NCERT Solutions for Class 9 Maths: Chapter Wise PDF 2024
Last Updated :
13 May, 2024
Mathematics is one of the most important subjects in Class 9th. There are certain topics in NCERT Class 9th Math from where various questions were asked in annual exams as well as competitive exams.
There are 15 chapters altogether in the NCERT Class 9 Math. We have created the detailed chapter-wise solution for NCERT Class 9 which is based on the latest CBSE Class 9 Syllabus.
NCERT Solutions Class 9 Maths Chapters (Updated Syllabus As per New CBSE Syllabus)
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Chapter 1 Number System
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Chapter 2 Polynomials
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Chapter 3 Coordinate Geometry
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Chapter 4 Linear Equations in Two Variables
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Chapter 5 Introduction to Euclids Geometry
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Chapter 6 Lines and Angles
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Chapter 7 Triangles
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Chapter 8 Quadrilaterals
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Chapter 9 Circles
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Chapter 10 Heron’s Formula
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Chapter 11 Surface Areas and Volumes
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Chapter 12 Statistics
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NCERT Solutions for Class 9 Maths Chapter 1 Number System
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials
NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables
NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclids Geometry
NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles
NCERT Solutions for Class 9 Maths Chapter 7 Triangles
NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals
NCERT Solutions for Class 9 Maths Chapter 9 Circles
NCERT Solutions for Class 9 Maths Chapter 10 Heron’s Formula
NCERT Solutions for Class 9 Maths Chapter 11 Heron’s Formula
NCERT Solutions for Class 9 Maths Chapter 12 Statistics
NCERT Solutions for Class 9 Maths (Old CBSE Syllabus)
Below is the chapter wise solution of class 9th Maths.
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NCERT Solutions for Class 9 Maths
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Download Class 9 Math NCERT Solution PDF
Click on the link below to download NCERT Class 9 Math Solution PDF.
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NCERT Class 9 Math Solution PDF
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Class 9 NCERT Math Solution
Following is the chapter wise solution of class 9 math.
Chapter 1 – Number System
Chapter 1 briefly covers the concept of rational and irrational numbers, real numbers, and their representation on the number line.
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Class 9 Maths NCERT Solutions Chapter 1 Exercises
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No Of Questions
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Exercise 1.1
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4 Questions & Solutions (4 short Answers)
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Exercise 1.2
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4 Questions & Solutions (4 short Answers)
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Exercise 1.3
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9 Questions & Solutions (8 short Answers, 1 long Answer)
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Exercise 1.4
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2 Questions & Solutions (2 long Answers)
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Exercise 1.5
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5 Questions & Solutions (4 short Answers, 1 long Answer)
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Exercise 1.6
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3 Questions & Solutions (3 short Answers)
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Resources for Class 9 Chapter 1 Number System
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Chapter 2 – Polynomials
The chapter Polynomials guides to learning polynomials of degree 1 (Linear polynomials), 2 (quadratic polynomials), 3 (cubic polynomials), etc. and terminology related to it. This chapter also covers the concept of factor theorem, algebraic identities of quadratic polynomials, split the middle theorem, algebraic identities for cubic polynomials, etc.
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Class 9 Maths NCERT Solutions Chapter 2 Exercises
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No Of Questions
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Exercise 2.1
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5 Questions (5 Short Answers)
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Exercise 2.2
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4 Questions (4 Short Answers)
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Exercise 2.3
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3 Questions (3 Short Answers)
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Exercise 2.4
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5 Questions (4 Short Answers, 1 Long Answer)
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Exercise 2.5 Set 1, Set 2
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16 Questions (9 Short Answers, 5 Long Answers, 2 Very Long Answers)
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Resources for Class 9 Chapter 2 Polynomials
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Chapter 3 – Coordinate Geometry
This chapter on coordinate geometry helps to learn the concepts of the Cartesian plane and various terminology related to it in detail. The chapter deals with problems on various subtopics like determining the x and y coordinates of a point in a cartesian plane, identifying quadrants, locating an object, and expressing it in the form of coordinates.
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Class 9 Maths NCERT Solutions Chapter 3 Exercises
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No Of Questions
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| Exercise 3.1 |
2 Questions (1 Short Answer, 1 Long Answer)
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| Exercise 3.2 |
2 Questions (2 Short Answers)
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| Exercise 3.3 |
2 Questions (1 Short Answer, 1 Long Answer)
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Resources for Class 9 Chapter 3 Coordinate Geometry
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Chapter 4 – Linear Equations in Two Variables
Linear equations in one variable have been already discussed in earlier classes that deal with Chapter unique solutions. Now, in this chapter linear equation comes with two variables like ax + by + c = 0. Thus, this chapter introduces the concepts like solutions including solving linear equations, graphical representation methods, and the depiction of parallel lines.
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Class 9 Maths NCERT Solutions Chapter 4 Exercises
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No Of Questions
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| Exercise 4.1 |
2 Questions & Solutions (2 Short Answers)
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| Exercise 4.2 |
4 Questions & Solutions (3 Short Answers, 1 Long Answer)
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| Exercise 4.3 |
8 Questions & Solutions (4 Short Answers, 4 Long Answers)
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| Exercise 4.4 |
2 Questions & Solutions (2 Long Answers)
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Resources for Class 9 Chapter 4 Linear Equations in Two Variables
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Chapter 5 – Introduction to Euclid’s Geometry
The next chapter for NCERT Class 9 Maths Solutions is Introduction to Euclid’s Geometry explains Euclid’s method of geometry and links it with modern-day geometry. Euclid’s five postulates deal with line segments, radii, perpendicular lines, and the variation of the fifth postulate. Euclid approached geometry by defining different axioms and postulates.
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Class 9 Maths NCERT Solutions Chapter 5 Exercises
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No Of Questions
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| Exercise 5.1 |
7 Questions (4 Short Answers, 3 Long Answers)
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| Exercise 5.2 |
2 Questions (1 Short Answer, 1 Long Answer)
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Resources for Class 9 Chapter 5 Introduction to Euclid’s Geometry
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Chapter 6 – Lines and Angles
Lines and Angles deals with the properties of the angle formed when two or more lines intersect each other and the properties of these angles formed. Also, provides an understanding of the basic definitions of various terms that are used in geometry.Â
Students learn about the different types of angles, pairs of angles, transversals, parallel lines, the angle sum property of triangles, and axioms associated with these concepts.
Chapter 7 – Triangles
This chapter gives a detailed description of the congruence of triangles, their rules, properties, and the inequalities in triangles.
Chapter 8 – Quadrilateral
The chapter Quadrilateral is all about the different types of quadrilaterals (rectangle, square, parallelogram, trapezium, etc) and their different properties like the angle sum property of a quadrilateral. Further, the last section of the chapter provides a brief introduction to the midpoint theorem and its converse.
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Class 9 Maths NCERT Solutions Chapter 8 Exercises
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No Of Questions
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| Exercise 8.1 |
12 Questions  (2 Short Answers, 6 Long Answers, 4 Very Long Answers)
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| Exercise 8.2 |
7 Questions (2 Short Answers, 3 Long Answers, 3 Very Long Answers)
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Resources for Class 9th Chapter 8 Quadrilateral
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Chapter 9 – Areas of Parallelograms and Triangles
As the name suggests Areas of parallelograms and Area of triangles are covered in this chapter. It gives the understanding of the formula to determine the areas of different closed shapes using the relation between the areas of different geometric shapes.
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Class 9 Maths NCERT Solutions Chapter 9 Exercises
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No Of Questions
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| Exercise 9.1 |
1 Question (1 Short Answer)
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| Exercise 9.2 |
6 Questions (5 Short Answers, 1 Long Answer)
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| Exercise 9.3 Set 1, Set 2 |
16 Questions (12 Short Answers, 4 Long Answers)
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| Exercise 9.4 |
8 Questions (4 Short Answers, 1 Long Answer, 3 Very Long Answers)
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Resources for Class 9 Chapter 9 Areas of Parallelograms and Triangles
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Chapter 10 – Circles
This chapter is related to the different properties and the terminology of the circles. The chapter Circles included various topics such as angles subtended by a chord at a point, perpendiculars dropped from the center to a chord, and how to calculate the distance of equal chords from the center. Other discussions include angles subtended by an arc of the circle, cyclic quadrilaterals, and their attributes.
| Class 9 Maths NCERT Solutions Chapter 10 Exercises |
No Of Questions
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| Exercise 10.1 |
2 Questions & Solutions (2 Short Answers)
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| Exercise 10.2 |
2 Questions & Solutions (2 Long Answers)
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| Exercise 10.3 |
3 Questions & Solutions (3 Long Answers)
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| Exercise 10.4 |
6 Questions & Solutions (6 Long Answers)
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| Exercise 10.5 |
12 Questions & Solutions (12 Long Answers)
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| Exercise 10.6 |
10 Questions & Solutions (10 Long Answers)
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Resources for Class 9 Chapter 10 Circles
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Chapter 11 – ConstructionsÂ
The chapter Constructions in this class helps to understand the approach to constructing different types of triangles for different given conditions. This chapter comprises two exercises in which the problems in Exercise 11.1 deal with the construction of a different angle or the bisector of a given angle, and Exercise 11.2 are related to the constructions of triangles, in the case when different parameters are given.
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Class 9 Maths NCERT Solutions Chapter 11 Exercises
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No Of Questions
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| Exercise 11.1 |
5 Questions(2 Short Answers, 2 Long Answer, 1 Very Long Answer)
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| Exercise 11.2 |
5 Questions (5 Very Long Answers)
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Resources for Class 9 Chapter 11 Constructions
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Chapter 12 – Heron’s Formula
This chapter discusses only Heron’s formula and its applications which are used to determine the area of a triangle when all three sides of the triangle are provided. The chapter comprises only two exercises, both Exercises 12.1 and 12.2 consist of problems related to the application of Heron’s formula.
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Class 9 Maths NCERT Solutions Chapter 12 Exercises
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No Of Questions
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| Exercise 12.1 |
6 Questions & Solutions (2 Short Answers, 2 Long Answers, 2 Very Long Answers)
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| Exercise 12.2 |
9 Questions & Solutions (4 Long Answers, 5 Very Long Answers)
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Resources for Class 9 Chapter 12 Heron’s Formula
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Chapter 13 – Surface Areas and Volumes
The chapter Surface areas and volumes mainly deal with the formula, to determine the surface areas and volumes of different shapes like cube, cuboid, and cylinder and their applications. The problems related to each topic of this chapter are discussed in nine different exercises.
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Class 9 Maths NCERT Solutions Chapter 13 Exercises
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No Of Questions
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| Exercise 13.1 |
8 Questions & Solutions (4 Short Answers, 4 Long Answers)
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| Exercise 13.2 |
11 Questions & Solutions (5 Short Answers, 6 Long Answers)
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| Exercise 13.3 |
8 Questions & Solutions (6 Short Answers, 2 Long Answers)
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| Exercise 13.4 |
9 Questions & Solutions (4 Short Answers, 5 Long Answers)
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| Exercise 13.5 |
9 Questions & Solutions (4 Short Answers, 5 Long Answers)
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| Exercise 13.6 |
8 Questions & Solutions (8 Short Answers)
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| Exercise 13.7 |
9 Questions & Solutions (9 Long Answers)
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| Exercise 13.8 |
10 Questions & Solutions (5 Short Answers, 5 Long Answers)
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| Exercise 13.9 |
3 Questions & Solutions (3 Long Answers)
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Resources for Class 9 Chapter 13 Surface Areas and Volumes
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Chapter 14 – StatisticsÂ
The chapter Statistics helps to learn the representation of data differently along with the frequency distribution. With the help of a total of four exercises the concept of graphical representation of data, using various graphs like Frequency polygons, Histograms, Bar graphs, etc.
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Class 9 Maths NCERT Solutions Chapter 14 Exercises
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No Of Questions
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| Exercise 14.1 |
2 Questions & Solutions (2 Short Answers)
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| Exercise 14.2 |
9 Questions & Solutions (9 Long Answers)
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| Exercise 14.3 |
9 Questions & Solutions (6 Short Answers, 3 Long Answers)
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| Exercise 14.4 |
6 Questions & Solutions (2 Short Answers, 4 Long Answers)
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Resources for Class 9 Maths Chapter 14 Statistics
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Chapter 15 – Probability
The last chapter covered in CBSE NCERT Solutions for class 9 math’s is chapter 15 Probability. Probability discusses the concept of the Chances of occurrence of a specific outcome in an experiment. This chapter consists of only one exercise which is based on the problems from everyday life examples to understand the experimental approach to probability.
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Class 9 Maths NCERT Solutions Chapter 15 Exercises
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No Of Questions
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| Exercise 15.1 |
10 Questions (4 Short Answers, 3 Long Answers, 3 Very Long Answers)
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Resources for Class 9 Chapter 15 Probability
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Important Resources for CBSE Class 9th by GeeksforGeeks
NCERT Solutions for Class 9 Maths – FAQs
Can I get solved answers for the questions from the NCERT Class 9 Maths chapters?
Yes, you can get solved answers for the questions from the NCERT Class 9 Maths chapters in this above article. All the solutions to the exercises are available here.
Should I daily solve the questions from the NCERT Solutions for Class 9 Maths?
It will be really helpful if you solve NCERT Solutions for Class 9 Maths on a regular basis. It will build a strong foundation on all the topics and after that, you can easily solve more complicated problems.
What are some important tips for Class 9 Maths Chapter 6 Lines and Angles?
This chapter teaches a number of properties that students must learn. The following tips can help you in optimizing this process.
- Answer a series of questions about the properties of angles created when a transversal intersects two or three parallel lines.
- Understand the logic underlying theorems like the triangle’s angle sum property.
- Make a mental note of how the angles relate to one another.
List out some important formulas from Class 9 Maths.
Important formulas from Geometry:
- Area of a triangle = ½ × b × h
- Perimeter of a triangle = a + b + c
- Area of parallelogram = b × h
- Perimeter of a parallelogram = 2(a + b)
Important formulas from Surface Area and volume:
- TSA of a cuboid = 2(lb + bh +lh)
- Volume of a cuboid = l×b×h
- TSA of a cube = 6a2
- Volume of a cube = a3
Important Algebraic Equations:
- (a + b)2 = a2 + b2 + 2ab
- (a – b)2 = a2 + b2 – 2ab
- (a + b) (a – b) = a2 – b2
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