I keep dropping marks in tests by making silly mistakes. Is that something I just have to get used to?

Great question!

I have, in a box of ancient relics upstairs, one of my GCSE mock papers. On the front of it is the number “100”, scribbled out and replaced by “99”; in the course of triple-checking my work (my head, they correctly reasoned, was big enough already) they found that I’d mis-measured a circle, enough to dock me a mark.

Sloppy, sloppy, sloppy. But you can bet I checked every circle’s radius twice in the real exam!

The thing to remember is: every mathematician makes mistakes. Stephen Hawking? Forever forgetting his brackets. Tim Gowers? Might as well toss a coin for his minus signs. Maryam Mirzakhani? Sometimes writes down $3 \times2 = 5$. Just like the rest of us.

The difference between a mathematician and a good mathematician, though, is that good mathematicians find their mistakes.

When I was a code-monkey, back in the day, I had a slip of paper next to my monitor with “IDIOT LIST” written on it. Whenever I made a mistake more than once, I wrote it down on the idiot list; it was the first thing I’d check when something wasn’t working.

After a while, I got used to checking for those mistakes and started spotting them early.

You can do the same thing - get hold of a notebook and, whenever you make a mistake you know you’ve made before, write it down. When you’re stuck, before you ask for help, check your notebook. You’ll get used to catching loose minus signs or arithmetic errors as a matter of course, and when you get to the exam, you’ll be on your toes for it.