How do I know when yellow split peas are cooked?
You probably haven't added enough water. Split peas are dried, cooking re-hydrates them, but only if there's enough to for them to absorb.  You need to add at least double the water as peas, a bit like rice in that respect. It's also possible you have old peas, or they are a variety that simply needs a longer cooking time. Hard water can also slow down cooking. 

Try using softened water if you can, and more of it. An overnight soak can also work wonders.