Here is a concise list of must know topics for doing well on the ACT:
1. Slope formula
2. Distance formula
3. Midpoint formula
4. Equation of a circle
5. Equations of lines (parallel and perpendicular)
6. Area and volume formulas of common shapes
7. Pythagorean theorem and Pythagorean triples.
9. Rules of exponents
14. Trigonometry(soh cah toa)
15. Special right triangles 30-60-90 and 45-45-90
16. Multiplication counting principle
17. Percentage problems
19. Graphs of lines and inequalities
20. Reading and interpreting charts and diagrams.
The key to doing well on the test is RECOGNIZING what the problem calls for and knowing which of the concepts above to apply. This is where experience makes all of the difference. I tutor students on the math section of the test and what I do is have them take a number of ACT tests on their own and then after each time we go over the ones that they miss and I point out what concept is DISGUISED in the problem and a more direct way of solving it. The experience gained is very valuable but it is experience that has to be gained by the student themselves through EXPERIENCE with the test and wrestling with the problems and learning when to apply the various topics mentioned above. This I feel is the best way to spend one's time in preparation for the math section of the test. Again, I am very familiar with the test and have helped many students improve their score but there isn't any secret beyond knowing the key topics and taking a lot of practice tests and have someone point out what to look for and apply to the ones that you miss. Someone just informed me today that their score went up a full 7 points since I started tutoring them. They put in the effort and there is still room for even more from this particular student.
Helping students succeed in math for over 15 years. Individualized attention makes the difference!