JEE Mains 2026 Syllabus PDF by NTA [Latest]: Download JEE Syllabus for Physics, Chemistry & Mathematics

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Chapters and Topics

Chapters and Topics

Oscillations

• Simple harmonic motion (SHM) and equations
• Energy in SHM
• Resonance and damping (qualitative)

Units and Measurement

• Units of measurement
• System of units
• SI Units, fundamental and derived units
• Least count, significant figures, Errors in measurements
• Dimensions of Physics quantities, dimensional analysis and its applications

Electrostatics

• Electric charges: conservation of charge, Coulomb's law, forces between two-point charges, forces between multiple charges, superposition principle and continuous charge distribution
• Electric field: electric field due to a point charge, electric field lines, electric
  dipole, electric field due to a dipole, torque on a dipole in a uniform electric
  field
• Electric flux, Gauss's law and its applications to find field due to infinitely longuniformly charged straight wire, uniformly charged infinite plane sheet anduniformly charged thin spherical shell
• Electric potential and its calculation for a point charge, electric dipole and system of charges, potential difference, equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field
• Conductors and insulators, dielectrics and electric polarization, capacitors and capacitance, the combination of capacitors in series and parallel and capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor

Kinematics

• The frame of reference
• Motion in a straight line
• Speed and velocity
• Uniform and non-uniform motion
• Average speed and instantaneous velocity
• Uniformly accelerated motion, velocity-time, position-time graph
• Relations for uniformly accelerated motion, relative velocity

Current Electricity

• Electric current: drift velocity, mobility and their relation with electric current, Ohm's law, electrical resistance, I-V characteristics of Ohmic and non-ohmic
  conductors, electrical energy and power, electrical resistivity and conductivity, series and parallel combinations of resistors, temperature dependence of resistance
• Internal resistance, potential difference and emf of a cell, a combination of cells
  in series and parallel
• Kirchhoff’s laws and their applications, Wheatstone bridge, Metre Bridge

Laws of Motion

• Force and inertia
• Newton’s first law of motion, momentum
• Newton’s second law of motion, impulse
• Newton’s third Law of motion
• Law of conservation of linear momentum and its applications
• Equilibrium of concurrent forces
• Static and Kinetic friction, laws of friction, rolling friction
• Dynamics of uniform circular motion, centripetal force and its applications
• Vehicle on a level circular road, vehicle on a banked road

Magnetic Effects of Current and Magnetism

• Biot-Savart law and its application to the current carrying circular loop, Ampere's law and its applications to infinitely long current carrying straight wire and solenoid
• Force on a moving charge in uniform magnetic and electric fields, force on a
  current-carrying conductor in a uniform magnetic field, the force between two parallel currents carrying conductors-definition of ampere, torque experienced by a current loop in a uniform magnetic field: Moving coil galvanometer, its sensitivity and conversion to ammeter and voltmeter
• Current loop as a magnetic dipole and its magnetic dipole moment, bar magnet as an equivalent solenoid, magnetic field lines, magnetic field due to a magnetic
  dipole (bar magnet) along its axis and perpendicular to its axis, torque on a
  magnetic dipole in a uniform magnetic field, para-, dia- and ferromagnetic
  substances with examples, the effect of temperature on magnetic properties

Work, Energy, and Power

• Work done by constant and variable force
• Kinetic and potential energy
• Work-energy theorem
• Power and efficiency
• The potential energy of a spring
• Conservation of mechanical energy
• Conservative and non-conservative forces
• Motion in a vertical circle
• Elastic and inelastic collisions in one and two dimensions

Electromagnetic Induction and Alternating Currents

• Electromagnetic induction: Faraday's law, induced emf and current, Lenz’s law, eddy currents, self and mutual inductance
• Alternating currents, peak and RMS value of alternating current/voltage, reactance and impedance, LCR series circuit, resonance, power in AC circuits, wattless current, AC generator and transformer

Rotational Motion

• Centre of mass of a two-particle system
• Centre of mass of a rigid body
• Basic concepts of rotational motion
• Moment of a force, torque
• Angular momentum, conservation of angular momentum and its applications
• The moment of inertia, the radius of gyration
• Values of moments of inertia for simple geometrical objects
• Parallel and perpendicular axes theorems and their applications
• Equilibrium of rigid bodies, rigid body rotation and equations of
  rotational motion
• Comparison of linear and rotational motions

Electromagnetic Waves

• Displacement current, electromagnetic waves and their characteristics, transverse nature of electromagnetic waves
• Electromagnetic spectrum(radiowaves, microwaves, infrared, visible, ultraviolet, X-rays, Gamma rays), applications of electromagnetic waves.

Gravitation

• Universal law of gravitation
• Acceleration due to gravity (variation and applications)
• Gravitational potential energy, gravitational potential
• Escape velocity, motion of a satellite, orbital velocity, time period and energy of the satellite
• Kepler’s laws of planetary motion

Optics

• Reflection of light, spherical mirrors, mirror formula. Refraction of light at
  plane and spherical surfaces, thin lens formula and lens maker formula, total
  internal reflection and its applications
• Magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism, microscope and astronomical telescope (reflecting and refracting ) and their magnifying powers
• Wave optics: wavefront and Huygens ‘Principle, laws of reflection and refraction using Huygens principle
• Interference: Young's double-slit experiment and expression for fringe width, coherent sources and sustained interference of light
• Diffraction due to a single slit, width of central maximum. Polarization: plane-polarized light, Brewster's law, uses of plane- polarizedlight and Polaroid.

Properties of Solids and Liquids

• Elastic behaviour, stress-strain relationship, Hooke's Law, Young's modulus, bulk modulus and modulus of rigidity
• Pressure due to a fluid column, Pascal's law and its applications, effect of gravityon fluid pressure, viscosity, Stoke’s law, terminal velocity, streamline andturbulent flow, critical velocity, Bernoulli's principle and its applications
• Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension: drops, bubbles and capillary rise
• Heat, temperature, thermal expansion, specific heat capacity, calorimetry, change of state, latent heat. Heat transfer: conduction, convection and radiation

Dual Nature of Matter and Radiation

• Alpha-particle scattering experiment
• Rutherford's model of atom, Bohr model, energy levels, hydrogen spectrum
• Composition and size of nucleus, atomic masses, mass-energy relation, mass defect, binding energy per nucleon and its variation with mass number, nuclear fission and fusion

Thermodynamics

• Thermal equilibrium and the concept of temperature
• Zeroth law of thermodynamics, heat, work and internal energy
• The first law of thermodynamics, isothermal and adiabatic processes
• The second law of thermodynamics: reversible and irreversible processes

Atoms and Nuclei

• Rutherford and Bohr’s atomic models
• Energy levels and spectra
• Radioactivity (α, β, γ decay)
• Mass defect, binding energy, nuclear fission and fusion

Kinetic Theory of Gases

• Equation of state of a perfect gas, work done on compressing a gas, kinetic theory of gases; assumptions
• Concept of pressure
• Kinetic interpretation of temperature
• RMS speed of gas molecules
• degrees of freedom, law of equipartition of energy and applications to specific heat capacities of gases,
• Mean free path, Avogadro's number

Electronic Devices

• Semiconductors, semiconductor diode: I-V characteristics in forward andreverse bias, diode as a rectifier; I-V characteristics of LED, the photodiode, solar cell, Zener diode, Zener diode as a voltage regulator
• Logic gates (OR. AND. NOT. NAND and NOR)

Waves

• Wave motion, longitudinal and transverse waves, speed of the travelling wave, displacement relation for a progressive wave
• Progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, beats.

Experiments

Experiments

The resistivity of the material of a given wire using a metre bridge.

Vernier Caliper -its use to measure the internal and external diameter and depth of a vessel.

The resistance of a given wire using Ohm's law.

Screw gauge-its use to determine the thickness/ diameter of thin sheet/wire.

Resistance and figure of merit of a galvanometer by half deflection method.

Simple Pendulum-dissipation of energy by plotting a graph between the square of amplitude and time.

The focal length of; (i) Convex mirror (ii) Concave mirror, and (ii) Convex lens, using the parallax method.

Metre Scale - the mass of a given object by the principle of moments.

The plot of the angle of deviation vs angle of incidence for a triangular prism.

Young's modulus of elasticity of the material of a metallic wire.

The refractive index of a glass slab using a travelling microscope.

Surface tension of water by capillary rise and effect of detergents.

Characteristic curves of a p-n junction diode in forward and reverse bias.

Co-efficient of Viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body.

Characteristic curves of a Zener diode and finding reverse breakdown voltage.

Speed of sound in air at room temperature using a resonance tube.

Identification of Diode. LED, Resistor. A capacitor from a mixed collection of such items.

Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.

                                                                                                                     Physical Chemistry

Chapter

Topics

Some Basic Concepts in Chemistry

• Matter and its nature
• Dalton's atomic theory, Concept of atom, molecule, element, and compound
• Laws of chemical combination
• Atomic and molecular masses
• Mole concept and molar mass, percentage composition
• Empirical and molecular formulae
• Chemical equations and stoichiometry

Atomic Structure

• Nature of electromagnetic radiation, photoelectric effect
• Spectrum of the hydrogen atom, Bohr model of a hydrogen atom and its postulates
• Derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr's model
• Dual nature of matter, de Broglie's relationship, Heisenberg uncertainty principle, elementary ideas of quantum mechanics, the quantum mechanical model of the atom and its important features
• Concept of atomic orbitals as one-electron wave functions
• Various quantum numbers (principal, angular momentum magnetic quantum numbers) and their significance, shapes of s, p and d - orbitals
• electron spin and spin quantum number, rules for filling electrons in orbitals – Aufbau principle, Pauli's exclusion principle rule, electronic configuration of elements and extra stability of half-filled and completely filled orbitals

Chemical Bonding and Molecular Structure

• Kossel-Lewis approach to chemical bond formation, the concept of ionic and covalent bond
• Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy.
• Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment, Valence Shell Electron Pair Repulsion (VSEPR ) theory, and shapes of simple molecules.
• Quantum mechanical approach to covalent bonding: Valence bond theory and its important features, the concept of hybridization involving s, p and d orbitals, resonance.
• Molecular Orbital Theory and Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, the concept of bond order, bond length and bond energy
• Elementary idea of metallic bonding, hydrogen bonding and its applications

Chemical Thermodynamics

• Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, statefunctions, entropy, types of processes.
• The first law of thermodynamics - Concept of work, heat, internal energy and enthalpy, heat capacity, molar heat capacity, Hess’s law of constant heat summation, Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution.
• The second law of thermodynamics - Spontaneity of processes, ΔS of the universe and ΔG of of thesystem as criteria for spontaneity. ΔG° (Standard Gibbs energy change) and equilibrium constant.

Solutions

• Different methods for expressing the concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both), the vapour pressure of solutions and Raoult's Law- Ideal and nonideal solutions
• Vapour pressure - composition, plots for ideal and non-ideal solutions, Colligative properties of dilute solutions - a relative lowering of vapour pressure, depression of freezing point, the elevation of boiling point and osmotic pressure
• Determination of molecular mass using colligative properties, abnormal value of molar mass, van’t Hoff factor, and its significance.

Equilibrium

• Meaning of equilibrium and the concept of dynamic equilibrium
• Equilibria involving physical processes: Solid-liquid, liquid-gas, gas-gas and solid-gas equilibria, Henry's law. General characteristics of equilibrium involving physical processes.
• Equilibrium involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, the significance of ΔG and ΔG° in chemical equilibrium, factors affecting equilibrium concentration, pressure, temperature, the effect of a catalyst, Le Chatelier’s principle.
• Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius, Bronsted - Lowry and Lewis) and their ionization, acid-base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ioneffect, hydrolysis of salts and pH of their solutions, the solubility of sparingly soluble salts, solubility productsand buffer solutions.

Redox Reactions and Electrochemistry

• Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number and balancing of redox reactions
• Electrolytic and metallic conduction, conductance in electrolytic solutions, molar conductivities and their variation with concentration, Kohlrausch’s law and its applications.
• Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentialsincluding standard electrode potential, half-cell and cell reactions, emf of a Galvanic cell and its measurement, Nernst equation and its applications, relationship between cell potential and Gibbs' energy change, dry cell and lead accumulator. 

Chemical Kinetics

• Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure, catalyst, elementary and complex reactions, order and molecularity of reactions
• Rate law, rate constant, and its units
• Differential and integral forms of zero and first-order reactions, their characteristics and half-lives 
• Effect of temperature on the rate of reactions, Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

                                                                                                              Inorganic Chemistry

Classification of Elements and Periodicity in Properties (Periodic Table)

• Modern periodic law and present form of the periodic table, s, p. d and f block elements, periodic trends in properties of elements, atomic and ionic radii
• ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity

p-block Elements

General characteristics of Groups 13 to 18 General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups, unique behaviour of the first element in each group.

• Group 13: Boron family – compounds like diborane, borax
• Group 14: Carbon family – allotropes, catenation, oxides of carbon
• Group 15: Nitrogen family – ammonia, nitric acid, oxides of nitrogen
• Group 16: Oxygen family – preparation and properties of ozone, sulfur compounds
• Group 17: Halogens – interhalogen compounds, properties of chlorine, Iodine test
• Group 18: Noble gases – structure and uses of xenon fluorides and oxides

Trends in acidic/basic nature, oxidation states, and anomalous behavior

d-block and f-block Elements

• Transition Elements - General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first-row transition elements - physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation, preparation, properties and uses of K2Cr2O7 
• Inner Transition Elements
  Lanthanoids - Electronic configuration, oxidation states and Lanthanoid contraction.
  Actinoids - Electronic configuration and oxidation states

Coordination Compounds

• Introduction to coordination compounds. Werner's theory, ligands, coordination number, denticity, chelation, IUPAC nomenclature of mononuclear coordination compounds, isomerism
• Bonding: Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties, importance of coordination compounds (in qualitative analysis, extraction of metals and in biological systems).

                                                                                                                  Organic Chemistry

Purification and Characterisation of Organic Compounds

• Purification - Crystallization, sublimation, distillation, differential extraction and chromatography-principles and their applications.
• Qualitative analysis - Detection of nitrogen, sulphur, phosphorus and halogens. Quantitative analysis (basic principles only) - Estimation of carbon, hydrogen, nitrogen, halogens, sulphur and phosphorus.
• Calculations of empirical formulae and molecular formulae, numerical problems in organic quantitative analysis,

Some Basic Principles of Organic Chemistry

• Tetravalency of carbon, shapes of simple molecules - hybridization (s and p): classification of organic compounds based on functional groups and those containing halogens, oxygen, nitrogen and sulphur, homologous series: Isomerism - structural and stereoisomerism. Nomenclature (Trivial and IUPAC)
  Covalent bond fission - Homolytic and heterolytic, free radicals, carbocations and carbanions, stability of carbocations and free radicals, electrophiles and nucleophiles. Electronic displacement in a covalent bond
  Inductive effect, electromeric effect, resonance and hyperconjugation.
• Common types of organic reactions- Substitution, addition, elimination and rearrangement

Hydrocarbons

• Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.
• Alkanes - Conformations: Sawhorse and Newman projections (of ethane), mechanism of halogenation of alkanes.
• Alkenes - Geometrical isomerism, mechanism of electrophilic addition, addition of hydrogen, halogens, water, hydrogen halides (Markownikoffs and peroxide effect), Ozonolysis and polymerization.
• Alkynes - Acidic character, addition of hydrogen, halogens, water and hydrogen halides, polymerization.
• Aromatic hydrocarbons - Nomenclature, benzene - structure and aromaticity, mechanism of electrophilic substitution, halogenation, nitration.
• Friedel-Craft's alkylation and acylation, directive influence of the functional group in mono-substituted benzene.

Organic Compounds Containing Halogens

• General methods of preparation, properties and reactions, nature of C-X bond, mechanisms of substitution reactions.
• Uses, environmental effects of chloroform, iodoform, freons and DDT

Organic Compounds Containing Oxygen

• General methods of preparation, properties, reactions and uses. 
  Alcohols: Identification of primary, secondary and tertiary alcohols, mechanism of dehydration.
• Phenols: Acidic nature, electrophilic substitution reactions, halogenation, nitration and sulphonation, Reimer-Tiemann reaction.
• Ethers: Structure.
• Aldehyde and Ketones: Nature of carbonyl group, nucleophilic addition to >C=Ogroup, relative reactivities of aldehydes and ketones, important reactions such as - Nucleophilic addition reactions(addition of HCN, NH3 and its derivatives), Grignard reagent, oxidation, reduction (Wolf Kishner andClemmensen), the acidity of � -hydrogen. Aldol condensation, Cannizzaro reaction, Haloform reaction, chemical tests to distinguish between aldehydes and ketones.
• Carboxylic Acids: Acidic strength and factors affecting it

Organic Compounds Containing Nitrogen

• Amines (primary, secondary, tertiary): structure, basicity, diazotization
• Diazonium salts: preparation and synthetic utility in azo dye formation
• Cyanides and isocyanides: nature and reduction

Biomolecules

• Carbohydrates: classification (mono-, di-, polysaccharides), glucose and its reactions
• Proteins: amino acids, peptide bond, structure (primary to quaternary)
• Vitamins and hormones: types and biological roles
• Enzymes: function and specificity
• Nucleic acids: structure of DNA and RNA, components (sugar, phosphate, nitrogen base)

S.No.

Principles Related to Practical Chemistry

1

Detection of extra elements (Nitrogen, Sulphur, halogens) in organic compounds;

2

Detection of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketones), carboxyl, and amino groups in organic compounds

3

The chemistry involved in the preparation of the following: l Inorganic compounds; Mohr’s salt, potash alum. l Organic compounds: Acetanilide, p-nitro acetanilide, aniline yellow, iodoform

4

The chemistry involved in the titrimetric exercises – Acids, bases, and the use of indicators, oxalic acid vs KMnO4, Mohr’s salt vs KMnO4

5

Chemical principles involved in the qualitative salt analysis: Cations – Pb2+, Cu2+, Al3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+ Anions- CO32−, S2-, SO42− ,NO3-, NO2-, Cl-, Br-, I- (Insoluble salts excluded)

6

Chemical principles involved in the following experiments: 1. Enthalpy of solution of CuSO4 2. Enthalpy of neutralization of strong acid and strong base. 3. Preparation of lyophilic and lyophobic sols. 4. Kinetic study of the reaction of iodide ions with hydrogen peroxide at room temperature.

Chapters and their Topics

Chapters and their Topics

Integral Calculus

• Integral as an anti-derivative
• Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
• Integration by substitution, by parts and by partial fractions
• Integration using trigonometric identities. Evaluation of simple integrals of the type
• The fundamental theorem of calculus, properties of definite integrals
• Evaluation of definite integrals, determining areas of the regions bounded by simple curves by simple curves in standard forms

Sets, Relations and Functions

• Sets and their representation
• Union, intersection and complement of sets and their algebraic properties
• Power set
• Relations, types of relations, equivalence relations, functions
• one-one, into and onto functions, the composition of functions

Differential Equations

• Ordinary differential equations, their order and degree
• Solution of differential equation by the method of separation of variables
• Solution of a homogeneous and linear differential equation of the type

Complex Numbers

• Complex numbers as ordered pairs of reals
• Representation of complex numbers in the form a + ib and their representation in a plane
• Argand diagram
• Algebra of complex numbers, modulus and argument (or amplitude) of a complex number
• Quadratic equations in real and complex number systems and their solutions
• Relations between roots and coefficients, nature of roots, the formation of
  quadratic equations with given roots

Coordinate Geometry

• Cartesian system of rectangular coordinates in a plane
• Distance formula, sections formula, locus, and its equation
• The slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis
• Straight line: Various forms of equations of a line, intersection of lines, angles
  between two lines, conditions for concurrence of three lines, the distance of a
  point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a
  triangle
• Circle, conic sections: A standard form of equations of a circle, the general
  form of the equation of a circle, its radius and centre, equation of a circle whenthe endpoints of a diameter are given, points of intersection of a line and a circle
  with the centre at the origin and sections of conics, equations of conic sections
  (parabola, ellipse and hyperbola) in standard forms.

Matrices and Determinants

• Matrices, algebra of matrices, type of matrices
• Determinants and matrices of order two and three
• Evaluation of determinants
• Determinants, area of triangles using determinants
• Adjoint and inverse of a square matrix
• Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

Three-Dimensional Geometry

• Coordinates of a point in space
• The distance between two points
• Section formula, direction ratios and direction cosines and the angle between two intersecting lines
• Equation of a line; Skew lines, the shortest distance betweenthem and its equation

Permutations and Combinations

• Fundamental principle of counting
• Permutations with/without repetition
• Combinations and their properties
• Meaning of P(n, r) and C(n, r)
• Simple applications

Vector Algebra

• Vectors and scalars
• The addition of vectors
• Components of a vector in two dimensions and three-dimensional spaces
• scalar and vector products

Binomial Theorem and Its Simple Applications

• Binomial theorem for a positive integral index
• General term and middle term and simple applications

Statistics and Probability

• Measures of dispersion
• Calculation of mean, median, mode of grouped and ungrouped dataC
• Calculation of standard deviation, variance and meandeviation for grouped and ungrouped data
• Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probabilitydistribution of a random variable
• Bayes’ theorem and independent events

Sequence and Series

• Arithmetic and geometric progressions
• Insertion of Arithmetic mean and geometric mean
• Geometric mean between two given numbers
• Relation between A.M and G.M

Trigonometry

• Trigonometrical identities and trigonometrical functions
• Inverse trigonometrical functions their properties

Limit, Continuity and Differentiability

• Real–valued functions, algebra of functions
• Polynomial, rational, trigonometric, logarithmic and exponential functions
• Inverse functions
• Graphs of simple functions
• Limits, continuity and differentiability
• Differentiation of the sum, difference, product and quotient of two functions
• Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite, and implicit functions
• Derivatives of order upto two, Applications of derivatives
• Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable

Relations and Functions

• Ordered pairs and Cartesian product
• Types of relations: reflexive, symmetric, transitive, equivalence
• Functions: one-one, onto, into; domain, co-domain, and range
• Composite and inverse of functions

Quadratic Equations

• Nature of roots, conditions for real, equal, or imaginary roots
• Graphical representation of quadratic functions
• Maximum and minimum values
• Relation between roots and coefficients

Differentiability

• Concept of differentiability
• Derivative as a rate of change
• Differentiability vs continuity
• Derivatives of composite, implicit and parametric functions