NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT textbook for Class 9. The students can download PDF of chapter-wise solutions to these problems, from the links provided further below on this page. These NCERT Solutions for Class 9 cover all the topics included in the NCERT textbook-like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

With the help of these Solutions of NCERT Books for Class 9 Maths, students can practise all types of questions from the chapters. The CBSE Class 9 Maths Solutions have been designed by our experts in a well-structured format to provide several possible methods of answering the problems and ensure a proper understanding of concepts. The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.

NCERT Class 9 Mathematics 

Chapter 1 Number System

Chapter 2 Polynomials

Chapter 3 Coordinate Geometry

Chapter 4 Linear Equations in Two Variables

Chapter 5 Introduction to Euclids Geometry

Chapter 6 Lines and Angles

Chapter 7 Triangles

Chapter 8 Quadrilaterals

Chapter 9 Areas of Parallelograms and Triangles

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Heron’s Formula

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics

Chapter 15 Probability

TERM ( 2021-2021) MCQ TYPES

UNIT- NUMBER SYSTEMS 1. NUMBER SYSTEM Review of representation of natural numbers, integers, rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers. 1. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as , √2,√3 and their representation on the number 2. Rationalization (with precise meaning) of real numbers of the type 1 𝑎+𝑏√𝑥 and 1 √𝑥+√√𝑦 (and their combinations) where x and y are natural number and a and b are integers. 3. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.) UNIT-ALGEBRA 2. LINEAR EQUATIONS IN TWO VARIABLES Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax+by+c=0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life with algebraic and graphical solutions being done simultaneously UNIT-COORDINATE GEOMETRY 3. COORDINATE GEOMETRY The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane. UNIT-GEOMETRY 4. LINES AND ANGLES 1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180˚ and the converse. 2. (Prove) If two lines intersect, vertically opposite angles are equal. 3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines. 4. (Motivate) Lines which are parallel to a given line are parallel. 5. (Prove) The sum of the angles of a triangle is 180˚. 6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. 5. TRIANGLES 1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2. (Motivate) 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). 3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence) 5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate) The sides opposite to equal angles of a triangle are equal. 7. (Motivate) The sides opposite to equal angles of a triangle are equal. UNIT-MENSURATION 6. HERON’S FORMULA Area of a triangle using Heron's formula (without proof) UNIT-STATISTICS & PROBABILITY 7. STATISTICS Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped, bar graphs, histograms

TERM 2 (2021 -2022)

UNIT-ALGEBRA 1. POLYNOMIALS Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities and their use in factorization of polynomials. UNIT-GEOMETRY 2. QUADRILATERALS 1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely. 3. (Motivate) In a parallelogram opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely. 6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse. 3. CIRCLES Through examples, arrive at definition of circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle. 1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse. 2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centres) and conversely. 4. (Motivate) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 5. (Motivate) Angles in the same segment of a circle are equal. 6. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse. 4. CONSTRUCTIONS 1. Construction of bisectors of line segments and angles of measure 60˚, 90˚, 45˚ etc., equilateral triangles. 2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle. UNIT-MENSURATION 5. SURFACE AREAS AND VOLUMES Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones. UNIT-STATISTICS & PROBABILITY 6. PROBABILITY History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on statistics).