middle school math formula sheet

Lemon

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31-01-2025

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This comprehensive formula sheet covers the key mathematical concepts typically encountered in middle school. Designed for quick reference and effective study, this guide will help you conquer your math challenges and ace those tests! Remember, understanding the why behind the formulas is as important as memorizing them. Use this sheet as a tool to reinforce your learning, not replace it.

Arithmetic

Number Properties

• Commutative Property: The order of numbers doesn't change the sum or product. a + b = b + a; a * b = b * a
• Associative Property: The grouping of numbers doesn't change the sum or product. (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 by each addend and then adding the products. a * (b + c) = (a * b) + (a * c)
• Identity Property of Addition: Adding zero to any number doesn't change its value. a + 0 = a
• Identity Property of Multiplication: Multiplying any 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

Order of Operations (PEMDAS/BODMAS)

Remember the order: 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 number.
• Constant: A fixed value.
• Expression: A combination of numbers, variables, and operations. Example: 3x + 5

Equations

• Equation: A statement showing two expressions are equal. Example: 2x + 4 = 10
• Solving Equations: Isolate the variable by performing inverse operations on both sides of the equation.

Inequalities

• Inequality: A statement showing two expressions are not equal. Uses symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).

Geometry

Perimeter and Area

• Perimeter: The distance around a shape.
• Area: The space inside a shape.

Common Shapes:

• Rectangle:
  • Perimeter: P = 2l + 2w (l = length, w = width)
  • Area: A = lw
• Square:
  • Perimeter: P = 4s (s = side length)
  • Area: A = s²
• Triangle:
  • Perimeter: P = a + b + c (a, b, c = side lengths)
  • Area: A = (1/2)bh (b = base, h = height)
• Circle:
  • Circumference: C = 2πr (r = radius) or C = πd (d = diameter)
  • Area: A = πr²

Volume

• Volume: The amount of space a three-dimensional object occupies.

Common 3D Shapes:

• Rectangular Prism: V = lwh (l = length, w = width, h = height)
• Cube: V = s³ (s = side length)

Statistics

Mean, Median, Mode, and Range

• Mean: The average (sum of values divided by the number of values).
• Median: The middle value when the data is ordered.
• Mode: The value that appears most frequently.
• Range: The difference between the highest and lowest values.

This formula sheet provides a solid foundation for middle school math. Remember to consult your textbook and teacher for more detailed explanations and examples. Good luck!