How to Stop Making Silly Mistakes on the AMC 10/12 (And Instantly Boost Your Score)

There is nothing more frustrating in competition math than reviewing your AMC 10 or 12 exam and realizing you missed the AIME cutoff because of a "silly mistake."

Silly mistakes can happen for a variety of reasons, but they are not unavoidable curses. By understanding exactly how and why they occur, you can systematically eliminate them from your test-taking process. Broadly speaking, careless errors fall into three main categories.

1. The "Rushing" Arithmetic Error

The most common type of silly mistake happens when you rush through the problem-solving process and your brain misfires on basic arithmetic.

This can look like writing $2 + 3 = 6$ because your brain accidentally calculated $2 \times 3 = 6$ without you realizing you were supposed to be doing addition. It can also look like hastily saying $0!$ (zero factorial) is $0$, when it is actually $1$.

Other mistakes in this category involve basic counting and fraction flips. For example, if a problem asks, "How many 3-digit numbers are there?" you cannot simply calculate $999 - 100$. You must remember the inclusive counting rule: $999 - 100 + 1$. Similarly, when a question specifically asks for the ratio $\dfrac{a}{b}$, a rushing student might accidentally solve for and select $\dfrac{b}{a}$, or perhaps even $\left(\dfrac{a}{b}\right)^2$.

These counting and arithmetic errors must be ruthlessly avoided. To fix this, you must build a mental habit: while doing every single computation, pause for a microsecond to re-ask yourself exactly what the computation is and whether you have done it correctly. For instance, as you write $2 + 3 = 6$, actively ask yourself, "The computation is 2 + 3. Is it 6? No, it's 5!" This active self-interrogation breaks the autopilot that causes slips.