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.
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