Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2461 : Act Math

If $x\ \blacklozenge \ y$ is defined by the formula $(x^{3}-y)^{2}-x$ , what is $2\ \blacklozenge \ 1$ equivalent to?

Possible Answers:

Correct answer:

Explanation:

The function $x\ \blacklozenge \ y$ is defined by $(x^{3}-y)^{2}-x$ . This means that for whatever value is in the space of the before the symbol $\blacklozenge$ , in our case 2, is inserted into any in the defined function:

$\dpi{100} (2^{3}-y)^{2}-2$

For the value that follows $\blacklozenge$ , the value of 1 in our case, is inserted into any variable in the defined function.

$\dpi{100} (2^{3}-1)^{2}-2$

Then simplify:

$(8-1)^{2}-2$

$7^{2}-2$

49-2

is our correct answer after all the simplification.

Report an Error

Example Question #2462 : Act Math

A dress that normally costs $80 before tax is on sale for 15% off. After the discount is subtracted, a 7% sale tax is added. What is the final price of the dress?

Possible Answers:

$\$50.76$

$\$72.00$

Need more information

$\$72.76$

$\$65.00$

Correct answer:

$\$72.76$

Explanation:

The word problem can be simplified into two steps. First, subtracting the 15% discount:

$New Price = (Original Price - (Original Price \cdot 0.15))$

Second, adding the sales tax to the result from the first step:

$Final Price = (New Price + (New Price \cdot 0.07))$

The percentage is represented as a decimal by dividing the percentage by 100.

So, for the numbers provided:

New Price = $(\$80.00-(\$80.00\cdot 0.15))=\$68.00$

Final Price = $\$68.00+(\$68.00\cdot 0.07)=\$72.76$

Report an Error

Example Question #2463 : Act Math

Evaluate the expression:

3(x-2) + y^2-xy

for x = 2 and y = -3

Possible Answers:

Correct answer:

Explanation:

Plug in the values for the variables and use PEMDAS to dictate the order of the operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Using this order of operations we get

(x-2) = 0 so the first part of the expression is .

Next we deal with the exponents,

-3^2 .

Then, we deal with the multiplication,

$2\cdot -3 = -6.$

Finally, we plug these simplified values back into the equation and solve,

9 - (-6) = 15 .

Report an Error

Example Question #2464 : Act Math

Tickets for a circus show cost $\$ 5$ each when bought in advance and $\$7$ each when bought at the door. The circus show's goal is to acquire at least $\$ 2,000$ in ticket sales. The show group sold 153 opening-night tickets in advance.

What is the minimum number of tickets they need to sell at the door on opening night to reach their goal?

Possible Answers:

200

177

176

293

154

Correct answer:

177

Explanation:

Since 153 tickets were sold in advance, the group earned a revenue of $153*\$ 5= \$ 765$ . In order to reach their goal of $\$ 2,000$ , they would still need to earn an extra $(\$ 2000-\$ 765)= \$ 1235.$

Since each ticket costs $\$ 7$ at the door, the theatre would need to sell $\$ 1235/7$ tickets, or 177 tickets (rounded to the next whole number).

Note: the answer is NOT 176 tickets, because if 176 tickets are sold, the revenue would be $(176*7) + (153*5) = \$ 1997$ , which does not reach the goal of $\$ 2,000$ .

Report an Error

Example Question #2465 : Act Math

If x=-4 , what is the value of $\frac{x^2-1}{x+1}$ ?

Possible Answers:

Correct answer:

Explanation:

Since x=-4 this value can be substituted for in the function.

$\frac{x^2-1}{x+1}}$

$=\frac{(-4)^2-1}{(-4)+1}$

$=\frac{16-1}{-3}$

Here, the denominator becomes , while the numerator becomes .

$=\frac{15}{-3}$

Hence,

$\frac{15}{-3} = -5$ .

Report an Error

Example Question #2466 : Act Math

If f(x) = 4x^2 + 2x - 4 , then f(-2) equals?

Possible Answers:

Correct answer:

Explanation:

When substituting (-2) for in the provided equation, we get

4(-2)^2 +2(-2) -4 ,

which can be simplified to

16-4-4 , or .

Report an Error

Example Question #31 : Evaluating Expressions

Question 20

In which month has Abraham collected the most stamps?

Possible Answers:

May

October

April

November

July

Correct answer:

May

Explanation:

May corresponds to the month Abraham collected the most stamps, adding 24 to his collection. April, July, October, and November correspond to 18, 6, 21, 12, respectively.

Report an Error

Example Question #2463 : Act Math

A company establishes a rewards program such that the bonus received by an employee is given by the model $b = \frac{s^3}{10}$ , where is the number of sales an employee completed. If Alex earned $2700 at the end of the month, how many sales has he completed?

Possible Answers:

27000

300

Correct answer:

Explanation:

Alex’s bonus of

$2700 = \frac{s^3}{10} \rightarrow 27000 = s^3\rightarrow s = 30.$

Report an Error

Example Question #2463 : Act Math

2x + 7 = |-7| , then $x = \:?$

Possible Answers:

-3.5

Correct answer:

Explanation:

|-7| = 7 . Thus

$2x + 7 = 7\rightarrow 2x = 0 \rightarrow x = 0$

Report an Error

Example Question #2464 : Act Math

Evaluate the folling expression given x=2 .

$x^3+\frac{2}{x}-4x^2+x!$

Possible Answers:

Correct answer:

Explanation:

To evaluate, simply plug in for . Thus:

$2^3+\frac{2}{2}-4*2^2+2!=8+1-16+2=-5$

Report an Error

View ACT Math Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

View ACT Math Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

View ACT Math Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

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

Popular Courses & Classes

MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Diego, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in Houston, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in Chicago, ISEE Courses & Classes in Miami, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in New York City, GRE Test Prep in Denver, ACT Test Prep in Phoenix, ACT Test Prep in Denver, ISEE Test Prep in San Diego, GMAT Test Prep in Washington DC, ISEE Test Prep in Seattle, ISEE Test Prep in Miami, MCAT Test Prep in Boston, GMAT Test Prep in Chicago

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

ACT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2461 : Act Math

Example Question #2462 : Act Math

Example Question #2463 : Act Math

Example Question #2464 : Act Math

Example Question #2465 : Act Math

Example Question #2466 : Act Math

Example Question #31 : Evaluating Expressions

Example Question #2463 : Act Math

Example Question #2463 : Act Math

Example Question #2464 : Act Math

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: