Is there a easy way to remember the equations for active systematic returns, expected active beta returns, active beta surprise and active benchmark timing return.

Don’t memorize the equations, just learn to understand what they measure. Come up with a quick one-liner for each and just learn that. Then you can come up with the formula yourself, or at least be able to make an educated guess.

Thanks for your reply, I am wondering why the AIMS has the word “calculate” .

with calculate you just have to know that adding the three; expected surprise and timing gives you the total active systematic return.