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What you'll find here

01

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02

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03

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Quick-lookup tables for common formulas, organized by subject.

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A glimpse at how lessons are structured on MathFlux.

Algebra

The Quadratic Formula

For ax² + bx + c = 0:

x = (-b ± √(b² - 4ac)) / (2a)

The value b² − 4ac (the discriminant) determines the nature of the roots:

  • > 0 — two distinct real roots
  • 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
  • = 0 — one repeated real root
  • < 0 — two complex conjugate roots
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Calculus

Fundamental Theorem of Calculus

This theorem links differentiation and integration:

∫ₐᵇ f(x) dx = F(b) − F(a)

Where F is any antiderivative of f, i.e. F′(x) = f(x). Consequences:

  • Integration and differentiation are inverse operations
  • Definite integrals reduce to antiderivative evaluation
  • Net signed area = difference of antiderivative values
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