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Discover Frequently Asked Math Questions and Their Answers

• How do you write the quadratic function #y=x^2+14x+11# in vertex form?
• How many points does #y=-2x^2+x-3# have in common with the vertex and where is the vertex in relation to the x axis?
• How do you solve #4x^4 - 16x^2 + 15 = 0#?
• How do you solve #2x^2+3x-2=0#?
• How do you solve #7(x-4)^2-2=54# using any method?
• How do you solve #x^2 + 5x + 6 = 0# algebraically?
• How do you use factoring to solve this equation #3x^2/4=27#?
• What is the vertex of # y = (1/8)(x – 5)^2 - 3#?
• How do you solve #| x^2+3x-2 | =2#?
• How do you solve #2x²+3x=5 # using the quadratic formula?
• How do you find the derivative of #y=tan(3x)# ?
• How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?
• How do you differentiate #(3+sin(x))/(3x+cos(x))#?
• What is the derivative of this function #sin^-1(x/4)#?
• What is the derivative of this function #y=sin^-1(2x)#?
• What is the derivative of this function #arcsec(x^3)#?
• What is the derivative of #y=sin(tan2x)#?
• How do you differentiate #cos(pi*x^2)#?
• What is the derivative of #f(x)=(x^2-4)ln(x^3/3-4x)#?
• What is the derivative of #y=3sin(x) - sin(3x)#?
• A triangle has corners at #(5 ,1 )#, #(2 ,9 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
• How can we find the area of irregular shapes?
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #24 #. What is the area of the triangle's incircle?
• An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #27 #, what are the possible coordinates of the triangle's third corner?
• A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?
• Circle A has a center at #(2 ,3 )# and a radius of #1 #. Circle B has a center at #(0 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
• A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?
• What is a quadrilateral that is not a parallelogram and not a trapezoid?
• Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#
• A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,9 )#, and #(4 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
• What is the GCF of the set #64, 16n^2, 32n#?
• How do you write the reciprocal number of 5?
• Jeanie has a 3/4 yard piece of ribbon. She needs one 3/8 yard piece and one 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Why?
• How do you find the GCF of #25k, 35j#?
• How do you write 132/100 in a mixed number?
• How do you evaluate the power #2^3#?
• How do you simplify #(4^6)^2 #?
• How do you convert 3.2 tons to pounds?
• How do you solve #\frac { 5} { 8} + \frac { 3} { 2} ( 4- \frac { 1} { 4} ) - \frac { 1} { 8}#?
• What are some acronyms for PEMDAS?
• How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?
• How do you determine whether the graph of #y^2+3x=0# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• How do you find the end behavior of #-x^3+3x^2+x-3#?
• How do you find the asymptotes for #(2x^2 - x - 38) / (x^2 - 4)#?
• How do you find the asymptotes for #f(x) = (x^2) / (x^2 + 1)#?
• How do you find the vertical, horizontal and slant asymptotes of: #(3x-2) / (x+1)#?
• How do you find the Vertical, Horizontal, and Oblique Asymptote given #s(t)=(8t)/sin(t)#?
• How do you find vertical, horizontal and oblique asymptotes for #(x^3+1)/(x^2+3x)#?
• How do you find vertical, horizontal and oblique asymptotes for #y = (4x^3 + x^2 + x + 5 )/( x^2 + 3x)#?
• What is a pooled variance?
• What is the mean, mode median and range of 11, 12, 13, 12, 14, 11, 12?
• What is the z-score of sample X, if #n = 81, mu= 43, St. Dev. =90, and E[X] =57#?
• The camera club has five members, and the mathematics club has eight. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club?
• How many permutations are there of the letter in the word baseball?
• How do you evaluate 6p4?
• What is the probability of #X= 6# successes, using the binomial formula?
• A lottery has a $100 000 first prize, a $25 000 second prize, and five $500 third prizes. A total of 50000 tickets are sold. What is the probability of winning a prize in this lottery?
• When a event is reported, the probability that is a negative event is 30%. What is the probability that 3 out of 5 reported events are negative?
• What is the median of 5, 19, 2, 28, 25?
• How do you solve this trigonometric equation?
• What is the frequency of #f(theta)= sin 3 t - cos2 t #?
• How do you evaluate #Sin(pi/2) + 6 cos(pi/3) #?
• How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=9, b=40, c=41?
• How do you express (5*pi)/4 into degree?
• Solve for θ on the interval [90°,180°]:2tanθ +19 = 0?
• Prove that #((cos(33^@))^2-(cos(57^@))^2)/((sin(10.5^@))^2-(sin(34.5^@))^2)= -sqrt2# ?
• A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3# and the angle between sides B and C is #pi/6#. If side B has a length of 26, what is the area of the triangle?
• How do you write the following in trigonometric form and perform the operation given #(sqrt3+i)(1+i)#?
• A triangle has sides A, B, and C. The angle between sides A and B is #(2pi)/3#. If side C has a length of #32 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Free Wolfram|Alpha Math Resources

Free help with your math—check your answers, quiz yourself, explore topics and more.

Wolfram|Alpha Website

Use the Wolfram|Alpha website for free to check answers, plot equations, balance chemical equations, visualize results, review interesting facts on a subject area and more.

Math Input on the Wolfram|Alpha Website

Use textbook notation to enter your math input and see it displayed in 2D. We've provided popular templates for you to use, as better visualization and quick editing mean faster results.

Wolfram|Alpha Mobile Apps

Use Wolfram|Alpha how and where you want with our natively designed apps. From additional features to specially designed keyboards, we’ve made it easy to use Wolfram|Alpha on the go.

Use Wolfram|Alpha to Practice

With Wolfram Problem Generator, each question is generated instantly, just for you. Quiz yourself with an unlimited number of questions until you feel confident in the subject area.

Wolfram|Alpha Calculators

Use our convenient calculator pages to input your queries into Wolfram|Alpha. Read more information on topic areas and explore example queries.

Wolfram|Alpha Math Topic Coverage

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge.

Wolfram|Alpha Pro Resources

Add more to your toolbox with Wolfram|Alpha Pro! Get step-by-step solution help, generate printable worksheets and more! Discounts are available for students and educators— go Pro now »

Learn with Step-by-Step Solutions

Unlock step-by-step calculators for calculus, algebra, trigonometry, equation solving and basic math. Gain more understanding of your math homework with step-by-step hints guiding you from problems to answers!

Use Step-by-Step Solutions on Your Device

Pro users can log in to their accounts in the Wolfram|Alpha iOS and Android apps to use step-by-step solutions on the go.

Textbook to Answers in a Snap with Photo Input

Input your math even faster with photo input. Enter your math problems using photo-based input to get you quickly to results and step-by-step solutions.

Enhanced Features for Wolfram Problem Generator

Wolfram|Alpha Pro subscribers get integrated step-by-step solutions and can create unlimited printable worksheets for study sessions and quizzes.

Web Apps Powered by Wolfram|Alpha

Easy inputs with our form-based interfaces get you straight to answers. Our Web App collections cover a wide variety of math topics, including algebra, calculus and more.

Wolfram|Alpha Notebook Edition Resources

The simplicity of Wolfram|Alpha with the computational capabilities of Mathematica— try it now »

Wolfram|Alpha Notebook Edition

Take Wolfram|Alpha to the next level with a unified software tool for desktop and cloud perfect for teaching and learning. Use free-form input to get instant answers to questions, create and customize graphs, and turn static examples into dynamic models.

Hands-on Start to Wolfram|Alpha Notebook Edition

Learn how to quickly create notebooks that combine calculations, graphics, interactive examples and notes; enter free-form input and get solutions; create 2D, 3D and interactive graphics with controls to dynamically change the parameters; and more.

Additional Resources

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• Join MathHelp.com

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• + more tests
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Lessons HW Guidelines Skills Survey

Need help with math? Start browsing Purplemath's free resources below!

What are Purplemath's lessons like?

Content Continues Below

MathHelp.com

Need a custom math course? K12 | College | Test Prep

How much do these lessons cost?

Purplemath's lessons cost nothing! These lessons are free, are intended for students (rather than for instructors), and are interlinked to help you find related material. There is a "Search" box on every page to help you find whatever math content you're looking for — without encountering ads masquerading as search results. Whether you're in middle school, high school, college, or university, these free algebra lessons can help you out!

How can I use Purplemath's lessons?

Purplemath's math lessons can be used in many ways:

• Read the lesson that relates to what you're about to study in class, so you get to class at least somewhat prepared.
• Print out the lesson that relates to what you're about to study in class, and use the margins, white space, or the backs of pages for taking notes in class.
• When the homework seems impossible and the textbook and your class notes aren't helping much, come to Purplemath for clarification.

Let Purplemath help you always be prepared!

Go to the lessons!

How should I be formatting my homework?

Neat homework can aid your comprehension and might make your teacher like you better. Purplemath's " Homework Guidelines for Mathematics " will give you a leg up, explaining in clear terms what your math teacher is looking for. The Guidelines link to examples of common errors, and demonstrate techniques that your instructors will love! In addition, students who get in the habit of explaining themselves clearly in their homework gain greater understanding of what they're doing, and therefore tend to do much better on their tests.

English teachers tell their students explicitly how to format their papers: what fonts, what page margins, what style guides, etc. Math teachers, on the other hand, frequently just complain amongst themselves in the faculty lounge about how messy their students' work is. Meanwhile, their students wonder why they've lost points on homework and tests.

Study these Guidelines , print out this " formatting " PDF, and improve your learning, retention, and test scores. Don't leave easy points on the table!

Go to the Guidelines!

How can I measure my study skills?

Many students, from time to time, wonder, "Do I have what it takes to succeed in math?" Much of one's success or failure in algebra can be laid at the feet of one's study habits. Do you have good math study habits? Take this survey and find out.

Go to the study-skills self-survey!

Personalized Help ($): Investigate hiring a qualified tutor in your local area (US only), or try e-mail tutoring from Purplemath's author. But for in-depth, quality, video-supported, at-home help, including self-testing and immediate feedback, try MathHelp.com . MathHelp.com comes highly recommended by homeschoolers, military service members, and other practical people. If you're needing more intensive help, give MathHelp.com a try!

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URL: https://www.purplemath.com/index.htm

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