 3\times (-11)=36+132=168$

$x=\frac{-b\pm \sqrt{D}}{2a}=\frac{-6\pm \sqrt{168}}{2\times 3}=\frac{-6\pm 2\sqrt{42}}{6}=\frac{-3\pm \sqrt{42}}{3}$

Then the roots are

$x=-\frac{3+\sqrt{42}}{3}=-1-\frac{\sqrt{42}}{3}$ and $x=\frac{3-\sqrt{42}}{3}=1-\frac{\sqrt{42}}{3}$ .

Report an Error

Example Question #42 : How To Find The Solution To An Equation

Find the roots of 4x^2-64=0 .

Possible Answers:

x=-4

x=4

x=-3 or

x=-4

x=4 or x=-4

x=-3

Correct answer:

x=4 or x=-4

Explanation:

$4x^2-64=0\Rightarrow 4x^2=64\Rightarrow x^2=16\Rightarrow x=\pm \sqrt{16}=\pm 4$

Therefore, x=4 or x=-4 .

Report an Error

Example Question #44 : Algebraic Concepts

Solve for :

4x^2-3x=0

Possible Answers:

x=0

x=0 or $x=-\frac{3}{4}$

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

x=0 or $x=\frac{3}{4}$

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

Correct answer:

x=0 or $x=\frac{3}{4}$

Explanation:

We can factor out an :

$4x^2-3x=0\Rightarrow x(4x-3)=0$

Therefore, x=0 or:

$4x-3=0\Rightarrow 4x-3+3=0+3\Rightarrow 4x=3\Rightarrow x=\frac{3}{4}$

Report an Error

View Tutors

Brittany
Certified Tutor

Xavier University of Louisiana, Bachelor in Arts, Elementary School Teaching. Concordia University-Seward, Masters in Educati...

View Tutors

Bagher
Certified Tutor

San Jose State University, Master's/Graduate, Physics.

View Tutors

Magda
Certified Tutor

Heritage College, Bachelor of Science, Education.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Atlanta, Physics Tutors in Chicago, Statistics Tutors in Atlanta, Chemistry Tutors in Los Angeles, SSAT Tutors in Miami, GMAT Tutors in Houston, Spanish Tutors in Chicago, Math Tutors in Denver, GRE Tutors in Seattle, ACT Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in Seattle, GRE Courses & Classes in Atlanta, ISEE Courses & Classes in Atlanta, ACT Courses & Classes in Houston, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Los Angeles, MCAT Courses & Classes in Denver, LSAT Courses & Classes in Boston, MCAT Courses & Classes in Seattle

Popular Test Prep

LSAT Test Prep in Atlanta, LSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Dallas Fort Worth, SAT Test Prep in Phoenix, SAT Test Prep in Philadelphia, SSAT Test Prep in Chicago, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Philadelphia, GRE Test Prep in Atlanta, ISEE Test Prep in San Diego

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 Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #31 : How To Find The Solution To An Equation

Example Question #41 : Algebraic Concepts

Example Question #41 : Algebraic Concepts

Example Question #41 : Equations

Example Question #741 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #746 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #747 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #748 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #42 : How To Find The Solution To An Equation

Example Question #44 : Algebraic Concepts

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: