NCERT Solutions For Class 9 Maths – Download in PDF (2021 – 2022)

NCERT solutions for class 9 maths English Medium and Hindi Medium both for CBSE and UP Board (High School) 2021 – 2022 in PDF form free download. NCERT Solutions for other subjects of class 9 are also given in the form of PDF file. CBSE board examinations completely in PDF form to download. During the preparation of these solutions, we were careful towards the accuracy, simplicity  and neatness of contents. If still there is any problem, please specify us, we will try to rectify as soon as possible. Students of class ix should feel the flow of reason while getting a result on solving a problem developing mastery of basic algebraic skills.

NCERT Solutions For Class 9 Maths

Download NCERT Solutions For Class 9 Maths in PDF

Chapter 1: Number Systems

Representation of terminating/non-terminating recurring decimals on the number line (and successive magnification method). Presentation of square roots of 2, 3 and other non-rational numbers. Rationalization of real numbers, laws of integral powers and rational exponents with positive real bases in Number Systems.

Chapter 2: Polynomials

Examples and definition of a polynomial, coefficient, degrees, zeroes and terms of a polynomial. Constant, linear, quadratic and cubic polynomials, monomials, binomials, trinomials. Factors and multiples, Remainder and factor theorems, factorization of a polynomials using factor theorem.

Chapter 3: Coordinate Geometry

In this chapter Coordinate Geometry we will study the concept of cartesian plane, coordinates of a point in this xy – plane, name, terms, notations and other terms associated with the coordinate plane. Abscissa and ordinate of a points. Plotting a point in xy – plane and naming it.

Chapter 4: Linear Equations in Two Variables

This chapter provides the introduction to the equation in two variables of the type ax + by + c = 0. Proving a linear equation has infinite number of solutions. Plotting a linear equation on graph and justification of any point on line. Problems based on Linear Equations in Two Variables in daily life.

Chapter 5: Introduction to Euclid’s Geometry

Euclid’s geometry and history of Indian geometry. Introduction to Euclid’s Geometry provides a way of defining the common geometrical shapes and terms. Euclid’s five postulates and redefining (equivalent versions) the fifth postulates.  Relationship between axiom, postulates and theorems.

Chapter 6: Lines and Angles

There are two theorems in Lines and Angles chapter which may be asked for proof. First is “If two lines intersect, vertically opposite angles are equal” and second is “The sum of the angles of a triangle is 180.”. Rest theorems are given for motivations and questions will be asked on the basis of all these theorems (Motivate/Prove).

Chapter 7: Triangles

In this chapter Triangles, two theorems (“Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence)” and “The angles opposite to equal sides of a triangle are equal.”) are given for proof and the rest will be asked in the form of applications/problems.

Chapter 8: Quadrilaterals

The chapter Quadrilaterals contains only one theorem( “The diagonal divides a parallelogram into two congruent triangles”) for proof. Other will be asked in the form of application and conceptual questions. Questions are on the basis of properties of quadrilaterals and combinations of it with triangles.

Chapter 9: Areas of Parallelograms and Triangles

The combinations of areas of parallelograms and triangles are given to prove in most of the question. Proof and questions based on “Parallelograms on the same base and between the same parallels have the same area” will be asked. Example of median may be used as theorem in most of the questions.

Chapter 10: Circles

“Equal chords of a circle subtend equal angles at the center” and “The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle” are given for proof in Circles. The other theorems are important for solving questions based on triangle, quadrilateral and circles.

Chapter 11: Constructions

There are two categories of constructions. One is Construction of bisectors of line segments and angles of measure 60, 90, 45 etc. The other is construction of a triangle given its base, sum/difference of the other two sides and one base angle & given perimeter and base angles.

Chapter 12: Heron’s Formula

Use of Heron’s  formula to find the area of triangles, quadrilaterals (dividing it into two triangles) and other polygons. Knowledge of formulae of plane figures will also help in doing questions.

Chapter 13: Surface Areas and Volumes

Students are familiar with surface areas and volumes as they have already studies mensuration in earlier classes. This chapter also contains problems based on surface areas and volumes of cube, cuboids, cylinders, cones, spheres and hemispheres. Conversion of one figure into the other comparing volumes is also given as an application of mensuration.

Chapter 14: Statistics

Introduction to statistics includes the presentation of data collected in raw form. Presentation of  data in tabular form by grouping them in proper intervals, drawing a bar graph, histogram or polygon. Finding the measure of central tendency mean, mode and median of raw data.

Chapter 15: Probability

Probability based on observation or frequency approach. Questions based on real life or day to day incidents. Toss of a coin, throwing a dice, based on deck of cards, etc. questions based on simple events.