This comprehensive formula sheet covers the essential mathematical concepts typically encountered in middle school. It's designed to be a handy reference for students, providing a quick overview of key formulas and their applications. Remember, understanding the underlying concepts is just as important as memorizing formulas!
Arithmetic
Number Properties
- Commutative Property: The order of numbers doesn't matter when adding or multiplying. a + b = b + a; a × b = b × a
- Associative Property: The grouping of numbers doesn't matter when adding or multiplying. (a + b) + c = a + (b + c); (a × b) × c = a × (b × c)
- Distributive Property: Multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products. a × (b + c) = (a × b) + (a × c)
- Identity Property of Addition: Adding zero to a number doesn't change its value. a + 0 = a
- Identity Property of Multiplication: Multiplying a number by one doesn't change its value. a × 1 = a
- Zero Property of Multiplication: Multiplying any number by zero results in zero. a × 0 = 0
Operations
- Addition: Combining quantities.
- Subtraction: Finding the difference between quantities.
- Multiplication: Repeated addition.
- Division: Splitting a quantity into equal parts.
- Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Algebra
Variables and Expressions
- Variable: A letter or symbol representing an unknown value.
- Algebraic Expression: A mathematical phrase containing variables, numbers, and operations. Example: 3x + 5y - 2
Equations and Inequalities
- Equation: A mathematical statement showing two expressions are equal. Example: 2x + 3 = 7
- Inequality: A mathematical statement comparing two expressions using < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Example: x + 2 > 5
Solving Equations
- Basic steps: Isolate the variable by performing inverse operations (addition/subtraction, multiplication/division) on both sides of the equation.
Geometry
Lines and Angles
- Complementary Angles: Two angles whose sum is 90°.
- Supplementary Angles: Two angles whose sum is 180°.
- Vertical Angles: Angles opposite each other when two lines intersect; they are equal.
- Linear Pair: Two adjacent angles that form a straight line; their sum is 180°.
Shapes
- Perimeter: The total distance around a polygon. (For rectangles: P = 2l + 2w)
- Area: The amount of space inside a two-dimensional shape.
- Rectangle: A = lw (length × width)
- Square: A = s² (side × side)
- Triangle: A = ½bh (½ base × height)
- Circle: A = πr² (π × radius²)
- Volume: The amount of space inside a three-dimensional shape.
- Rectangular Prism: V = lwh (length × width × height)
- Cube: V = s³ (side × side × side)
Data Analysis
Mean, Median, Mode, and Range
- Mean (Average): The sum of the numbers divided by the number of numbers.
- Median: The middle number when the numbers are arranged in order.
- Mode: The number that appears most frequently.
- Range: The difference between the highest and lowest numbers.
This formula sheet provides a foundation for middle school math. Remember to consult your textbook and teacher for more detailed explanations and examples. Practice regularly to master these concepts!
