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February 2, 2018

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26 Need to Know Math Concepts for the ACT

February 13, 2018

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

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

    2. 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.

    3. Mode: The number that appears most often.

  7. Powers, Exponents, and Roots

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

      1. Ex. x² * x⁵ = x⁷

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

      1. Ex. x⁷ / x² = x⁵

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

      1. (x²)⁴ = x⁸

    4. Any number raised to 0 equals 1

      1. Ex. 10170  = 1

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

    1. │-2 │= 2 and │2│ = 2

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

    1. 2, 5, 8, 11, 14 or 15, 10, 5, 0, -5

  10. Geometric sequence: There is a common multiple

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

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

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

    1. A diameter is the longest chord of any circle

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

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

  15. Consecutive: Numbers that follow each other directly.

    1. Ex. 5, 6, 7

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

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

    1. Ex. -1 or 17

  17. Real number: Any number that is not imaginary

    1. Ex. -17 , pi ,  3.666666667

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

    1. Ex. √(-16) = 4i or  √(-25) = 5i

    2. Remember: i² = -1

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

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

    2. 1 is not a prime number

    3. 2 is the only even prime number

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

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

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

    1. Ex. pi, √(7), 1/3

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

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

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

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

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

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

  25. 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.

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

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

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

    1. 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

 

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