Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Expressions

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Evaluating Expressions

High and low 2

Above is a graph which gives the high and low temperatures, in degrees Celsius, over a one week period for Washington City. Temperature given in degrees Celsius can be converted to the Fahrenheit scale using the following formula, where and are the temperature expressed in degrees Celsius and degrees Fahrenheit, respectively:

F =1.8 C + 32

In degrees Fahrenheit, what was the highest temperature of the week shown (Nearest whole degree)?

Possible Answers:

$64 ^{\circ }F$

$84^{\circ }F$

$79 ^{\circ }F$

$69 ^{\circ }F$

$74 ^{\circ }F$

Correct answer:

$79 ^{\circ }F$

Explanation:

The highest temperature during the week was $26 ^{\circ } C$ , which, as can be seen in the graph, was reached on Tuesday and Friday. Setting C= 26 in the given formula:

F =1.8 C + 32

$F =1.8 \cdot 26 + 32$

=46.8 + 32

= 78.8

Rounded to the nearest whole number, this is $79 ^{\circ }F$ .

Report an Error

Example Question #61 : Expressions

High and low 2

Above is a graph which gives the high and low temperatures, in degrees Fahrenheit, over a one week period for Washington City. Temperature given in degrees Fahrenheit can be converted to the Celsius scale using the following formula, where and are the temperature expressed in degrees Celsius and degrees Fahrenheit, respectively:

$C = \frac{5}{9} (F-32)$ .

In degrees Celsius, what was the high temperature on Thursday, June 11 (nearest whole degree)?

Possible Answers:

$-5^{\circ } C$

$-10^{\circ } C$

$0^{\circ } C$

$10^{\circ } C$

$5^{\circ } C$

Correct answer:

$-5^{\circ } C$

Explanation:

The high temperature for Thursday was $23 ^{\circ }$ Fahrenheit. Convert this to the Celsius temperature scale by setting F= 23 in the given formula and evaluating:

$C = \frac{5}{9} (F-32)$

$C = \frac{5}{9} (23-32)$

$C = \frac{5}{9} (-9)$

C = -5

In degrees Celsius, Thursday's high temperature was $-5^{\circ } C$ .

Report an Error

Example Question #62 : Expressions

represents a positive quantity and represents a negative quantity.

$x^{2} = 99$

$y^{2} = 11$

Evaluate $x^{3}- 3x^{2}y+3xy^{2}- y^{3}$ .

Possible Answers:

$704 \sqrt{11}$

None of the other choices gives the correct response.

$-88 \sqrt{11}$

$88 \sqrt{11}$

$-704 \sqrt{11}$

Correct answer:

$704 \sqrt{11}$

Explanation:

$x^{3}- 3x^{2}y+3xy^{2}- y^{3}$ can be recognized as the cube of the binomial x-y , so

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

$x^{2} = 99$ ,

so, taking the square root of both sides,

$x = \pm \sqrt{99}$

By the Product of Radicals rule, simplify:

$x = \pm \sqrt{9} \cdot \sqrt{11}$

$= \pm 3 \sqrt{11}$

Since represents a positive quantity, we choose

$x = 3\sqrt{11}$

$y^{2} = 11$ ,

so, taking the square root of both sides,

$y = \pm \sqrt{11}$

Since represents a negative quantity.

$y = - \sqrt{11}$

Substituting:

$x^{3}- 3x^{2}y+3xy^{2}- y^{3}$

$= (x-y)^{3}$

$=\left [ (3 \sqrt{11}) - \left ( -\sqrt{11}\right ) \right ] ^{3}$

$= (4 \sqrt{11}) ^{3}$

By the Product of Powers rule, this is

$4 ^{3} \cdot (\sqrt{11}) ^{3}$

$= 4 ^{3} \cdot (\sqrt{11}) ^{2} \cdot \sqrt{11}$

$=64 \cdot 11 \cdot \sqrt{11}$

$= 704 \sqrt{11}$

Report an Error

Example Question #43 : Evaluating Expressions

represents a positive quantity and represents a negative quantity.

$x^{2} = 60$

$y^{2} = 15$

Evaluate $x^{3}+3x^{2}y+3xy^{2}+ y^{3}$ .

Possible Answers:

$-15\sqrt{15}$

$15\sqrt{15}$

$-405\sqrt{15}$

$405\sqrt{15}$

Correct answer:

$15\sqrt{15}$

Explanation:

$x^{3}+3x^{2}y+3xy^{2}+ y^{3}$ can be recognized as the cube of the binomial x+y , so

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

$x^{2} = 60$ ,

so, taking the square root of both sides,

$x = \pm \sqrt{60}$

By the Product of Radicals rule, simplify:

$x = \pm \sqrt{4} \cdot \sqrt{15}$

$= \pm 2\sqrt{15}$

Since represents a positive quantity, we choose

$x = 2\sqrt{15}$

$y^{2} = 15$ ,

so, taking the square root of both sides,

$y = \pm \sqrt{15}$

Since represents a negative quantity.

$y = - \sqrt{15}$

Substituting:

$x^{3}+3x^{2}y+3xy^{2}+ y^{3}$

$= (x+y)^{3}$

$=\left [ (2 \sqrt{15}) + \left ( -\sqrt{15}\right ) \right ] ^{3}$

$= ( \sqrt{15}) ^{3}$

$= ( \sqrt{15}) ^{2} \cdot \sqrt{15}$

$= 15\sqrt{15}$

Report an Error

Example Question #51 : How To Evaluate Algebraic Expressions

and both represent positive quantities.

$x^{2} = 48$

$y^{2} = 12$

Evaluate $x^{3}+ y^{3}$ .

Possible Answers:

$72\sqrt{3}$

$-216\sqrt{3}$

$-72\sqrt{3}$

$216\sqrt{3}$

Correct answer:

$216\sqrt{3}$

Explanation:

One way to evaluate $x^{3}+ y^{3}$ is to note that, as the sum of cubes, this can be factored as

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

$x^{2} = 48$ ,

and is positive, so, using the Product of Radicals Rule,

$x = \sqrt{48} = \sqrt{16} \cdot \sqrt{3} = 4 \sqrt{3}$

$y^{2} = 12$ , and is positive, so, similarly,

$y = \sqrt{1 2}= \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3}$

$xy = 4 \sqrt{3} \cdot 2 \sqrt{3} = 4 \cdot 2 \cdot \sqrt{3} \cdot \sqrt{3} = 4 \cdot 2 \cdot 3 = 24$

Therefore, substituting for $x, y,xy, x^{2}, y^{2}$ in the factored expression:

$x^{3}+ y^{3}$

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

$= ( 4 \sqrt{3} +2 \sqrt{3})(48-24+12)$

$= (6\sqrt{3})(36)$

$= 216\sqrt{3}$

Report an Error

Example Question #52 : How To Evaluate Algebraic Expressions

High and low 2

The above double line graph gives the high and low temperatures, in degrees Celsius, for each day in a given week in Washington City. Temperatures given in terms of the Celsius scale can be converted to degrees Farhrenheit using this formula:

F = 1.8C + 32

where and are the temperature expressed in degrees Celsius and degrees Fahrenheit, respectively.

In degrees Fahrenheit, what was the low temperature for Tuesday, June 9 (nearest whole degree?)

Possible Answers:

$85^{\circ } F$

$79^{\circ } F$

$72^{\circ } F$

$66^{\circ } F$

$59^{\circ } F$

Correct answer:

$66^{\circ } F$

Explanation:

The low temperature for Tuesday was $19^{\circ } C$ . This can be converted to degrees Fahrenheit by setting C = 19 in the formula and evaluating :

F = 1.8C + 32

$= 1.8 \cdot 19 + 32$

= 34.2+ 32

=66.2

This rounds to $66 ^{\circ } F$ .

Report an Error

Example Question #53 : How To Evaluate Algebraic Expressions

If Sandy is running at a pace of $\frac{12\: \text{meters}}{\text{sec}}$ , find how fast sandy is running in $\frac{\text{meters}}{\text{year}}$ .

Possible Answers:

$\frac{37843\:\text{meters}}{\text{year}}$

$\frac{3784320\:\text{meters}}{\text{year}}$

$\frac{12\:\text{meters}}{\text{year}}$

$\frac{378432000\:\text{meters}}{\text{year}}$

$\frac{2000\:\text{meters}}{\text{year}}$

Correct answer:

$\frac{378432000\:\text{meters}}{\text{year}}$

Explanation:

To convert into $\frac{\text{meters}}{\text{year}}$ , we will do the following conversions

$\frac{12\: \text{meters}}{\text{sec}}\cdot\frac{60\:\text{sec}}{\text{min}}\cdot\frac{60\:\text{min}}{\text{hour}}\cdot\frac{24\:\text{hour}}{\text{day}}\cdot\frac{365\:\text{days}}{\text{year}}=\frac{378432000\:\text{meters}}{\text{year}}$

Report an Error

Example Question #54 : How To Evaluate Algebraic Expressions

$\begin{tabular}{cccc} x & \vline & y\\ \hline 0 & \vline & 2\\ 1& \vline &7 \\ 2 & \vline & 12\\ 3 & \vline & 17 \end{tabular}$

Find the equation of a line that fits the above data.

Possible Answers:

y=5x-2

y=5x+2

y=5x

y=2x+5

y=-5x+2

Correct answer:

y=5x+2

Explanation:

We can use point slope form to determine the equation of a line that fits the data.

Point slope form is y-y_0=m(x-x_0) , where (x_0, y_0) , and is the slope, where $m=\frac{y_2-y_1}{x_2-x_1}$ .

Let y_2=17 , y_1=12 , x_2=3 , and x_1=2 .

$m=\frac{17-12}{3-2}=5$

If we do this for every other point, we will see that they have the same slope of .

y-y_0=5(x-x_0)

Now let x_0=0 , and y_0=2 .

y-2=5(x-0)

y-2=5x

y=5x+2

Report an Error

Example Question #55 : How To Evaluate Algebraic Expressions

The equation for the universal gravitation is $F_g=\frac{Gm_1m_2}{r^2}$ , $m_1=\text{mass of object 1}$ , $m_2=\text{mass of object 2}$ , $r=\text{radius between masses}$ , and is the universal gravitational constant. If $m_1=10 \ kg$ , $m_2=20 \ kg$ , $r=100\ m$ , and $G=6.67408 \times 10^{-11} m^3 kg^{-1} s^{-2}$ , what is the Force equal to? Round to the nearest tenth.

Hint: $\frac{\text{kg\:m}}{s^2}=1 \text{Newton}$

Possible Answers:

$F_g=1.3\times10^{-9}N$

$F_g=1.3\times10^{-11}N$

$F_g=1.3\times10^{-8}N$

$F_g=1.3\times10^{-10}N$

$F_g=1.3\times10^{-12} N$

Correct answer:

$F_g=1.3\times10^{-12} N$

Explanation:

All we need to do is plug in the values into the equation.

$F_g=\frac{Gm_1m_2}{r^2}$

$F_g=\frac{(6.67408 \times 10^{-11} m^3 kg^{-1} s^{-2})10\: kg\: 20\: kg}{(100m)^2}$

$F_g=\frac{(6.67408 \times 10^{-11} m^3 kg^{-1} s^{-2})200\: kg^2}{10000m^2}$

$F_g=\frac{(6.67408 \times 10^{-11} m^3 kg^{-1} s^{-2})1\: kg^2}{50m^2}$

$F_g=1.3\times10^{-12}\frac{\text{kg m}}{s^2}$

$F_g=1.3\times10^{-12}N$

Report an Error

Example Question #56 : How To Evaluate Algebraic Expressions

Given a right triangle $\Delta ABC$ whose $m\angle C=90^\circ$ and $\sin B=$ $\frac{2}{3}$ , find $\cos A$ .

Possible Answers:

$72^\circ$

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

To solve for $\cos A$ first identify what is known.

The question states that $\Delta ABC$ is a right triangle whose $m\angle C=90^\circ$ and $\sin B=$ $\frac{2}{3}$ . It is important to recall that any triangle has a sum of interior angles that equals 180 degrees.

Therefore, to calculate $\cos A$ use the complimentary angles identity of trigonometric functions.

$\cos A=\sin \left ( 90-A\right )$

and since B=90-A , then

$\cos A=\sin B$

$\cos A=\frac{2}{3}$

Report an Error

View SAT Mathematics Tutors

Aaqib
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Neuroscience.

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Zachary
Certified Tutor

Yale University, Bachelor of Science, Biology, General.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Houston, GMAT Courses & Classes in Denver, GRE Courses & Classes in Washington DC, Spanish Courses & Classes in New York City, Spanish Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Chicago, ISEE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in Atlanta, ACT Test Prep in Los Angeles, GMAT Test Prep in Denver, GRE Test Prep in Phoenix, ISEE Test Prep in Boston, GRE Test Prep in Washington DC, SSAT Test Prep in Atlanta, MCAT Test Prep in San Diego, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Boston

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 Math : Expressions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #41 : Evaluating Expressions

Example Question #61 : Expressions

Example Question #62 : Expressions

Example Question #43 : Evaluating Expressions

Example Question #51 : How To Evaluate Algebraic Expressions

Example Question #52 : How To Evaluate Algebraic Expressions

Example Question #53 : How To Evaluate Algebraic Expressions

Example Question #54 : How To Evaluate Algebraic Expressions

Example Question #55 : How To Evaluate Algebraic Expressions

Example Question #56 : How To Evaluate Algebraic Expressions

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: