JEE ADVANCED Exam Preparation Program

General Topics

• Concept of atoms and molecules
• Dalton’s atomic theory
• Mole concept
• Chemical formulae
• Balanced chemical equations
• Calculations based on the mole concept and stoichiometry
  
  • Oxidation–reduction reactions
  • Neutralisation reactions
  • Displacement reactions
    
• Concentration terms:
  
  • Mole fraction
  • Molarity
  • Molality
  • Normality

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States of Matter: Gases and Liquids

Gaseous State

• Gas laws and the ideal gas equation
• Absolute scale of temperature
• Deviation from ideality
• van der Waals equation
• Kinetic theory of gases
  
  • Average velocity
  • Root mean square velocity
  • Most probable velocity
  • Relation with temperature
    
• Law of partial pressures
• Diffusion of gases

Intermolecular Interactions & Liquids

• Types of intermolecular interactions
• Distance dependence of intermolecular forces
• Effect on physical properties
• Vapour pressure
• Surface tension
• Viscosity

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Atomic Structure

• Bohr model
• Spectrum of hydrogen atom
• Wave–particle duality
• de Broglie hypothesis
• Heisenberg uncertainty principle
• Quantum mechanical model of hydrogen atom (qualitative)
  
  • Energies
  • Quantum numbers
  • Wave function and probability density (plots only)
  • Shapes of s, p and d orbitals
    
• Aufbau principle
• Pauli’s exclusion principle
• Hund’s rule

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Chemical Bonding and Molecular Structure

• Orbital overlap and covalent bond
• Hybridisation (s, p and d orbitals only)
• Molecular orbital energy diagrams (homonuclear diatomic species up to Ne₂)
• Hydrogen bonding
• Polarity of molecules
• Dipole moment
• VSEPR model
• Shapes of molecules:
  
  • Linear
  • Angular
  • Trigonal planar
  • Square planar
  • Pyramidal
  • Square pyramidal
  • Trigonal bipyramidal
  • Tetrahedral
  • Octahedral

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Chemical Thermodynamics

• Intensive and extensive properties
• State functions
• First law of thermodynamics
• Internal energy
• Work (pressure–volume work only)
• Heat
• Enthalpy
• Heat capacity
• Standard state
• Hess’s law
• Enthalpy of reaction, fusion, vaporization, lattice enthalpy
• Second law of thermodynamics
• Entropy
• Gibbs free energy
• Criteria for equilibrium and spontaneity

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Chemical and Ionic Equilibrium

Chemical Equilibrium

• Law of mass action
• Significance of ΔG and ΔG°
• Equilibrium constant (Kp and Kc)
• Reaction quotient
• Le Chatelier’s principle
  
  • Effect of concentration
  • Effect of temperature
  • Effect of pressure

Ionic Equilibrium

• Solubility product (Ksp) and applications
• Common ion effect
• pH and buffer solutions
• Acids and bases (Brønsted and Lewis concepts)
• Hydrolysis of salts

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Electrochemistry

• Electrochemical cells and cell reactions
• Standard electrode potentials
• Electrochemical work
• Nernst equation
• Electrochemical series
• EMF of galvanic cells
• Faraday’s laws of electrolysis
• Electrolytic conductance
  
  • Specific conductivity
  • Equivalent conductivity
  • Molar conductivity
    
• Kohlrausch’s law
• Batteries:
  
  • Primary batteries
  • Secondary batteries
  • Fuel cells
    
• Corrosion

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Chemical Kinetics

• Rate of chemical reactions
• Order and molecularity
• Rate law
• Rate constant
• Half-life
• Differential and integrated rate equations
  
  • Zero order reactions
  • First order reactions
    
• Temperature dependence of rate constant
  
  • Arrhenius equation
  • Activation energy
    
• Catalysis:
  
  • Homogeneous catalysis
  • Heterogeneous catalysis
  • Activity and selectivity of solid catalysts
  • Enzyme catalysis and its mechanism

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Solid State

• Classification of solids
• Crystalline state
• Seven crystal systems
  
  • Cell parameters: a, b, c
  • Angles: α, β, γ
    
• Close-packed structures of solids
  
  • Cubic close packing (ccp/fcc)
  • Hexagonal close packing (hcp)
    
• Packing in:
  
  • Face-centred cubic (fcc)
  • Body-centred cubic (bcc)
  • Hexagonal close-packed (hcp) lattices
    
• Nearest neighbours
• Ionic radii and radius ratio
• Point defects

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Solutions

• Henry’s law
• Raoult’s law
• Ideal and non-ideal solutions
• Colligative properties:
  
  • Lowering of the vapour pressure
  • Elevation of boiling point
  • Depression of freezing point
  • Osmotic pressure
    
• van’t Hoff factor

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Surface Chemistry

Adsorption

• Elementary concepts of adsorption
• Physisorption
• Chemisorption
• Freundlich adsorption isotherm

Colloids

• Types of colloids
• Methods of preparation
• General properties

Emulsions & Micelles

• Emulsions (definitions and examples)
• Surfactants
• Micelles

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Classification of Elements and Periodicity in Properties

• Modern periodic law
• Present form of the periodic table
• Electronic configuration of elements
• Periodic trends in:
  
  • Atomic radius
  • Ionic radius
  • Ionization enthalpy
  • Electron gain enthalpy
  • Valence
  • Oxidation states
  • Electronegativity
  • Chemical reactivity

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Hydrogen

• Position of hydrogen in the periodic table
• Occurrence and isotopes
• Preparation, properties, and uses of hydrogen
• Hydrides:
  
  • Ionic hydrides
  • Covalent hydrides
  • Interstitial hydrides
    
• Physical and chemical properties of water
• Heavy water
• Hydrogen peroxide:
  
  • Preparation
  • Reactions
  • Uses
  • Structure
    
• Hydrogen as a fuel

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s-Block Elements

Alkali and Alkaline Earth Metals

• Reactivity towards:
  
  • Air
  • Water
  • Dihydrogen
  • Halogens
  • Acids
    
• Reducing nature (including solutions in liquid ammonia)
• Uses of these elements
  

Compounds

• General characteristics of:
  
  • Oxides
  • Hydroxides
  • Halides
  • Salts of oxoacids

Anomalous Behaviour

• Lithium
• Beryllium

Important Compounds

Sodium Compounds:

• Sodium carbonate
• Sodium chloride
• Sodium hydroxide
• Sodium hydrogen carbonate

Calcium Compounds:

• Calcium oxide
• Calcium hydroxide
• Calcium carbonate
• Calcium sulphate

(Preparation, properties, and uses)

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p-Block Elements

General Trends (Groups 13–17)

• Oxidation states
• Trends in chemical reactivity
• Anomalous properties of:
  
  • Boron
  • Carbon
  • Nitrogen
  • Oxygen
  • Fluorine

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Group 13

• Reactivity towards acids, alkalis, halogens
• Preparation, properties, and uses of:
  
  • Borax
    Orthoboric acid
  • Diborane
  • Boron trifluoride
  • Aluminium chloride
  • Alums
    
• Uses of boron and aluminium

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Group 14

• Reactivity towards water and halogens
• Allotropes of carbon and their uses
• Preparation, properties, and uses of:
  
  • Carbon monoxide
  • Carbon dioxide
  • Silicon dioxide
  • Silicones
  • Silicates
  • Zeolites

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Group 15

• Reactivity towards hydrogen, oxygen, halogens
• Allotropes of phosphorus
• Preparation, properties, and uses of:
  
  • Dinitrogen
  • Ammonia
  • Nitric acid
  • Phosphine
  • Phosphorus trichloride
  • Phosphorus pentachloride
    
• Oxides of nitrogen
• Oxoacids of phosphorus

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Group 16

• Reactivity towards hydrogen, oxygen, halogens
• Simple oxides
• Allotropes of sulphur
• Preparation/manufacture, properties, and uses of:
  
  • Dioxygen
  • Ozone
  • Sulphur dioxide
  • Sulphuric acid
    
• Oxoacids of sulphur

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Group 17

• Reactivity towards hydrogen, oxygen, metals
• Preparation/manufacture, properties, and uses of:
  
  • Chlorine
  • Hydrogen chloride
  • Interhalogen compounds
    
• Oxoacids of halogens
• Bleaching powder

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Group 18

• Chemical properties and uses
• Compounds of xenon with fluorine and oxygen

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d-Block Elements

• Oxidation states and their stability
  
• Standard electrode potentials
  
• Interstitial compounds
  
• Alloys
  
• Catalytic properties
  
• Applications
  
• Preparation, structure, and reactions of oxoanions of:
  
  • Chromium
    
  • Manganese
    

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f-Block Elements

• Lanthanoid contraction
  
• Actinoid contraction
  
• Oxidation states
  
• General characteristics
  

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Coordination Compounds

• Werner’s theory
  
• Nomenclature
  
• Isomerism:
  
  • Cis–trans isomerism
    
  • Ionization isomerism
    
• Hybridisation and geometries of mononuclear coordination compounds:
  
  • Linear
    
  • Tetrahedral
    
  • Square planar
    
  • Octahedral
    
• Bonding:
  
  • Valence Bond Theory (VBT)
    
  • Crystal Field Theory (CFT) (octahedral and tetrahedral fields)
    
• Magnetic properties (spin-only formula)
  
• Colour of 3d-series coordination compounds
  
• Ligands and spectrochemical series
  
• Stability of coordination compounds
  
• Importance and applications
  
• Metal carbonyls
  

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Isolation of Metals

• Metal ores and their concentration
  
• Extraction of crude metal from concentrated ores:
  
  • Thermodynamic principles (Iron, Copper, Zinc)
    
  • Electrochemical principles (Aluminium)
    
• Cyanide process (Silver and Gold)
  
• Refining of metals
  

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Principles of Qualitative Analysis

Cations (Groups I to V)

• Ag⁺
  
• Hg₂²⁺
  
• Cu²⁺
  
• Pb²⁺
  
• Fe³⁺
  
• Cr³⁺
  
• Al³⁺
  
• Ca²⁺
  
• Ba²⁺
  
• Zn²⁺
  
• Mn²⁺
  
• Mg²⁺
  

Anions

• Nitrate
  
• Halides (excluding fluoride)
  
• Carbonate and bicarbonate
  
• Sulphate
  
• Sulphide
  

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Environmental Chemistry

• Atmospheric pollution
  
• Water pollution
  
• Soil pollution
  
• Industrial waste
  
• Strategies to control environmental pollution
  
• Green chemistry
  

Basic Principles of Organic Chemistry

• Hybridisation of carbon
• Sigma (σ) and pi (π) bonds
• Shapes of simple organic molecules
• Aromaticity
• Structural and geometrical isomerism
• Stereoisomerism:
  
  • Enantiomers
  • Diastereomers
  • Meso compounds
    (R,S and E,Z configurations excluded)
    
• Determination of empirical and molecular formulae (combustion method only)
• IUPAC nomenclature:
  
  • Hydrocarbons
  • Simple cyclic hydrocarbons
  • Mono-functional and bi-functional derivatives
    
• Hydrogen bonding effects
• Electronic effects:
  
  • Inductive effect
  • Resonance
  • Hyperconjugation
    
• Acidity and basicity of organic compounds
• Reactive intermediates:
  
  • Carbocations
  • Carbanions
  • Free radicals
    
• Homolytic and heterolytic bond cleavage

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Alkanes

• Homologous series
• Physical properties:
  
  • Melting points
  • Boiling points
  • Density
  • Effect of branching
    
• Conformations:
  
  • Ethane (Newman projection)
  • Butane (Newman projection)
    
• Preparation:
  
  • From alkyl halides
  • From aliphatic carboxylic acids
    
• Reactions:
  
  • Combustion
  • Halogenation (including allylic and benzylic halogenation)
  • Oxidation

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Alkenes and Alkynes

• Physical properties:
  
  • Boiling points
  • Density
  • Dipole moments
    
• Preparation by elimination reactions
• Acid-catalysed hydration (stereochemistry excluded)
• Metal acetylides
• Reactions:
  
  • With KMnO₄
  • With ozone (ozonolysis)
  • Reduction
  • Electrophilic addition with X₂, HX, HOX (X = halogen)
  • Peroxide effect
    
• Cyclic polymerisation of alkynes

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Benzene

• Structure of benzene
• Electrophilic substitution reactions:
  
  • Halogenation
  • Nitration
  • Sulphonation
  • Friedel–Crafts alkylation
  • Friedel–Crafts acylation
    
• Effect of directing groups (monosubstituted benzene)

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Phenols

• Physical properties
• Preparation
• Electrophilic substitution reactions:
  
  • Halogenation
  • Nitration
  • Sulphonation
    
• Reimer–Tiemann reaction
• Kolbe reaction
• Esterification
• Etherification
• Aspirin synthesis
• Oxidation and reduction reactions

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Alkyl Halides

• Rearrangement reactions of alkyl carbocation
• Grignard reactions
• Nucleophilic substitution reactions
• Stereochemical aspects of substitution

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Alcohols

• Physical properties
• Reactions:
  
  • Esterification
  • Dehydration (formation of alkenes and ethers)
  • Reaction with sodium
  • Reaction with phosphorus halides
  • Reaction with ZnCl₂/concentrated HCl
  • Reaction with thionyl chloride
    
• Conversion of alcohols into:
  
  • Aldehydes
  • Ketones
  • Carboxylic acids

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Ethers

• Preparation by Williamson’s synthesis
• C–O bond cleavage reactions

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Aldehydes and Ketones

Preparation:

• From acid chlorides and nitriles
• Aldehydes from esters
• Benzaldehyde from toluene and benzene

Reactions:

• Oxidation and reduction
• Oxime and hydrazone formation
• Aldol condensation
• Cannizzaro reaction
• Haloform reaction
• Nucleophilic addition reactions with RMgX, NaHSO₃, HCN, alcohols, and amines

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Carboxylic Acids

Physical Properties

Preparation:

• From nitriles
• From Grignard reagents
• Hydrolysis of esters and amides
• Preparation of benzoic acid from alkylbenzenes

Reactions:

• Reduction
• Halogenation
• Formation of esters
• Formation of acid chlorides
• Formation of amides

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Amines

Preparation:

• From nitro compounds
• From nitriles
• From amides

Reactions:

• Hoffmann bromamide degradation
• Gabriel phthalimide synthesis
• Reaction with nitrous acid
• Azo coupling reaction of diazonium salts of aromatic amines
• Sandmeyer and related reactions of diazonium salts
• Carbylamine reaction
• Hinsberg test
• Alkylation and acylation reactions

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Haloarenes

Reactions:

• Fittig reaction
• Wurtz–Fittig reaction
• Nucleophilic aromatic substitution in haloarenes and substituted haloarenes
  (excluding benzyne mechanism and cine substitution)

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Biomolecules

Carbohydrates:

• Classification
• Monosaccharides and disaccharides (glucose and sucrose)
• Oxidation and reduction
• Glycoside formation
• Hydrolysis of disaccharides (sucrose, maltose, lactose)
• Anomers

Proteins:

• Amino acids
• Peptide linkage
• Structure of peptides (primary and secondary)
• Types: fibrous and globular proteins

Nucleic Acids:

• Chemical composition and structure of DNA and RNA

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Polymers

• Types of polymerization: addition and condensation
• Homopolymers and copolymers
• Natural rubber and cellulose
• Nylon, Teflon, Bakelite, PVC
• Biodegradable polymers
• Applications of polymers

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Chemistry in Everyday Life

• Drug–target interaction
• Therapeutic action and examples (structures excluded) of:
  
  • Antacids
  • Antihistamines
  • Tranquilizers
  • Analgesics
  • Antimicrobials
  • Antifertility drugs
    
• Artificial sweeteners (names only)
• Soaps, detergents, and cleansing action

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Practical Organic Chemistry

• Detection of elements: nitrogen, sulphur, and halogens
• Detection and identification of functional groups:
  
  • Hydroxyl (alcoholic and phenolic)
  • Carbonyl (aldehyde and ketone)
  • Carboxyl
  • Amino
  • Nitro

Sets, Relations and Functions

Sets:

• Representation of sets
• Types of sets: empty, finite, infinite
• Algebra of sets
• Union, intersection, complement, difference, symmetric difference
• Algebraic properties of set operations
• De Morgan’s laws (for a finite number of sets)
• Practical problems based on set operations

Relations:

• Cartesian product of finite sets
• Ordered pairs
• Domain and codomain
• Equivalence relation

Functions:

• Function as a special case of relation
• Functions as mappings
• Domain, codomain and range
• One-to-one, onto, into functions
• Even and odd functions
• Invertible functions
• Special functions:
  
  • Polynomial
  • Trigonometric
  • Exponential
  • Logarithmic
  • Power
  • Absolute value
  • Greatest integer
    
• Sum, difference, product, and composition of functions

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Algebra

Complex Numbers:

• Algebra of complex numbers
• Addition, multiplication, conjugation
• Polar representation
• Modulus and principal argument
• Triangle inequality
• Cube roots of unity
• Geometric interpretation

Quadratic Equations:

• Fundamental Theorem of Algebra (statement only)
• Quadratic equations with real coefficients
• Relations between roots and coefficients
• Formation of quadratic equations
• Symmetric functions of roots

Sequences and Series:

• Arithmetic progression (AP)
• Geometric progression (GP)
• Arithmetic and geometric means
• Sum of finite AP and GP
• Infinite geometric series
• Sum of the first n natural numbers
• Sum of squares and cubes of the first n natural numbers

Other Topics:

• Logarithms and their properties
• Permutations and combinations
• Binomial theorem (positive integral index)
• Properties of binomial coefficients

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Matrices

• Matrices as rectangular arrays of real numbers
• Equality of matrices
• Addition and scalar multiplication
• Matrix multiplication
• Transpose of a matrix
• Elementary row and column transformations
• Determinant of a square matrix (order ≤ 3)
• Adjoint and inverse of matrix (order ≤ 3)
• Properties of matrix operations
• Diagonal, symmetric, and skew-symmetric matrices
• Solution of simultaneous linear equations (two or three variables)

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Probability and Statistics

Probability:

• Random experiments
• Sample space
• Types of events: impossible, simple, compound
• Addition and multiplication rules
• Conditional probability
• Independence of events
• Total probability
• Bayes’ Theorem
• Probability using permutations and combinations

Statistics:

• Measures of central tendency: mean, median, mode
• Measures of dispersion: mean deviation, variance, standard deviation
• Grouped and ungrouped data
• Frequency distribution (same mean, different variance)
• Random variable
• Mean and variance of a random variable

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Trigonometry

• Trigonometric functions
• Periodicity and graphs
• Addition and subtraction formulae
• Multiple and sub-multiple angle formulae
• General solutions of trigonometric equations
• Inverse trigonometric functions (principal value only)
• Elementary properties of inverse trigonometric functions

---

Analytical Geometry

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Two Dimensions (2D)

Basic Coordinate Geometry:

• Cartesian coordinates
• Distance between two points
• Section formula
• Shift of origin

Straight Lines:

• Equation of a straight line (various forms)
• Angle between two lines
• Distance of a point from a line
• Lines through the intersection of two given lines
• Angle bisectors between two lines
• Concurrency of lines

Triangle Geometry:

• Centroid
• Orthocentre
• Incentre
• Circumcentre

Circle:

• Equation of a circle (various forms)
• Tangent, normal, and chord
• Parametric equations
• Intersection of:
  
  • Circle and line
  • Two circles
    
• Circle through the intersection points of:
  
  • Two circles
  • Circle and line

Conic Sections:

• Parabola (standard form, focus, directrix, eccentricity)
• Ellipse (standard form, focus, directrix, eccentricity)
• Hyperbola (standard form, focus, directrix, eccentricity)
• Parametric equations
• Tangent and normal equations

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Three Dimensions (3D Geometry)

• Distance between two points
• Direction ratios and direction cosines
• Equation of a straight line in space
• Skew lines
• Shortest distance between two lines
• Equation of a plane
• Distance of a point from a plane
• Angle between:
  
  • Two lines
  • Two planes
  • Line and plane
    
• Coplanar lines

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Differential Calculus

Limits and Continuity

• Limit of a function
• Continuity of a function
• Limit and continuity of sum, difference, product, and quotient
• L’Hospital’s Rule
• Continuity of composite functions
• Intermediate Value Theorem

Differentiation

• Derivative of a function
• Derivatives of sum, difference, product, quotient
• Chain rule
• Derivatives of:
  
  • Polynomial
  • Rational
  • Trigonometric
  • Inverse trigonometric
  • Exponential
  • Logarithmic functions

Applications of Derivatives

• Tangents and normals
• Increasing and decreasing functions
• Second-order derivatives
• Maximum and minimum values
• Rolle’s Theorem
• Lagrange’s Mean Value Theorem
• Geometric interpretation of theorems
• Derivatives (up to second order) of implicit functions
• Geometric interpretation of derivatives

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Integral Calculus

Integration

• Integration as the inverse of differentiation
• Indefinite integrals of standard functions
• Definite integrals as the limit of sums
• Properties of definite integrals
• Fundamental Theorem of Integral Calculus

Methods of Integration

• Integration by parts
• Substitution method
• Partial fractions

Applications

• Area bounded by simple curves

Differential Equations

• Formation of ordinary differential equations
• Homogeneous differential equations (first order, first degree)
• Separation of variables
• Linear first-order differential equations

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Vectors

• Addition of vectors
• Scalar multiplication
• Dot product
• Cross product
• Scalar triple product
• Vector triple product
• Geometrical interpretations of vector operations