Formularium
Formula collection
Algebra
Contents
- Real numbers
- Number line
- Operator precedence
- Parenthesis
- Sign
- Parenthesis and sign
- Fractions
- Notable products
- Notable products
- Newton’s binomial
- Polynomial
- Zero polynomial
- First degree polynomial
- Second degree polynomial
- Polynomials of higher degree
- Exponents
- Definition exponents
- Negative exponent
- Sign of exponent
- Properties exponents
- Rationale exponent
- Square roots
- Definition square root
- Properties square root
- Roots
- Definition roots
- Properties roots
- Logarithms
- Definition logarithm
- Notable logarithms
- Properties logarithms
- Absolute value
- Absolute value
- Properties absolute value
- Divisibility
- Divisibility
- Common multiples/divisors
- Euclidean Division
- Prime Numbers
- Summations
- Definition
- Operations on summations
- Summation identities
Linear algebra
Contents
Trigonometry
Contents
- Angle
- Degree
- Radian
- Angles
- Connection between radians and degrees
- Trigonometric numbers
- Trigonometric numbers in a right triangle
- Trigonometric numbers in the unit circle
- Definitions
- Pythagorean identities
- Common trigonometric values
- Related angles
- Triangle measurement
- Right triangles
- Random triangles
- Trigonometric identities
- Pythagorean identities
- Angle sum and difference identities
- Double-angle formulae
- Power-reduction formulae
- Tangent half-angle substitution
- Simpson’s formulas
Geometry
Contents
- Plane Geometry
- Points
- Lines
- Triangles
- Circles
- Plane Figures
- Concepts
- Figures
- Synthetic Solid Geometry
- Axioms
- Relative position
- Analytic Solid Geometry
- Equations of a line
- Equations of a plane
- Relative position of lines
- Relative position of a line and a plane
- Relative position of planes
- Solids
- Concepts
- Figures
- Vectors
- Definitions of vectors
- Adding vectors
- Scalar multiplication of vectors
- Norm of a Vector
- Dot Product of Two Vectors
Real functions
Contents
- Real Functions
- Definitions
- Characteristics of Real Functions
- Polynomials
- Polynomial
- Degree after operations
- Euclidean Division
- Polynomial Functions
- General
- Polynomial Functions of Degree 0
- Polynomial Functions of Degree 1
- Polynomial Functions of Degree 2
- Rational functions
- Basic function
- Homographic functions
- Rational functions
- Exponential Functions
- Exponential Functions
- Logarithmic Functions
- Logarithmic Function
- Main Property of Logarithmic Functions
- Trigonometric Functions
- Sine Function
- Cosine Function
- Tangent Function
Analyse
Contents
- Limits
- Definition
- Limit properties
- Calculating infinity
- Indeterminate forms
- Properties of limits
- Limits of polynomials
- Limits of rational functions
- Trig limits
- Special limits
- L’Hospital’s rule
- Asymptotes
- Vertical asymptotes (V.A.)
- Horizontal asymptotes (H.A.)
- Oblique asymptotes (S.A.)
- Derivatives
- Definition of the derivative
- Base derivatives
- Differentiation of exponential and logaritmic functions
- Differentiation of trigonometric functions
- Differentiation formulas
- Higher Derivatives
- Function Analysis
- Tangent Line
- Increasing and Decreasing of a Function
- Integrals
- Definitions
- Properties of integrals
- Base integrals
- Integration rules
- Integration of Rational Functions
- Applications of Definite Integrals
Complex Numbers
Contents
- Complex Numbers
- Definitions of Complex Numbers
- Operations on Complex Numbers
- Powers of Complex Numbers
- Square Root of a Complex Number
- Complex Quadratic Equations
- Binomial Equations
- Polar Form
- Polar Form
- Operations in Polar Form
- Euler’s Formula
- de Moivre’s Formula
- Polynomials with Complex Coefficients
- Definitions
- Divisibility
Statistics
Physics
Contents
- Optics
- Snell’s Law
- Lens Formula
- Pressure
- Hydrostatic Pressure
- Buoyant Force in a Fluid
- Gas Laws
- Ideal Gas Law
- Boyle’s Law
- Thermodynamics
- First Law of Thermodynamics
- Heat Transfer
- Heat Capacity
- Heat of Fusion
- Heat of Vaporization
- Electrostatics
- Coulomb’s Law
- Electric Field Due to a Point Charge
- Electric Potential Due to a Point Charge
- Relationship Between Electric Field and Potential
- Capacitance of a Capacitor
- Energy Stored in a Capacitor
- Continuity Equation (Gauss’ Law for Electricity)
- Electromagnetism
- Lorentz force on a moving charge in a magnetic field
- Lorentz force on a current-carrying conductor in a magnetic field
- Magnetic field around a long straight current-carrying wire
- Magnetic field in the core of a long solenoid
- Magnetic flux
- Biot-Savart law
- Ampère’s law
- Faraday’s law of electromagnetic induction
- Lenz’s law
- Maxwell’s equations
- Speed of light in vacuum
- Nuclear Physics
- Activity of a Radioactive Substance
- Number of Remaining Nuclei After Time \(t\)
- Relationship of the Decay Constant with the Half-life
- Kinematics
- Displacement with Constant Velocity
- Velocity with a Constant Acceleration
- Displacement with a Constant Acceleration
- Dynamics
- Newton’s Second Law
- Newton’s Law of Universal Gravitation
- Weight of an Object Near the Earth’s Surface
- Work Done by a Force
- Power
- Spring Force
- Kinetic Energy
- Potential Energy in a Gravitational Field
- Potential Energy in a Spring
- Centripetal Acceleration
- Oscillations and Waves
- Simple Harmonic Oscillation
- Wave Equation
- Relation between Angular Frequency and Period
- Relation between Wavelength, Speed, and Frequency
- Period of a Simple Harmonic Oscillation
- Harmonic Frequencies in a Closed Pipe
- Sound
- Speed of Sound in a Medium
- Doppler Effect for a Stationary Observer
- Sound Intensity
- Sound Level
- Physical Constants
- Atmospheric Pressure
- Gravitation
- Speed of Light in Vacuum
- Planck’s Constant
- Gas Constant
- Charge of an Electron
- Density
- Thermal Properties
- Electrostatics
- Energy
- Masses of Fundamental Particles