Windows Memory Diagnostic (WMD) is an excellent free memory testing program. It is comprehensive, but also very easy to use.
FREE Fast Way to TEST for Faulty RAM Modules NO Downloads Required Windows Memory Diagnostics
The BIOS in your computer tests your memory during POST, but it is an extremely basic test. To really determine if your RAM is failing, you should run a comprehensive memory test using a program like Windows Memory Diagnostic.
I recommend testing your memory with Memtest86 first, but you should always test a second time with another memory testing tool to be sure. Windows Memory Diagnostic should be that second tool.
While it's not the best RAM testing tool out there, it's a great second option:
