I want to take the ACT; however, I have not taken pre calculus and I don’t know how well I would score. Does the ACT only ask about the basics of precalculus? Do the math sections primarily focus on other types of math such as algebra II ? Should I take the exam? I am considering taking this test since people say they score better on the ACT than on the SAT most of the time.
You will be fine. It covers the following math topics: Alg (I & II), Geometry, and a small amount of trig. Normally (just like with the SAT), if you have the Algebra, Geometry, and Algebra II experience then you will be able to work around the topics. Purchase a prep book if you’re not sure. I think you should take it. You will be fine. However, I’m not sure if you’re taking the SAT or not but I recommend taking both and seeing which one you like better. Best of luck! 
There are only a few precalc topics on the ACT. For example, my ACT had a question about the equation of an ellipse.
You can take the ACT an be very successful without Pre-calc. There are only 4 trig questions.
Do not let this stop you!