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Algebra

Equations, inequalities, functions, and polynomials.

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Geometry

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Shapes, angles, transformations, and proofs.

Calculus

Limits, derivatives, integrals, and series.

θ

Trigonometry

Sine, cosine, tangent, and their applications.

σ

Statistics

Data analysis, probability, and distributions.

Linear Algebra

Vectors, matrices, and transformations.

Number Theory

Primes, divisibility, and modular arithmetic.

δ

Differential Equations

First-order, second-order, and Laplace transforms.

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What you'll find here

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01

Step-by-step explanations

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Concepts are broken down with plain language so you understand the reasoning, not just the result.

02

Worked examples

Solved problems show how to apply each formula and technique in practice.

03

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Visual aids for abstract concepts — especially useful for geometry, calculus, and linear algebra.

04

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Exercises at different difficulty levels for each topic.

05

Formula reference sheets

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

06

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Sample content

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Algebra

The Quadratic Formula

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

Fundamental Theorem of Calculus

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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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