**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!

It was really helpful, thank you so much