What does “MATH ERROR” mean?

SHORT ANSWER: this means you have just asked the calculator to do a sum it doesn’t like. The three most common reasons for getting this error message are:

1) you have tried to divide by zero: forbidden in maths! If you type in $3\div 0$ you are asking the calculator “zero times by what equals three?” Of course there is no such number: zero multiplied by anything is zero.

2) you have tried to square root a negative number: e.g. $\sqrt{25}$. The answer can’t be 5 because $5^2=+25$ and it can’t be -5 because $(-5)^2=+25$. Whatever number you multiply by itself, you will never get -25, so there is no answer.

3) you have tried to find $cos^{-1}$ or $sin^{-1}$ of a number bigger than 1 or smaller than -1. But the graphs of sin and cos both stay between -1 and +1, so asking the calculator where $cos(θ) = 2$ for instance is gong to be impossible.

You will also get a Math Error if the answer is larger than a googol ($=10^{100}$). The calculator can handle 69! but not 70! The ! in maths means factorial, so 70! = 1x2x3x…x69x70 = too large for my poor calculator to work out. Try it for yourself.

AT GCSE: this probably means you have done something wrong – go back and check!

AT A-LEVEL: this need not mean you have done anything wrong! It may mean that your equation has no solutions: for instance, if you are trying to find out where two curves meet, a Math Error would indicate that they don’t meet anywhere. You will also get a Math Error if you try to take the logarithm of zero or a negative number (why is this?).

AT FURTHER MATHS A-LEVEL: we change the rules to extend the number system. For instance, we allow the square root of negative numbers (forbidden at GCSE) by introducing “complex numbers“. These beautiful numbers are not really so complicated as they sound. Think of them as being like negative numbers: they don’t actually exist, but that doesn’t stop them being useful!

There are many other ways to get a Math Error message – why not see if you can find some? HINT: ask your calculator to do something absurd. Try using all the different buttons!