→ Simples Formules → Einfache Formeln

Arithmetic

Numbers

→    Decomposition of an Integer Number in Prime Factors →    Simplification of a Fraction with an Integer Numerator and Denominator →    Additon of two Fractions with Integer positive Numerator and Denominator →    Subtraction of two Fractions with Integer positive Numerator and Denominator →    Largest common Divisor of two positive Integers →    Largest common Divisor of a set of positive Integers →    Smallest common Multiple of two positive Integers →    Smallest common Multiple of a set of positive Integers →    Convert Decimal to HexaDecimal (Base16) →    Convert Decimal to Binary (Base2) →    Convert HexaDecimal (Base16) to Decimal →    Convert Binary (Base2) to Decimal →    Convert a Number between any Bases

Combination Analysis

→   : Factorials: Product of the n first integers →   Arrangements of n éléments taken k at a time (in order) →   Combinations of n éléments taken k at a time (without order)

Algebra

Matrices and Determinants

→    Inverse Matrix of a two-dimensional Matrix →    Inverse Matrix of a three-dimensional Matrix →    Inverse Matrix of a four-dimensional Matrix →    Determinant of a two-dimensional Matrix →    Determinant of a three-dimensional Matrix →    Determinant of a four-dimensional Matrix →    Two-dimensional Matrix x two-dimensional Vector →    Three-dimensional Matrix x three-dimensional Vector →    Four-dimensional Matrix x four-dimensional Vector

Analysis

Calculus

→    Simple Integrals

Geometry

Areas

→    Any Triangle: Lengthes an Angles →    Any Triangle: Incircle →    Any Triangle: Circumcircle →    Any Triangle: Excircles →    Rectangular Triangle →    Isoceles Triangle →    Equilateral Triangle →    Trapeze →    Square →    Rectangle →    Parallelogram →    Rhombus →    Circle →   Power of an inner point for the circle →   Power of an outer point for the circle →    Circular Segment, Chord and circular Arc

Volume

→    Cube (regular hexahedron) →    Square Pyramid →    Straight-sided Pyramid trunk with square bases →    Regular Tetrahedron →    Sphere →    Sphere Segment →    Ellipsoïd →    Straight Cone →    Straight truncated Cone

→    Regular torus

Analytical Geometry

→    Straight-Line: Intersections with the Axes determined from the Equation →    Straight-Line: Equation determined from two points →    Two straight Lines: Intersection Point →    Parabola: Characteristics determined from the Equation →    Parabola: Equation determined from Focal Point and Guideline →    Parabola: Equation determined from the Y-value (Intersection with Y-axis) and the two Roots →    Parabola: Equation determined from the Coordinates of the Vertex and the two Roots →    Parabola: Equation determined from three Points →    Section of Parabola and non-vertical Line →    Intersection of two Parablolas →    Sine, Cosine, Tangent: Period, Frequency, Phase ..

Physics

Forces

→    Resultant of two non-parallel Forces →    Work, strength, and speed of a constant Force in the direction of Movement →    Work, power and speed of a constant Force not in the direction of Movement →    Moment of a Force, Momentum →    Weight at Sea Level →    The Archimedes Force in a Liquid →    The Archimedes Force in a Gas →    The Archimedes Buoyancy in floating Bodies →    The General Attraction Law (Newton) →    The Spring Law (Hooke) →    The Inclined Plane →    The Lever →    The Hoist

Motion

→    Uniform Unaccelerated Motion →    Uniformly Accelerated Motion →    Uniformly Accelerated Movement (2) →    Uniformly accelerated motion, inclined force to movement →    Vertical Drop →    Horizontal Throw →    Oblique Throw →    Uniform Circular Motion →    Simple Pendulum →    Simple Spring Pendulum

Pressure

→    The Pressure →    The Hydrostatic Pressure

Waves

→    The Progressive Transverse Wave →    The Stationary Wave →    DifFraction of a Wave through a Slot

Optics

→    Propagation of Light in a Refractive Medium: Refractive Index, Velocity, Wavelength →    Refraction (Law of Descartes) →    Diffraction by a Grating →    Refraction through a Prism →    Convergent Lens →    Divergent Lens

Acoustics

→    Acoustic Frequency emitted by a Vibrating String →    Sound generated by an Open Pipe →    Sound frequency generated by a Closed Pipe →    Doppler Effect in the Air (Galilean Reference System)

Electricity

→    Electron, Charge, Current and Current Density →    Coulomb's Law →    Resistance →    Ohm's Law: Resistance, Intensity, Voltage (Potential Difference),Power →    Two Resistors in series →    Two Resistors in parallel →    The Electric Field →    The Flat Capacitor: Characteristics →    Charging a Flat Capacitor across a Resistance circuit →    Unloading a Flat Capacitor in a Resistance circuit →    Two Capacitors connected in Series →    Two Capacitors connected in Parallel →    Empty Potentiometer →    Potentiometer with User Circuit

Magnetism

→    Magnetic Field Strength H generated by a straight line Current →    Magnetic Field Strength H generated by a Coil Current →    Magnetic Field Strength H in a Solenoid →    Relationship between Magnetic Flux Density and Magnetic Field Strength →    Inductance of a Magnet →    Two Magnetic Induction Coils connected in Series →    Two Solenoids connected in Parallel →    Force affecting a Charge moving in a Magnetic Field (Lorenz) →    Force acting on a linear conductor moved in a Magnetic field (Lorenz) →    Reciprocal Force between two Linear Conductors

The Atom

→    The Nucleus: Mass and Binding Energy of its Particles →    The Law of Radioactive Decay →    Radioactivity of the Nuclei →    Radiation Doses

Quantic

→    Propagation of Light in Empty Space: Waves and Photons →    The Photoelectric Effect →    The Atom of Bohr

Heat

→    Heat, Temperature and Heat Capacities →    Heat exchange, Thermal Balance →    Heat produced in Calorimeter, Heat output (thermal), Water Equivalent →    Determination of Heat Capacity and the Water Equivalent of a Calorimeter →    Linear Dilation of a Solid →    Dilatation of a Solid Surface →    Dilatation of a Solid Volume →    Change of the Density of a Solid with the TTemperature →    Dilatation of a Liquid →    Change of the Density of a Liquid with the Temperature →    Thermal Conductivity →    Thermal Radiation Strength

Chemistry

Molar Volume

→   Number of Moles of a Substance →   Number of Moles and molecules of a Substance →   Number of Moles of a gas

Gas

→    Law of Ideal Gases: n, P, V, and T →    Law of ideal gases: m, M, ρ n, P, V, and T →    Gas Laws according to Van der Waals: n, P, V, and T

Solutions

→    Molarity of a Solution (one Solute) →    Mass Concentration of a Solution (one Solute) →    Molality of a Solution (one Solute) →    Mole Fractions in a mixture of two substances →    All Concentrations of a Solution (one Solute) →    Ebullioscopy: Boiling Temperature Increase of a Solution (Molarity, non-dissociated Solute) →    Ebullioscopy: Boiling Temperature Increase of a Solution (Molarity, dissociated Solute, Van'tHoff Factor) →    Cryoscopy: Lowering of the Melting Temperature of a Solution (Molarity, non-dissociated Solute) →    Ebullioscopy: Lowering of the melting Temperature of a Solution (Molarity, dissociated Solute, Van'tHoff factor) →    Osmotic Pressure of the Dilute Aqueous Solution (Molarity, dissociated or non-dissociated Solute) →    Capillarity

Chemical Kinetics

→      Reaction Speed ​​:( Definition) →      Reaction of Order 0 (One Reagent A, v = k) →      Reaction of Order 1 (One Reagent A, v = kc A ) →      Reaction of Order 2 (One Reagent A, v = kc A 2 ) →      Reaction of Order 2 (Two Reagents A and B, v = kc A c B ) →      Reaction Constant as a Function of Temperature

Chemical Equilibrium

→   A ⇄ B →   A+B ⇄ C (eventually A=B)> (Note: in the case of 2A → C, thus A + A → C, it is necessary to double the Molarity of a A found in Equilibrium!) →   A ⇄ B+C (eventually C=B) →   A + B ⇄ C+D (eventually C=D or A=B) →   A + B + C ⇄ D (eventually A=B=C or A=B) →   D ⇄ A + B + C(eventually A=B=C or A=B) →   A + B + C ⇄ D + E (eventually A=B=C or A=B or D = E) →   D + E ⇄ A + B + C (eventually A=B=C or A=B or D = E) →   A + B + C ⇄ D + E + F (eventually A=B=C or A=B or D=E=F or D=E)

Thermochemistry

→   Volume work at constant pressure

Solubility

→     Product of Solubility of Ionic Substances

Colligative properties

→       Cryoscopy of the Undissociated Substance →       Cryoscopy of Dissociated Substance (Degree of Dissociation, Van't Hoff factor) →       Ebullioscopy of Undissociated Substance →       Ebullioscopy of Dissociated Substance (Degree of Dissociation, Van't Hoff factor) →       Osmotic Pressure of Undissociated Substance →       Osmotic Pressure of a Dissociated Substance (Degree of Dissociation, Van't Hoff factor)

pH

→       Definition of pH →       Definition of pOH, Relationship to pH →       pH Value of a Strong Acid →       pH of a Strong Base →       pH of a Weak Acid →       pH of a Weak Base →       Buffer pH →       pH Value when a Strong (mono) Acid (HCl, HBr, HI, HNO3) reacts with a Strong (mono)Base(NaOH, KOH) →       pH of an Ampholyte which is titrated by a strong (mono) Base(NaOH, KOH) →       pH Value in the Titration of a Strong (mono) Base(NaOH, KOH) with a Strong (mono) Acid, HBr, HI, HNO 3 ) →       pH Value in the Titration of a Weak (mono) Acid with a Strong (mono) Base(NaOH, KOH) →       pH Value in the Titration of a Weak (mono) Basewith a Strong (mono) Acid (HCl, HBr, HI, HNO 3 )

Economy

Loan

→       Constant Amortization - Declining Annuity →       Increasing Amortization - Constant Annuity →       Individual Payment, Annual Interest Rate and Interest Rates →       Periodic Investment, Periodic Interest and Interest Rates