NCERT Solutions for Class 9 Math
The NCERT solutions for Mathematics Textbook as prescribed by CBSE Schools is strictly based on latest pattern of Central Board of Secondary Education for the Board Exams 2020. Math is one of the most important subject for Class 1students. NCERT Textbook of Class 9 Math build the basic fundamental which will help you at higher levels. If you want to opt Science stream in upper classes then you must clear all the concept and doubts. Solving NCERT Solutions for Class 9 Math will memorize all the important formulas and theories that are important for the examination. Being a part of Studyrankers, we are committed to provided most accurate and detailed answers of every NCERT questions. These solutions are simple and prepared in a way so that you can easily grasp the concepts related to each question. If you are facing any type of problem then you can take help from here. You can use the links provided below to start reading you problematic chapter.
- NCERT Solutions of Chapter 1 Number Systems
- NCERT Solutions of Chapter 2 Polynomials
- NCERT Solutions of Chapter 3 Coordinate Geometry
- NCERT Solutions of Chapter 4 Linear Equations in Two Variables
- NCERT Solutions of Chapter 5 Introduction to Euclid’s Geometry
- NCERT Solutions of Chapter 6 Lines and Angles
- NCERT Solutions of Chapter 7 Triangles
- NCERT Solutions of Chapter 8 Quadrilaterals
- NCERT Solutions of Chapter 9 Areas of Parallelograms and Triangles
- NCERT Solutions of Chapter 10 Circles
- NCERT Solutions of Chapter 11 Constructions
- NCERT Solutions of Chapter 12 Heron’s Formula
- NCERT Solutions of Chapter 13 Surface Areas and Volumes
- NCERT Solutions of Chapter 14 Statistics
- NCERT Solutions of Chapter 15 Probability
Benefits of NCERT Solutions for 9th Class Math
These NCERT Solutions are prepared by our expert Math Faculty and accurate and detailed. These will be helpful in revising important formulas. We have added figures wherever necessary so that you can understand it easily. Through these solutions students can strengthen their problem-solving skills. Students can understand the problem easily and in less time.
The first chapter of Class 9 Math Textbook is Number Systems and the chapter ends with Probability. We have provided all the important details of each chapter below.
Chapter 1: Number Systems
We all know about the numbers and it’s different types. In earlier classes we have discussed about rational numbers, whole numbers, integers, natural numbers. The expanded version of number line is discussed here. Rational and Irrational numbers are represented on number lines with geometrical methods. In this chapter contains the representation of terminating/non-terminating recurring decimals on the number line (and successive magnification method). It has been discussed how to represent the root of any number √x on number line. We will also learn to represent √3.5, √2.4 etc on number Line. Rationalisation of Irrational numbers is discussed. Laws of integral powers and rational exponents with positive real bases in Number system is discussed. 6 NCERT exercises have given to make chapter understand well.
Chapter 2: Polynomials
We know what algebraic expression means. Polynomials are the special kind of algebraic expression where power of variable is always a natural number. This chapter explains various aspects of polynomial and the detailed terminologies related to it very clearly. Require number of illustrative examples are also there. Definition of a polynomial, degrees, coefficient, zeroes and terms of a polynomial are explained. After that different types of Polynomials – Linear, Constant, quadratic and cubic polynomials, monomials, binomials, trinomials are discussed. Next topics discussed are Factors and multiples, Remainder and factor theorems, factorization of polynomials using factor theorem. The chapter has total of 4 exercises for better learning.
Chapter 3: Coordinate Geometry
The third chapter coordinate geometry is all about related position of different points. It is about the point of The chapter has 3 exercises in total. Here we will be discussing the concept of cartesian plane also known as the XY plane. We will be learning about coordinates of a point in this XY– plane. Also we will be learning names, terms, notations and other terms associated with the coordinate plane. We will discuss the meaning of Abscissa and ordinate of a points. Abscisa is for X coordinate and Ordinate is for Y-coordiante. After that, we will we learn how to place a point in the XY Plane.
Chapter 4: Linear Equations in Two Variables
This chapter will take you through the introduction to the equation in two variables of the type ax + by + c = 0. Here the condition is that a≠0, b≠0. Questions are asked to prove that a linear equation has an infinite number of solutions. Also question regarding plotting a linear equation on graph is asked. It is taught how to represent real time problems in form of linear Equations in two variables. Questions are asked on converting general life problem in linear equation in two variables. Also, questions are asked regarding representing linear equation on XY plane and straight line.
Chapter 5: Introduction to Euclid’s Geometry
Geometry is an ancient concept. It is all about studying different defined figures and interesting things about it. The chapter starts with an introduction of geometry and some information regarding history of Indian geometry. Introduction to Euclid’s Geometry make us understand that how should we define the common geometrical shapes. The difference between axioms, postulates and theorems is discussed. Euclids Postulates of geometry are discussed. The chapter has two exercises to make you understand chapter better.
Chapter 6: Lines and Angles
After discussing various postulates of geometry in chapter 5, in chapter 6 we start with geometrical figures of Lines and angles. These are the basics of Geometry. Line and angles has been introduced to us in previous classes. Here their various aspects are discussed. There are two exercises in this book. The chapter has theorems in Lines and Angles chapter. Proofs can also be asked in examinations. First type of proof is “If two lines intersect, vertically opposite angles are equal” and second proof that is asked is “The sum of the angles of a triangle is 180.” Other theorems are also there. Questions are asked all these concepts.
Chapter 7: Triangles
A geometrical figure bounded by three line segments is known as Triangle. This chapter has a total of 5 exercises to make us understand the concepts of congruency and Inequality in triangles. In congruency we discuss how two triangles are said to be congruent. Five such criteria are discussed. They are SSS, SAS, ASA, AAS, and RHS. After the concepts related to inequalities are discussed. When we say inequality we are discussing about signs like <,> and =. Such concepts are discussed about the sides of triangle. One of such examples is sum of side of two sides are more than third. Some proofs are asked from this chapter related to concept of Inequality.
Chapter 8: Quadrilaterals
Quadrilaterals are geometrical figures having four sides. Different types of quadrilaterals like Parallelogram and rhombus are discussed with their important properties. The chapter Quadrilaterals consists of only two exercises. The chapter has only one theorem which is asked for proof. Others will be asked in the form of application and conceptual questions. Most of these questions are asked in form of given geometrical figures and shapes. The theorems are needed to be used wisely to solve problems.
Chapter 9: Areas of Parallelograms and Triangles
Area is the unit First the meaning of area is explained. Areas of parallelograms and triangles and their combinations are discussed in this chapter. Few kinds of proof regarding areas or different combinations of areas can be asked. Example of median may be used as theorem in most of the questions. There are four exercises in the chapter to understand such area related concepts.
Chapter 10: Circles
We all know what circle is. Mathematically, it is the collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane. In class IX, We will be discussing some interesting topics related to circle, 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. Questions are asked which can be solved using these concepts effectively. The chapter has been discussed in the form of important and interesting problems based on geometrical figures. These topics will be discussed with the help of six exercises.
Chapter 11: Constructions
In the chapter it is discussed how to construct certain geometrical figures, you will be learning two categories of constructions. There are two exercises. One is Construction of bisectors of the line segments and angles of measure including 60°, 90°, 45° etc. The other category which you will be learning is construction of a triangle with its base, sum/difference of the other two sides and one base angle & given perimeter and base angles given. So, students will be asked to learn the construction with understanding geometrical logic behind it.
Chapter 12: Heron’s Formula
We know how to find area of triangle when altitude and base is given. Heron’s formula is the formula for finding area of triangle when length of three sides is given. This formula was given by ancient mathematician Herons. There are only two exercises in this chapter. In the first exercise it has been discussed how to find the area of a triangle if sides of triangle. In next it has been taught how to find area of Quadrilateral if length of its sides and one of the diagonal is given. That makes two triangles. The area of quadrilateral will be some of the areas of these two triangles.
Chapter 13: Surface Areas and Volumes
Mensuration has already been discussed in the previous class. It is about finding surface areas and volumes of some definite geometrical three dimensional figures like of cube, cuboids, cylinders, cones, spheres and hemispheres. Conversion of one of the figures into another, comparing volumes is also given as an application of mensuration. Some real time problems are discussed in nine exercises of the chapter.
Chapter 14: Statistics
We have seen charts in newspapers, magazines related to certain data. Here in this chapter, Statistics is explained simply as the collection of data on different aspects of the life of people, which is useful to the State and interpretation and drawing of inferences from the data. With a total of four exercises, Introduction to statistics includes the presentation of data collected in a raw form. Building blocks of this chapter are presentation of data in tabular form by grouping them in a regular intervals, histogram or polygon, bar graph drawing. Measure of central tendency mean and mode and median of raw data are also discussed. Questions are asked to find these for given data.
Chapter 15: Probability
Probability is the science of finding chance of an event. It is the method to find the chance of occurrence of any event mathematically. Here, in class IX, we will be discussing about the experimental approach to find the probability of given conditions. The probability of certain elements depends upon the condition that how things have been going on in the past. If a coin is tossed 10 times, 7 times its tail probability of tail is more than head in next toss. This is based on experiments. One NCERT exercise is enough to understand the concept.