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Formula Book for Quick Revision - AIEEE
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COMPENDIUM - MATHEMATICS
5
1. Partial Fractions
1
2. Inequalities
3. Complex Numbers
3.1 Modulus Amplitude form of a complex number
3.2 Properties of Modulus and amplitude
3.3 Geometrical Representation
3.4 Demoivre's Theorem
3.5 Euler's Formula
Cube Roots of Unity
4. Quadratic Equations and Expressions
4.1 The Roots of the Quadratic Equation
4.2 Relation Between the Roots and coefficients
4.3 Sign of the Roots
4.4 Nature of the Roots
1
4.5 Symmetrical function of the roots
4.6 Formation of a Quadratic Equation whose roots are known
4.7 Common Roots
5. Quadratic Expressions
5.1 Sign of a Quadratic expression
5.2 Maximum and Minimum Values
5.3 Geometrically, the equation y=ax2+bx+c represents a Parabola
5.4 Position of roots of a Quadratic Equation
6. Progressions
Definition
Means
7. Permutations and combinations
7.1 Permutation
7.6 Combination
8.Binomial Theorem
Series involving Binomial Coefficients
9.Determinant
Solutions of Linear Simultaneous equations by using determinants - Cramer's Rule
Consistency of Equations
Homogeneous linear Equations
Matrices
II. PROBABILITY
1.Mutually Exclusive Events
2.Independent Events
Conditional Probability
5.Baye's Rule
III.Trigonometry
1.Trigonometrical Ratios
2.Functions of Compound Angles
3.Transformations of sums into products and viceversa
4.Identities relating to the angles of a Triangle
1
5.Relations between the sides and Triangles of a Triangle
8.General Solutions of Equations
9.Inverse Circular Functions
IV. Analytical Geometry
1.Points
Conditions for three points to be collinear
2.Locus
3.(a) Standard forms of equations to a straight line
b) Other Forms
4.Position of a Point with respect to a line
5.a)Length of the Perpendicular
5.b Sign of the PErpendicular
6.Two or More Lines
7.Circles
7.1 Equation to the Circle
7.2 A Circle can be Made to Satisfy any three geometrical conditions such as
8. The Length of the Tangent from the point
9.Tangent to the Circle
10.Two or More Circles
11.Parabola
12.Ellipse
13.Hyperbola
Rectangular Hyperbola
V.DIFFERENTIAL CALCULUS
1. Functions
1.1 Classification of Functions
a.Single valued and Many Valued:
b.Implicit and Explicit Functions
c.Polynomial of X
d.Rational Function
e.Algebraic Function
1.2 Limits
a.Laws on Limits
b.Some Important Limits
1.3 Continuous and Discontinuous functions
2. Differentiation
2.1 Some general theorems on differentiation
Function
Derivative
3.Geometrical Meaning of Derivative
4. Derivative as a Measurer
5.Monotonic Functions
6.Maxima and Minima
7.Rolle's Theorem
8.Mean Value Theorem
9.L'Hospitals Rule
VI.INTEGRAL CALCULUS
1.Integration
2.Two Results on Integration
3.Methods of Integration
a) Integration by Parts
b)Integration of rational algebraic equations
c) Special cases
g)integration of Irrational functions
4.Properties of Definite Integrals
5.Reduction Formulae
6.Limit of a series as a definite integral
7.Areas and Volumes
8.Differential Equations
Linear differential Equation
VII.VECTOR ALGEBRA
1.Scalar and vector
2.Position Vector
3.Components of a Vector
4.Unit Vectors
5.Addition and Subtraction
Scalar product
Vector Product
Scalar Triple Product
Vector Triple Product
VIII.THREE DIMENSIONAL COORDINATE GEOMETRY
Section Formula
Standard form of the equation of a plane
Equation of a line in space
Skew Lines
Equations to a Sphere
COMPENDIUM- CHEMISTRY
1.PHYSICAL CHEMISTRY
1.Atomic Structure
Bohr's Model of Atom
Radical Probability Distribution Curves
Spherical (Radical) Nodes and Nodal Plane
Angular Node or Planar Node
2. BONDING AND MOLECULAR STRUCTURE
Dipole Moment of Polar Molecules
Percentage of Ionic Character of a Covalent bond
Dipole Moment and Percentage of ionic character
Predicting the type of hybridisation of the central atom in a molecule/ion other than complex Ions:
Predicting Geometry of species using VSEPR Theory
3.NUCLEAR CHEMISTRY
4.BEHAVIOUR OF GASES
5.STOICHIOMETRY AND VOLUMETRIC ANALYSIS
I.Mole Concept
2.Calculation of molecular Weight
3.Calculation of Equivalent Weight
4.Relationship Between Normality and Molarity
6.SOLUTIONS
1.Strength of Solutions
2.Colligative Properties
3.Raoult's Law
4.Relationship between mole fraction of the components of an ideal solution in the vapour pressure
5.Relationship Between mole fraction of a component in the vapour phase and total pressure of an ideal solution:
6.Calculation of boiling point of a liquid at a given pressure, when the boiling point at some pressure is given(use Clausius Clapayron equation)
4.Relationship Between different colligative properties
7.Chemical Equilibrium
1.Equilibrium Constant
2.Van't Hoff Equation
3.Ionic Equilibrium:Ostwald's dilution law
Relative Strengths of acids
Ionic Product of water
pH of buffer solutions
Buffer Capacity
Common Ion Effect
4. Hydrolysis of Salts
Salt of a weak acid and strong base
Salt of a weak base and strong acid
salt of a weak acid and weak base
8.Energetics
Variation of Enthalpy change or internal energy change with temperature
Trouton's Rule
Criteria of Sponataneity
9.CHEMICAL KINETICS
1.Order of a Reaction
2.Molecularity of a Reaction
3.Expressions for rate constant of different orders
4.Units of k Rate Constant
5.Some typical linear plots for reactions of different orders
a) Plots of rate vs concentration(Rate=k(concentration)
b) Plots from Integrated rate Equations(concentration vs Time)
c) Plots of Half Lives vs Concentration
d0 Expression for t1/2 for first order reaction
e)Expression for t1/2 for nth order Reaction
11.Calculation of order of reaction from two different half-lives:
Rate Law for Reversible Reaction
Application of Kholrausch's law
Faraday's Law of Electrolysis
1
I Law of Faraday
II Law of Faraday
II.Inorganic Chemistry
1.Periodic classification and Electronic Configuration
2.Atomic Radius
3.Ionisation Potential
4.Electron Affinity
5.Electronegativity
6.Oxidation States
7.Diagonal Relationship
Types of Compounds
According to VSEPR theory
Hydrides
Oxides
Carbides
Extractive Metallurgy
Gradation in Properties of elements and their compounds (Group Wise)
Transition Elements(d-Block Elements)
Coordination Compounds
III.Organic Chemistry
Concepts
ISomerism
Alkanes
Alkenes
Alkynes
Arenes
Halogen Compounds
Alcohols
Phenols
Ethers
Carbonyl Compounds
Carboxylic Acids
Nitrogen Compounds
Carbohydrates, Amino Acids and Polymers
COMPENDIUM PHYSICS
1.Units and Dimensions
1.1 Significant Figures
1.2 Error Analysis
2.Mechanics
2.1 Some Definitions
2.2 Graphical Solution of Rectilinear Motion problems
2.3 Equations for Rectilinear Motion
2.4 Motion Under Gravity
2.5 Relative Motion of two Particles
2.6 Dependent Motions
2.7 Vectors
2.8 Projectile Motion
2.9 Circular Motion
Motion in Vertical Circle
Newton's Second Law
Elevator or Lift
Systems of Varying Mess
Forces and Free Body Diagrams
Normal Reaction
Maximum Frictional Force
Pulley Systems
2.10 Fictitious Forces
2.11 Work, Power, Energy
Kinetic Energy
Potential Energy
The Work Energy Theorem
Conservative Force
2.12 Conservation of Momentum
i.Principle of Conservation of Momentum
ii.Newton's Experimental Law
Rigid Body Statics
Resultant of parallel Forces
i.Two like parallel Forces
ii.Two Unlike parallel forces
2.13 Rigid Body Dynamics
Centre of a Mass of a System of Particles
A System of two Bodies with force of Interaction only
Two Bodies with CM moving with force of interaction only
2.14 Angular Momentum
2.15 Gravitation
2.16 Elasticity
2.17 Simple Harmonic Motion
2.18 Fluid Mechanics
An Ideal Liquid
Pressure
Principle of Archimedes
Pascal's Law
Equation of Continuity
Bernoulli's Equation
Velocity of Efflux
Surface tension
Capillary Rise Method
Jaeger's Method
Jaeger's Method
Bonding Energy,Eo
Viscosity
Poissuille's formula
Stoke's Law
3.Thermal Physics
3.1 Expansions of Solids and Liquids
Temperature
Linear Expansivity
Thermal Stress
Calorimetry
3.2 Ideal Gases and Thermodynamics
Molar Heat Capacities
Slope of PV Diagram
3.3 Kinetic Theory of Gases
i.Pressure of an Ideal Gas
ii.Root mean Square Velocity
iii.Equipartition of Energy
Real or Van der Waal's gas
3.4 Transmission of Heat
Thermal Conductivity
Thermal Resistence
Stefan Boltzmann Law
Prevost's Theory
Kirchoff's Law in blackbody Radiation
4.Sound
4.1 Wave Motion
4.2 Vibrating Air Columns
4.3 Propagation of Sound in Solids
4.4 Propagation of Sound in Gases
4.5 Doppler Effect
4.6 Intensity of Sound
4.7 Beats
5.Electricity and Magnetism
5.1 Electrostatics
Electric Field due to dipole
a. at a point P on axis
b. At a point on equator (at distance r)
Electric dipole in uniform electric field
Electric Flux (and Gauss Law)
Near a thin flat sheet of charge of surface charge density
Near a conductor of any shape
Motion of a charged particle in an electric field
Force on a Surface charge per unit area
Electric field due to a ring of charge q at a distance x along the axial line
Electric field due to a disc of charge density, at a distance x along the axial line
Electric field to finite line of charge of linear charge density
Electric field due to a charged spherical shell of radius R
Electric field due to a solid sphere of charge density p
5.2 Electric Currents
Current
Ohm's Law
Joule's Law
KIrchoff's Rules
Combination of n cells in series
m cells in parallel
Wheat stone bridge
Terrestrial Magnetism
Meters to Measure current and voltage
Voltmeter
Inductance in groups
Series
Parallel
When Mutual M Inductance is Involved
5.3 Magnetism and Electromagnetic Induction
Lorentz Force
Flemings Left Hand Rule
Biosavart Rule
Magnetic Field Intensity
Permanent Magnets
Current Loop
Moving Coil Galvanometer
Electromagnetic Induction
Mutual Inductance
Cyclotron
CR Circuit
LS Oscillations (Analogy with Mass and Spring)
6.Optics
New Cartesian Conversion
6.1 Reflection and Refraction
Laws of Reflection
1
Rotation of Mirrors
Laws of Refraction
Refraction Through Prism
Deviation without Dispersion
i.Refraction at Spherical Surfaces
ii.Refraction at Curved Surface
6.2 Interference
7.Modern Physics
1
7.1 Atomic Physics
7.2 Nuclear Physics
i.Law of Radioactive Decay
ii.Variation of mass with velocity
Examination
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