CBSE Class 9 Mathematics Concepts, makes students to understand all the concepts of class 9 maths chapter-wise as it covers all the topics and subtopics provided in the syllabus of class 9 maths. GeeksforGeeks provided the following chapter-wise notes that contain numbers of theorems with their proper explanations, formulae with their applications, and graphs that need to accelerate students’ knack of practicing problems and boost their interest to pursue maths in higher classes.
Chapter 1: Number Systems
The numeral or number system is the combination of natural, integers, rational, irrational, and real numbers. This lesson covers the entire concepts of the numeral system and its types, representation on the number line, laws of rational exponents, and integral powers.
- Number System
- Decimal Expansion of Real Numbers
- Operations on Real numbers
- Laws of exponents for real numbers
- nth roots of a number
Chapter 2: Polynomials
Polynomial is an expression that comprises variables and coefficients which involves the operations like addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
- Polynomials in One Variable
- Zeroes of a polynomial
- Remainder Theorem
- Multiplying Polynomials
- Algebraic Identities of Polynomials
- Standard Algebraic Identities
Chapter 3: Coordinate Geometry
The coordinate geometry is a part of geometry where the position of the points on the plane is described with the help of an ordered pair of numbers called coordinates.
Chapter 4: Linear Equations in Two Variables
Any equation which can be defined in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables.
- Linear Equations and their solutions
- Graph of a linear equation in two variables
- Equations of Lines Parallel to the x-axis and y-axis
Chapter 5: Introduction to Euclid’s Geometry
Euclidean geometry is the branch of geometry that deals with the study of geometrical shapes and figures based on different axioms and theorems. This study basically provides a brief explanation for flat surfaces.
Chapter 6: Lines and Angles
In geometry, Lines and Angles are defined as figures that are made up of infinite points extending indefinitely in both directions. Lines are straight and have length and breadth, while an angle is a figure from which two rays emerge from a common point.
Chapter 7: Triangles
Geometrically, a triangle is defined as a three-sided polygon consist of three edges and three vertices. The most important and applied property of a triangle is its Angle sum property which means the sum of the internal angles of a triangle is equal to 180 degrees only.
- Congruence of Triangles
- Properties of triangles
- Angle Sum Property of a Triangle
- Inequalities in a triangle
- Theorem – Angle opposite to equal sides of an isosceles triangle are equal
Chapter 8: Quadrilateral
A quadrilateral is a plane geometrical figure which has four sides and has four corners or vertices. Typically, quadrilaterals are rectangle, square, trapezoid, and kite or irregular and uncharacterized figures with four sides.
- Angle sum property of a quadrilateral
- Types of quadrilateral
- Properties of Parallelograms
- MidPoint Theorem
- Kite – Quadrilaterals
Chapter 9: Areas of Parallelograms and Triangles
The area of a plane figure is described as the amount of the planar surface covered by a closed geometric figure like rectangle, square, etc. The area of a parallelogram is equal to the product of its
Chapter 10: Circles
A circle is a geometrical shape which is defined as the locus of points that moves in a plane so that its distance from a fixed point is always constant. This fixed point is the Centre of the circle while the fixed distance from it is called the radius of the circle.
- Circles and its Related Terms
- Circle Theorems
- Theorem – There is one and only one circle passing through three given non-collinear points
- Theorem – The sum of opposite angles of a cyclic quadrilateral is 180°
Chapter 11: Constructions
Construction helps to understand the approach to construct different types of triangles for different given conditions using a ruler and compass of required measurements.
Chapter 12: Heron’s Formula
In this chapter, a formula called Heron’s formula is introduced which helps to determine the area of the triangle when three sides of its being given. The application of this formula also helps to find the area of other different polygons also.
Chapter 13: Surface Areas and Volumes
Surface area and volume are the measures calculated for a three-dimensional geometrical shape like a cube, cuboid, sphere etc. The surface area of any given object is the area occupied by the surface of the object while volume is the amount of space available in an object.
Chapter 14: Statistics
Statistics is the study of the representation, collection, interpretation, analysis, presentation, and organization of data. In other words, it is a mathematical way to collect, summarize data. The representation of data differently along with the frequency distribution.
- Presentation of data
- Graphical representation of Data
- Bar graphs and Histograms
- Central Tendency
- Mean, Median, Mode, and Range
Chapter 15: Probability
The Probability in this class includes basic probability theory, which is also used in the probability distribution, to learn the possibility of outcomes for a random experiment and to find the probability of a single event to occur, when the total number of possible outcomes.