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Mathematics · Part 2

Class 10 Mathematics

Real Numbers

Introduction The Fundamental Theorem of Arithmetic

HCF and LCM, the Prime Way

Practice: Factors, HCF and LCM

Revisiting Irrational Numbers

Practice: Proving Irrationality

Summary

Polynomials

Introduction Geometrical Meaning of the Zeroes of a Polynomial

Practice: Zeroes from Graphs

Relationship between Zeroes and Coefficients of a Polynomial

Practice: Zeroes and Coefficients

Summary

Pair of Linear Equations in Two Variables

Introduction Graphical Method of Solution of a Pair of Linear Equations

Practice: Graphing Pairs of Equations

Algebraic Methods of Solving a Pair of Linear Equations

Practice: Substitution Method

Elimination Method

Practice: Elimination Method

Summary

Quadratic Equations

Introduction Quadratic Equations

Practice: Recognising Quadratic Equations

Solution of a Quadratic Equation by Factorisation

Practice: Solving by Factorisation

Nature of Roots

Practice: Nature of Roots

Summary

Arithmetic Progressions

Introduction Arithmetic Progressions

Practice: Identifying and Building APs

nth Term of an AP

Practice: The nth Term of an AP

Sum of First n Terms of an AP

Practice: Sums, Sequences and Word Problems

Practice: AP Challenge Problems (Optional)

Summary

Triangles

Introduction Similar Figures

Practice: Recognising Similar Figures

Similarity of Triangles

Practice: The Basic Proportionality Theorem

Criteria for Similarity of Triangles

Practice: Similarity Criteria in Action

Summary

Coordinate Geometry

Introduction Distance Formula

Practice: Coordinate Distances

Section Formula

Practice: Dividing Segments in a Ratio

Summary

Introduction to Trigonometry

Introduction Trigonometric Ratios

Practice: Ratios in a Right Triangle

Trigonometric Ratios of Some Specific Angles

Practice: Ratios of Special Angles

Trigonometric Identities

Practice: Trigonometric Identities

Summary

Some Applications of Trigonometry

Heights and Distances

Practice: Elevation and Depression

Summary

Circles

Introduction Tangent to a Circle

Practice: Tangent Perpendicularity

Number of Tangents from a Point on a Circle

Practice: Tangent Lengths and Angles

Summary

Areas Related to Circles

Areas of Sector and Segment of a Circle

Practice: Sectors and Segments

Summary

Surface Areas and Volumes

Introduction Surface Area of a Combination of Solids

Practice: Surface Area of Combined Solids

Volume of a Combination of Solids

Practice: Volume of Combined Solids

Summary

Statistics

Introduction Mean of Grouped Data

Practice: Mean of Grouped Data

Mode of Grouped Data

Practice: Mode of Grouped Data

Median of Grouped Data

Practice: Mean, Median and Mode

Summary

Probability

Probability — A Theoretical Approach

Practice: Theoretical Probability

Summary

Class 10 Science

Chemical Reactions and Equations

Introduction Chemical Equations

Practice: Writing and Balancing Equations

Types of Chemical Reactions

Practice: Types of Reactions

Have You Observed the Effects of Oxidation Reactions in Everyday Life?

Chapter Review: Mixed Practice

Summary

Acids, Bases and Salts

Introduction Understanding the Chemical Properties of Acids and Bases

Practice: Reactions of Acids and Bases

What do All Acids and All Bases Have in Common?

Practice: Ions in Solution

How Strong are Acid or Base Solutions?

Practice: The pH Scale

More About Salts

Practice: Salts and Their Uses

Chapter Review: Mixed Practice

Summary

Metals and Non-metals

Introduction Physical Properties

Practice: Physical Properties

Chemical Properties of Metals

Practice: Reactivity of Metals

How do Metals and Non-metals React?

Practice: Ionic Compounds

Occurrence of Metals

Corrosion

Practice: Extraction and Corrosion

Chapter Review: Mixed Practice

Summary

Carbon and its Compounds

Introduction Bonding in Carbon – The Covalent Bond

Practice: Covalent Bonding

Versatile Nature of Carbon

Practice: Hydrocarbons and Nomenclature

Chemical Properties of Carbon Compounds

Practice: Reactions of Carbon Compounds

Some Important Carbon Compounds – Ethanol and Ethanoic Acid

Soaps and Detergents

Practice: Ethanol, Ethanoic Acid and Soaps

Chapter Review: Mixed Practice

Summary

Life Processes

Introduction What are Life Processes?

Nutrition

Practice: Nutrition

Respiration

Practice: Respiration

Transportation

Practice: Transportation

Excretion

Practice: Excretion

Chapter Review: Mixed Practice

Summary

Control and Coordination

Introduction Animals – Nervous System

Practice: The Nervous System

Coordination in Plants

Practice: Coordination in Plants

Hormones in Animals

Practice: Hormones

Chapter Review: Mixed Practice

Summary

How do Organisms Reproduce?

Introduction Do Organisms Create Exact Copies of Themselves?

Practice: Variation

Modes of Reproduction Used by Single Organisms

Practice: Asexual Reproduction

Sexual Reproduction

Practice: Sexual Reproduction

Chapter Review: Mixed Practice

Summary

Heredity

Introduction Accumulation of Variation During Reproduction

Practice: Variation

Heredity

Practice: Mendel and Sex Determination

Chapter Review: Mixed Practice

Summary

Light – Reflection and Refraction

Introduction Reflection of Light

Spherical Mirrors

Practice: Spherical Mirrors

Refraction of Light

Practice: Refraction and Refractive Index

Practice: Lenses, Lens Formula and Power

Chapter Review: Mixed Practice

Summary

The Human Eye and the Colourful World

Introduction The Human Eye

Defects of Vision and their Correction

Practice: The Eye and Its Defects

Refraction of Light through a Prism

Dispersion of White Light by a Glass Prism

Atmospheric Refraction

Scattering of Light

Practice: Prism, Dispersion and Scattering

Chapter Review: Mixed Practice

Summary

Electricity

Introduction Electric Current and Circuit

Electric Potential and Potential Difference

Practice: Current and Potential Difference

Circuit Diagram

Ohm's Law

Factors on which the Resistance of a Conductor Depends

Practice: Ohm's Law and Resistance

Resistance of a System of Resistors

Practice: Series and Parallel Circuits

Heating Effect of Electric Current

Electric Power

Practice: Heating Effect and Power

Chapter Review: Mixed Practice

Summary

Magnetic Effects of Electric Current

Introduction Magnetic Field and Field Lines

Practice: Magnetic Field Lines

Magnetic Field due to a Current-carrying Conductor

Practice: Field due to a Current

Force on a Current-carrying Conductor in a Magnetic Field

Domestic Electric Circuits

Practice: Force on a Conductor and Domestic Circuits

Chapter Review: Mixed Practice

Summary

Our Environment

Introduction Eco-System — What are its Components?

Practice: Ecosystems and Food Chains

How do our Activities Affect the Environment?

Practice: Ozone and Waste

Chapter Review: Mixed Practice

Summary

Class 11 Physics · Part 1

Units and Measurement

Introduction The International System of Units

Practice: Units and the SI

Significant Figures

Practice: Significant Figures

Dimensions of Physical Quantities

Dimensional Formulae and Dimensional Equations

Dimensional Analysis and its Applications

Practice: Dimensions and Dimensional Analysis

Summary

Motion in a Straight Line

Introduction Instantaneous Velocity and Speed

Practice: Position, Velocity and Speed

Acceleration

Practice: Acceleration and Motion Graphs

Kinematic Equations for Uniformly Accelerated Motion

Practice: Equations of Motion

Relative Velocity

Practice: Relative Velocity

Summary

Motion in a Plane

Introduction Scalars and Vectors

Multiplication of Vectors by Real Numbers

Addition and Subtraction of Vectors — Graphical Method

Practice: Scalars, Vectors and Graphical Addition

Resolution of Vectors

Vector Addition — Analytical Method

Practice: Resolution and Analytical Addition

Motion in a Plane

Motion in a Plane with Constant Acceleration

Practice: Motion in a Plane

Projectile Motion

Uniform Circular Motion

Practice: Projectile and Circular Motion

Summary

Laws of Motion

Introduction Aristotle's Fallacy

The Law of Inertia

Newton's First Law of Motion

Practice: Inertia and the First Law

Newton's Second Law of Motion

Practice: The Second Law and Impulse

Newton's Third Law of Motion

Conservation of Momentum

Equilibrium of a Particle

Practice: Third Law, Momentum and Equilibrium

Common Forces in Mechanics

Circular Motion

Solving Problems in Mechanics

Practice: Friction, Circular Motion and Free-Body Diagrams

Summary

Work, Energy and Power

Introduction Notions of Work and Kinetic Energy: The Work-Energy Theorem

Work

Kinetic Energy

Practice: Scalar Product, Work and Kinetic Energy

Work Done by a Variable Force

The Work-Energy Theorem for a Variable Force

Practice: Variable Force and the Work-Energy Theorem

The Concept of Potential Energy

The Conservation of Mechanical Energy

The Potential Energy of a Spring

Practice: Potential Energy and Conservation of Mechanical Energy

Power

Collisions

Practice: Power and Collisions

Summary

System of Particles and Rotational Motion

Introduction Centre of Mass

Motion of Centre of Mass

Linear Momentum of a System of Particles

Practice: Centre of Mass and Linear Momentum

Vector Product of Two Vectors

Angular Velocity and its Relation with Linear Velocity

Torque and Angular Momentum

Practice: Vector Product, Torque and Angular Momentum

Equilibrium of a Rigid Body

Practice: Equilibrium of a Rigid Body

Moment of Inertia

Kinematics of Rotational Motion about a Fixed Axis

Practice: Moment of Inertia and Rotational Kinematics

Dynamics of Rotational Motion about a Fixed Axis

Angular Momentum in Case of Rotation about a Fixed Axis

Practice: Rotational Dynamics and Angular Momentum

Summary

Gravitation

Introduction Kepler's Laws

Universal Law of Gravitation

The Gravitational Constant

Practice: Kepler's Laws and the Law of Gravitation

Acceleration due to Gravity of the Earth

Acceleration due to Gravity below and above the Surface of Earth

Practice: Acceleration due to Gravity

Gravitational Potential Energy

Escape Speed

Practice: Gravitational Potential Energy and Escape Speed

Earth Satellites

Energy of an Orbiting Satellite

Practice: Earth Satellites and Orbital Energy

Summary

Class 11 Physics · Part 2

Mechanical Properties of Solids

Introduction Stress and Strain

Hooke's Law

Stress-Strain Curve

Practice: Stress, Strain and the Stress-Strain Curve

Elastic Moduli

Practice: Elastic Moduli

Applications of Elastic Behaviour of Materials

Practice: Applications of Elasticity

Summary

Mechanical Properties of Fluids

Introduction Pressure

Practice: Pressure and Pascal's Law

Streamline Flow

Bernoulli's Principle

Practice: Streamline Flow and Bernoulli's Principle

Viscosity

Practice: Viscosity and Stokes' Law

Surface Tension

Practice: Surface Tension

Summary

Thermal Properties of Matter

Introduction Temperature and Heat

Measurement of Temperature

Ideal-Gas Equation and Absolute Temperature

Practice: Temperature Scales and the Ideal-Gas Equation

Thermal Expansion

Practice: Thermal Expansion

Specific Heat Capacity

Calorimetry

Change of State

Practice: Specific Heat, Calorimetry and Change of State

Heat Transfer

Newton's Law of Cooling

Practice: Heat Transfer and Newton's Law of Cooling

Summary

Thermodynamics

Introduction Thermal Equilibrium

Zeroth Law of Thermodynamics

Heat, Internal Energy and Work

First Law of Thermodynamics

Practice: Zeroth and First Laws

Specific Heat Capacity

Thermodynamic State Variables and Equation of State

Practice: Specific Heat Capacity and State Variables

Thermodynamic Processes

Practice: Thermodynamic Processes

Second Law of Thermodynamics

Reversible and Irreversible Processes

Carnot Engine

Practice: Second Law and Carnot Engine

Summary

Kinetic Theory

Introduction Molecular Nature of Matter

Behaviour of Gases

Practice: Molecular Nature and Behaviour of Gases

Kinetic Theory of an Ideal Gas

Practice: Kinetic Theory of an Ideal Gas

Law of Equipartition of Energy

Specific Heat Capacity

Mean Free Path

Practice: Equipartition, Specific Heat and Mean Free Path

Summary

Oscillations

Introduction Periodic and Oscillatory Motions

Simple Harmonic Motion

Practice: Periodic Motion and Simple Harmonic Motion

Simple Harmonic Motion and Uniform Circular Motion

Velocity and Acceleration in Simple Harmonic Motion

Practice: Reference Circle, Velocity and Acceleration

Force Law for Simple Harmonic Motion

Energy in Simple Harmonic Motion

Practice: Force Law and Energy in SHM

The Simple Pendulum

Practice: The Simple Pendulum

Summary

Waves

Introduction Transverse and Longitudinal Waves

Displacement Relation in a Progressive Wave

Practice: Types of Waves and the Wave Equation

The Speed of a Travelling Wave

Practice: Speed of a Travelling Wave

The Principle of Superposition of Waves

Reflection of Waves

Beats

Practice: Superposition, Standing Waves and Beats

Summary

Class 11 Chemistry · Part 1

Class 11 Chemistry · Part 2

Class 11 Mathematics

Sets

Introduction Sets and their Representations

Practice: Roster and Set-Builder Form

The Empty Set

Finite and Infinite Sets

Equal Sets

Practice: Empty, Finite and Equal Sets

Subsets

Universal Set

Practice: Subsets and Intervals

Venn Diagrams

Operations on Sets

Practice: Union, Intersection and Difference

Complement of a Set

Practice: Complement of a Set

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Relations and Functions

Introduction Cartesian Products of Sets

Practice: Cartesian Products

Relations

Practice: Domain and Range of a Relation

Functions

Practice: Is It a Function?

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Trigonometric Functions

Introduction Angles

Practice: Degree and Radian Measure

Trigonometric Functions

Practice: Signs and Values of Trig Ratios

Trigonometric Functions of Sum and Difference of Two Angles

Practice: Proving Trig Identities

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Complex Numbers and Quadratic Equations

Introduction Complex Numbers

Algebra of Complex Numbers

The Modulus and the Conjugate of a Complex Number

Practice: Complex Number Arithmetic

Argand Plane and Polar Representation

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Linear Inequalities

Introduction Inequalities

Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

Practice: Solving Linear Inequalities

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Permutations and Combinations

Introduction Fundamental Principle of Counting

Practice: The Multiplication Principle

Permutations

Practice: Factorial Notation

Derivation of the Formula for nPr

Permutations When All the Objects Are Not Distinct Objects

Practice: Permutations and Arrangements

Combinations

Practice: Combinations and Selections

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Binomial Theorem

Introduction Binomial Theorem for Positive Integral Indices

Practice: Binomial Expansions

Chapter Review: Mixed Practice

Summary

Sequences and Series

Introduction Sequences

Series

Practice: Terms of a Sequence

Geometric Progression (G. P.)

Relationship Between A.M. and G.M.

Practice: Geometric Progressions

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Straight Lines

Introduction Slope of a Line

Practice: Coordinates and Slope

Various Forms of the Equation of a Line

Practice: Equations of a Line

Distance of a Point From a Line

Practice: Distance From a Line

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Conic Sections

Introduction Sections of a Cone

Circle

Practice: Circle Equations

Parabola

Practice: Parabola Equations

Ellipse

Practice: Ellipse Equations

Hyperbola

Practice: Hyperbola Equations

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Introduction to Three Dimensional Geometry

Introduction Coordinate Axes and Coordinate Planes in Three Dimensional Space

Coordinates of a Point in Space

Practice: Points and Octants in Space

Distance between Two Points

Practice: Distance in Three Dimensions

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Limits and Derivatives

Introduction Intuitive Idea of Derivatives

Limits

Limits of Trigonometric Functions

Practice: Evaluating Limits

Derivatives

Practice: Derivatives and Differentiation Rules

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Statistics

Introduction Measures of Dispersion

Range

Mean Deviation

Practice: Mean Deviation

Variance and Standard Deviation

Practice: Variance and Standard Deviation

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Probability

Event

Practice: Classifying Events

Axiomatic Approach to Probability

Practice: Computing Probabilities

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Class 12 Physics · Part 1

Electric Charges and Fields

Introduction Electric Charge

Conductors and Insulators

Basic Properties of Electric Charge

Coulomb's Law

Forces between Multiple Charges

Practice: Charges and Coulomb's Law

Electric Field

Electric Field Lines

Electric Flux

Electric Dipole

Dipole in a Uniform External Field

Practice: Electric Field and Dipoles

Continuous Charge Distribution

Gauss's Law

Applications of Gauss's Law

Practice: Gauss's Law

Chapter Review: Mixed Practice

Summary

Electrostatic Potential and Capacitance

Introduction Electrostatic Potential

Potential due to a Point Charge

Potential due to an Electric Dipole

Potential due to a System of Charges

Equipotential Surfaces

Practice: Potential and Equipotential Surfaces

Potential Energy of a System of Charges

Potential Energy in an External Field

Electrostatics of Conductors

Dielectrics and Polarisation

Practice: Potential Energy, Conductors and Dielectrics

Capacitors and Capacitance

The Parallel Plate Capacitor

Effect of Dielectric on Capacitance

Combination of Capacitors

Energy Stored in a Capacitor

Practice: Capacitors

Summary

Current Electricity

Introduction Electric Current

Electric Currents in Conductors

Ohm's Law

Drift of Electrons and the Origin of Resistivity

Limitations of Ohm's Law

Practice: Current, Drift and Ohm's Law

Resistivity of Various Materials

Temperature Dependence of Resistivity

Electrical Energy, Power

Practice: Resistivity, Temperature and Power

Cells, emf, Internal Resistance

Cells in Series and in Parallel

Practice: Cells and Their Combinations

Kirchhoff's Rules

Wheatstone Bridge

Practice: Kirchhoff's Rules and Wheatstone Bridge

Chapter Review: Mixed Practice

Summary

Moving Charges and Magnetism

Introduction Magnetic Force

Motion in a Magnetic Field

Practice: Magnetic Force and Motion in a Field

Magnetic Field due to a Current Element, Biot-Savart Law

Magnetic Field on the Axis of a Circular Current Loop

Practice: Biot-Savart Law and Circular Loops

Ampere's Circuital Law

The Solenoid

Practice: Ampere's Law and the Solenoid

Force between Two Parallel Currents, the Ampere

Torque on Current Loop, Magnetic Dipole

The Moving Coil Galvanometer

Practice: Parallel Currents, Torque and the Galvanometer

Chapter Review: Mixed Practice

Summary

Magnetism and Matter

Introduction The Bar Magnet

Practice: The Bar Magnet

Magnetism and Gauss's Law

Magnetisation and Magnetic Intensity

Magnetic Properties of Materials

Practice: Magnetisation and Magnetic Materials

Summary

Electromagnetic Induction

Introduction The Experiments of Faraday and Henry

Magnetic Flux

Faraday's Law of Induction

Practice: Flux and Faraday's Law

Lenz's Law and Conservation of Energy

Motional Electromotive Force

Practice: Lenz's Law and Motional EMF

Inductance

AC Generator

Practice: Inductance and the AC Generator

Chapter Review: Mixed Practice

Summary

Alternating Current

Introduction AC Voltage Applied to a Resistor

Representation of AC Current and Voltage by Rotating Vectors — Phasors

Practice: RMS Values and Phasors

AC Voltage Applied to an Inductor

AC Voltage Applied to a Capacitor

Practice: Reactance of an Inductor and a Capacitor

AC Voltage Applied to a Series LCR Circuit

Practice: Series LCR Circuit and Resonance

Power in AC Circuit: The Power Factor

Transformers

Practice: Power Factor and Transformers

Summary

Electromagnetic Waves

Introduction Displacement Current

Practice: Displacement Current

Electromagnetic Waves

Practice: Electromagnetic Waves

Electromagnetic Spectrum

Practice: Electromagnetic Spectrum

Summary

Class 12 Physics · Part 2

Ray Optics and Optical Instruments

Introduction Reflection of Light by Spherical Mirrors

Practice: Spherical Mirrors

Refraction

Total Internal Reflection

Practice: Refraction and Total Internal Reflection

Refraction at Spherical Surfaces and by Lenses

Practice: Lenses and Lens Combinations

Refraction through a Prism

Optical Instruments

Practice: Prisms and Optical Instruments

Summary

Wave Optics

Introduction Huygens Principle

Refraction and Reflection of Plane Waves using Huygens Principle

Practice: Huygens Principle and Wavefronts

Coherent and Incoherent Addition of Waves

Interference of Light Waves and Young's Experiment

Practice: Interference and Young's Experiment

Diffraction

Polarisation

Practice: Diffraction and Polarisation

Summary

Dual Nature of Radiation and Matter

Introduction Electron Emission

Photoelectric Effect

Experimental Study of Photoelectric Effect

Practice: Electron Emission and the Photoelectric Experiment

Photoelectric Effect and Wave Theory of Light

Einstein's Photoelectric Equation: Energy Quantum of Radiation

Particle Nature of Light: The Photon

Practice: Einstein's Equation and the Photon

Wave Nature of Matter

Practice: Matter Waves

Summary

Atoms

Introduction Alpha-particle Scattering and Rutherford's Nuclear Model of Atom

Practice: Alpha-particle Scattering and Rutherford's Model

Atomic Spectra

Bohr Model of the Hydrogen Atom

Practice: Bohr Model and Energy Levels

The Line Spectra of the Hydrogen Atom

De Broglie's Explanation of Bohr's Second Postulate of Quantisation

Practice: Hydrogen Spectrum and de Broglie's Explanation

Summary

Nuclei

Introduction Atomic Masses and Composition of Nucleus

Size of the Nucleus

Practice: Composition and Size of the Nucleus

Mass-Energy and Nuclear Binding Energy

Nuclear Force

Practice: Mass Defect, Binding Energy and Nuclear Force

Radioactivity

Nuclear Energy

Practice: Radioactivity and Nuclear Energy

Summary

Semiconductor Electronics: Materials, Devices and Simple Circuits

Introduction Classification of Metals, Conductors and Semiconductors

Intrinsic Semiconductor

Extrinsic Semiconductor

Practice: Energy Bands and Semiconductors

p-n Junction

Semiconductor Diode

Practice: p-n Junction and the Diode

Application of Junction Diode as a Rectifier

Practice: Rectifiers and Diode Circuits

Summary

Class 12 Chemistry · Part 1

Class 12 Chemistry · Part 2

Class 12 Mathematics · Part 1

Relations and Functions

Introduction Types of Relations

Practice: Relations and Equivalence Classes

Types of Functions

Practice: One-One and Onto Functions

Composition of Functions and Invertible Function

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Inverse Trigonometric Functions

Introduction Basic Concepts

Practice: Principal Values of Inverse Trig Functions

Properties of Inverse Trigonometric Functions

Practice: Simplifying Inverse Trig Expressions

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Matrices

Introduction Matrix

Types of Matrices

Practice: Building and Sizing Matrices

Operations on Matrices

Practice: Matrix Arithmetic and Products

Transpose of a Matrix

Symmetric and Skew Symmetric Matrices

Practice: Transpose, Symmetric and Skew-Symmetric

Invertible Matrices

Practice: Invertible Matrices

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Determinants

Introduction Determinant

Practice: Evaluating Determinants

Area of a Triangle

Practice: Area and Collinearity

Minors and Cofactors

Practice: Minors and Cofactors

Adjoint and Inverse of a Matrix

Practice: Adjoint and Inverse

Applications of Determinants and Matrices

Practice: Solving Systems with Matrices

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Continuity and Differentiability

Introduction Continuity

Practice: Testing Continuity

Differentiability

Practice: Chain Rule

Practice: Implicit and Inverse Trigonometric Derivatives

Exponential and Logarithmic Functions

Practice: Exponential and Logarithmic Derivatives

Logarithmic Differentiation

Practice: Logarithmic Differentiation

Derivatives of Functions in Parametric Forms

Practice: Parametric Derivatives

Second Order Derivative

Practice: Second Order Derivatives

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Application of Derivatives

Introduction Rate of Change of Quantities

Practice: Rates of Change

Increasing and Decreasing Functions

Practice: Increasing and Decreasing Functions

Maxima and Minima

Practice: Maxima and Minima

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Class 12 Mathematics · Part 2

Integrals

Introduction Integration as an Inverse Process of Differentiation

Practice: Antiderivatives by Inspection

Methods of Integration

Practice: Integration by Substitution

Practice: Trigonometric Integrals

Integrals of Some Particular Functions

Practice: Standard Forms and Completing the Square

Integration by Partial Fractions

Practice: Partial Fractions

Integration by Parts

Practice: Integration by Parts

Practice: Integrals of Square-Root Quadratics

Definite Integral

Fundamental Theorem of Calculus

Practice: Evaluating Definite Integrals

Evaluation of Definite Integrals by Substitution

Practice: Definite Integrals via Substitution

Some Properties of Definite Integrals

Practice: Properties of Definite Integrals

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Application of Integrals

Introduction Area under Simple Curves

Practice: Areas under Curves

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Differential Equations

Introduction Basic Concepts

Practice: Order and Degree

General and Particular Solutions of a Differential Equation

Practice: Verifying Solutions

Methods of Solving First Order, First Degree Differential Equations

Practice: Variables Separable

Practice: Homogeneous Equations

Practice: Linear Differential Equations

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Vector Algebra

Introduction Some Basic Concepts

Types of Vectors

Practice: Vectors and Their Types

Addition of Vectors

Multiplication of a Vector by a Scalar

Practice: Components, Sums and Section Formula

Product of Two Vectors

Practice: Dot Product and Projections

Practice: Cross Product

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Three Dimensional Geometry

Introduction Direction Cosines and Direction Ratios of a Line

Practice: Direction Cosines and Ratios

Equation of a Line in Space

Angle between Two Lines

Shortest Distance between Two Lines

Practice: Lines in Space

Chapter Review: Mixed Practice

Summary

Linear Programming

Introduction Linear Programming Problem and its Mathematical Formulation

Practice: Graphical Solutions

Chapter Review: Mixed Practice

Summary

Probability

Introduction Conditional Probability

Practice: Conditional Probability

Multiplication Theorem on Probability

Independent Events

Practice: Multiplication Rule and Independence

Bayes' Theorem

Practice: Total Probability and Bayes' Theorem

Miscellaneous Examples

Chapter Review: Mixed Practice

Summary

Basic Models

Grading the AI

Precision and Recall

Introduction Precision and Recall The F1-Score The Tradeoff... Again Not the End Code with Python Summary

Visualizing Performance

Introduction Building ROC Curves What Makes A Good ROC Curve?AUC: Area Under the Curve Considerations Code with Python Summary

Testing Your AI

Introduction Our Previous Approach K-Fold Cross-Validation Leave-One-Out Cross Validation (LOOCV)See For Yourself Which K Should You Pick?Conclusion Code with Python Summary

Underfitting and Overfitting

Introduction Visualization LOESS Regression K-Nearest Neighbors Conclusion Code with Python Summary

AI That Thinks

Decision Trees

Introduction Decision Tree Where To Partition?Information Gain Another Look At Our Decision Tree The Problem of Perturbations Going Beyond A Single Tree Code with Python Summary

Random Forest

Introduction Ensemble Learning Bagging Method Variance in Composition Conclusion Code with Python Summary

Neural Networks

Introduction Computational Graphs Activation Functions Backpropagation: How Networks Learn See for yourself The Deep Learning Universe Code with Python Summary

Advanced & Ethical AI

Reinforcement Learning

Introduction Simulation Line World Grid World Where Do We Go From Here?Code with Python Summary

Equality Of Odds

Introduction Measuring Fairness How Can We Actually Fix the Bias?Conclusion Code with Python Summary

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AI / ML

Class 10 — CBSEBuy · ₹599

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Class 10 Mathematics

Real Numbers

Polynomials

Pair of Linear Equations in Two Variables

Quadratic Equations

Arithmetic Progressions

Triangles

Coordinate Geometry

Introduction to Trigonometry

Some Applications of Trigonometry

Circles

Areas Related to Circles

Surface Areas and Volumes

Statistics

Probability

Class 10 Science

Chemical Reactions and Equations

Acids, Bases and Salts

Metals and Non-metals

Carbon and its Compounds

Life Processes

Control and Coordination

How do Organisms Reproduce?

Heredity

Light – Reflection and Refraction

The Human Eye and the Colourful World

Electricity

Magnetic Effects of Electric Current

Our Environment

Class 11 Physics · Part 1

Units and Measurement

Motion in a Straight Line

Motion in a Plane

Laws of Motion

Work, Energy and Power

System of Particles and Rotational Motion

Gravitation

Class 11 Physics · Part 2

Mechanical Properties of Solids

Mechanical Properties of Fluids

Thermal Properties of Matter

Thermodynamics

Kinetic Theory

Oscillations

Waves

Class 11 Chemistry · Part 1

Class 11 Chemistry · Part 2

Class 11 Mathematics

Sets

Relations and Functions

Trigonometric Functions

Complex Numbers and Quadratic Equations

Linear Inequalities

Permutations and Combinations

Binomial Theorem

Sequences and Series

Straight Lines

Conic Sections

Introduction to Three Dimensional Geometry

Limits and Derivatives

Statistics

Probability

Class 12 Physics · Part 1

Electric Charges and Fields

Electrostatic Potential and Capacitance

Current Electricity

Moving Charges and Magnetism

Magnetism and Matter

Electromagnetic Induction

Alternating Current

Electromagnetic Waves

Class 12 Physics · Part 2

Ray Optics and Optical Instruments