formula chart for algebra 1

2 min read 01-02-2025

Algebra 1 can feel overwhelming with its numerous formulas and concepts. This comprehensive chart breaks down essential formulas, providing context and examples to help you master Algebra 1. Understanding these formulas is key to success in higher-level math courses.

Key Algebraic Concepts and Formulas

This section outlines core algebraic concepts and their corresponding formulas. Remember to always understand the why behind the formula, not just the how.

1. Order of Operations (PEMDAS/BODMAS)

This dictates the sequence in which calculations should be performed:

Parentheses/ Brackets
Exponents/ Orders
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Example: 3 + 2 × (4 - 1)² = 3 + 2 × 3² = 3 + 2 × 9 = 3 + 18 = 21

2. Real Numbers and Properties

Understanding the properties of real numbers is crucial for simplifying expressions and solving equations.

Commutative Property: a + b = b + a and a × b = b × a
Associative Property: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)
Distributive Property: a(b + c) = ab + ac
Identity Property: a + 0 = a and a × 1 = a
Inverse Property: a + (-a) = 0 and a × (1/a) = 1 (where a ≠ 0)

3. Linear Equations

Linear equations represent a straight line when graphed. The standard form is Ax + By = C.

Slope-Intercept Form: y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Point-Slope Form: y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a point on the line.
Slope Formula: m = (y₂ - y₁) / (x₂ - x₁)

Example: Find the slope of the line passing through points (2, 4) and (5, 10).

m = (10 - 4) / (5 - 2) = 6 / 3 = 2

4. Systems of Linear Equations

Solving systems of equations involves finding the values of variables that satisfy all equations simultaneously. Methods include substitution, elimination, and graphing.

Substitution: Solve one equation for one variable, then substitute it into the other equation.
Elimination: Multiply equations by constants to eliminate a variable when adding the equations.

5. Inequalities

Inequalities represent relationships where one quantity is greater than, less than, greater than or equal to, or less than or equal to another. Solving inequalities follows similar rules to solving equations, except that multiplying or dividing by a negative number reverses the inequality sign.

6. Polynomials

Polynomials are expressions involving variables raised to non-negative integer powers.

Adding and Subtracting Polynomials: Combine like terms.
Multiplying Polynomials: Use the distributive property (FOIL method for binomials).
Factoring Polynomials: Reverse the multiplication process to express the polynomial as a product of simpler expressions (e.g., greatest common factor, difference of squares, trinomial factoring).

7. Quadratic Equations

Quadratic equations are of the form ax² + bx + c = 0.

Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a
Factoring: Factor the quadratic expression and set each factor to zero.
Completing the Square: Manipulate the equation to create a perfect square trinomial.

8. Exponents and Radicals

Exponents represent repeated multiplication, while radicals (like square roots and cube roots) are the inverse operation.

Exponent Rules: xᵃ × xᵇ = x⁽ᵃ⁺ᵇ⁾; (xᵃ)ᵇ = x⁽ᵃˣᵇ⁾; xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾; x⁰ = 1 (x ≠ 0); x⁻ᵃ = 1/xᵃ
Radical Rules: √(a × b) = √a × √b; √(a / b) = √a / √b

This chart provides a foundation for understanding Algebra 1. Remember to practice regularly and seek help when needed. Consistent effort will lead to mastery of these concepts.