College Algebra
Formula & Equation Cheat Sheet
Introduction — The Foundation of All STEM Mathematics ›
This College Algebra Cheat Sheet condenses the equations, identities,
and algebra skills that power every future STEM course.
Mastering this page means easier Calculus, clearer Physics, and faster problem solving across engineering and computer science.
Continue full lessons at thestemmajor.com.
Mastering this page means easier Calculus, clearer Physics, and faster problem solving across engineering and computer science.
Continue full lessons at thestemmajor.com.
Symbols and Notations ›
Algebra Reference Sheet | AuthorJonathanDavid.com
Algebra
General Symbols and Notations
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| Symbol | Meaning | Example |
|---|---|---|
| = | Equal | 0 = 0 |
| ≠ | Not equal | 1 ≠ 0 |
| ± | Plus or Minus | x = ±a ⇒ x = a or x = −a |
| ∓ | Minus or Plus | x = ∓a ⇒ x = −a or x = a |
| iff, ⇔ | If and only if | p ⇒ q and q ⇒ p then p ⇔ q |
| ⇒ | Implies | p ⇒ q |
| < | Less than | x − a < 0 ⇒ x < a |
| ≤ | Less than equal | x − a ≤ 0 ⇒ x ≤ a |
| ≥ | Greater than equal | x − a ≥ 0 ⇒ x ≥ a |
| > | Greater than | x − a > 0 ⇒ x > a |
| × | Times | 2 × 3 = 6 |
| * or · | Multiplication | 2 * 3 = 6 or 2 · 3 = 6 |
| ( )( ) | Multiplication | (2)(3) = 6 |
| = 6 | ||
| [ ][ ] | Multiplication | [2][3] = 6 |
| [( )( )]^( )( ) | Exponential Multiplication | [(2)(3)]³⁻²(3 − 2) = 6 |
| ∞ | Infinity | Never ends |
| Δ | Displacement or change of | Δx = x − x₀ |
| Σ | Summation | Σₙ₌₁³ aₙxⁿ = a₁x¹ + a₂x² + a₃x³ |
| θ | Theta reserved for angles | θ = π/4 = 45° |
| f(x) | Function of x | f(x) = xⁿ + … |
| f(x, y) | Function of x and y | f(x, y) = (xy)ⁿ + … |
| ∈ | In or element of | x ∈ [a, b) means a ≤ x < b |
| ∀ | For all | ∀x (for all x) |
| ∴ | Therefore | x − a = 0 ⇔ x = a ∴ x = a |
| ∵ | Because | ∵ x − a = 0, x = a |
| ≡ | Equivalent | (−2, 3) ≡ −2 < x < 3 |
| ( , ) | Open interval | (−2, 3) = −2 < x < 3 |
| [ , ] | Closed interval | [2, 3] = 2 ≤ x ≤ 3 |
| ⊂ | Proper subset | A ⊂ B ⇒ B ⊄ A |
| ⊆ | Subset (equal) | A ⊆ B ⇒ A = B |
| [ , ) | Half-open interval | [1, 4) = 1 ≤ x < 4 |
| { … } | Set of numbers | {1, 3, 5, 7} |
| ∪ | Union | {1,2,3} ∪ {3,4,5} = {1,2,3,4,5} |
| ∩ | Intersection | {1,2,3} ∩ {3,4,5} = {3} |
| ℝ | Real numbers | (−∞, ∞) |
| P(x₀, y₀) | Point | (1, f(1)) |
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Functions, Graphs, and Interpretation ›
Understanding functions visually allows you to predict behavior,
check answers instantly, and prepare for calculus concepts.
Why Algebra Determines STEM Success ›
Students who become fluent in algebra reduce study time,
increase exam scores, and transition smoothly into calculus,
physics, and programming logic.
Discover more from Author Jonathan David
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