top of page

26 Need to Know Math Concepts for the ACT

  • Alex Theoharides
  • Feb 13, 2018
  • 3 min read

The ACT math section isn't so much hard as it is tricky. Unlike school where you spend a few weeks working on a unit and then take a test on it, the ACT math test covers material that goes back as far as middle school for some students. One of the first steps in getting a great math score is mastering these 26 key concepts.

  1. Sum: Addition

  2. Difference: Subtraction

  3. Product: Multiplication

  4. Quotient: Division

  5. Order of Operations / PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

  6. Mean, Median, Mode

  7. Mean means average: Add up all the numbers and divide by how many items there are.

  8. Median: Put the numbers in order from smallest to largest. Then find the number in the exact middle. If the number is even, find the average of the 2 number in the middle.

  9. Mode: The number that appears most often.

  10. Powers, Exponents, and Roots

  11. When you multiply common bases with exponents, add the exponents

  12. Ex. x² * x⁵ = x⁷

  13. When you divide common bases with exponents, subtract the exponents

  14. Ex. x⁷ / x² = x⁵

  15. When you raise a base with an exponent to another exponent, multiply the exponents

  16. (x²)⁴ = x⁸

  17. Any number raised to 0 equals 1

  18. Ex. 10170 = 1

  19. Absolute Value: The distance from zero on the number line. It is the positive version of a number.

  20. │-2 │= 2 and │2│ = 2

  21. Arithmetic sequence: There is a common difference or addition

  22. 2, 5, 8, 11, 14 or 15, 10, 5, 0, -5

  23. Geometric sequence: There is a common multiple

  24. 3, 9, 27, 81 or 45, 15, 3, 1, 1/3

  25. Bisect: To cut an angle or line in half

  26. Chord: Any line segment that both ends on a circle

  27. A diameter is the longest chord of any circle

  28. Complement: Two angles that add up to 90°

  29. Supplement: Two angles that add up to 180°

  30. Consecutive: Numbers that follow each other directly.

  31. Ex. 5, 6, 7

  32. Consecutive odd numbers: 5, 7, 9, 11

  33. Integer: Any number that doesn’t have a decimal or a fraction.

  34. Ex. -1 or 17

  35. Real number: Any number that is not imaginary

  36. Ex. -17 , pi , 3.666666667

  37. Imaginary numbers: The square root of a negative number

  38. Ex. √(-16) = 4i or √(-25) = 5i

  39. Remember: i² = -1

  40. Prime Numbers: Can only be divided by 1 and themselves

  41. Ex. 2, 3, 5, 7, 11, 13

  42. 1 is not a prime number

  43. 2 is the only even prime number

  44. Rational number: Any number that ends or repeats.

  45. Ex. 7, -4.83, 3/4, 0.1616161616161616...

  46. Irrational: A number that doesn’t end or repeat.

  47. Ex. pi, √(7), 1/3

  48. Greatest Common Factor: The largest number a group of numbers can be divided by.

  49. Ex. The greatest common factor of 50 & 75 is 25

  50. Least Common Multiple: The smallest number that a group of numbers can multiply into.

  51. Ex. The least common multiple of 4 & 7 is 28

  52. Percent increase/decrease: Find the difference between the two numbers. Then divide the difference by the original.

  53. Ex. Find the percent increase from 3 to 5: Difference is 2, original is 3. The percent increase is 2/3 or 66%.

  54. Probability: The chance you get the result you want. Divide the number of times you get what you want by the total times that is possible.

  55. Ex. If there are 5 red balls in a bag of 20 balls, what is the probability you randomly pull out a red ball?

  56. Want is 5, total is 20, 5/20 is 1/4 or 25%

  57. Sandwich problems AKA The Fundamental Counting Principle: Multiply the amount of items in each category by each other.

  58. Ex. If they ask how many possible combinations of sandwiches can be made with 4 types of bread, 3 types of cheese, and 5 types of meat: Multiply 4 X 3 X 5 = 60

2 Comments


zhao sunny
zhao sunny
6 hours ago

For mastering multiplication, especially up to the multiplication chart 1-100, having visual aids and practice tools is key. Online platforms often provide free printable charts that kids can use for reference, as well as interactive games and exercises. These resources can cater to different learning styles and make the process of memorizing times tables more dynamic. The combination of visual charts, practice opportunities, and gamified learning can significantly boost a child's understanding and recall of multiplication facts, setting a strong foundation for future math success.

Like

zhao sunny
zhao sunny
6 hours ago

A free multiplication chart is an invaluable aid for any student learning their times tables. Whether it's a printable chart they can keep on their desk or an interactive online version, seeing the patterns visually can greatly help with memorization. Many online resources also offer blank charts for practice or charts that go up to 1-100, providing a comprehensive tool. These resources make it easier for parents and teachers to support children as they build this fundamental math skill, often incorporating games to keep learning enjoyable.

Like
Featured Posts
Recent Posts
Archive
Search By Tags
Follow Us
  • Facebook Basic Square
  • Twitter Basic Square
  • Google+ Basic Square
bottom of page