Geometry

  1. Area of a Triangle Formula
  2. Perimeter of a Triangle Formula
  3. Area of a Square Formula
  4. Perimeter of a Square Formula
  5. Area of a Rectangle Formula
  6. Perimeter of a Rectangle Formula
  7. Area of a Circle Formula
  8. Circumference of a Circle Formula
  9. Sector Area Formula
  10. Arc Length of a Circle Formula
  11. Area of a Parallelogram Formula
  12. Perimeter of a Parallelogram Formula
  13. Area of a Rhombus Formula
  14. Perimeter of a Rhombus Formula
  15. Area of a Trapezoid Formula
  16. Perimeter of a Trapezoid Formula
  17. Volume of a Cube Formula
  18. Surface Area of a Cube Formula
  19. Face Diagonal of a Cube Formula
  20. Space Diagonal of a Cube Formula
  21. Volume of a Cylinder Formula
  22. Surface Area of a Cylinder Formula
  23. Volume of a Cone Formula
  24. Surface Area of a Cone Formula
  25. Volume of a Sphere Formula
  26. Surface Area of a Sphere Formula
  27. Volume of a Prism Formula
  28. Surface Area of a Prism Formula
  29. Volume of a Pyramid Formula
  30. Surface Area of a Pyramid Formula
  31. Volume of a Torus Formula
  32. Surface Area of a Torus Formula
  33. Pythagorean Theorem Formula
  34. Distance between Two Points Formula
  35. Midpoint Formula
  36. Slope Formula
  37. Equation of a Line
  38. Slope-Intercept Form
  39. Point-Slope Form
  40. Standard Form of a Line
  41. Equation of a Circle
  42. Parabola, Ellipse, and Hyperbola Equations
  43. Transformations (Translation, Rotation, Reflection, Scaling)
  44. Similarity and Congruence Theorems

Algebra

  1. Quadratic Formula
  2. Discriminant of a Quadratic Equation
  3. Factoring Quadratics
  4. Completing the Square
  5. Difference of Squares
  6. Sum and Difference of Cubes
  7. Polynomial Long Division
  8. Synthetic Division
  9. Binomial Theorem
  10. Arithmetic Sequence Formulas
  11. Geometric Sequence Formulas
  12. Harmonic Sequence Formulas
  13. Exponential Growth and Decay
  14. Compound Interest Formula
  15. Simple Interest Formula
  16. Rational Expressions and Equations
  17. Linear Equations and Inequalities
  18. System of Equations (Substitution, Elimination)
  19. Matrix Operations (Addition, Subtraction, Multiplication)
  20. Determinants and Cramer’s Rule
  21. Inverse of a Matrix
  22. Eigenvalues and Eigenvectors

Calculus

  1. Power Rule
  2. Product Rule
  3. Quotient Rule
  4. Chain Rule
  5. Derivative of Exponential Functions
  6. Derivative of Logarithmic Functions
  7. Derivative of Trigonometric Functions
  8. Integration by Parts
  9. Integration by Substitution
  10. Definite Integrals
  11. Indefinite Integrals
  12. Fundamental Theorem of Calculus
  13. L’Hôpital’s Rule
  14. Taylor and Maclaurin Series
  15. Mean Value Theorem
  16. Riemann Sum
  17. Gradient and Directional Derivative
  18. Partial Derivatives
  19. Multiple Integrals (Double and Triple Integrals)
  20. Surface Integrals and Line Integrals
  21. Vector Calculus (Divergence, Curl)
  22. Stokes’ Theorem
  23. Green’s Theorem
  24. Laplace Transform
  25. Fourier Series and Transforms

Trigonometry

  1. Trigonometric Ratios (Sine, Cosine, Tangent, etc.)
  2. Inverse Trigonometric Functions
  3. Law of Sines
  4. Law of Cosines
  5. Sine Rule
  6. Cosine Rule
  7. Tangent Rule
  8. Angle Sum and Difference Identities
  9. Double Angle Formulas
  10. Half Angle Formulas
  11. Sum and Product Identities
  12. Pythagorean Identities
  13. Secant, Cosecant, and Cotangent Identities
  14. Polar Coordinates Conversion
  15. De Moivre’s Theorem

Statistics and Probability

  1. Mean, Median, and Mode
  2. Range, Variance, and Standard Deviation
  3. Z-Scores
  4. Normal Distribution
  5. Binomial Distribution
  6. Poisson Distribution
  7. Probability Density Functions (PDF)
  8. Cumulative Distribution Functions (CDF)
  9. Bayes’ Theorem
  10. Permutations and Combinations
  11. Factorial Notation
  12. Expected Value
  13. Variance of Random Variables
  14. Covariance and Correlation
  15. Hypothesis Testing
  16. Chi-Square Distribution
  17. T-Distribution
  18. Confidence Intervals
  19. Simple Linear Regression
  20. Multiple Regression Analysis
  21. ANOVA (Analysis of Variance)
  22. Standard Error

Logarithms and Exponentials

  1. Logarithmic Properties (Product, Quotient, Power Rules)
  2. Change of Base Formula
  3. Exponential Growth and Decay Models
  4. Compound Interest Formula
  5. Solving Exponential Equations
  6. Solving Logarithmic Equations
  7. Natural Logarithms and Euler’s Constant (e)
  8. Inverse Functions of Exponentials and Logarithms
  9. Logarithmic Differentiation

Vectors and Complex Numbers

  1. Vector Addition and Subtraction
  2. Scalar Multiplication
  3. Dot Product of Vectors
  4. Cross Product of Vectors
  5. Magnitude and Direction of a Vector
  6. Unit Vectors
  7. Complex Number Basics (Real and Imaginary Parts)
  8. Polar Form of Complex Numbers
  9. Euler’s Formula
  10. De Moivre’s Theorem
  11. Roots of Complex Numbers

Sequences and Series

  1. Arithmetic Sequence Formulas
  2. Geometric Sequence Formulas
  3. Harmonic Sequence Formulas
  4. Sum of an Arithmetic Series
  5. Sum of a Geometric Series
  6. Infinite Series and Convergence
  7. Power Series
  8. Taylor Series
  9. Maclaurin Series
  10. Binomial Series Expansion

Differential Equations

  1. First-Order Differential Equations
  2. Second-Order Differential Equations
  3. Homogeneous Equations
  4. Non-Homogeneous Equations
  5. Separation of Variables
  6. Laplace Transform for Differential Equations
  7. Eigenvalue Problems
  8. Fourier Series Solutions
  9. Partial Differential Equations (PDEs)
  10. Heat Equation, Wave Equation, and Laplace Equation

Number Theory

  1. Prime Factorization
  2. Greatest Common Divisor (GCD)
  3. Least Common Multiple (LCM)
  4. Modular Arithmetic
  5. Euclidean Algorithm
  6. Euler’s Totient Function
  7. Fermat’s Little Theorem
  8. Chinese Remainder Theorem
  9. Divisibility Rules
  10. Sum of Divisors
  11. Perfect Numbers and Amicable Numbers

Miscellaneous Topics

  1. Fibonacci Sequence
  2. Golden Ratio
  3. Fractals and Recursive Patterns
  4. Game Theory Basics
  5. Graph Theory (Vertices, Edges, Paths)
  6. Cryptography Basics (RSA Algorithm)
  7. Linear Programming and Optimization
  8. Markov Chains
  9. Probability Generating Functions
  10. Queue Theory Formulas
  11. Monte Carlo Methods
  12. Boolean Algebra