25 Math Problems You MUST Know for the ACT
Author;
3rPrep 2020-12-10
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 3R Prep 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.
- Word Problems – 99% of the ACT math is word problems. More, less, fewer, higher, lower, double, half, etc.
- Properties of Integers. 90% + of the numbers used by the ACT are integers. Even, odd, positive, negative, consecutive, prime, factor, multiple, square, etc.
- 1/a + 1/b = (a + b)/ab. 1/2 + 1/3 = (2+3)/(2*3)
- Arithmetic = add/subtract. Geometric = multiply/divide.
- Part+Part=Whole.
- Rates & Proportions.
- Increase, decrease, percent of a percent, interest.
- Algebraic Operations & solving equations. Combine like terms – watch out for negative signs. Easy – don’t miss these.
- Algebraic Inequalities – graph them quickly.
- Absolute Value.
- Exponents, roots, logarithms.
- Linear Functions. ax+by=c & y=mx+b
- Coordinate Geometry in the xy-plane.
- Systems of Equations
- Evaluate f(x).
- Quadratics, parabolas, factor and FOIL.
- Lines & Angles. l is parallel to m, l||m
- Triangles, right, isosceles, 3-4-5
- Quadrilaterals, squares, rectangles, trapezoids.
- Circles & sectors. They love the angle of a piece of a pie chart.
- Multiple Geometry Figures. Big Area – Small Area is usually the answer.
- Two SOHCAHTOA questions, usually straightforward.
- Average, Mean, Median, rarely mode.
- Probability
- Counting, Factorials, Permutations, & Combinations.
