Course Overview

The study of fundamental and advanced Mathematical concepts is the main subject of Mathematics courses. Theoretical understanding of number systems, data handling, algebra, geometry, trigonometry, etc. is covered in the Mathematics courses. Candidates may pursue courses related to Maths at the undergraduate, graduate, or doctorate levels.
All About Mathematics Courses
The Mathematics courses focus on the study of Mathematics, with particular attention paid to the study of numbers, structure, transition, and space. After completing the Mathematics courses, candidates will discover employment prospects in the Financial, Information Technology, and research industries.

The entire Mathematics courses’ curriculum comprises Vector analysis and Geometry, advanced Calculus, integral Calculus and Trigonometry, Algebra, and Mathematical methods.
Why Study Mathematics Courses?
Critical Thinking Skills: Mathematics courses teach students to analyze problems logically, break them down into smaller, manageable parts, and develop systematic approaches to finding solutions.
Versatility: Studying Mathematics courses opens doors to diverse career paths and provides a solid foundation for further specialization in specific fields.
Career Opportunities: Graduates of Mathematics courses are highly sought after in the job market. Many industries, such as technology, finance, data science, engineering, and research, require individuals with strong mathematical skills.
Innovation and Discovery: Studying Mathematics courses can lead to groundbreaking research and contribute to advancements in society.
Quantitative Literacy: Mathematics courses provide students with the skills to interpret data, assess risk, and make informed judgments, both in their personal lives and as responsible citizens.
Intellectual Stimulation: Studying Mathematics courses challenges the mind, fosters curiosity, and encourages the exploration of abstract concepts.
Mathematics Syllabus
Mathematics courses are customised programmes that include the fundamentals of Advanced Mathematics such as calculus, geometry, algebra, number theory, differential equations, and many more.

Because of the diverse dynamics of the subjects, the Mathematics courses teach students how to execute and solve hard mathematical problems to arrive at a definitive result.

Candidates can check the Mathematics syllabus in the table given below:

Mathematics is the study of amount, pattern, arrangement, structure, and connection. It keeps growing from simple actions of counting, measuring, and examining symmetrical shapes. The main thing is to use logical thinking and numerical calculations to discover the best solutions to problems. Maths is the solution to many problems and hence has various branches, that give solutions in different fields.

Mathematics is broadly classified into two parts— pure mathematics and applied mathematics. This article will cover the concept of branches in mathematics— Arithmetic, Geometry, Algebra, Calculus, Topology, Trigonometry, Number theory, Probability and Statistics, and the various sub-categories of these branches.

Table of Content:
Number Theory
Arithmetic
Geometry
Algebra
Calculus
Trigonometry
Probability and Statistics
Topology

What are Main Branches of Mathematics?
Mathematics has different parts or areas of focus. Each part deals with specific kinds of problems and uses unique methods. Some major branches include:

Number theory
Arithmetic
Geometry
Algebra
Calculus
Topology
Trigonometry
Probability and Statistics
Number Theory
Number Theory is a branch of mathematics that explores the properties and relationships of numbers. Instead of dealing with calculations and operations, it focuses on understanding the fundamental nature of integers and their patterns. In other words, it’s like studying the building blocks of numbers.

Whole Numbers
Whole numbers are the numbers we use for counting things. They start from zero and go on without any fractions or decimals. They are the natural numbers we use in our daily lives for simple counting and basic calculations.

Prime Numbers
Prime numbers are a central concept in Number Theory. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers, except for 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11. The fundamental theorem of arithmetic states that every natural number greater than 1 can be uniquely expressed as a product of prime numbers.

Divisibility Rules
Divisibility rules are guidelines that help determine whether one number is divisible by another without performing the actual division. These rules are practical tools in Number Theory for understanding the relationships between numbers.

Divisibility Tests
Prime Factorization
Number System
The number system is a method of representing and expressing quantities using numerical symbols. It encompasses different types of numbers, such as natural numbers, integers, rational numbers, and irrational numbers. The number system provides a structured way to count, measure, and perform mathematical operations.

Complex Number
A complex number is a mathematical concept that combines both real and imaginary components. It is expressed in the form a+bi, where a is the real part, b is the imaginary part, and i represents the imaginary unit (√-1). Complex numbers find applications in various fields, including engineering and physics, for solving equations that involve square roots of negative numbers.

Key Concepts of Number Theory:

Numbers
Natural Numbers
Integers
Rational Numbers
Real Numbers
Arithmetic
Arithmetic is a part of math that deals with numbers and basic operations like adding, subtracting, multiplying, and dividing. It also covers more complicated stuff like percentages, logarithms, exponentiation, and square roots. The word “arithmetic” comes from the Greek word “arithmos,” which means numbers.
According to a big idea called the fundamental theorem of arithmetic, any number bigger than 1 can be broken down into prime numbers in a unique way, except for the order they’re in. A smart guy named Carl Friedrich Gauss came up with this theory in 1801.

Arithmetic isn’t just about simple math. It also includes more advanced concepts like limits and exponents. Even though it’s the basic and most important part of math, we use arithmetic every day in regular life, like when we’re calculating stuff or working on problems.

Arithmetic Operation
Arithmetic operations are the basic calculations we do with numbers. It includes addition, where we combine numbers, subtraction, where we take away one number from another, multiplication, which is like repeated addition, and division, where we split a quantity into equal parts. These operations are the building blocks of math and help us solve everyday problems.

Addition
Subtraction
Multiplication
Division
Fractions and Decimals
Fractions represent parts of a whole. They have a numerator (the top number) representing the part we have and a denominator (the bottom number) representing the whole. Decimals are another way of showing parts of a whole, using a point to separate the whole number part from the fractional part. Understanding fractions and decimals helps us work with quantities that are not whole numbers, making math more flexible and applicable in various situations.

Arithmetic Progression
Arithmetic progression is a mathematical concept that deals with a sequence of numbers where the difference between any two consecutive terms is constant. In simpler terms, each number in the sequence is obtained by adding a fixed value to the previous one. This constant difference is known as the common difference. Arithmetic progressions find applications in various fields, including mathematics, physics, and finance. Understanding the properties and formulas associated with arithmetic progressions is essential for solving problems involving the predictable patterns these sequences exhibit.

Key Concepts on Arithmetic:

Addition of Fractions
Subtracting Fractions
Multiplication of Fractions
Division of Fractions
Geometry
Geometry is a branch of mathematics, focuses on the shapes and sizes of objects, how they relate to each other, and the characteristics of space. The term “geometry” comes from the Ancient Greek words geo, meaning “earth,” and metric, meaning “measuring.” Euclid, who is a Greek mathematician, is recognized as the “father of geometry.” This field covers angles, shapes, sizes, and various geometric objects in both 2D (like circles, triangles, squares) and 3D (3D shapes such as cubes, cones, spheres).

In geometry, one studies special properties of these shapes. Basic terms involved include points, lines, line segments, angles, coordinate planes, different surfaces, shapes, and solids. Geometry finds practical use in our daily lives, particularly in GPS for navigation and in manufacturing industries. It wouldn’t be an exaggeration to say that geometry is one of the most practical branches of mathematics in the world.

Shapes and Figures
Polygons
2D and 3D Shapes
Angles and Lines
Types of Angles
Parallel and Perpendicular Lines
Coordinate Geometry
Key Concepts on Geometry:

Triangles
Quadrilateral
Circle
Area and Perimeter Formulas
Algebra
Algebra is Branch of Mathematics that deals with variables, symbols, numbers, and the rules to work with them. It’s a way to represent problems or situations using mathematical expressions. In algebra, we use variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to create meaningful expressions. Algebra helps solve equations and figure out unknown quantities, such as interest, proportions, and percentages. Key terms in algebra include variables, constants, coefficients, expressions, and equations.

Algebra isn’t just about solving equations; it includes other operations and concepts like polynomial equations. It’s crucial in mathematics and finds applications in diverse fields like physics, chemistry, engineering, economics, and accounting. Algebra helps uncover missing or unknown values in mathematical expressions or equations, making it an essential tool in problem-solving across various disciplines.

Solving Equations
This involves figuring out the values that make mathematical expressions true. It’s like solving puzzles where you need to find the missing pieces.

Linear Equations
Quadratic Equations
Systems of Equations
Polynomials
In algebra, we deal with expressions containing variables and coefficients. These are like mathematical terms with letters and numbers, and we learn to work with them to solve problems.

Polynomial Basics
Factoring Polynomials
Inequalities
Inequalities is like breaking down a complex algebraic expression into simpler parts. It’s similar to breaking a big problem into smaller, more manageable pieces, making it easier to understand and solve.

Solving Inequalities
Systems of Inequalities
Set Theory
Set theory is a branch of mathematics that deals with the study of sets, which are collections of distinct elements. It explores the relationships and interactions among these sets, utilizing concepts such as union, intersection, and complement to analyze their properties.

Relation and Function
Relation and function theory investigates the connections between sets of elements. A relation is a pairing of elements from different sets, while a function is a specific type of relation where each element from one set is associated with exactly one element in another set. This area of mathematics explores how elements relate to each other within various mathematical structures.

Linear Algebra
Linear algebra focuses on vector spaces and linear mappings between these spaces. It deals with the study of systems of linear equations and their solutions, emphasizing concepts such as matrices, determinants, eigenvalues, and eigenvectors.

Matrices
: Matrices are rectangular arrays of numbers, symbols, or expressions organized in rows and columns. They are used to represent linear transformations, solve systems of linear equations, and perform various operations in linear algebra.
Vector: A vector, on the other hand, is a quantity characterized by magnitude and direction. It is often represented as an ordered list of numbers. Vectors are used to describe physical quantities such as displacement, velocity, or force.
Key Concepts on Algebra:

Algebraic Expression
Domain and Range
Matrix Operations
Determiant
Vector Operations
Calculus
Calculus is a highly advanced Branches of Mathematics, with different levels like pre-calculus, advanced calculus, accelerated multivariable calculus, differential calculus, and integral calculus. It’s originally called “infinitesimal calculus” or “the calculus of infinitesimals,” focusing on continuous change, similar to how geometry studies shapes. The main ideas in calculus are limits, functions, integrals, and infinite series.

People use calculus to find areas of complex shapes, analyze survey data, ensure vehicle safety, and understand changing conditions in systems. Economists, architects, medical experts, statisticians, and others use calculus as a language. It’s a crucial part of pure mathematics and widely applied in various fields.

Limits and Continuity
Limits in calculus are like boundaries that a function approaches as the input values get closer and closer to a certain point. It helps us understand the behavior of a function at specific points and is a fundamental concept in calculus.

Differentiation
Differentiation or Derivatives measure how a function changes as its input changes. They represent the rate of change or the slope of a function at a given point. Derivatives are crucial in understanding motion, rates, and various real-world scenarios where things are changing.

Integrals
Integrals, on the other hand, deal with the accumulation of quantities. They help find the total or accumulated effect of a changing quantity. Integrals are used to calculate areas under curves, representing the total “amount” within a certain range. They have applications in areas like physics, where they are used to calculate things like displacement, velocity, and acceleration.

Indefinite Integrals
Definite Integrals
Key Concepts on Calculus:

Differentiation Formulas
Integration Formulas
Application of Derivatives
Area under Curve
Area between Curves
Trigonometry
Trigonometry is a part of mathematics that looks at how the sides and angles of triangles are connected. The word “trigonometry” comes from Greek words: “trigonon,” meaning triangle, and “metron,” meaning measure. Trigonometry is all about studying the angles and sides of triangles to figure out distances and lengths. The functions that show how triangles’ sides and angles relate are called trigonometric functions. There are six main trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Trigonometric Functions
Trigonometric functions are tools in trigonometry that describe the relationships between the angles and sides of triangles. The six primary trigonometric functions are:

Sine (sin): The ratio of the length of the side opposite an angle to the hypotenuse in a right-angled triangle.
Cosine (cos): The ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle.
Tangent (tan): The ratio of the length of the side opposite an angle to the length of the adjacent side in a right-angled triangle.
Cotangent (cot): The reciprocal of the tangent, equal to the ratio of the length of the adjacent side to the side opposite an angle.
Secant (sec): The reciprocal of the cosine, equal to the ratio of the hypotenuse to the length of the adjacent side.
Cosecant (csc): The reciprocal of the sine, equal to the ratio of the hypotenuse to the length of the side opposite an angle.
Trigonometric Identities
Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables within their domains. Some fundamental trigonometric identities include:

Pythagorean Identities
Reciprocal Identities
Double Angle Formulas
Inverse Trigonometry
Inverse trigonometry involves finding angles when the values of trigonometric ratios are given. It’s like working backward from the result to find the angle. In mathematics, this helps in solving problems where you know the trigonometric ratio but need to find the corresponding angle.

Articles to be Read

Trigonometric Ratios
Trigonometry Formulas
Trigonometric Table
Inverse Trigonometric Functions
Height and Distance
Probability and Statistics
Probability and Statistics stand as a crucial and somewhat underestimated part of mathematics. Compared to other branches like calculus, it’s often considered more accessible. This branch employs mathematical concepts to foresee likely events by organizing, analyzing, and interpreting data. It relies on a set of rules and formulas to make these predictions.

It’s a relatively recent addition to the mathematical family but has become indispensable in both scientific and social sciences. Probability and Statistics is about the laws and principles governing numerical data and random events. It’s a surprising field, always offering new insights.

Today, there’s a growing demand for professionals skilled in Probability and Statistics, particularly in roles like data analysts and scientists. This illustrates the increasing importance of this branch in addressing real-world challenges and making informed predictions.

Probability Distributions
Probability distributions are mathematical functions that describe the likelihood of different outcomes in a set of possible events. These distributions provide a way to understand and quantify the uncertainty or randomness associated with various situations. In statistics and probability theory, probability distributions can be discrete or continuous.

Discrete Probability Distributions
Continuous Probability Distributions
Descriptive Statistics
Descriptive statistics involve methods for summarizing and presenting data to provide a clear and concise understanding of its main features. These statistical techniques include measures such as mean, median, mode, range, and standard deviation. Descriptive statistics aim to organize and describe the main characteristics of a dataset, offering insights into its central tendency, dispersion, and distribution.

Inferential Statistics
Inferential statistics draw conclusions and make predictions about a population based on a sample of data. These methods involve using probability theory to estimate parameters and test hypotheses. Common inferential statistical techniques include hypothesis testing, confidence intervals, and regression analysis. Inferential statistics are crucial in making generalizations from limited data to broader populations.

Regression and Correlation
Regression and correlation are statistical methods used to analyze relationships between variables. Regression helps predict one variable based on the values of another, identifying the strength and direction of the relationship. Correlation measures the degree of association between two variables, indicating whether they move together or in opposite directions. These techniques are valuable in fields such as economics, biology, and social sciences for understanding and predicting interdependencies between variables.

Key Concepts on Probability and Statistics:

Events in Probability
Bayes Theorem
Frequency Distribution
Central Tendency
Standard Deviation
Topology
Topology is a part of mathematics that looks at the unchanging features of spaces even when you smoothly change their shape. It’s often called “rubber-sheet geometry” because, like rubber, objects can stretch and shrink without breaking. Imagine turning a square into a circle without tearing it; that’s the kind of transformation we’re talking about. However, a figure 8 can’t transform into a square or a circle without breaking.

For instance, think of a coffee cup and a donut. Topologically, they are the same because you can turn one into the other by bending and stretching, but you can’t turn a coffee cup or a donut into a pretzel without breaking or gluing.

Topology is a relatively recent addition to mathematics, with most research happening since 1900. Some of its subfields include general topology (or point set topology), combinatorial topology, algebraic topology, and differential topology. People use topology in various areas of math, like understanding differential equations, studying dynamical systems, exploring knot theory, and examining Riemann surfaces in complex analysis.

List of Branches of Mathematics
The branches and sub-branches of mathematics are listed below:

Arithmetic
Algebra
Geometry
Trigonometry
Calculus
Statistics
Number Theory
Discrete Mathematics
Linear Algebra
Abstract Algebra
Mathematical Logic
Set Theory
Differential Equations
Topology
Combinatorics
Probability Theory
Mathematical Analysis
Game Theory
Cryptography
Mathematical Physics
Actuarial Science
Operations Research
Optimization.

Chapter Name:

Number Theory –
Number theory is an area of mathematics that studies the set of positive whole numbers, such as 1, 2, 3, 4, 5, 6, etc., known as natural numbers.

Number theory makes the connections between various types of numbers easier. In number theory, numbers have been divided into different categories such as:

Odd Numbers – 1, 3, 5, 7, 9, 11, 13, 15, 17, 19…..
Even Numbers – 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 . . .
Square Numbers – 4, 9, 16, 25, 36, 49, 64, 81,100 . . .
Cube Numbers – 8, 27, 64, 125, 216, 343, 512 . . .
Prime Numbers – 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,53, 59, 61 . . .
Composite Numbers – 4, 6, 8, 9, 10, 12, 14, 15, 16,18, 20, 21, 22, 24 . . .
1 (modulo 4) Numbers – 1, 5, 9, 13, 17, 21, 25, . . .
3 (modulo 4) Numbers – 3, 7, 11, 15, 19, 23, 27, . . .
Triangular Numbers – 3, 6, 10, 15, 21, 28, 36, 45,. . .
Perfect Numbers – 6, 28, 496, 8128, . . .
Fibonacci Numbers -1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. . .
Key Concepts in Number Theory

Number System: Gain a comprehensive understanding of the
Number System in Maths
, covering its fundamental concepts and types.
Numbers: Explore the world of
Numbers
, their classifications, and properties.
Prime Numbers: Delve into the intriguing world of
Prime Numbers
and their significance in mathematics.
Real Numbers: Understand the concept of
Real Numbers
, their characteristics, and applications.
Rational Numbers: Learn about
Rational Numbers
and their place in the number system.
Algebra
Algebra is the area of mathematics that helps represent conditions or problems into mathematical expressions. These expressions include variables like x,y, and z and operations like addition, subtraction, multiplication, and division implemented on them.

Key Concepts

Algebraic Expression: Discover the basics of
Algebraic Expressions
and their various forms.
Polynomials: Get to know about
Polynomials
, their structure, and types.
Equation in Maths: Explore the fundamental concept of an
Equation in Maths
.
Quadratic Equation: Dive into the details of
Quadratic Equations
and their solutions.
Cubic Equation: Understand the complexities of
Cubic Equations
and how to solve them.
Geometry
Geometry is the Mathematics section concerned with the dimensions, sizes, angles, and forms of a wide range of items we see every day. There are various types of geometry such as plane geometry, three-dimensional geometry, solid geometry, etc.

Key Concepts

Geometric Shapes: Get acquainted with various
Geometric Shapes
.
Types of Polygons: Explore the
Types of Polygons
and their properties.
Triangle: Learn about the properties and types of
Triangles
.
Quadrilateral: Understand the characteristics of
Quadrilaterals
.
Circle: Delve into the properties and equations of
Circles
.
Types of Angles: Familiarize yourself with the
Types of Angles
in geometry.
Arithmetic
Arithmetic is a branch of mathematics that includes the operations of numbers. This field of mathematics serves as the foundation for students to understand mathematics and implement it in real life.

Key Concepts

What is Arithmetic: Learn about the basics of
Arithmetic
and its importance.
Arithmetic Operations: Familiarize yourself with various
Arithmetic Operations
.
Addition: Master the fundamental operation of
Addition
.
Division: Understand the process and rules of
Division
.
Arithmetic Progression: Explore the concept of
Arithmetic Progression
and its applications.
Combinatorics
A branch of mathematics called combinatorics is concerned with the investigation of finite discrete structures. Enumerations of the sets of elements and the study of permutations and combinations are covered. It describes the characteristics of mathematical relations.

Key Concepts

Permutation Combination: Master the concepts of
Permutation and Combination
.
Binomial Theorem: Understand the
Binomial Theorem
and its applications.
Topology
Topology studies properties of spaces that are invariant under any continuous deformation. Because the objects may be stretched and contracted like rubber sheets yet cannot be broken, it is frequently referred to as “rubber-sheet geometry”.

Calculus
Calculus is a field of mathematics that is concerned with the computation of instantaneous rates of change (differential calculus) and the summing of an infinite number of minor elements to find a single whole.

Key Concepts in Calculus

Derivatives: Grasp the concept of
Derivatives
in calculus.
Differentiation Formulas: Learn about various
Differentiation Formulas
.
Integration: Dive into the process of
Integration
and its significance.
Integration Formulas: Familiarize yourself with key
Integration Formulas
.
Differential Equations: Understand the role of
Differential Equations
in calculus.
Application of Derivatives: Discover the
Application of Derivatives
in various fields.
Limits: Learn about the concept of
Limits
in calculus.
Statistics and Probability
The two most crucial ideas in mathematics are probability and statistics. Probability is mainly about chance, and statistics, on the other hand, is about how we manage varied data using various methods.

It enables in the easy and clear simplification of very complex data. We discuss the probability of various outcomes if we are unsure about how an event will turn out. Statistics is the study of these probabilistically determined occurrences.

Key Concepts For Statistics,

Central Tendency: Learn about measures of
Central Tendency
.
Frequency Distribution: Explore the concept of
Frequency Distribution
.
Standard Deviation: Understand the calculation and significance of
Standard Deviation
.
Mean: Discover how to calculate the
Mean
of a dataset.
Median: Learn about finding the
Median
in statistics.
Mode: Understand what the
Mode
is and how to find it.
Key Concepts For Probability,

Sample Space: Get to know about
Sample Space in Probability
.
Events in Probability: Understand
Events in Probability
.
Bayes Theorem: Explore the
Bayes Theorem
and its applications.
Card Probability: Learn about
Card Probability
.
Coin Toss Probability: Understand the
Coin Toss Probability Formula
.
Set Theory
This branch of mathematics studies sets, which are basically the collection of things or objects or data.

Key Concepts in Set Theory

Set Theory: Explore the fundamental principles of
Set Theory
.
Subsets: Understand what
Subsets
are in set theory.
Union of Sets: Learn about the
Union of Sets
and how it’s formed.
Intersection of Sets: Discover the concept of
Intersection of Sets
.
Venn Diagram: Visualize set relationships with
Venn Diagrams
.
Trigonometry
Trigonometry is the field of mathematics that deals with certain angles’ functions and how to use such functions in computations. There are six popular trigonometric functions for an angle.

Sine (sin)
Cosine (cos)
Tangent (tan)
Cotangent (cot)
Secant (sec)
Cosecant (csc)

Key Concepts in Trigonometry

Trigonometry Ratios: Familiarize yourself with
Trigonometric Ratios
.
Trigonometry Table: Refer to the
Trigonometry Table
for quick calculations.
Trigonometry Formulas: Learn key
Trigonometry Formulas
.
Trigonometric Identities: Understand
Trigonometric Identities
and their uses.
Height and Distance: Apply trigonometry to solve
Height and Distance
problems.
How to learn Maths?
Maths is a simple as well as a tricky subject. Maths is fun to explore but tough to excel. At GeeksforGeeks, you can clear all fundamental concepts and build a strong foundation in this subject. When you get a good grip and clear understanding of this subject, your brain will think logically and help you grasp the concepts in all other subjects with excellent efficiency.

We are providing learning materials for students of Class 8 to 12 based on the latest syllabus approved by CBSE. In these classes, Maths for students understand the important concepts of Maths, like basic geometry, decimals, algebra, ratio, and proportions, etc. Our experts at GeeksforGeeks have curated the concepts in such an interactive manner for the students which helps students to grasp the basics of any topic in the most efficient way possible.

With the help of animations and creative ways, our experts have tried their level best to ensure that the students in the best way possible understand concepts. The sole purpose is to make maths easy to learn and implement the concepts with ease when solving problems.

Basic Maths
The basics of Maths involve arithmetic operations such as :

Addition(+)
Subtraction(-)
Multiplication(x)
Division(/)
To grasp these basic concepts most efficiently, Maths for students need to practice questions and solve worksheets based on them. Concepts like HCF and LCM, multiples, and factors, will be introduced to students in their secondary classes.

Class 8-12 Maths Syllabus
There are various simple and advanced concepts in Mathematics. These concepts are taught to students according to their difficulty and complexity level. Basic concepts like numbers, addition, subtraction, multiplication, division, place value, etc are taught to kids first, and later enhanced concepts such as ratios, percentages, algebra, trigonometry, mensuration, etc are taught. Advanced Concepts like Integration and differentiation, Permutation and combination, and Probability, are included in secondary school.

Class 8 Maths Syllabus
Class 9 Maths Syllabus
Class 10 Maths Syllabus
Class 11 Maths Syllabus
Class 12 Maths Syllabus

Chapter 1: Rational Numbers

Introduction to the rational number
Negative of a number
Representation of Rational Numbers on the Number Line
Rational Number between Two Rational Numbers
Chapter 2: Linear Equations in One Variable

Introduction to Linear Equations in one variable
Solving Equations that have Linear Expressions on one Side and Numbers on the Other Side
Some Applications
Solving Equations having the Variable on both sides
Some More Applications
Reducing Equations to Simpler Form
Equations Reducible to the Linear Form
Chapter 3: Understanding Quadrilaterals

Introduction to Quadrilaterals
Polygons: Classification of polygons, Diagonals, Concave and Convex polygons, Regular and irregular polygons
Angle sum property
Some of the Measures of the Exterior Angles of a Polygon
Kinds of Quadrilaterals:
Trapezium
,
Kite
Parallelogram, Elements of parallelogram, Angles of a parallelogram, Diagonals of parallelogram
Some Special Parallelograms: Rhombus, Rectangle, Square
Chapter 4: Practical Geometry

Introduction to Construction
Constructing a Quadrilateral
When four sides and one diagonal given
When two diagonals and three sides are given
When two adjacent sides and three angles are given
When three sides and two included angles are given
When other special properties are known.
Some Special Cases
Chapter 5: Data Handling

Looking for Information
Organizing Data
Grouping Data (Bars with a Difference)
Circle Graph or Pie Chart (Drawing Pie Charts)
Chance and Probability (Getting A Result, Equally Likely Outcomes, Linking Chances To Probability, Outcomes As Events, Chance And Probability Related To Real Life)

Squares and Square Roots

Introduction to Square and Square Roots
Properties of Square Numbers
Some More Interesting Patterns
Finding the Square of a Number (Other Patterns in Squares, Pythagorean Triplets)
Methods to Find Square Roots
Square Roots of Decimals
Estimating Square Root
Chapter 7: Cubes and Cube Roots

Introduction to Cube and Cube Roots
Cubes (Some Interesting Patterns, Smallest Multiple that is a Perfect Cube)
Methods to Find Cube Roots
Chapter 8: Comparing Quantities

Recalling Ratios and Percentages
Finding the Increase and Decrease Percent
Finding Discounts
Prices Related to Buying and Selling (Profit and Loss)
Sales Tax/Value Added Tax/Goods and Services Tax
Compound Interest
Deducing a Formula for Compound Interest
Rate Compounded Annually or Half Yearly (Semi-Annually)
Applications of Compound Interest Formula
Chapter 9: Algebraic Expressions and Identities

What are Expressions?
Terms, Factors, and Coefficients
Monomials, Binomials, and Polynomials
Like and Unlike Terms
Addition and Subtraction of Algebraic Expressions
Multiplication of Algebraic Expressions: Introduction
Multiplying a Monomial by a Monomial
Multiplying a Monomial by a Polynomial
Multiplying a Polynomial by a Polynomial
What is an Identity?
Standard Identities
Applying Identities
Chapter 10: Visualizing Solid Shapes

Introduction to Visualizing Solid Shapes
View of 3D-Shapes
Mapping Space Around Us
Faces, Edges and Vertices
Chapter 11: Mensuration

Introduction to Mensuration
Area of Trapezium
Area of General Quadrilateral
Area of Polygons
Solid Shapes
Surface Area of Cube, Cuboid, and Cylinder
Volume of Cube, Cuboid, and Cylinder
Volume and Capacity
Chapter 12: Exponents and Powers

Introduction to Exponents and Powers
Powers with Negative Exponents
Laws of Exponents

Chapter 13: Direct and Inverse Proportions

Introduction to Direct and Inverse Proportions
Direct Proportion
Inverse Proportion
Chapter 14: Factorization

What is Factorisation?
Division of Algebraic Expressions
Can you Find the Error?
Chapter 15: Introduction to Graphs

Introduction (Bar Graph, Pie Graph, Histogram, Line Graph)
Linear Graphs (Location of a Point, Coordinates)
Some Applications
Chapter 16: Playing with Numbers

Introduction
Numbers in General Form
Game with Numbers
Letters for Digits
Test of Divisibility (Divisibility by 10, Divisibility by 5, Divisibility by 2, Divisibility by 9 and 3)