# 26 Need to Know Math Concepts for the ACT

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.

Sum: Addition

Difference: Subtraction

Product: Multiplication

Quotient: Division

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

Mean, Median, Mode

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

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.

Mode: The number that appears most often.

Powers, Exponents, and Roots

When you multiply common bases with exponents, add the exponents

Ex. x² * x⁵ = x⁷

When you divide common bases with exponents, subtract the exponents

Ex. x⁷ / x² = x⁵

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

(x²)⁴ = x⁸

Any number raised to 0 equals 1

Ex. 10170 = 1

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

│-2 │= 2 and │2│ = 2

Arithmetic sequence: There is a common difference or addition

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

Geometric sequence: There is a common multiple

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

Bisect: To cut an angle or line in half

Chord: Any line segment that both ends on a circle

A diameter is the longest chord of any circle

Complement: Two angles that add up to 90°

Supplement: Two angles that add up to 180°

Consecutive: Numbers that follow each other directly.

Ex. 5, 6, 7

Consecutive odd numbers: 5, 7, 9, 11

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

Ex. -1 or 17

Real number: Any number that is not imaginary

Ex. -17 , pi , 3.666666667

Imaginary numbers: The square root of a negative number

Ex. √(-16) = 4i or √(-25) = 5i

Remember: i² = -1

Prime Numbers: Can only be divided by 1 and themselves

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

1 is not a prime number

2 is the only even prime number

Rational number: Any number that ends or repeats.

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

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

Ex. pi, √(7), 1/3

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

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

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

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

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

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

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.

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

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

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

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