We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : SAT Subject Test in Math II

Study concepts, example questions & explanations for SAT II Math II

Create An Account

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Matrices

Give the determinant of the matrix $\begin{bmatrix} a&5 \\ a& 7 \end{bmatrix}$

Possible Answers:

$12-a^{2}$

-2a

12a

$a^{2}-12$

Correct answer:

Explanation:

The determinant of the matrix $\begin{bmatrix} A& B\\ C& D \end{bmatrix}$ is

$\begin{vmatrix} A& B\\ C& D \end{vmatrix} = AD - BC$ .

Substitute A = C = a , B = 5, D = 7 :

$\begin{vmatrix} a& 5\\ a& 7 \end{vmatrix} = a \cdot 7 - a \cdot 5 = 7a - 5a = 2a$

Report an Error

Example Question #3 : Matrices

Multiply:

$\begin{bmatrix} x&5 \\ 6& x \end{bmatrix}\begin{bmatrix} 3\\ 4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix}3x+20\\ 4x+18 \end{bmatrix}$

$\begin{bmatrix} 3x&15 \\ 24& 4 x \end{bmatrix}$

$\begin{bmatrix}3x+15\\ 4x+24\end{bmatrix}$

$\begin{bmatrix}3x+24 \\ 4x+15\end{bmatrix}$

$\begin{bmatrix} 3x&5 \\ 24& x \end{bmatrix}$

Correct answer:

$\begin{bmatrix}3x+20\\ 4x+18 \end{bmatrix}$

Explanation:

The product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.

Multiply each row in the first matrix by the column matrix by multiplying elements in corresponding positions, then adding the products, as follows:

$\begin{bmatrix} x&5 \\ 6& x \end{bmatrix}\begin{bmatrix} 3\\ 4 \end{bmatrix}$

$= \begin{bmatrix} x \cdot 3 + 5 \cdot 4\\ 6 \cdot 3 + x \cdot 4 \end{bmatrix}$

$= \begin{bmatrix}3x+20\\ 4x+18 \end{bmatrix}$

Report an Error

Example Question #1 : Matrices

Let $A = \begin{bmatrix} 3& 2\\ 4& 3\\ -5& 0 \end{bmatrix}$ .

Give $A^{-1}$ .

Possible Answers:

$A = \begin{bmatrix} -3&-4 &5 \\ -2 & -3 & 0 \end{bmatrix}$

$A = \begin{bmatrix} -2& -3\\ -3& -4\\ 0& 5 \end{bmatrix}$

$A = \begin{bmatrix} -3& -2\\ -4& -3\\ 5& 0 \end{bmatrix}$

$A^{-1}$ is not defined.

$A = \begin{bmatrix} 5&-4 &-3 \\ 0 & -3 & -2 \end{bmatrix}$

Correct answer:

$A^{-1}$ is not defined.

Explanation:

has three rows and two columns; since the number of rows is not equal to the number of columns, is not a square matrix, and, therefore, it does not have an inverse.

Report an Error

Example Question #1 : Matrices

Define matrix $A = \begin{bmatrix} 4& 5\\ 6&7 \\ 8& 9 \end{bmatrix}$ .

For which of the following matrix values of is the expression A+B defined?

I: $B = \begin{bmatrix} 4& 5\\ 6&7 \\ 8& 9 \end{bmatrix}$

II: $B = \begin{bmatrix} 4& 5\\ 6&7 \end{bmatrix}$

III: $B = \begin{bmatrix} 3 & 4& 5\\ 5 & 6&7 \\ 7 & 8& 9 \end{bmatrix}$

Possible Answers:

I only

I and II only

II and II only

I and III only

I, II, and III

Correct answer:

I only

Explanation:

For the matrix sum A+B to be defined, it is necessary and sufficent for and to have the same number of rows and the same number of columns. has three rows and two columns; of the three choices, only (I) has the same dimensions.

Report an Error

Example Question #7 : Matrices

Let $A = \begin{bmatrix} 5& -4\\ -2& -7 \end{bmatrix}$ and be the 2 x 2 identity matrix.

Let A - B = I .

Which of the following is equal to ?

Possible Answers:

$B = \begin{bmatrix} 4& -5 \\ -3& -8\end{bmatrix}$

$B = \begin{bmatrix} 4& -3 \\ -1& -8\end{bmatrix}$

$B = \begin{bmatrix} 3& -5 \\ -3& -9\end{bmatrix}$

$B = \begin{bmatrix} 5& -5 \\ -3& -7\end{bmatrix}$

$B = \begin{bmatrix} 4& -4 \\ -2& -8\end{bmatrix}$

Correct answer:

$B = \begin{bmatrix} 4& -4 \\ -2& -8\end{bmatrix}$

Explanation:

The 2 x 2 identity matrix is $I =\begin{bmatrix} 1& 0\\ 0& 1 \end{bmatrix}$ .

A - B = I , or, equivalently,

B = A - I ,

$B = \begin{bmatrix} 5& -4\\ -2& -7 \end{bmatrix} - \begin{bmatrix} 1& 0\\ 0& 1 \end{bmatrix}$

Subtract the elements in the corresponding positions:

$B = \begin{bmatrix} 5-1& -4-0\\ -2-0& -7 -1\end{bmatrix}$

$B = \begin{bmatrix} 4& -4 \\ -2& -8\end{bmatrix}$

Report an Error

Example Question #81 : Mathematical Relationships

$A = \begin{bmatrix} x+8& 7\\ 5& x - 7 \end{bmatrix}$

$B = \begin{bmatrix} 4&x-6 \\ x-7 & 2 \end{bmatrix}$

Calculate: A+B

Possible Answers:

$\begin{bmatrix} x+12& x+1\\ x-12 & x - 9 \end{bmatrix}$

$\begin{bmatrix} x+12& x+1\\ x-2 & x - 5 \end{bmatrix}$

$\begin{bmatrix} x+12& x+1\\ x-2 & x - 9 \end{bmatrix}$

$\begin{bmatrix} x+12& x+1\\ x-12 & x - 9 \end{bmatrix}$

$\begin{bmatrix} x+12& x-13\\ x-12 & x - 9 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} x+12& x+1\\ x-2 & x - 5 \end{bmatrix}$

Explanation:

To add two matrices, add the elements in corresponding positions:

$A + B = \begin{bmatrix} x+8& 7\\ 5& x - 7 \end{bmatrix} + \begin{bmatrix} 4&x-6 \\ x-7 & 2 \end{bmatrix}$

$= \begin{bmatrix} x+8 + 4& 7+ \left ( x-6 \right )\\ 5+\left ( x - 7 \right ) & x - 7 +2 \end{bmatrix}$

$= \begin{bmatrix} x+12& x+1\\ x-2 & x - 5 \end{bmatrix}$

Report an Error

Example Question #81 : Mathematical Relationships

Solve for :

$\begin{vmatrix} N + 1& 6 \\ 6& N - 1 \end{vmatrix} = 12$

Possible Answers:

N = -7 or N = 7

N = 0

$N = -\sqrt{47}$ or $N = \sqrt{47}$

The equation has no solution.

N = 12

Correct answer:

N = -7 or N = 7

Explanation:

The determinant of a matrix can be evaluated as follows:

$\begin{vmatrix} A&B \\ C&D \end{vmatrix} = AD - BC$

Therefore, the equation can be rewritten:

$\begin{vmatrix} N + 1& 6 \\ 6& N - 1 \end{vmatrix} = 12$

$\left ( N + 1 \right )\left (N - 1 \right ) - 6 \cdot 6= 12$

$N^{2} - 1 -3 6 = 12$

$N^{2} - 37= 12$

$N^{2} - 37+ 37 = 12 + 37$

$N^{2} = 49$

$N = \pm \sqrt{49} = \pm 7$

The solution set is

N = -7 or N = 7 .

Report an Error

Example Question #11 : Matrices

Multiply:

$\begin{bmatrix} x& 8\\ -6& t \end{bmatrix}\begin{bmatrix} t& x \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} tx +8x\\xt-6t \end{bmatrix}$

$\begin{bmatrix} tx +6x& xt-8t \end{bmatrix}$

The matrices cannot be multiplied.

$\begin{bmatrix} tx +8x&xt-6t \end{bmatrix}$

$\begin{bmatrix} tx +6x\\xt-8t \end{bmatrix}$

Correct answer:

The matrices cannot be multiplied.

Explanation:

Two matrices can be multiplied if and only if the number of columns in the first matrix and the number of rows in the second are equal. The first matrix has two columns; the second matrix has one row. This violates the condition, so they cannot be multiplied in this order.

Report an Error

Example Question #92 : Mathematical Relationships

Evaluate:

$\begin{vmatrix} x-1& 3\\ 3& x+1 \end{vmatrix}$

Possible Answers:

$x^{2}-10$

-6x

$x^{2}+8$

$x^{2}-8$

Correct answer:

$x^{2}-10$

Explanation:

The determinant of the matrix $\begin{bmatrix} A& B\\ C& D \end{bmatrix}$ is

$\begin{vmatrix} A& B\\ C& D \end{vmatrix} = AD - BC$ .

Substitute A = x-1, B = C = 3,D = x+1 :

$\begin{vmatrix} x-1& 3\\ 3& x+1 \end{vmatrix}$

$= (x-1)(x+1) - 3 \cdot 3$

$=x^{2} -1 - 9$

$=x^{2} -10$

Report an Error

Example Question #12 : Matrices

Define $A = \begin{bmatrix} 5& 8\\ 4 & 6 \end{bmatrix}$ .

Give $A^{-1}$ .

Possible Answers:

$A^{-1} = \begin{bmatrix} -2\frac{1}{2} &4\\2 & -3 \end{bmatrix}$

$A^{-1} = \begin{bmatrix} -3&4\\2 & -2\frac{1}{2} \end{bmatrix}$

$A^{-1} = \begin{bmatrix} -3&-4\\-2 & -2\frac{1}{2} \end{bmatrix}$

$A^{-1} = \begin{bmatrix} -2\frac{1}{2} &-4\\-2 & -3 \end{bmatrix}$

$A^{-1}$ is not defined.

Correct answer:

$A^{-1} = \begin{bmatrix} -3&4\\2 & -2\frac{1}{2} \end{bmatrix}$

Explanation:

The inverse of a 2 x 2 matrix $\begin{bmatrix} A& B\\ C& D \end{bmatrix}$ , if it exists, is the matrix

$\frac{\begin{bmatrix} D& -B\\ -C&A \end{bmatrix}}{\begin{vmatrix} A& B\\ C& D \end{vmatrix}}= \frac{\begin{bmatrix} D& -B\\ -C&A \end{bmatrix}}{AD - BC}$ .

First, we need to establish that the inverse is defined, which it is if and only if the determinant $AD - BC \neq 0$ .

Set A = 5, B = 8, C = 4, D = 6 , and check:

$AD - BC = 5 \cdot 6 - 8 \cdot 4 =30 - 32 = -2$

The inverse exists.

The process: First, switch the upper-left and lower-right entries, and change the other two entries to their opposites:

$\begin{bmatrix} 5& 8\\ 4 & 6 \end{bmatrix} \rightarrow \begin{bmatrix} 6&- 8\\ -4 & 5 \end{bmatrix}$

Then divide the new matrix elementwise by the determinant of the original matrix, which is .

The inverse is

$\frac{\begin{bmatrix} 6&- 8\\ -4 & 5\end{bmatrix} }{-2}$

$= \begin{bmatrix} \frac{6}{-2}& \frac{-8}{-2}\\ \\ \frac{-4}{-2} & \frac{5}{-2} \end{bmatrix}$

$= \begin{bmatrix} -3&4\\2 & -2\frac{1}{2} \end{bmatrix}$

Report an Error

View SAT Subject Test in Mathematics Level 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View SAT Subject Test in Mathematics Level 2 Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View SAT Subject Test in Mathematics Level 2 Tutors

Gregory
Certified Tutor

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

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Washington DC, Statistics Tutors in Atlanta, French Tutors in San Diego, ACT Tutors in Dallas Fort Worth, French Tutors in Washington DC, MCAT Tutors in Philadelphia, French Tutors in Denver, Math Tutors in Washington DC, MCAT Tutors in Dallas Fort Worth, GRE Tutors in Atlanta

Popular Courses & Classes

ISEE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Boston, GMAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Boston, ACT Courses & Classes in Boston, SAT Courses & Classes in Chicago, ISEE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Seattle

Popular Test Prep

ACT Test Prep in Boston, GMAT Test Prep in New York City, ACT Test Prep in Philadelphia, MCAT Test Prep in Seattle, MCAT Test Prep in Philadelphia, GMAT Test Prep in Seattle, ISEE Test Prep in Denver, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Seattle, GRE Test Prep in Seattle

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 II Math II : SAT Subject Test in Math II

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #4 : Matrices

Example Question #3 : Matrices

Example Question #1 : Matrices

Example Question #1 : Matrices

Example Question #7 : Matrices

Example Question #81 : Mathematical Relationships

Example Question #81 : Mathematical Relationships

Example Question #11 : Matrices

Example Question #92 : Mathematical Relationships

Example Question #12 : Matrices

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: