NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Maths include solutions to all the problems of NCERT Class 9 Maths along with step by step explanations. Along with the Class 9 Maths NCERT Solutions, Important topics, Multiple Choice Questions, and Important Questions have also been provided for the students.

NCERT Solutions for Class 9 Maths cover important chapters such as Number System, Polynomials, Coordinate Geometry, Euclid’s Geometry, Quadrilaterals, Circles, Triangles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc. Practicing and preparing for the exams through the Class 9 Maths NCERT Solutions can help the students clear their basics and understand the related concepts.

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NCERT Solutions for Class 9 Maths: Chapter-wise Solutions

The chapter-wise NCERT Solutions for Class 9 Maths are given below: 

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Class 9th Maths Chapters

NCERT Solutions for Class 9 Maths Chapter-wise Solutions are provided below:

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Chapter 1 Number Systems

• Definition: Number sysytem is representation of numbers using digits or symbols in a consistent manner.
• Weightage in Board Exam: Chapter 1 Number Systems belongs to Unit 1 Number Systems which has a weightage of 10 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • Review of representation of natural numbers, integers, and rational numbers on the number line
  • Examples of non-recurring/non-terminating decimals 
  • Definition of nth root of a real number
  • Rationalization (with precise meaning) of real number
  • Recall of laws of exponents with integral powers

Chapter 1 Number System: Additional Resources

• Definition: An algebric expression that consists of variables and coefficients is known as polynomials.
• Weightage in Board Exam: Chapter 2 Polynomials belongs to Unit 2 Algebra which has a weightage of 20 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • This chapter covers algebraic expressions called polynomial and various terminologies related to them.
  • Definition, terms, examples and counterexamples, coefficient and Degree of a polynomial, zero, constant, linear, cubic, and quadratic polynomials.
  • Remainder theorem and Factor theorem with examples, monomials, binomials, and trinomials.

Chapter 2 Polynomials: Additional Resources

• Definition: Coordinate geometry is the branch of geometry where position of points on a plane is defined by their coordinates.
• Weightage in Board Exam: Chapter 3 Coordinate Geometry belongs to Unit 3 Coordinate Geometry which has a weightage of 04 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • Cartesian plane, terms, and various terms associated with the coordinate plane.
  • Plotting a point in the XY plane and the naming process of this point.

Chapter 3 Coordinate Geometry: Additional Resources

• Definition: An expression in the form of, ax + by + c = 0, where a, b and c are real numbers and a and b are not equal to 0, is called a linear equation in two variables. 
• Weightage in Board Exam: Chapter 4 Linear Equations in Two Variables belongs to Unit 2 Algebra which has a weightage of 20 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • Introduction to two-variable linear equations of the type ax+by+c=0.
  • Using bar graph to plot linear equation, and justify any point on a line.
  • Graphs and examples of linear equations.
  • Ratio and proportion.

Chapter 4 Linear Equations in Two Variables: Additional Resources

• Definition: Euclid Geometry is the study of plane and solid figures on the basis of axioms and theorems propounded by a mathematician Euclid.
• Weightage in Board Exam: Chapter 5 Introduction to Euclid’s Geometry belongs to Unit 4 Geometry which has a weightage of 27 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • Introduction of Indian geometry as it has some base in Euclid’s geometry.
  • Defining geometrical terms and shapes.

Chapter 5 Introduction to Euclid’s Geometry: Additional Resources

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Chapter 6 Lines and Angles

• Definition: A line is a row of closely spaced dots that extent to infinity in two directions and when such two lines intersect each other an angle is formed. 
• Weightage in Board Exam: Chapter 6 Lines and Angles belongs to Unit 4 Geometry which has a weightage of 27 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • Theorems on angles and lines that can be asked for proof.
  • The first theorem which will be asked for proof is “If the two lines are intersecting each other, then the vertically opposite angles formed will be equal”.
  • Also, the second proof that is asked is, “The sum of all the angles formed in a triangle is 180°”. 

Chapter 6 Lines and Angles: Additional Resources

• Definition: A three sided polygon consisting three edges and three vertices, is known as a triangle. The sum of all the three angles of a triangle is always 180°.
• Weightage in Board Exam: Chapter 7 Triangles belongs to Unit 4 Geometry which has a weightage of 27 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered:
  • Congruent Figures and the rules of congruence. 
  • There are two theorems that are given as proof while the other is used in the problems or applications.
  • Properties of inequalities and triangles.

Chapter 7 Triangles: Additional Resources

• Definition: A polygan that has four edges, four vertices and four angles is called a quadrilateral.
• Weightage in Board Exam: Chapter 8 Quadrilaterals belongs to Unit 4 Geometry which has a weightage of 27 marks in the CBSE Class 9 Maths Examination.
• The chapter comprises the properties related to quadrilateral and their combinations with the triangles and detailed coverage of polygon curve angle.

Chapter 8 Quadrilaterals: Additional Resources

• Definition: Area of a triangle and parallelogram is the region occupied by them in two dimensional plane. 
• Important Topics:
  • Areas of Triangle 
  • Parallelogram 
  • Combinations of Areas of Triangle and Parallelograms

Chapter 9 Areas of Triangles and Parallelogram: Additional Resources

Please note: Chapter 9 Areas of Triangles and Parallelogram has been omitted for Syllabus 2022-23.

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Chapter 10 Circles

• Definition: Circle is a locus (path) of a point which is, at all points, is equidistant from another fixed point (center).
• Weightage in Board Exam: Chapter 10 Circles belongs to Unit 4 Geometry which has a weightage of 27 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered: 
  • Equal chords and their distance from the center
  • Chord of a point and angle subtended by it
  • Angles that are subtended by an arc of a circle 
  • Cyclic quadrilaterals 

Chapter 10 Circles: Additional Resources

• Definition: Accurate drawings and measurements of shapes, lines and angles in geometry is termed as construction.
• Important Topics Covered:
  • Categories of Construction
  • Construction of a triangle along with its base, difference, or sum of the remaining two sides, and one base angle with base angle and parameters are given.
  • Construction of bisectors for the line segments and measuring angles that include 45/60/90, etc.

Chapter 11 Constructions:  Additional Resources

Please note: Chapter 11 Constructions has been omitted for Syllabus 2022-23.

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Chapter 12 Heron’s Formula

• Definition: Not dpending on the angles of a triangle, Heron’s formula gives the area of a triangle using length all the three sides. The formula is given by Area = √s(s-a)(s-b)(s-c); where s is the perimeter of the triangle. 
• Weightage in Board Exam: Chapter 12 Heron’s Formula belongs to Unit 5 Mensuration which has a weightage of 13 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered: 
  • Extended concepts from Area of Triangle
  • Finding Area of triangles, Quadrilaterals, and various types of Polygons
  • Formula for plane figures 

Chapter 12 Heron’s Formula: Additional Resources

• Definition: The surface area of an object is the complete area/region the object occupies whilst the volume the amount of space an object occupies is called its volume.
• Weightage in Board Exam: Chapter 13 Surface Areas and Volume belongs to Unit 5 Mensuration which has a weightage of 13 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered: 
  • Volume of cylinders, cubes, cuboids, cones, hemispheres, and Spheres
  • Conversion of one figure into another, and compare volumes of two figures

Chapter 13 Surface Area and Volume: Additional Resources

• Definition: The branch of mathematics that deals with collectiong, analysing and interpreting the data is called statistics.
• Weightage in Board Exam: Chapter 14 Statistics belongs to Unit 6 Statistics and Probability which has a weightage of 06 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered: 
  • Collection of data
  • Presentation of data in the form of a table, bar chart, histograms, and frequency polygons

  • Mean, mode, and median for data (ungrouped)

Chapter 14 Statistics: Additional Resources

• Definition: Probability deals with the possibility of any event to occur and is calculated as the ratio of number of favourable outcomes to th ethe total number of outcomes.
• Weightage in Board Exam: Chapter 15 Probability belongs to Unit 6 Statistics and Probability which has a weightage of 06 marks in the CBSE Class 9 Maths Examination.
• Important Topics Covered: 
  • Repeated experiments, incidents like throwing dice, coin tossing, the probability for a deck of cards, and simple events

  • Observed frequency approach to probability

Chapter 15 Probability: Additional Resources

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