Efficient Math Commands for Wolfram Alpha

Wolfram Alpha is a free, online, computational engine. It provides some of the power of a computational algebra system (CAS) such as Maple or Mathematica without having to learn the proper syntax. However, it takes a little bit of practice to get WA to give exactly what you want.

Here, I’ll give a list of queries that are commonly used in math classes:

  • Solving an equation in one variablesolve 3x^2-1=0 
  • Solving an equation for one variable in terms of anothersolve 3x+2y=-8 for y
  • Factor an expression: factor (4x^2-16y^2) 
  • Simplify an expression: simplify (x+3(x+2)^2-2(x-y)) 
  • Plot a function:  plot x^3-x^2
  • Plotting a function on a given intervalplot sin(x), x=-pi..pi
  • Take the derivative of a function: derivative of (x^3+sin(x))
  • Higher derivatives: second derivative of (x^3+sin(x)) 
  • Higher derivatives, symbolic:  d^2/dx^2(x^3+sin(x))
  • Integration:  integrate (x^3+sin (x))
  • Definite Integrals: integrate (x^3+sin (x)), x=-2..3 
There are many, many more cool things you can do with Wolfram Alpha and I have only scratched the surface here. But the commands above should take care of most of the solving equations and graphing chapters in algebra, and the differentiation and integration material in calculus. I’ve told my students about it so that they can check their homework.
One thing to note is that WA will often give both graphical and algebraic representations for solutions of equations. It really helps students to connect those concepts.  However, it is not going to help a student set up and solve a word problem or help them to interpret a solution or a graph. If you’re interested in teaching or learning both math concepts and skills, then WA is an extremely useful tool.


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Hi! I am an associate professor of mathematics at Kean University, NJ. In this blog, I share insights and resources for mathematics in secondary and higher education.

2 Responses

  1. Maria H. Andersen
    Maria H. Andersen at |

    With Wolfram Alpha you actually don’t need as much text as you’ve written here. For plots, factoring, simplifying, derivatives, and indefinite integrals, all you need to type is the expression (like x^3+sinx), and it will automatically do all of those things (you’ll only get factoring if the expression has an “alternate [factored] form”

  2. Reva Narasimhan
    Reva Narasimhan at |

    Thanks, Maria. However, there are situations where one may need just to solve an equation, or plot something in a specified interval. I have a preference for being specific in my commands for a CAS. But if one wants to see what all that can be done with a function, what you suggest is quicker.

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