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 variable:  solve 3x^2-1=0 
  
• Solving an equation for one variable in terms of another:  solve 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 interval:  plot 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.