## 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.

1. Crop Production and Management
2. Microorganisms: Friend and Foe
3. Synthetic Fibres and Plastics
4. Materials: Metals and Non-Metals
5. Coal and Petroleum
6. Combustion and Flame
7. Conservation of Plants and Animals
8. Cell – Structure and Functions
9. Reproduction in Animals
10. Reaching the Age of Adolescence
11. Force and Pressure
12. Friction
13. Sound
14. Chemical Effects of Electric Current
15. Some Natural Phenomena
16. Light
17. Stars and Solar System
18. Pollution of Air and Water
1. Rational Numbers
2. Linear Equations in One Variable
4. Practical Geometry
5. Data Handling
6. Squares and Squares Roots
7. Cubes and Cube Roots
8. Comparing Quantities
9. Algebraic Expressions and Identties
10. Visualizing Solid Shapes
11. Mensuration
12. Exponents and Powers
13. Direct and Inverse Proportions
14. Factorization
15. Introduction to Graphs
16. Playing with Numbers
1. Matter in Our Surroundings
2. Is Matter Around us Pure
3. Atoms and Molecules
4. Structure of the Atom
5. The Fundamental Unit of Life
6. Tissues
7. Diversity in Living Organisms
8. Motion
9. Force and Laws of Motion
10. Gravitation
11. Work and Energy
12. Sound
13. Why do we Fall Ill
14. Natural Resources
15. Improvement in Food Resources
1. Number Systems
1. Introduction
2. Irrational Numbers
3. Real Numbers and Their Decimal Expansions
4. Representing Real Numbers on the Number Line
5. Operations on Real Numbers
6. Laws of Exponents for Real Numbers
7. Summary
2. Polynomials
1. Introduction
2. Polynomials in One Variable
3. Zeroes of a Polynomial
4. Remainder Theorem
5. Factorisation of Polynomials
6. Algebraic Identities
7. Summary
3. Coordinate Geometry
1. Introduction
2. Cartesian System
3. Plotting a Point in the Plane if its Coordinates are given
4. Summary
4. Linear Equations in Two Variables
1. Introduction
2. Linear Equations
3. Solution of a Linear Equation
4. Graph of a Linear Equation in Two Variables
5. Equations of Lines Parallel to x-axis and y-axis
6. Summary
5. Introduction to Euclid’s Geometry
1. Introduction
2. Euclid’s Definitions, Axioms and Postulates
3. Equivalent Versions of Euclid’s Fifth Postulate
4. Summary
6. Lines and Angles
1. Introduction
2. Basic Terms and Definitions
3. Intersecting Lines and Non-intersecting Lines
4. Pairs of Angles
5. Parallel Lines and a Transversal
6. Lines Parallel to the Same Line
7. Angle Sum Property of a Triangle
8. Summary
7. Triangles
1. Introduction
2. Congruence of Traingles
3. Criteria for Congruence of Traingles
4. Some Properties of a triangle
5. Some More Criteria for Congruence of Triangles
6. Inequalities in a Triangle
7. Summary
1. Introduction
2. Angle Sum Property of  a Quadrilaterals
4. Properties of a Parallelogram
5. Another Condition for a Quadrilateral to be a Parallewlgoram
6. The mid-point Theorem
7. Summary
9. Areas of Parallelograms and Triangles
1. Introduction
2. Figures on the Same Base and between the Same Parallels
3. Parallelograms on the same base and between the same Parallels
4. Triangles on the same base and between the same parallels
5. Summary
10. Circles
1. Introduction
2. Circles and its Related Terms: A Review
3. Angle Subtended by a Chord at a POint
4. Perpendicular from the Centre to a Chord
5. Circle Through Three Points
6. Equal Chords and their Distances from the Centre
7. Angle Subtended by an Arc of a Circle
9. Summary
11. Constructions
1. Introduction
2. Basic Constructions
3. Some Constructions of Triangles
4. Summary
12. Heron’s Formula
1. Introduction
2. Area of a Triangle – by Heron’s Formula
3. Application of Heron’s Formula in Finding Areas of Quadrilaterals
4. Summary
13. Surface Areas and Volumes
1. Introduction
2. Surface Area of a Cuboid and Cube
3. Surface Area of A right Circular Cylinder
4. Surface Area of a Right Circular Cone
5. Surface Area of a Sphere
6. Volume of a Cuboid
7. Volume of a Cylinder
8. Volume of a Right Circular Cone
9. Volume of a Sphere
10. Summary
14. Statistics
1. Introduction
2. Collection of Data
3. Presentation of Data
4. Geographical Representation of Data
5. Measures of Central Tendency
6. Summary
15. Probability
1. Introduction
2. Probability – an Experimental Approach
3. Summary
1. Chemical Reactions and Equations
2. Acids, Bases and Slats
3. Metals and Non-metals
4. Carbon and its Compounds
5. Periodic Classification of Elements
6. Life Processes
7. Control and Coordination
8. How Organisms Reproduce?
9. Heredity and Evolution
10. Light – Reflection and Refraction
11. Human Eye and Colourful World
12. Electricity
13. Magnetic Effects of Electric Current
14. Sources of Energy
15. Our Environment
16. Management of Natural Resources
1. Real Numbers
1. Introduction
2. Euclid’s Division Lemma
3. The Fundamental Theorem of Arithmetic
4. Revisiting Irrational Numbers
5. Revisiting Rational Numbers and Their Decimal Expansions
6. Summary
2. Polynomials
1. Introduction
2. Geometrical Meaning of the Zeroes of a Polynomial
3. Relationship between Zeroes and Coefficients of a Polynomial
4. Division Algorithm for Polynomials
5. Summary
3. Pair of Linear Equations in Two Variables
1. Introduction
2. Pair of Linear Equations in Two Variables
3. Graphical Method of Solution of a Pair of Linear Equations
4. Algebraic Methods of Solving a Pair of Linear Equations
5. Substitution Method
6. Elimination Method
7. Cross-Multiplication Method
8. Equations Reducible to a Pair of Linear Equations in Two Variables
9. Summary
1. Introduction
3. Solution of a Quadratic Equation by Factorisation
4. Solution of a Quadratic Equation by Completing the Square
5. Nature of Roots
6. Summary
5. Arithmetic Progressions
1. Introduction
2. Arithmetic Progressions
3. nth Term of an AP
4. Sum of First n Terms of an AP
5. Summary
6. Triangles
1. Introduction
2. Similar Figures
3. Similarity of Triangles
4. Criteria for Similarity of Triangles
5. Areas of Similar Triangles
6. Pythagoras Theorem
7. Summary
7. Coordinate Geometry
1. Introduction
2. Distance Formula
3. Section Formula
4. Area of a Triangle
5. Summary
8. Introduction to Trigonometry
1. Introduction
2. Trigonometric Ratios
3. Trigonometric Ratios of Some Specific Angles
4. Trigonometric Ratios of Complementary Angles
5. Trigonometric Indentities
6. Summary
9. Some Applications of Trigonometry
1. Introduction
2. Heights and Distances
3. Summary
10. 10. circles
1. Introduction
2. Tangent to a Circle
3. Number of Tangents from a Point on a Circle
4. Summary
11. Construction
1. Introduction
2. Division of a Line Segment
3. Construction of Tangents to a Circle
4. Summary
12. Areas Related to Circles
1. Introduction
2. Surface Area of a Combination of Solids
3. The volume of a Combination of Solids
4. Conversion of Solid from One Shape to Another
5. Frustum of a Cone
6. Summary
13. 14. Statistics
1. Introduction
2. Mena of Grouped Data
3. Mode of Grouped Data
4. Median of Grouped Data
5. Graphical Representation of Cumulative Frequency Distribution
6. Summary
14. Probability
1. Introduction
2. Probability – AtTheoretical Approach
3. Summary
1. ### 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

• 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
• 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
• 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

### 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 sin2x + cos2x = 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 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
1. ### 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 −
• 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

• 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
• 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

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