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Formula Book for Quick Revision AIEEE
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COMPENDIUM MATHEMATICS
1. ALGEBRA
1. Partial Fractions
2.Inequalities
3. Complex Numbers
Quadratic Equations and Expressions
Quadratic Expressions
Progressions
7. Permutation and Combination
8. Binomial Theorem
9. Determinant
II.Probability
III. Trigonometry
1. Trigonometric Ratios
2. Transformations of sums into products and viceversa
3. Functions of Compound Angles
4. Identities relating to the angles of a triangle
5. Relations between the sides and angles of a triangle
6. Area of the triangle
7. Inradius (r) and Exradii (r1,r2,r3)
8. General Solutions of equations
9. Inverse Circular functions
IV. Analytical Geometry
1. Points
2. Locus
3. Standard forms of equations to a straight line
4. Position of a point with respect to a line
6. Two or more lines
5. Length of the Perpendicular
7. Circles
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
14. Rectangular Hyperbola
V. Differential Calculus
1. Functions
2. Differentiation
3. Geometrical Meaning of a derivative
4. Derivative as a rate measurer
5. Monotonic Functions
6. Maxima and Minima
7. Rolle's Theorem
8. L' Hospital's Rule
VI. Integral Calculus
1. Integration
2. Two Results on integration
3. Methods of Integration
Methods by SUbstitution
Some standard substitutions
Integral by Parts
Integration of rational equations
Special Cases
Integration of irritational 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
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VII. Vector Algebra
1. Scalar and Vector
2. Equal Vectors
3. Addition and Subtraction
4. Scalar Product
5. Vector product
6. Scalar Triple Product
7. Vector Triple Product
VIII.Three Dimensional Coordinate Geometry
2. Section Formula
3. Standard form of the equation of a plane
4. Equation of a line in space
5. Skew Lines
6. Equation to a Sphere
COMPENDIUM - CHEMISTRY
1. Physical Chemistry
1. Atomic Structure
2. Bohr's Model of Atom
Radial Probability Distribution curves
Spherical (radial) Nodes and nodal Plane
Angular node or planar node
2. Bonding and Molecular Structure
i) Dipole and molecular Structure
2. Percentage of ionic character of a covalent bond
3. Dipole moment and percentage of ionic character
4. Predicting the type of hybridization of the central atom in a molecule/ion other than complex ions
5. Predicting geometry of species using VSEPR theory
6. M.O.Theory
3. Nuclear Chemistry
Radioactivity
Disintegration Series
Isosters
4. Behaviour of Gases
5. Stoichiometry and Volumetric Analysis
1. Mole Concept
2. Calculation of molecular weight
3. Calculation of equivalent weight
4. Relationship between molality and molarity
6. Solutions
1. Strengths of solutions
2. Colligative Properties: Raoult's Law
3. Relationship between mole fraction of the components of an ideal solution in the vapour phase:
4. Relationship between mole fraction of a component in the vapour phase and total pressure of an ideal solution
5. Calculation of boiling point of a liquid at a given pressure, When the boiling point at same other pressure is given (use Calausius Clapeyron Equation)
6.Relationship between different colligative properties
7. Chemical Equilibrium
1. Equilibrium Constant
2. Ionic Equilibrium: Ostwald's dilution law
Relative strength of acids
Ionic Product of water
pH of buffer solutions
Buffer capacity
Common Ion Effect
3. Solubility Product
4. Hydrolysis of salts
a. Salt of a weak acid and strong base
b. Salt of a weak base and strong acid
c. Salt of a Weak acid and weak base
8.Energetics
1. Mathematical formula of first law
2. Expression of work of expansion
Work done in isothermal reversible expansion of an ideal gas
3. Application of first law to different types of processes
4. Variation of enthalpy change or internal energy change with temperature
5. Criteria of Spontaniety
9. Chemical Kinetics
1. Order of a reaction
2. Molecularity of a reaction
3. Expressions for rate constant for reaction of different orders:
5. Some typical linear plots of different orders
Plots of rate vs Concentration ( Rate =k (Concentration)
Some typical linear plots fr 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
11. Calculation of order of reaction from two different half- lives:
14. Rate law for reactions involving parallel or side reactions, both following first order reaction Kinetics
15. Rate law for reversible reaction
10. Electrochemistry
Application of Kholrausch's Law
11. Representation of a galvanic cell and construction of a galvanic cell
12. Nernest equation for electrode potential
EMF of a concentration cell
19. Faradays Law of Electrolysis
i. I Law of Faraday
ii. IInd Law of Faraday
21. Predicting products of Electrolysis
II. Organic Chemistry
1. Periodic classification and Electronic Configuration
2.Types of Compounds
3. Extractive Metallurgy
4. Gradation in properties of elements and their compounds (Group Wise)
5. Transition elements(d- Block Elements)
6. Coordination Compounds
III. Organic Chemistry
1. Concepts
2. Alkanes
3. Alkenes
4. Alkynes
5. Arenes
6. Halogen Compounds
7. Alcohols
8. Phenols
9. Ethers
10. Carbonyl Compounds
11. Carboxylic Acids
12. Nitrogen Compounds
13. Carbohydrates, Amino Acids and Polymers
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Compendium - Physics
1. Units and Dimensions
2. Mechanics
2.1 Some Definitions
Distance
Displacement
Velocity
Acceleration
Average Speed
Average Velocity
Average Acceleration
Uniform Velocity
Uniform Acceleration
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
Addition of Vectors
Subtraction of Vectors
Paralleleogram of Vectors
Relative Velocity
Resolution of Vectors
Sine Law of Triangle
Cosine Law of Triangle
Unit Vector
Direct Cosines of a vector
Products of scalars and vectors
2.8 Projectile Motion
2.9 Circular Motion
2.10 Fictitious Forces
2.11 Work, Power and Energy
2.12 Conservation of momentum
2.13 Rigid Body Dynamics
2.14 Angular momentum
2.15 Gravitatiion
2.16 Elasticity
2.17 Simple Harmonic Motion
2.18 Fluid Mechanics
3. Thermal Physics
3.1 Expansions of Solids and Liquids
3.2 Ideal gases and Thermodynamics
3.3 Kinetic Theory of gases
3.4 Transmission of Heat
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
5. Electricity and Magnetism
5.1 Electrostatics
5.2 Electric Currents
5.3 Magnetism and Electromagnetic Induction
6. Optics
New Cartesian Convention
Reflection and Refraction
4.2 Interference
7. Modern Physics
7.1 Atomic Physics
7.2 Nuclear physics
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