## Kerala Board

## PHYSICS-XI

#### CHAPTER I: UNITS AND MEASUREMENTS

- Units of measurements
- System of Units
- S I Units
- Fundamental and Derived units
- Least count
- Significant figures
- Errors in measurements
- Dimensions of Physics quantities
- Dimensional analysis and its applications

#### CHAPTER II: MOTION IN A STRAIGHT LINE

- The frame of reference
- Motion in a straight line
- Position- time graph
- 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

#### CHAPTER III: MOTION IN A PLANE

- Scalars and Vectors
- Vector Addition and Subtraction
- Scalar and vector products
- Unit Vector
- Resolution of a Vector
- Relative Velocity
- Motion in a plane
- Projectile Motion
- Uniform Circular Motion

#### CHAPTER IV: LAWS OF MOTION

- Force and inertia
- Newton’s First law of motion: Momentum
- Newton’s Second Law of motion
- Impulses: 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
- Examples of circular motion (vehicle on level circular road, vehicle on banked road)

#### CHAPTER V: WORK, ENERGY AND POWER

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

#### CHAPTER VI: SYSTEM OF PARTICLES AND ROTATIONAL MOTION

- Centre of the mass of a two-particle system
- Centre of the 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

#### CHAPTER VII: GRAVITATION

- The universal law of gravitation
- Acceleration due to gravity and its variation with altitude and depth
- Kepler’s law of planetary motion
- Gravitational potential energy
- Gravitational potential
- Escape velocity
- Motion of a satellite
- Orbital velocity
- Time period and energy of satellite

#### CHAPTER VIII: MECHANICAL PROPERTIES OF SOLIDS

- Elastic behaviour
- Stress-strain relationship
- Hooke’s Law
- Young’s modulus
- Bulk modulus
- Modulus of rigidity
- Poisson’s ratio
- Elastic energy

#### CHAPTER XI: MECHANICAL PROPERTIES OF FLUIDS

- Pressure due to a fluid column
- Pascal’s law and its applications
- Effect of gravity on fluid pressure
- Viscosity
- Stokes’ law
- Terminal velocity
- Streamline
- Turbulent 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

#### CHAPTER X: THERMAL PROPERTIES OF MATTER

- Heat
- Temperature
- Thermal expansion
- Specific heat capacity
- Calorimetry
- Change of state
- Latent heat
- Heat tansfer conduction, convection, and radiation
- Thermal conductivity
- Qualitative ideas of Blackbody radiation
- Wein’s displacement Law
- Stefan’s law
- Greenhouse effect

#### CHAPTER XI: THERMODYNAMICS

- Thermal equilibrium
- Zeroth law of thermodynamics
- The concept of temperature
- Heat, work, and internal energy
- The first law of thermodynamics
- Isothermal and adiabatic processes
- The second law of thermodynamics
- Reversible and irreversible processes
- Heat engine and refrigerator

#### CHAPTER XII: KINETIC THEORY

- Equation of state of a perfect gas
- Work done on compressing a gas
- Kinetic theory of gases - assumptions
- The 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

#### CHAPTER XIII: OSCILLATIONS

- Oscillations and periodic motion - time period, frequency
- Displacement as a function of time
- Periodic functions
- Simple harmonic motion (S.H.M.) and its equation’s phase
- Oscillations of a spring -restoring force and force constant
- Energy in S.H.M
- Kinetic and potential energies
- Simple pendulum - derivation of expression for its time period

#### CHAPTER XIV: WAVES

- Wave motion
- Longitudinal and transverse waves
- Speed of travelling wave
- Displacement relation for a progressive wave
- Principle of superposition of waves
- Reflection of waves
- Standing waves in strings and organ pipes
- Fundamental mode and harmonics- Beats

## PHYSICS-XII

#### CHAPTER I: ELECTRIC CHARGES AND FIELDS

- 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 Lines
- Electric Flux
- Electric Dipole
- Dipole in a Uniform External Field
- Gauss’s Law
- Applications of Gauss’s Law
- Field due to infinitely long straight uniformly charged wire
- Field due to uniformly charged infinite plane sheet

#### CHAPTER II: ELECTROSTATIC POTENTIAL AND CAPACITANCE

- 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 infnitely long uniformly charged straight wire
- Uniformly charged infinite plane sheet
- Uniformly 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 capacitances
- The combination of capacitors in series and parallel
- Capacitance of a parallel plate capacitor with and without dielectric medium between the plates
- Energy stored in a capacitor

#### CHAPTER III: CURRENT ELECTRICITY

- Electric current
- Drift velocity
- Mobility and their relation with electric current
- Ohm’s law
- Electrical resistance
- V-I 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
- Kirchhoffs raws and their applications
- Wheatstone bridge
- Metre Bridge
- Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells
- Measurement of internal resistance of a cell

#### CHAPTER IV: MOVING CHARGES AND MAGNETISM

- Biot - Savart law and its application to current carrying circular loop
- Ampere’s law
- 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
- Conversion to ammeter and voltmeter

#### CHAPTER V: MAGNETISM AND MATTER

- 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
- Electromagnets and factors affecting their strengths
- Permanent magnets

#### CHAPTER VI: ELECTROMAGNETIC INDUCTION

- Electromagnetic induction
- Faraday’s law
- Induced emf and current
- Lenz’s Law
- Eddy currents
- Self and mutual inductance

#### CHAPTER VII: ALTERNATING CURRENT

- 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
- Transformer

#### CHAPTER VIII: ELECTROMAGNETIC WAVES

- Displacement current
- Electromagnetic waves and their characteristics
- Transverse nature of electromagnetic waves
- Electromagnetic spectrum(radio waves, microwaves, infrared, visible, ultraviolet. X-rays. Gamma rays)
- Applications of e.m. waves

#### CHAPTER IX: RAY OPTICS AND OPTICAL INSTRUMENTS

- Ray Optics
- Reflection of light
- spherical mirrors
- mirror formula
- Refraction of light at plane and spherical surfaces
- Thin lens formula
- 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

#### CHAPTER X: WAVE OPTICS

- 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
- Sustained interference of light
- Diffraction due to a single slit
- Width of central maximum
- Polarization
- Plane-polarized light
- Brewster’s law
- Uses of plane-polarized light and Polaroid

#### CHAPTER XI: DUAL NATURE OF RADIATION AND MATTER

- Dual nature of radiation
- Photoelectric effect
- Hertz and Lenard’s observations
- Einstein’s photoelectric equation: particle nature of light
- Matter waves-wave nature of particle, de Broglie relation
- Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained)

#### CHAPTER XII: ATOMS

- Alpha-particle scattering experiment
- Rutherford’s model of atom
- Bohr model
- Energy level’s hydrogen spectrum
- de Broglie’s Explanation of Bohr’s
- Second Postulate of Quantisation

#### CHAPTER XIII: NUCLEI

- 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 fussion

#### CHAPTER XIV: SEMICONDUCTOR ELECTRONICS: MATERIALS, DEVICES AND SIMPLE CIRCUITS

- Semiconductors
- Semiconductor diode
- I-V characteristics in forward and reverse bias
- Diode as a rectifier
- I-V characteristics of LED
- The photodiode
- Solar cell and Zener diode
- Zener diode as a voltage regulator
- Junction transistor
- Transistor action
- Characteristics of transistor
- Transistor as an amplifier (CE configuration)
- Basic idea of analog and digital signals
- Logic gates (OR. AND. NOT. NAND and NOR)

## CHEMISTRY-XI

#### UNIT I: SOME BASIC CONCEPTS OF 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
- Molar mass
- Percentage composition
- Empirical and molecular formulae
- Chemical equations and stoichiometry

#### UNIT II: STRUCTURE OF ATOM

- Discovery of Electron, Proton and Neutron
- Atomic number
- Isotopes and isobars
- Thomson’s model and its limitations
- Rutherford’s model and its limitations
- Bohr’s model and its limitations
- Nature of electromagnetic radiation
- photoelectric effect
- Spectrum of the hydrogen atom
- Bohr model of a hydrogen atom - 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
- Quantum mechanics
- The quantum mechanical model of the atom, its important features
- Concept of atomic orbitals as one-electron wave functions
- Variation of 𝚿 and 𝚿2 with r for ls and 2s orbitals
- Various quantum numbers (principal, angular momentum, and 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 and Hund’s rule
- Electronic configuration of elements
- Extra stability of half-filled and completely filled orbitals

#### UNIT III: CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES

- Significance of classification
- Modem 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

#### UNIT IV: CHEMICAL BONDING AND MOLECULAR STRUCTURE

- Kossel - Lewis approach to chemical bond formation
- The concept of ionic and covalent bonds
- 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 - its important features
- The concept of hybridization involving s, p, and d orbitals
- Resonance
- Molecular orbital Theory - 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 application

#### UNIT V: THERMODYNAMICS

- Fundamentals of thermodynamics: system and surroundings
- Extensive and intensive properties
- State functions
- Types of processes
- The first law of thermodynamics
- Concept of work
- Heat and internal energy
- Enthalpy
- Heat capacity
- Molar heat capacity
- Hess’s laws 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 the system as criteria for spontaneity
- ΔG° (Standard Gibbs energy change)
- Equiliribrium constant

#### UNIT VI: EQUILIBRIUM

- Meaning of equilibrium
- The concept of dynamic equilibrium
- Equilibria involving physical processes: Solid-liquid, liquid - 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 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)
- Ionization constants
- Ionization of water
- pH scale
- Common ion effect
- Hydrolysis of salts and pH of their solutions
- The solubility of sparingly soluble salts and solubility products
- Buffer solutions

#### UNIT VII: REDOX REACTIONS

- Electronic concepts of oxidation and reduction
- Redox reactions
- Oxidation number
- Rules for assigning oxidation number
- 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 cells
- Galvanic cells
- Different types of electrodes
- Electrode potentials including 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
- Fuel cells

#### UNIT VIII: ORGANIC CHEMISTRY: SOME BASIC PRINCIPLES AND TECHNIQUES

- 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
- 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

#### UNIT IX: 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 monosubstituted benzene

## CHEMISTRY-XII

#### UNIT I: 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 non-ideal solutions
- Vapour pressure - composition
- Plots for ideal and non-ideal solutions
- Colligative properties of dilute solutions - a relative lowering of vapour pressure
- Depression of mass freezing point
- The elevation of boiling point
- Osmotic pressure
- Determination of molecular mass using colligative properties
- Abnormal value of molar mass
- Van’t Hoff factor and its significance

#### UNIT II: ELECTROCHEMISTRY

- Electronic concepts of oxidation and reduction
- Redox reactions
- Oxidation number
- Rules for assigning oxidation number
- 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 cells
- Galvanic cells
- Different types of electrodes
- Eectrode potentials including 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
- Fuel cells

#### UNIT III: CHEMICAL KINETICS

- Rate of a chemical reaction
- Factors affecting the rate of reactions concentration, temperature, pressure, and 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
- The effect of temperature on the rate of reactions
- Arrhenius theory
- Activation energy and its calculation
- Collision theory of bimolecular gaseous reactions (no derivation)

#### UNIT IV: d - 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 K2CrO7, and KMnO4
- Lanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences
- Actinoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences
- Actinoids - Electronic configuration, oxidation states and comparison with lathanoids.

#### UNIT V: COORDINATION COMPOUNDS

- Introduction to coordination compounds
- Werner’s theory
- Ligands
- Co-ordination number
- Denticity
- Chelation
- IUPAC nomenclature of mononuclear co-ordination compounds
- Isomerism
- Bonding-Valence bond approach and basic ideas of Crystal field theory
- Colour and magnetic properties
- Importance of co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems)

#### UNIT VI: HALOALKANES AND HALOARENES

- 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

#### UNIT VII: ALCOHOLS, PHENOLS AND ETHERS

- 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

#### UNIT VIII: ALDEHYDES, KETONES AND CARBOXYLIC ACIDS

- General methods of preparation, properties, reactions, and uses
- Aldehyde and Ketones
- Nature of carbonyl group
- Nucleophilic addition to >C=O group
- 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 and Clemmensen)
- The acidity of α-hydrogen
- Aldol condensation
- Cannizzaro reaction
- Haloform reaction
- Chemical tests to distinguish between aldehydes and Ketones
- Carboxylic Acids Acidic strength and factors affecting it

#### UNIT IX: AMINES

- General methods of preparation
- Properties, reactions, and uses
- Amines: Nomenclature, classification structure, basic character, and identification of primary, secondary, and tertiary amines and their basic character
- Diazonium Salts: Importance in synthetic organic chemistry

#### UNIT X: BIOMOLECULES

- General introduction and importance of biomolecules
- CARBOHYDRATES - Classification
- Aldoses and ketoses: monosaccharides (glucose and fructose)
- constituent monosaccharides of oligosaccharides (sucrose, lactose, and maltose)
- PROTEINS - Elementary Idea of α-amino acids
- Peptide bond
- Polypeptides
- Proteins:primary, secondary, tertiary, and quaternary structure (qualitative idea only)
- Denaturation of proteins
- Enzymes
- VITAMINS - Classification and functions
- NUCLEIC ACIDS - Chemical constitution of DNA and RNA
- Biological functions of nucleic acids
- Hormones (General introduction)

## MATHEMATICS-XI

#### CHAPTER I: SETS

- Sets and their representation: Union, intersection, complement of sets, Power set
- Algebraic properties of sets

#### CHAPTER II: RELATIONS & FUNCTIONS

- Relation
- Ordered pairs.Cartesian product of sets
- Number of elements in the Cartesian product of two finite sets
- Cartesian product of the set of reals with itself (upto R x R x R)
- Definition of relation
- Pictorial diagrams
- Domain
- Co-domain and range of a relation
- Function as a special type of relation
- One-one, into and onto functions
- The composition of functions
- Pictorial representation of a function, domain, co-domain and range of a function
- Real valued functions, domain and range of these functions
- Constant
- Identity
- Polynomial
- Rational
- Modulus
- Signum
- Exponential
- Logarithmic and greatest integer functions with their graphs
- Sum, difference, product and quotients of functions

#### CHAPTER III: TRIGONOMETRIC FUNCTIONS

- Positive and negative angles
- Measuring angles in radians and in degrees and conversion from one measure to another
- Definition of trigonometric functions with the help of unit circle
- Truth of the identity sin 2x + cos 2x = 1 , for all x
- Signs of trigonometric functions
- Domain and range of trigonometric functions and their graphs
- Expressing sin (x±y) and cos (x±y) in terms of sin x , sin y ,cos x & cos y and their simple applications
- Deducing identities like the following: tan(x ± y) = tan x ± tan y / 1 ± tan x tan y , cot(x ± y) = cot x cot y ± 1 / cot y ± cot x sin α ± sin β = 2sin(½(α ± β))cos(½(α ∓ β)) cos α + cos β = 2cos(½(α + β))cos(½(α − β)) cos α − cos β = −2sin(½(α + β))sin(½(α − β)) Identities related to sin 2x , cos 2x ,tan 2x ,sin 3x ,cos 3x and tan 3x
- General solution of trigonometric equations of the type sin y = sin a , cos y = cos a and tan y = tan a
- Trigonometrical identities and trigonometrical functions
- Inverse trigonometrical functions
- Properties of inverse trigonometrical functions

#### CHAPTER IV: COMPLEX NUMBERS AND QUADRATIC EQUATIONS

- Introduction to Complex Numbers
- Complex numbers as ordered pairs of reals
- Representation of complex numbers in the form a + ib and their representation in a plane
- Modulus
- Algebra of complex number
- Argand diagram and argument (or amplitude) of a complex number
- Quadratic equations in real system and their solutions Relations between roots and co-efficient
- Nature of roots
- The formation of quadratic equations with given roots

#### CHAPTER V: LINEAR INEQUALITIES

- Linear inequalities
- Algebraic solutions of linear inequalities in one variable and their representation on the number line
- Graphical solution of linear inequalities in two variables
- Graphical method of finding a solution of system of linear inequalities in two variables

#### CHAPTER VI: PERMUTATIONS AND COMBINATIONS

- The fundamental principle of counting
- Permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r)
- Simple applications

#### CHAPTER VII: BINOMIAL THEOREM

- Binomial theorem for a positive integral index
- General term and middle term
- Simple applications

#### CHAPTER VIII: SEQUENCE AND SERIES

- Arithmetic and Geometric progressions
- Insertion of arithmetic means between two given numbers
- Geometric means between two given numbers
- Relation between A.M and G.M

#### CHAPTER IX: STRAIGHT LINES

- Various forms of equations of a line
- Angles between two lines
- Intersection of lines
- Conditions for concurrence of three lines
- the distance of a point from a line
- Co-ordinate of the centroid
- Orthocentre and circumcentre of a triangle

#### CHAPTER X: CONIC SECTIONS

- A standard form of equations of a circle
- The general form of the equation of a circle,its radius
- Central equation of a circle when the endpoints of a diameter are given
- Points of intersection of a line and a circle with the centre at the origin
- Sections of conics
- Equations of parabola in standard form
- Equations of ellipse in standard forms
- Equations of hyperbola in standard forms

#### CHAPTER XI: INTRODUCTION TO THREE-DIMENSIONAL GEOMETRY

- Coordinates of a point in space
- Directions ratio and direction cosines
- The angle between two intersecting lines
- The distance between two points
- Section formula
- Skew lines
- The shortest distance between them Skew lines
- The shortest distance between them and its equation
- Equations of a line

#### CHAPTER XII: LIMITS AND DERIVATIVES

- Functions
- Graphs of simple functions
- Algebra of functions
- Rational
- Polynomial function
- Trigonometric function
- Inverse function
- Limits
- Differentiation of the sum, difference, product, and quotient of two functions
- Differentiation of trigonometric functions
- Logarithmic Functions & its Derivatives
- Differentiation of Exponential
- Inverse trigonometric and implicit functions
- Differentiation of composite function
- Derivatives of order up to two
- Rate of change of quantities
- Applications of derivatives
- Increasing and decreasing functions
- Maxima and minima of functions of one variable

#### CHAPTER XIII: STATISTICS

- Measures of discretion
- Calculation of mean, median, mode of grouped and ungrouped data
- Mean deviation for grouped and ungrouped data
- Calculation of standard deviation, variance, for grouped and ungrouped data
- Analysis of frequency distributions with equal means but different variances

#### CHAPTER XIV: PROBABILITY

- Probability of an event
- Addition theorems of probability
- Multiplication theorems of probability
- Baye’s theorem, probability distribution of a random variate

## MATHEMATICS-XII

#### CHAPTER I: RELATIONS AND FUNCTIONS

- Relation
- Type of relations
- Equivalence relations
- One to one and onto functions
- Composition functions
- Inverse of a function
- Binary operations

#### CHAPTER II: Inverse Trigonometrical Functions

- Definition, range, domain, principal value branches
- Graphs of inverse trigonometric functions
- properties of inverse trigonometrical functions

#### CHAPTER III: Matrices

- Concept
- Notation
- Order
- Equality
- Types of matrices
- Zero matrix
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Addition, multiplication and scalar multiplication of matrices
- Simple properties of addition
- Multiplication and scalar multiplication
- Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
- Concept of elementary row and column operations
- Invertible matrices and proof of the uniqueness of inverse, if it exists; (here all matrices will have real entries)

#### CHAPTER IV: Determinants

- Determinant of a square matrix (up to 3 x 3 matrices)
- Properties of determinants
- Minors
- Cofactors and applications of determinants in finding the area of a triangle
- Adjoint and inverse of a square matrix
- Consistency, inconsistency and number of solutions of system of linear equations by examples
- Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix
- Cramer’s Rule and its applications
- Matrices
- Algebra of matrices
- Type of matrices and matrices of order two and three
- Determinants
- Evaluation of determinants
- Adjoint and evaluation of inverse of a square matrix using determinants
- Area of triangles using determinants
- Test of consistency
- Solution of simultaneous linear equations in two or three variables using matrices

#### CHAPTER V: CONTINUITY AND DIFFERENTIABILITY

- Functions
- Graphs of simple functions
- Algebra of functions
- Rational
- Polynomial function
- Trigonometric function
- Inverse function
- Limits
- continuity and differentiability
- Differentiation of the sum, difference, product, and quotient of two functions
- Differentiation of trigonometric functions
- Logarithmic Functions & its Derivatives
- Differentiation of Exponential
- Inverse trigonometric and implicit functions
- Differentiation of composite function
- Derivatives of order up to two
- Rate of change of quantities
- Applications of derivatives

#### CHAPTER VI: APPLICATIONS OF DERIVATIVE

- Geometrical application-tangent and normal at a point
- Rolle’s theorem and Mean value theorem and their geometrical interpretation (without proof)
- Derivative as a rate measure-introduction,
- Increasing and decreasing function
- Approximation (without proof)
- Maxima and minima
- Introduction of extrema and extreme values
- Maxima and minima in a closed interval
- First derivative test
- Second derivative test

#### CHAPTER VII: INTEGRATION

- Integral as an anti-derivative
- Fundamental theorem of calculus
- Fundamental integral involving algebraic
- Trigonometric, exponential and logarithms functions
- Integrations by substitution
- Integration by parts and by partial fractions
- Integration using trigonometric identities
- Evaluation of simple integrals of the type ∫ 𝑑𝑥 𝑥 2+𝑎2 , ∫ 𝑑𝑥 √𝑥 2 ± 𝑎2 , ∫ 𝑑𝑥 𝑎2− 𝑥 2 , ∫ 𝑑𝑥 √𝑎2− 𝑥 2 , ∫ 𝑑𝑥 𝑎𝑥2+𝑏𝑥+𝑐 ,∫ 𝑑𝑥 √𝑎𝑥2+ 𝑏𝑥+𝑐 , ∫ (𝑝𝑥+𝑞)𝑑𝑥 𝑎𝑥2+𝑏𝑥+𝑐 , ∫ (𝑝𝑥+𝑞)𝑑𝑥 √𝑎𝑥2+ 𝑏𝑥+𝑐
- Evaluation of simple integrals of the type ∫ √𝑎 2 ± 𝑥 2 𝑑𝑥 , ∫√𝑥 2 − 𝑎 2 𝑑𝑥
- The properties of definite integrals
- Evaluation of definite integrals
- Determining areas of the regions bounded by simple curves in standard form
- Indefinite integrals-methods of integration
- Substitution method
- Integrals of the various types
- Integration by parts (reduction formulae are not expected)
- Integration by partial fraction-factors involving repeated and non-repeated linear factors
- Non-repeated quadratic factors
- Definite integral-definite integral as a limit of sum
- Fundamental theorem of integral calculus (without proof)
- Evaluation of definite integral 1) by substitution, 2) integration by parts
- Properties of definite integrals

#### CHAPTER VIII: APPLICATIONS OF DEFINITE INTEGRAL

- Area under the curve
- Area bounded by curve and axis (simple problems)
- Area bounded by two curves
- Volume of solid of revolution-volume of solid obtained by revolving the area under the curve about the axis (simple problems)

#### CHAPTER IX: DIFFERENTIAL EQUATION

- Definition-differential equation
- Order
- Degree
- General solution
- Particular solution of differential equation
- Formation of differential equation-formation of differential equation by eliminating arbitary constants (at most two constants)
- Solution of first order and first degree differential equation-variable separable method
- Homogeneous differential equation (equation reducible to homogeneous form are not expected)
- Linear differential equation
- Applications : population growth, bacterial colony growth, surface area, Newton’s laws of cooling, radioactive decay

#### CHAPTER X: VECTORS ALGEBRA

- Vectors and scalars
- Magnitude and direction of a vector
- Direction cosines/ratios of vectors
- Types of vectors (equal, unit, zero, parallel and collinear vectors)
- Position vector of a point
- Negative of a vector
- Components of a vector
- Addition of vectors
- Multiplication of a vector by a scalar
- Position vector of a point dividing a line segment in a given ratio
- Scalar (dot) product of vectors
- Projection of a vector on a line
- Vector (cross) product of vectors

#### CHAPTER XI: THREE-DIMENSIONAL GEOMETRY

- Direction cosines/ratios of a line joining two points
- Cartesian and vector equation of a line
- Coplanar and skew lines
- Shortest distance between two lines
- Cartesian and vector equation of a plane
- Angle between (i) two lines (ii) two planes (iii) a line and a plane
- Distance of a point from a plane
- Vectors and scalars
- The addition of vectors
- Components of a vector in two dimensions and threedimensional space
- Scalar products
- Vector products
- Coordinates of a point in space,directions ratios and direction cosines
- The angle between two intersecting lines
- The distance between two points
- Section formula
- Skew lines
- The shortest distance between them Skew lines
- The shortest distance between them, and its equation
- Equations of a line

#### CHAPTER XII: LINEAR PROGRAMMING

- Introduction
- Definition of related terminology such as constraints, objective function, optimization
- Different types of linear programming (L.P.) problems
- Mathematical formulation of L.P. Problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions
- Feasible and infeasible solutions
- Optimal feasible solutions (up to three non-trivial constraints)

#### CHAPTER XIII: PROBABILITY

- Multiplication theorem on probability Conditional probability
- Independent events
- Total probability
- Baye’s theorem
- Random variable and its probability distribution mean and variance of random variable
- Repeated independent (Bernoulli) trials and Binomial distribution
- Probability of an event
- Addition theorems of probability
- Multiplication theorems of probability
- Baye’s theorem
- Probability distribution of a random variate

## BIOLOGY-XI

#### UNIT I: DIVERSITY OF LIVING ORGANISMS

##### The Living World

- What is living?
- Biodiversity
- Need for classification
- Taxonomy & Systematics
- Concept of species and taxonomical hierarchy
- Binomial nomenclature

##### Biological Classification

- Five kingdom classification
- Salient features and classification of Monera
- Protista and Fungi into major groups
- Lichens
- Viruses and Viroids

##### Plant Kingdom

- Salient features and classification of plants into major groups - Algae, Bryophyta, Pteridophyta, Gymnospermae and Angiospermae (salient and distinguishing features and a few examples of each category)
- Angiosperms - classification up to class, characteristic features and examples

##### Animal Kingdom

- Salient features and classification of animals
- Non-chordates up to phyla level and chordates up to class level (salient features and distinguishing features of a few examples of each category)
- (No live animals or specimen should be displayed)

#### UNIT II: STRUCTURAL ORGANISATION IN ANIMALS AND PLANTS

##### Morphology of Flowering Plants

- Morphology and modifications
- Morphology of different parts of flowering plants: root, stem, leaf, inflorescence, flower, fruit and seed
- Description of families: Fabaceae, Solanaceae and Liliaceae (to be dealt along with the relevant experiments of the Practical Syllabus)

##### Anatomy of Flowering Plants

- Anatomy and functions of different tissues and tissue systems in dicots and monocots
- Secondary growth
- Anatomy and functions of different parts of flowering plants
- Tissues

##### Structural Organisation in Animals

- Animal tissues
- Morphology
- Anatomy and functions of different systems(digestive, circulatory, respiratory, nervous and reproductive)

- of an insect-cockroach (a brief account only)

#### UNIT III: CELL: STRUCTURE AND FUNCTION

##### Cell-The Unit of Life

- Cell theory and cell as the basic unit of life
- Structure of prokaryotic and eukaryotic cell
- Plant cell and animal cell
- Cell membrane
- Cell wall
- Cell envelope
- Cell organelles structure and function
- Endomembrane system-endoplasmic reticulum
- Golgi bodies
- Lysosomes
- Vacuoles
- Mitochondria
- Ribosomes
- Plastids
- Micro bodies
- Cytoskeleton
- Cilia
- Flagella
- Centrioles
- Nucleus-nuclear membrane
- Chromatin(ultra structure and function)
- Nucleolus

##### Biomolecules

- Chemical constituents of living cells
- Biomolecules-structure
- Function of proteins
- Carbodydrates
- Lipids
- Nucleic acids
- Enzymes-types
- Properties
- Enzyme action
- Classification and nomenclature of anzymes

##### Cell Cycle and Cell Division

#### UNIT IV: PLANT PHYSIOLOGY

##### Photosynthesis in Higher Plants

- Photosynthesis
- Photosynthesis as a means of Autotrophic nutrition
- Site of photosynthesis take place
- Pigments involved in Photosynthesis(Elementary idea)
- Photochemical
- Biosynthetic phases of photosynthesis
- Cyclic and non cyclic and photophosphorylation
- Chemiosmotic hypothesis
- Photorespiration C3 and C4 pathways
- Factors affecting photosynthesis

##### Respiration in Plants

- Respiration
- Exchange gases
- Cellular respiration-glycolysis
- Fermentation (anaerobic)
- TCA cycle and electron transport system (aerobic)
- Energy relations-Number of ATP molecules generated
- Amphibolic pathways
- Respiratory quotient

##### Plant - Growth and Development

- Plant growth and development
- Seed germination
- Phases of Plant growth and plant growth rate
- Conditions of growth
- Differentiation, dedifferentiation and redifferentiation
- Sequence of developmental process in a plant cell
- Growth regulator sauxin, gibberellin, cytokinin, ethylene, ABA

#### UNIT V: HUMAN PHYSIOLOGY

##### Breathing and Exchange of Gases

- Respiratory organs in animals (recall only)
- Respiratory system in humans
- Mechanism of breathing and its regulation in humans-Exchange of gases
- Transport of gases
- Regulation of respiration Respiratory volumes
- Disorders related to respiration-Asthma
- Emphysema
- Occupational respiratory disorders

##### Body Fluids and Circulation

- Composition of blood
- Blood groups
- Coagulation of blood
- Composition of lymph and its function
- Human circulatory system-Structure of human heart
- Blood vessels
- Cardiac cycle, cardiac output, ECG
- Double circulation
- Regulation of cardiac activity
- Disorders of circulatory system-Hypertension
- Coronary artery disease
- Angina pectoris
- Heart failure

##### Excretory Products and their Elimination

- Modes of excretion- Ammonotelism, ureotelism, uricotelism
- Human excretory system-structure and fuction
- Urine formation
- Osmoregulation
- Regulation of kidney function-Renin
- Angiotensin
- Atrial Natriuretic Factor
- ADH and Diabetes insipidus
- Role of other organs in excretion
- Disorders
- Uraemia, Renal failure, Renal calculi, Nephritis
- Dialysis and artificial kidney

##### Locomotion and Movement

- Types of movement
- Ciliary
- Fiagellar
- Muscular
- Skeletal muscle-contractile proteins
- Muscle contraction
- Skeletal system and its functions(To be dealt with the relevant practical of Practical syllabus)
- Joints
- Disorders of muscular and skeletal system
- Myasthenia gravis, Tetany, Muscular dystrophy
- Arthritis
- Osteoporosis
- Gout

##### Neural control and Coordination

- Neuron and nerves
- Nervous system in humans central nervous system
- peripheral nervous system and visceral nervous system
- Generation and conduction of nerve impulse
- Reflex action
- Sensory perception
- Sense organs
- Elementary structure and functions of eye and ear

##### Chemical Coordination and Integration

- Endocrine glands and hormones
- Human endocrine system
- Hypothalamus
- Pituitary
- Pineal
- Thyroid
- Parathyroid
- Adrenal
- Pancreas
- Gonads
- Mechanism of hormone action(Elementary Idea)
- Role of hormones as messengers and regulators
- Hypo-and hyperactivity and related disorders
- Common disorders e.g. Dwarfism
- Acromegaly
- Cretinism
- Goiter
- Exopthalmic goiter
- Diabetes
- Addison’s disease (Imp: Diseases and disorders mentioned above to be dealt in brief)

## BIOLOGY-XII

#### UNIT I: REPRODUCTION

##### Sexual Reproduction in Flowering Plants

- Flower structure
- Development of male and female gametophytes
- Pollination-types, agencies and examples
- Outbreeding devices; Pollen-Pistil interaction
- Double fertilization
- Post fertilization events- Development of endosperm and embryo
- Development of seed and formation of fruit
- Special modes apomixis parthenocarpy, polyembryony
- Significance of seed and fruit formation

##### Human Reproduction

- Male and female reproductive systems
- Microscopic anatomy of testis and ovary
- Gametogenesis-spermatogenesis
- Oogenesis
- Menstrual cycle
- Fertilisation
- Embryo development upto blastocyst formation
- Implantation
- Pregnancy and placenta formation(Elementary idea)
- Parturition (Elementary idea)
- Lactation (Elementary idea)

##### Reproductive Health

- Need for reproductive health and prevention of sexually transmitted diseases (STD)
- Birth control-Need and Methods
- Contraception and Medical Termination of Pregnancy (MTP)
- Amniocentesis
- Infertility and assisted reproductive technologies — IVF, ZIFT, GIFT (Elementary idea for general awareness)

#### UNIT II: GENETICS AND EVOLUTION

##### Principles of Inheritance and Variation

- Heredity and variation
- Mendelian Inheritance
- Deviations from Mendelism
- Incomplete dominance
- Co-dominance
- Multiple alleles
- Inheritance of blood groups
- Pleiotropy
- Elementary idea of polygenic inheritance
- Chromosome theory of inheritance
- Chromosomes and genes
- Sex determination -
- In humans
- Birds
- Honey bee
- Linkage and crossing over
- Sex linked inheritance -
- Haemophilia
- Colour blindness
- Mendelian disorders in humans -
- Thalassemia
- Chromosomal disorders in humans
- Down’s syndrome
- Turner’s syndrome
- Klinefelter’s syndromes

##### Molecular Basis of Inheritance

- Search for genetic material
- And DNA as genetic material
- Structure of DNA
- RNA
- DNA packaging
- DNA replication
- Central dogma
- Transcription
- Genetic code
- Translation
- Gene expression and regulation- Lac Operon
- Genome and human genome project
- DNA finger printing
- Protein biosynthesis

##### Evolution

- Evolution: Origin of life
- Biological evolution and evidences for biological evolution from Paleontology
- Comparative anatomy
- Embryology and molecular evidence
- Darwin’s contribution
- Modern Synthetic theory of Evolution
- Mechanism of evolution
- Variation(Mutation and Recombination)
- Natural Selection with examples
- Types of natural selection
- Gene flow and genetic drift
- Hardy-Weinberg’s principle
- Adaptive Radiation
- Human evolution

#### UNIT III: BIOLOGY AND HUMAN WELFARE

##### Human Health and Diseases

- Health and Disease
- Pathogens
- Parasites causing human diseases
- Malaria
- Filariasis
- Ascariasis
- Typhoid
- Pneumonia
- Common cold
- Amoebiasis
- Ring worm
- Dengue
- Chikungunya
- Basic concepts of immunology
- Vaccines
- Cancer
- HIV and AIDS
- Adolescence
- Drug and alcohol abuse
- Tobacco abuse

##### Microbes in Human Welfare

- Microbes in human welfare
- In household food processing
- Industrial production
- Sewage treatment
- Energy generation
- As biocontrol agents and biofertilizers
- Antibiotics
- Production and judicious use

#### UNIT IV: BIOTECHNOLOGY AND ITS APPLICATIONS

##### Biotechnology - Principles and Processes

##### Biotechnology and its Application

- Application of Biotechnology in health and agriculture
- Human insulin
- Vaccine production
- Gene therapy
- Genetically modified organisms-Bt crops
- Transgenic Animals
- Biosafety issues-Biopiracy and patents

#### UNIT V: ECOLOGY AND ENVIRONMENT

##### Organisms and Populations

- Organisms and environment Population interactions mutualism, competition. predation, parasitism
- Population attributes-growth, birth rate and death rate, age distribution

##### Ecosystem

- Ecosystem: Patterns, components
- Productivity and decomposition
- Energy flow
- Pyramids of number
- Biomass
- Energy