Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1023 : Algebra

If $f(x)=x^{3} +\frac{4}{x} + \frac{x^{2}}{2}$ what is $f\left ( 4 \right )$

Possible Answers:

Correct answer:

Explanation:

$f(x)=x^{3} +\frac{4}{x} + \frac{x^{2}}{2}$

$f(4)=4^{3} +\frac{4}{4} + \frac{4^{2}}{2}$

$f(4)=64 + 1 + 8$

$f(4)=73$

Report an Error

Example Question #1022 : Algebra

If $f(x)=x+\frac{1}{x}$ , find the value of f(4) .

Possible Answers:

$\frac{17}{4}$

$\frac{41}{4}$

Correct answer:

$\frac{17}{4}$

Explanation:

f(4) = 4 + 1/4 = 16/4 + 1/4 = 17/4

Report an Error

Example Question #1023 : Algebra

If f(x) = x + 8 and g(x) = x^2 + x , what is g(f(3)) ?

Possible Answers:

104

132

100

Correct answer:

132

Explanation:

g is a function of f, and f is a function of 3, so you must work inside out.

f(3) = 11

g(f(3)) = g(11) = 121 + 11 = 132

Report an Error

Example Question #1021 : Algebra

Jamie buys a new fish tank. It is 45% full. She adds seven more liters of water, and it is 65% full. What is the capacity of Jamie's new fish tank?

Possible Answers:

48 liters

None of the other answers are correct.

22 liters

35 liters

27 liters

Correct answer:

35 liters

Explanation:

The algebraic expression for x, the capacity of the fishtank is:

$0.45x+7=0.65x$

$0.45x+7-0.45x=0.65x-0.45x$

$0.2x=7$

$0.2x\times\frac{1}{0.2}=7\times\frac{1}{0.2}$

$x=35\hspace{1 mm}L$

The capacity of the fishtank is 35 liters.

Report an Error

Example Question #101 : Algebraic Functions

f(x)=2x+6

g(x)=3x-3

2f(x)-g(x)+2=?

Possible Answers:

5x + 11

x + 5

x + 11

7x + 17

x + 17

Correct answer:

x + 17

Explanation:

When we multiply a function by a constant, we multiply each value in the function by that constant. Thus, 2f(x) = 4x + 12. We then subtract g(x) from that function, making sure to distribute the negative sign throughout the function. Subtracting g(x) from 4x + 12 gives us 4x + 12 - (3x - 3) = 4x + 12 - 3x + 3 = x + 15. We then add 2 to x + 15, giving us our answer of x + 17.

Report an Error

Example Question #102 : Algebraic Functions

If $f(t)=6+(4-t)^2$ , what is the smallest possible value of $f(t)$ ?

Possible Answers:

Correct answer:

Explanation:

This equation describes a parabola whose vertex is located at the point (4, 6). No matter how large or small the value of t gets, the smallest that f(t) can ever be is 6 because the parabola is concave up. To prove this to yourself you can plug in different values of t and see if you ever get anything smaller than 6.

Report an Error

Example Question #61 : How To Find F(X)

If $f(x)=x^{2}+3$ , then $f(x+h)=$ ?

Possible Answers:

$x^{2}+3+h$

$x^{2}+h^{2}+3$

$x^{2}+2xh+h^{2}$

$x^{2}+h^{2}$

$x^{2}+2xh+h^{2}+3$

Correct answer:

$x^{2}+2xh+h^{2}+3$

Explanation:

To find $f(x+h)$ when $f(x)=x^{2}+3$ , we substitute $(x+h)$ for $x$ in $f(x)$ .

Thus, $f(x+h)=(x+h)^{2}+3$ .

We expand $(x+h)^{2}$ to $x^{2}+xh+xh+h^{2}$ .

We can combine like terms to get $x^{2}+2xh+h^{2}$ .

We add 3 to this result to get our final answer.

Report an Error

Example Question #62 : How To Find F(X)

Let $f(x)$ and $g(x)$ be functions such that $f(x)=\frac{1}{x-3}$ , and $f(g(x))=g(f(x))=x$ . Which of the following is equal to $g(x)$ ?

Possible Answers:

$\frac{4}{x}$

$\frac{3x+1}{x}$

$\frac{1}{x+3}$

$\frac{x}{x+3}$

$\frac{x}{x-3}$

Correct answer:

$\frac{3x+1}{x}$

Explanation:

If $\dpi{100} h(x)$ and $\dpi{100} k(x)$ are defined as inverse functions, then $\dpi{100} h(k(x))=k(h(x))=x$ . Thus, according to the definition of inverse functions, $\dpi{100} f(x)$ and $\dpi{100} g(x)$ given in the problem must be inverse functions.

If we want to find the inverse of a function, the most straighforward method is usually replacing $\dpi{100} f(x)$ with $\dpi{100} y$ , swapping $\dpi{100} y$ and $\dpi{100} x$ , and then solving for $\dpi{100} y$ .

We want to find the inverse of $f(x)=\frac{1}{x-3}$ . First, we will replace $\dpi{100} f(x)$ with $\dpi{100} y$ .

$y = \frac{1}{x-3}$

Next, we will swap $\dpi{100} x$ and $\dpi{100} y$ .

$x = \frac{1}{y-3}$

Lastly, we will solve for $\dpi{100} y$ . The equation that we obtain in terms of $\dpi{100} x$ will be in the inverse of $\dpi{100} f(x)$ , which equals $\dpi{100} g(x)$ .

We can treat $x = \frac{1}{y-3}$ as a proportion, $\frac{x}{1} = \frac{1}{y-3}$ . This allows us to cross multiply and set the results equal to one another.

$x(y-3)= 1$

We want to get y by itself, so let's divide both sides by x.

$y-3=\frac{1}{x}$

Next, we will add 3 to both sides.

$y=\frac{1}{x}+3$

To combine the right side, we will need to rewrite 3 so that it has a denominator of $\dpi{100} x$ .

$y=\frac{1}{x}+3 = \frac{1}{x}+\frac{3x}{x}=\frac{3x+1}{x}$

The answer is $\frac{3x+1}{x}$ .

Report an Error

Example Question #1034 : Algebra

$\small \textup{The function}\, f(x)\, \textup{is defined as }f\left ( x\right )=5x-2$ .

$\small \small f\left ( 4\right )-f\left ( 2\right )=\,?$

Possible Answers:

$\small 6$

$\small 8$

$\small 14$

$\small 2$

$\small 10$

Correct answer:

$\small 10$

Explanation:

$\small f\left ( x\right )=5x - 2$

$\small f\left ( 4\right )=5\left ( 4\right )-2 = 18$

$\small f\left ( 2\right )=5\left ( 2\right )-2 = 8$

$\small 18-8 = 10$

Report an Error

Example Question #105 : Algebraic Functions

Let the function f be defined by f(x)=x-t. If f(12)=4, what is the value of f(0.5*t)?

Possible Answers:

Correct answer:

Explanation:

First we substitute in 12 for x and set the equation up as 12-t=4. We then get t=8, and substitute that for t and get f(0.5*8), giving us f(4). Plugging 4 in for x, and using t=8 that we found before, gives us:

f(4) = 4 - 8 = -4

Report an Error

View PSAT Mathematics Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View PSAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View PSAT Mathematics Tutors

Nico
Certified Tutor

New York University, Bachelors, Philosophy.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in San Francisco-Bay Area, Computer Science Tutors in Seattle, French Tutors in Dallas Fort Worth, SAT Tutors in New York City, LSAT Tutors in Denver, Spanish Tutors in Miami, Statistics Tutors in San Diego, Computer Science Tutors in Miami, Computer Science Tutors in Chicago, GRE Tutors in Philadelphia

Popular Courses & Classes

SSAT Courses & Classes in Miami, ACT Courses & Classes in Seattle, LSAT Courses & Classes in Boston, ISEE Courses & Classes in Atlanta, ISEE Courses & Classes in Boston, ACT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, GRE Courses & Classes in New York City, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, ACT Test Prep in Seattle, SSAT Test Prep in New York City, GMAT Test Prep in Philadelphia, SAT Test Prep in Washington DC, GRE Test Prep in Chicago, ISEE Test Prep in Phoenix, GMAT Test Prep in San Diego, LSAT Test Prep in Denver, LSAT Test Prep in San Francisco-Bay Area

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

PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1023 : Algebra

Example Question #1022 : Algebra

Example Question #1023 : Algebra

Example Question #1021 : Algebra

Example Question #101 : Algebraic Functions

Example Question #102 : Algebraic Functions

Example Question #61 : How To Find F(X)

Example Question #62 : How To Find F(X)

Example Question #1034 : Algebra

Example Question #105 : Algebraic Functions

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: