## CBSE (Central Board of Secondary Education)

The curriculum is aimed to encompass CBSE syllabus. The ‘fundamental’ and ‘additional’ modules in our curriculum, in addition, to give a deeper and clearer understanding of subjects will also enrich students ability for competitive exams.

## CBSE (Central Board of Secondary Education)

The curriculum is aimed to encompass CBSE syllabus. The ‘fundamental’ and ‘additional’ modules in our curriculum, in addition, to give a deeper and clearer understanding of subjects will also enrich students ability for competitive exams.

## Courses Available Online and Offline

### Class 8th

Students who passed 7th grade and moving to 8th grade may join us for our group tutoring sessions or may opt for one-on-one sessions. We teach all courses over a full academic year. We offer two sciences (Physics & Chemistry) and Mathematics.

Our full-length tests are in accordance with CBSE.

### Class 9th

Students who passed 8th grade and moving to 9th grade may join us for our group tutoring sessions or may opt for one-on-one sessions. We teach all courses over a full academic year. We offer two sciences (Physics & Chemistry) and Mathematics.

Our full-length tests are in accordance with CBSE.

### Class 10th

Students who passed 9th grade and moving to 10th grade may join us for our group tutoring sessions or may opt for one-on-one sessions. We teach all courses over a full academic year. We offer two sciences (Physics & Chemistry) and Mathematics.

Our full-length tests are in accordance with CBSE.

### Class 11th

Students who passed 10th grade and moving to 11th grade may join us for our group tutoring sessions or may opt for one-on-one sessions. We teach all courses over a full academic year. We offer Physics and Mathematics courses.

Our full-length tests are in accordance with CBSE.

### Class 12th

Students who passed 11th grade and moving to 12th grade may join us for our group tutoring sessions or may opt for one-on-one sessions. We teach all courses over a full academic year. We offer Physics and Mathematics courses.

Our full-length tests are in accordance with CBSE.

- Crop Production and Management
- Microorganisms: Friend and Foe
- Synthetic Fibres and Plastics
- Materials: Metals and Non-Metals
- Coal and Petroleum
- Combustion and Flame
- Conservation of Plants and Animals
- Cell – Structure and Functions
- Reproduction in Animals
- Reaching the Age of Adolescence
- Force and Pressure
- Friction
- Sound
- Chemical Effects of Electric Current
- Some Natural Phenomena
- Light
- Stars and Solar System
- Pollution of Air and Water

- Rational Numbers
- Linear Equations in One Variable
- Understanding Quadrilaterials
- Practical Geometry
- Data Handling
- Squares and Squares Roots
- Cubes and Cube Roots
- Comparing Quantities
- Algebraic Expressions and Identties
- Visualizing Solid Shapes
- Mensuration
- Exponents and Powers
- Direct and Inverse Proportions
- Factorization
- Introduction to Graphs
- Playing with Numbers

- Matter in Our Surroundings
- Is Matter Around us Pure
- Atoms and Molecules
- Structure of the Atom
- The Fundamental Unit of Life
- Tissues
- Diversity in Living Organisms
- Motion
- Force and Laws of Motion
- Gravitation
- Work and Energy
- Sound
- Why do we Fall Ill
- Natural Resources
- Improvement in Food Resources

- Number Systems
- Introduction
- Irrational Numbers
- Real Numbers and Their Decimal Expansions
- Representing Real Numbers on the Number Line
- Operations on Real Numbers
- Laws of Exponents for Real Numbers
- Summary

- Polynomials
- Introduction
- Polynomials in One Variable
- Zeroes of a Polynomial
- Remainder Theorem
- Factorisation of Polynomials
- Algebraic Identities
- Summary

- Coordinate Geometry
- Introduction
- Cartesian System
- Plotting a Point in the Plane if its Coordinates are given
- Summary

- Linear Equations in Two Variables
- Introduction
- Linear Equations
- Solution of a Linear Equation
- Graph of a Linear Equation in Two Variables
- Equations of Lines Parallel to x-axis and y-axis
- Summary

- Introduction to Euclid’s Geometry
- Introduction
- Euclid’s Definitions, Axioms and Postulates
- Equivalent Versions of Euclid’s Fifth Postulate
- Summary

- Lines and Angles
- Introduction
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle
- Summary

- Triangles
- Introduction
- Congruence of Traingles
- Criteria for Congruence of Traingles
- Some Properties of a triangle
- Some More Criteria for Congruence of Triangles
- Inequalities in a Triangle
- Summary

- Quadrilaterals
- Introduction
- Angle Sum Property of a Quadrilaterals
- Types of Quadrilaterals
- Properties of a Parallelogram
- Another Condition for a Quadrilateral to be a Parallewlgoram
- The mid-point Theorem
- Summary

- Areas of Parallelograms and Triangles
- Introduction
- Figures on the Same Base and between the Same Parallels
- Parallelograms on the same base and between the same Parallels
- Triangles on the same base and between the same parallels
- Summary

- Circles
- Introduction
- Circles and its Related Terms: A Review
- Angle Subtended by a Chord at a POint
- Perpendicular from the Centre to a Chord
- Circle Through Three Points
- Equal Chords and their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilaterals
- Summary

- Constructions
- Introduction
- Basic Constructions
- Some Constructions of Triangles
- Summary

- Heron’s Formula
- Introduction
- Area of a Triangle – by Heron’s Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Summary

- Surface Areas and Volumes
- Introduction
- Surface Area of a Cuboid and Cube
- Surface Area of A right Circular Cylinder
- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Volume of a Cuboid
- Volume of a Cylinder
- Volume of a Right Circular Cone
- Volume of a Sphere
- Summary

- Statistics
- Introduction
- Collection of Data
- Presentation of Data
- Geographical Representation of Data
- Measures of Central Tendency
- Summary

- Probability
- Introduction
- Probability – an Experimental Approach
- Summary

- Chemical Reactions and Equations
- Acids, Bases and Slats
- Metals and Non-metals
- Carbon and its Compounds
- Periodic Classification of Elements
- Life Processes
- Control and Coordination
- How Organisms Reproduce?
- Heredity and Evolution
- Light – Reflection and Refraction
- Human Eye and Colourful World
- Electricity
- Magnetic Effects of Electric Current
- Sources of Energy
- Our Environment
- Management of Natural Resources

- Real Numbers
- Introduction
- Euclid’s Division Lemma
- The Fundamental Theorem of Arithmetic
- Revisiting Irrational Numbers
- Revisiting Rational Numbers and Their Decimal Expansions
- Summary

- Polynomials
- Introduction
- Geometrical Meaning of the Zeroes of a Polynomial
- Relationship between Zeroes and Coefficients of a Polynomial
- Division Algorithm for Polynomials
- Summary

- Pair of Linear Equations in Two Variables
- Introduction
- Pair of Linear Equations in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Algebraic Methods of Solving a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross-Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Summary

- Quadratic Equations
- Introduction
- Quadratic Equations
- Solution of a Quadratic Equation by Factorisation
- Solution of a Quadratic Equation by Completing the Square
- Nature of Roots
- Summary

- Arithmetic Progressions
- Introduction
- Arithmetic Progressions
- nth Term of an AP
- Sum of First n Terms of an AP
- Summary

- Triangles
- Introduction
- Similar Figures
- Similarity of Triangles
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Pythagoras Theorem
- Summary

- Coordinate Geometry
- Introduction
- Distance Formula
- Section Formula
- Area of a Triangle
- Summary

- Introduction to Trigonometry
- Introduction
- Trigonometric Ratios
- Trigonometric Ratios of Some Specific Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometric Indentities
- Summary

- Some Applications of Trigonometry
- Introduction
- Heights and Distances
- Summary

- 10. circles
- Introduction
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Summary

- Construction
- Introduction
- Division of a Line Segment
- Construction of Tangents to a Circle
- Summary

- Areas Related to Circles
- Introduction
- Surface Area of a Combination of Solids
- The volume of a Combination of Solids
- Conversion of Solid from One Shape to Another
- Frustum of a Cone
- Summary

- 14. Statistics
- Introduction
- Mena of Grouped Data
- Mode of Grouped Data
- Median of Grouped Data
- Graphical Representation of Cumulative Frequency Distribution
- Summary

- Probability
- Introduction
- Probability – AtTheoretical Approach
- Summary

### Unit I: Physical World and Measurement

**Chapter 1: Physical World**- Physics – scope and excitement
- Nature of physical laws
- Physics, technology and society

**Chapter 2: Units and Measurements**- Need for measurement
- Units of measurement
- Systems of units −
- SI units
- Fundamental and derived units

- Length, mass and time measurements
- Accuracy and precision of measuring instruments
- Errors in measurement
- Significant figures
- Dimensions of physical quantities
- Dimensional analysis and its applications

### Unit II: Kinematics

**Chapter 3: Motion in a Straight Line**Frame of reference

Motion in a straight line

Position-time graph

Speed and velocity

Elementary concepts of differentiation and integration for describing motion

Uniform and non-uniform motion

Average speed and instantaneous velocity

Uniformly accelerated motion

Velocity time

Position-time graphs

Relations for uniformly accelerated motion (graphical treatment)

**Chapter 4: Motion in a Plane**- Scalar and vector quantities
- Position and displacement vectors
- general vectors and their notations
- equality of vectors, multiplication of vectors by a real number
- addition and subtraction of vectors
- Relative velocity
- Unit vector
- Resolution of a vector in a plane – rectangular components
- Scalar and Vector product of vectors
- Motion in a plane
- Cases of uniform velocity and uniform acceleration-projectile motion
- Uniform circular motion

### Unit III: Laws of Motion

**Chapter 5: Laws of Motion**Intuitive concept of force

Inertia

Newton’s first law of motion

momentum and 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

lubrication

Dynamics of uniform circular motion:

Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on banked road)

### Unit IV: Work, Energy and Power

**Chapter–6: Work, Energy and Power**- Work done by a constant force and a variable force
- Kinetic energy
- Work-energy theorem
- Power
- The notion of potential energy
- The potential energy of a spring
- Conservative forces
- Conservation of mechanical energy (kinetic and potential energies)
- Non-conservative forces
- Motion in a vertical circle
- Elastic and inelastic collisions in one and two dimensions

### Unit V: Motion of System of Particles and Rigid Body

**Chapter 7: System of Particles and Rotational Motion**Centre of mass of a two-particle system

momentum conservation and centre of mass motion

Centre of mass of a rigid body

Centre of mass of a uniform rod

Moment of a force

Torque

angular momentum

laws of conservation of angular momentum and its applications

Equilibrium of rigid bodies

rigid body rotation and equations of rotational motion

comparison of linear and rotational motions

Moment of inertia

radius of gyration

Values of moments of inertia, for simple geometrical objects (no derivation)

Statement of parallel and perpendicular axes theorems and their applications

### Unit VI: Gravitation

**Chapter 8: Gravitation**- Keplar’s laws of planetary motion
- The universal law of gravitation
- Acceleration due to gravity and its variation with altitude and depth
- Gravitational potential energy and gravitational potential
- Escape velocity
- Orbital velocity of a satellite
- Geo-stationary satellites

### Unit VII: Properties of Bulk Matter

**Chapter–9: Mechanical Properties of Solids**- Elastic behavior
- Stress-strain relationship
- Hooke’s law
- Young’s modulus
- Bulk modulus
- Shear modulus of rigidity
- Poisson’s ratio
- Elastic energy

**Chapter–10: Mechanical Properties of Fluids**Pressure due to a fluid column

- Pascal’s law and its applications (hydraulic lift and hydraulic brakes)
- Effect of gravity on fluid pressure
- Viscosity
- Stokes’ law
- terminal velocity
- streamline and turbulent flow
- critical velocity
- Bernoulli’s theorem and its applications
- Surface energy and surface tension
- angle of contact
- excess of pressure across a curved surface
- application of surface tension ideas to drops
- bubbles and capillary rise

**Chapter–11: Thermal Properties of Matter**- Heat, temperature, thermal expansion
- Thermal expansion of −
- Solids
- Liquids
- Gases

- Anomalous expansion of water
- Specific heat capacity
- Cp, Cv – calorimetry
- Change of state
- Latent heat capacity
- Heat transfer −
- Conduction
- Convection
- radiation

- Thermal conductivity
- Qualitative ideas of Blackbody radiation
- Wein’s displacement Law
- Stefan’s law
- Greenhouse effect

### Unit VIII: Thermodynamics

**Chapter 12: Thermodynamics**- Thermal equilibrium and definition of temperature
- Zeroth law of thermodynamics

- Heat, work and internal energy
- First law of thermodynamics
- Isothermal and adiabatic processes
- Second law of thermodynamics −
- Reversible and irreversible processes

- Heat engine and refrigerator

### Unit IX: Behaviour of Perfect Gases and Kinetic Theory of Gases

**Chapter–13: Kinetic Theory**Equation of state of a perfect gas

Work done in 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 equi-partition of energy (statement only) and application to specific heat capacities of gases

Concept of mean free path

Avogadro’s number

### Unit X: Oscillations and Waves

**Chapter 14: Oscillations**Periodic motion – time period, frequency, displacement as a function of time

Periodic functions

Simple harmonic motion (S.H.M) and its equation

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

Free, forced and damped oscillations (qualitative ideas only), resonance

**Chapter–15: Waves**- Wave motion
- Transverse and longitudinal waves
- speed of wave motion
- 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
- Doppler effect

### Unit-I: Sets and Functions

**Chapter 1: Sets**

- Sets and their representations
- Empty set
- Finite and Infinite sets
- Equal sets. Subsets
- Subsets of a set of real numbers especially intervals (with notations)
- Power set
- Universal set
- Venn diagrams
- Union and Intersection of sets
- Difference of sets
- Complement of a set
- Properties of Complement Sets
- Practical Problems based on sets

**Chapter 2: Relations & Functions**

Ordered pairs

Cartesian product of sets

Number of elements in the cartesian product of two finite sets

Cartesian product of the sets of real (up to R × R)

Definition of −

Relation

Pictorial diagrams

Domain

Co-domain

Range of a relation

Function as a special kind of relation from one set to another

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

Greatest integer functions (with their graphs)

Sum, difference, product and quotients of functions.

**Chapter 3: Trigonometric Functions**

Positive and negative angles

Measuring angles in radians and in degrees and conversion of one into other

Definition of trigonometric functions with the help of unit circle

Truth of the sin

^{2}x + cos^{2}x = 1, for all xSigns of trigonometric functions

Domain and range of trigonometric functions and their graphs

Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x

General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

### Unit-II: Algebra

**Chapter 1: Principle of Mathematical Induction**

Process of the proof by induction −

Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers

The principle of mathematical induction and simple applications

**Chapter 2: Complex Numbers and Quadratic Equations**

Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations

Algebraic properties of complex numbers

Argand plane and polar representation of complex numbers

Statement of Fundamental Theorem of Algebra

Solution of quadratic equations in the complex number system

Square root of a complex number

**Chapter 3: 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 solution of system of linear inequalities in two variables

**Chapter 4: Permutations and Combinations**

- Fundamental principle of counting
- Factorial n
- (n!) Permutations and combinations
- Derivation of formulae and their connections
- Simple applications.

**Chapter 5: Binomial Theorem**

- History
- Statement and proof of the binomial theorem for positive integral indices
- Pascal’s triangle
- General and middle term in binomial expansion
- Simple applications

**Chapter 6: Sequence and Series**

- Sequence and Series
- Arithmetic Progression (A.P.)
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.)
- General term of a G.P.
- Sum of n terms of a G.P.
- Arithmetic and Geometric series infinite G.P. and its sum
- Geometric mean (G.M.)
- Relation between A.M. and G.M.

### Unit-III: Coordinate Geometry

**Chapter 1: Straight Lines**

Brief recall of two dimensional geometries from earlier classes

Shifting of origin

Slope of a line and angle between two lines

Various forms of equations of a line −

Parallel to axis

Point-slope form

Slope-intercept form

Two-point form

Intercept form

Normal form

General equation of a line

Equation of family of lines passing through the point of intersection of two lines

Distance of a point from a line

**Chapter 2: Conic Sections**

Sections of a cone −

Circles

Ellipse

Parabola

Hyperbola − a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section.

Standard equations and simple properties of −

Parabola

Ellipse

Hyperbola

Standard equation of a circle

**Chapter 3. Introduction to Three–dimensional Geometry**

- Coordinate axes and coordinate planes in three dimensions
- Coordinates of a point
- Distance between two points and section formula

### Unit-IV: Calculus

**Chapter 1: Limits and Derivatives**

Derivative introduced as rate of change both as that of distance function and geometrically

Intuitive idea of limit

Limits of −

Polynomials and rational functions

Trigonometric, exponential and logarithmic functions

Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions

The derivative of polynomial and trigonometric functions

### Unit-V: Mathematical Reasoning

**Chapter 1: Mathematical Reasoning**

Mathematically acceptable statements

Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics

Validating the statements involving the connecting words difference between contradiction, converse and contrapositive

### Unit-VI: Statistics and Probability

**Chapter 1: Statistics**

Measures of dispersion −

Range

Mean deviation

Variance

Standard deviation of ungrouped/grouped data

Analysis of frequency distributions with equal means but different variances.

**Chapter 2: Probability**

- Random experiments −
- Outcomes
- Sample spaces (set representation)

- Events −
- Occurrence of events, ‘not’, ‘and’ and ‘or’ events
- Exhaustive events
- Mutually exclusive events
- Axiomatic (set theoretic) probability
- Connections with the theories of earlier classes

- Probability of −
- An event
- probability of ‘not’, ‘and’ and ‘or’ events

### Unit I: Electrostatics

**Chapter 1: Electric Charges and Fields**Electric Charges −

Conservation of charge

Coulomb’s law-force between two point charges

Forces between multiple charges

Superposition principle

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 uniform electric field.

Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).

**Chapter-2: Electrostatic Potential and Capacitance**Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges

Equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field

Conductors and insulators, free charges and bound charges inside a conductor

Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.

### Unit II: Current Electricity

**Chapter 3: Current Electricity**Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current

Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity

Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance

Internal resistance of a cell, potential difference and EMF of a cell, combination of cells in series and in parallel

Kirchhoff’s laws and simple 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

### Unit III: Magnetic Effects of Current and Magnetism

**Chapter 4: Moving Charges and Magnetism**Concept of magnetic field −

Oersted’s experiment

Biot – Savart law and its application to current carrying circular loop

Ampere’s law and its applications to infinitely long straight wire

Straight and toroidal solenoids

Force on a moving charge in uniform magnetic and electric fields

Cyclotron

Force on a current-carrying conductor in a uniform magnetic field

Force between two parallel current-carrying conductors-definition of ampere

Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.

**Chapter 5: Magnetism and Matter**Current loop as a magnetic dipole and its magnetic dipole moment

Magnetic dipole moment of a revolving electron

Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis

Torque on a magnetic dipole (bar magnet) in a uniform magnetic field −

Bar magnet as an equivalent solenoid

Magnetic field lines

Earth’s magnetic field

Magnetic elements

Para-, dia- and ferro – magnetic substances, with examples

Electromagnets and factors affecting their strengths

Permanent magnets

### Unit IV: Electromagnetic Induction and Alternating Currents

**Chapter 6: Electromagnetic Induction**- Electromagnetic induction −
- Faraday’s laws
- Induced EMF and current
- Lenz’s Law
- Eddy currents

- Self and mutual induction.

**Chapter 7: Alternating Current**- Alternating currents −
- Peak and RMS value of alternating current/voltage
- Reactance and impedance
- LC oscillations (qualitative treatment only)
- LCR series circuit
- Resonance
- Power in AC circuits
- Wattless current

- AC generator and transformer

### Unit V: Electromagnetic waves

**Chapter 8: Electromagnetic Waves**Basic idea of displacement current, Electromagnetic waves, their characteristics, their transverse nature (qualitative ideas only).

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.

### Unit VI: Optics

**Chapter 9: Ray Optics and Optical Instruments**Ray Optics −

Reflection of light

Spherical mirrors

Mirror formula

Refraction of light

Total internal reflection and its applications

Optical fibres

Refraction at spherical surfaces

Lenses

Thin lens formula

Lensmaker’s formula

Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror

Refraction and dispersion of light through a prism.

Scattering of light – blue colour of sky and reddish appearance of the sun at sunrise and sunset

Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers

**Chapter 10: Wave Optics**Wave optics: Wave front and Huygen’s principle, reflection and refraction of plane wave at a plane surface using wave fronts

Proof of laws of reflection and refraction using Huygen’s 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

Resolving power of microscopes and astronomical telescopes

Polarisation, plane polarised light Brewster’s law, uses of plane polarised light and Polaroids

### Unit VII: Dual Nature of Matter and Radiation

**Chapter 11: 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 particles, de Broglie relation

Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained).

### Unit VIII: Atoms & Nuclei

**Chapter 12: Atoms**- Alpha-particle scattering experiment
- Rutherford’s model of atom
- Bohr model
- Energy levels
- Hydrogen spectrum

**Chapter 13: Nuclei**- Composition and size of −
- Nucleus
- Atomic masses
- Isotopes
- Isobars
- Isotones

- Radioactivity alpha, beta and gamma particles/rays and their properties
- Radioactive decay law
- Mass-energy relation −
- Mass defect
- Binding energy per nucleon and its variation with mass number
- Nuclear fission
- Nuclear fusion

### Unit IX: Electronic Devices

**Chapter 14: Semiconductor Electronics: Materials, Devices and Simple Circuits**Energy bands in conductors, semiconductors and insulators (qualitative ideas only)

Semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier

Special purpose p-n junction diodes: LED, photodiode, solar cell and Zener diode and their characteristics, zener diode as a voltage regulator

Junction transistor, transistor action, characteristics of a transistor and transistor as an amplifier (common emitter configuration), basic idea of analog and digital signals, Logic gates (OR, AND, NOT, NAND and NOR).

### Unit X: Communication Systems

**Chapter 15: Communication Systems**Elements of a communication system (block diagram only)

Bandwidth of signals (speech, TV and digital data)

Bandwidth of transmission medium

Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation, satellite communication

Need for modulation, amplitude modulation and frequency modulation, advantages of frequency modulation over amplitude modulation

Basic ideas about internet, mobile telephony and global positioning system (GPS).

### Unit I: Relations and Functions

**Chapter 1: Relations and Functions**

- Types of relations −
- Reflexive
- Symmetric
- transitive and equivalence relations
- One to one and onto functions
- composite functions
- inverse of a function
- Binary operations

**Chapter 2: Inverse Trigonometric Functions**

- Definition, range, domain, principal value branch
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions

### Unit II: Algebra

**Chapter 1: Matrices**

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices.

Operation on matrices: Addition and multiplication and multiplication with a scalar

Simple properties of addition, multiplication and scalar multiplication

Noncommutativity 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 2: Determinants**

Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle

Ad joint 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

### Unit III: Calculus

**Chapter 1: Continuity and Differentiability**

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions

Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions

Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives

Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation

**Chapter 2: Applications of Derivatives**

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normal, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)

Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)

**Chapter 3: Integrals**

Integration as inverse process of differentiation

Integration of a variety of functions by substitution, by partial fractions and by parts

Evaluation of simple integrals of the following types and problems based on them

$\int \frac{dx}{x^2\pm {a^2}’}$, $\int \frac{dx}{\sqrt{x^2\pm {a^2}’}}$, $\int \frac{dx}{\sqrt{a^2-x^2}}$, $\int \frac{dx}{ax^2+bx+c} \int \frac{dx}{\sqrt{ax^2+bx+c}}$

$\int \frac{px+q}{ax^2+bx+c}dx$, $\int \frac{px+q}{\sqrt{ax^2+bx+c}}dx$, $\int \sqrt{a^2\pm x^2}dx$, $\int \sqrt{x^2-a^2}dx$

$\int \sqrt{ax^2+bx+c}dx$, $\int \left ( px+q \right )\sqrt{ax^2+bx+c}dx$

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)

Basic properties of definite integrals and evaluation of definite integrals

**Chapter 4: Applications of the Integrals**

Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only)

Area between any of the two above said curves (the region should be clearly identifiable)

**Chapter 5: Differential Equations**

Definition, order and degree, general and particular solutions of a differential equation

Formation of differential equation whose general solution is given

Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree

Solutions of linear differential equation of the type −

dy/dx + py = q, where p and q are functions of x or constants

dx/dy + px = q, where p and q are functions of y or constants

### Unit IV: Vectors and Three-Dimensional Geometry

**Chapter 1: Vectors**

Vectors and scalars, magnitude and direction of a vector

Direction cosines and direction ratios of a vector

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

Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors

**Chapter 2: Three – dimensional Geometry**

Direction cosines and direction ratios of a line joining two points

Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines

Cartesian and vector equation of a plane

Angle between −

Two lines

Two planes

A line and a plane

Distance of a point from a plane

### Unit V: Linear Programming

**Chapter 1: Linear Programming**

- Introduction
- 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 (bounded and unbounded)
- Feasible and infeasible solutions
- Optimal feasible solutions (up to three non-trivial constraints)

### Unit VI: Probability

**Chapter 1: Probability**

- Conditional probability
- Multiplication theorem on 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

## PHYSICS, CHEMISTRY and MATH

Class: 8th| 9th| 10th

## PHYSICS and MATH

Class: 11th| 12th

New Batches Commencing in October. Students appearing for 2022 Exams may join our online or classroom batches.

**Limited Seats Available**