| Unit Name | Marks |
| Unit 1: Number System | 08 |
| Unit 2: Algebra | 17 |
| Unit 3: Coordinate Geometry | 04 |
| Unit 4: Geometry | 28 |
| Unit 5: Mensuration | 13 |
| Unit 6: Statistics and Probability | 10 |
| Total | 80 |
How to Prepare for Competitive Exam Through NCERT Class 9 Solutions
NCERT is the fundamental book that provides a basic understanding of the topics that are taught in Class 9. For most of the competitive exams and Olympiad, the basic foundation of the students needs to be very solid. For this, students must start building their concepts from Class 9. This is the stage from where the self-study begins playing a major role in students’ life.
The pressure of studies is less in Class 9 so students can use this time to learn other things as per their interest. Also, they can start their preparation for the Olympiad and other competitive exams at this stage. NCERT Solution for Class 9 will also help in this preparation. Whatever the concepts students will learn, it will help them further in solving the problems of competitive exams.
Apart from NCERT Solutions, students can also get other preparation material at CONCEPT ACADEMY such as previous years papers, Syllabus, CONCEPT study notes, Sample papers, important questions for all the classes to prepare more efficiently. Keep Learning and stay tuned for further updates on CBSE and other competitive exams such as OLYMPIADS & NTSE.
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
The chapter Coordinate Geometry includes the concepts of the cartesian plane, coordinates of a point in xy – plane, terms, notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more. Students, in this chapter, will also be studying the concepts of Abscissa and ordinates of a point as well plotting and naming a point in xy – plane. There are 3 exercises in this chapter that contain questions revolving around the topics mentioned in the chapter, helping the students get thorough with the concepts.
Along with recalling the knowledge of linear equations in one variable, this chapter will introduce the students to the linear equation in two variables, i.e., ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. There are 4 exercises in this chapter that consists of questions related to finding the solutions of a linear equation, plotting a linear equation on the graph and other topics discussed in the chapter.
Chapter 5 Introduction to Euclids Geometry
This chapter discusses Euclid’s approach to geometry and tries to link it with the present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms. Students will be taken deeper into the topic of axioms, postulates and theorems with the two exercises present in the chapter.
This chapter revolves around the theorems present in the topics of Lines and Angles. Students might often be asked to prove the statements given in the questions. There are 3 exercises in the chapter solving which students would be able to understand the concepts covered in the chapter thoroughly. There are four axioms and eight theorems covered in the chapter.
In this chapter, students will study in detail about the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles. The chapter has a total of 5 exercises, in which the students are asked “to-prove” as well as application-level problems. With this chapter, students will also learn to prove the properties that they learnt in earlier classes. The chapter also teaches the students to apply the various congruence rules while solving the problems. There are about eight theorems covered in this chapter.
Chapter 8 Quadrilaterals
A figure obtained by joining four points in order is called a quadrilateral. This chapter takes the students to the depth of the topics of Quadrilaterals. The chapter contains 2 exercises that contain only one theorem to prove. However, there are a total of nine theorems that can be used to solve the application or conceptual level questions asked. Angle sum property of a Quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem are taught explained in this chapter to help the students in learning the concepts thoroughly.
Chapter 9 Areas of Parallelograms and Triangles
In this chapter, an attempt is being made to consolidate the knowledge about the formulae for finding the areas of different figures, by studying relationships between the areas of geometric figures provided they lie on the same base and between the same parallels. This study will also be useful in the understanding of some results on ‘similarity of triangles’. The chapter contains 4 exercises of which, most of the questions ask the students to prove the statement given
Chapter 10 Circles
A circle can be defined as a collection of all the points in a plane, at a fixed distance from a fixed point in the plane. Topics like Angle Subtended by a Chord at a Point, Equal Chords and their respective distances from the Centre, the Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals and other terms related to circles are covered in this chapter. A total of twelve theorems are present in this chapter, learning which the students will get a clearer idea of the concepts taught. There are 6 exercises in this chapter which consist of questions from all the concepts present in the chapter.
Chapter 11 Constructions
In this chapter, students will learn some basic constructions. The method learnt will then be used to construct certain kinds of triangles. There are 2 exercises present in this chapter, of which the first exercise deals with the construction of a certain angle or the bisector of a given angle. On the other hand, the second exercise deals with the constructions of triangles when different parameters are given.
Chapter 12 Heron’s Formula
The chapter discusses Heron’s formula, which can be used to calculate the area of a triangle when the length of all three sides is given. In this method, there is no need to calculate the angles or other distances in the triangle. This formula can be used not only to find the area of triangles but also to find the areas of quadrilaterals and other polygons by dividing them into triangles. There are 2 exercises in this chapter which help the student in understanding the method of solving the problems based on Heron’s formula.
Chapter 13 Surface Areas and Volumes
In this chapter, students shall learn to find the surface areas and volumes of cuboids and cylinders in details and broaden the study to some other solids such as cones and spheres. This chapter is just an extended version of the chapter mensuration in which the students learnt about the surface areas and volumes in earlier classes. There are 8 exercises in this chapter, and these exercises contain problems that are based on surface areas and volumes of different solids such as cubes, cuboids, spheres, cylinders, cones, and hemispheres.
Chapter 14 Statistics
The branch of Mathematics in which the extraction of meaningful information is studied is known as Statistics. It can also be defined as the collection of data on different aspects of the life of people, useful to the State. The chapter teaches about the different presentation of the data, including the frequency distribution as well. The chapter also helps the students learn the graphical representation of data, using different graphs such as Bar graphs, Histograms, Frequency polygons etc. The chapter also lets the students learn the measure of central tendency mean, median and mode of the raw data. A total of 4 exercises are present in the chapter that includes problems related to all these concepts.
Chapter 15 Probability
The collection of some outcomes of an experiment is known as an event of an experiment. The chances of occurrence of an event are known as probability. In this chapter, students will learn to measure the chance of occurrence of a particular outcome in an experiment. This chapter contains only 1 exercise. The problems covered in this exercise are based on real-life incidents, enhancing the interest of the students in solving the questions