25 Math Problems You MUST Know for the ACT

25 Math Concepts you MUST know for the ACT!

Phil McCaffrey

 

ACT Math – Top 25 ACT Math Concepts.

 

I read, analyze, and teach ACT Math problems 4 to 6 hours per day, 5 days per week, sometimes more. Doesn’t sound like fun to anyone but a real geek like me. But I love it, and I love helping the teenagers who come to 3RPrep for help. When the SAT was changing a few years ago, I convinced David to be my partner (because he is way better at grammar than I am), and we painstakingly counted every “type” (or concept) of question on the ACT. I just looked at the list of math question types and tried to identify the ones that are on almost EVERY test.

 

Stay tuned. I am going to make a very short lesson with an example problem or two from every concept.

 

  1. Word Problems – 99% of the ACT math is word problems. More, less, fewer, higher, lower, double, half, etc.
  2. Properties of Integers. 90% + of the numbers used by the ACT are integers. Even, odd, positive, negative, consecutive, prime, factor, multiple, square, etc.
  3. 1/a + 1/b = (a + b)/ab. 1/2 + 1/3 = (2+3)/(2*3)
  4. Arithmetic = add/subtract. Geometric = multiply/divide.
  5. Part+Part=Whole.
  6. Rates & Proportions.
  7. Increase, decrease, percent of a percent, interest.
  8. Algebraic Operations & solving equations. Combine like terms – watch out for negative signs. Easy – don’t miss these.
  9. Algebraic Inequalities – graph them quickly.
  10. Absolute Value.
  11. Exponents, roots, logarithms.
  12. Linear Functions. ax+by=c & y=mx+b
  13. Coordinate Geometry in the xy-plane.
  14. Systems of Equations
  15. Evaluate f(x).
  16. Quadratics, parabolas, factor and FOIL.
  17. Lines & Angles. l is parallel to m, l||m
  18. Triangles, right, isosceles, 3-4-5
  19. Quadrilaterals, squares, rectangles, trapezoids.
  20. Circles & sectors. They love the angle of a piece of a pie chart.
  21. Multiple Geometry Figures. Big Area – Small Area is usually the answer.
  22. Two SOHCAHTOA questions, usually straightforward.
  23. Average, Mean, Median, rarely mode.
  24. Probability
  25. Counting, Factorials, Permutations, & Combinations.

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