If you want to do well in Science, you need Maths. You may have heard this saying, but the concept has stood true beyond the tests of time. Maths has brought revolutionary innovations and has impacted the fields of other core Sciences like Physics and Chemistry. It is the language of logic, and by studying it extensively, you learn how to problem-solve better and master the art of thinking abstractly.
Our NCERT Maths PDFs will not only boost your confidence by giving you a quick refresher and overview of key concepts covered in the syllabus but also prepare you for any upcoming competitive exams. The IIT and JEE which are two of the most popular national competitive tests even base their question paper patterns from excerpts contained in NCERT textbooks, which makes studying these all the more important for any student who is seriously aspiring to crack engineering or college-level entrance tests. Below given are the chapter wise details for Class 9 Maths NCERT Books.
Chapter 1: Number System
In this chapter, students will learn about the concept of an irrational number, real numbers, and their decimal expansions, they will also learn the techniques of real numbers on the number line, different kinds of operations on real numbers, and about the laws of exponents for real numbers. Overall there are 7 exercises, solve the questions and in case of any doubt refer to our book. As we provide a step-by-step description of each question for making you perfect in the number system.
Chapter 2: Polynomial
Polynomial is a type of algebraic expression. In previous classes, you understood factorization of algebraic expression, so apply those concepts and learn some new concepts while solving polynomials. Here students will familiarize themselves with the concept of polynomials in one variable, zeros of a polynomial, remainder theorem, factorization of polynomials, and algebraic identities. There are 7 exercises in this chapter. Solve them and take our book help in case you are unable to get the desired answer or if you find it difficult to solve any question.
Chapter 3: Coordinate geometry
In earlier classes you studied the location of points on a particular line. And now in this chapter you will learn how to locate a point which is not present on that line, but at some other place. In this chapter students will be introduced to the concept of the Cartesian system, plotting a point in the plane if its coordinates are given. Make yourself aware of the X and Y axis and plot a point using a graph. There are 5 exercises in this chapter including the summary.
Chapter 4: Linear Equations and Two variables
In previous classes you understood linear equations in one variable and now it’s the time to add one more variable. In this chapter, students will understand what is a linear equation, solving linear equations, graphical representation of linear equations in two variables, equations of lines parallel to the x-axis, and y-axis. Like other chapters there are 5 exercises including the summary exercise. Attempt all the questions for knowing your practice, and consult our book in case you need any help.
Chapter 5: Introduction To Euclid’s Geometry
Here students will learn about Euclid’s definition, axioms, and postulates, equivalent versions of Euclid’s fifth postulate. There is a theorem in this chapter which states that two distinct lines can’t have more than one common point. Solve the exercises, know about the postulates of Euclid for grasping the chapter in a better way. And yes for any kind of difficulty refer to our book containing solutions of all exercises.
Chapter 6: Lines and Angles
In chapter 5 students understood that minimum two points are needed to draw a line, they also became aware of some axioms. Now, this chapter introduces students to the basic terms and definition of line and angles. Students will learn about intersecting and non-intersecting lines, pairs of angles, transversal and parallel lines, lines parallel to the same line, and finally the angle sum property of a triangle. And like previous chapters, this chapter also ends up with exercises.
Chapter 7: Triangles
In your previous classes you learnt about triangles and their properties and in chapter 6 you understood about some triangle properties. Students will learn about the congruence of triangles, criteria for congruence of triangles, properties of a triangle, and inequalities in a triangle in this chapter. Congruent triangles are those triangles who are equal in size or you can say replica of each other. Learn more about congruent triangles and solve the exercises at the end.
Chapter 8: Quadrilaterals
In previous chapters students learnt about triangles which have three angles. Now add one more angle in the figure and see what comes up. A quadrilateral has 4 angles. Here, students will learn about the angle sum property of quadrilaterals, different types of quadrilaterals, properties of a parallelogram, conditions that make a quadrilateral parallelogram. Finally, students will be introduced to the concept of the mid-point theorem. So learn the new concepts and take our help in case you are stuck somewhere.
Chapter 9: Areas of parallelogram and triangles
In this chapter, students will learn about figures having the same base and between the same parallels, parallelograms on the same base and between the same parallels, triangles on the same base and between the same parallels. Also learn about trapezium. There are 4 exercises in this chapter. Solve each of them, initially you may find them difficult, but try to attempt them by yourself and take guidance from our book in case of any doubt.
Chapter 10: Circles
Here students will learn what is a circle and its related terms, the angle of a chord at a point, perpendicular from the center to a chord, circle through three points, equal chords and their distance from the center, the angle subtended by the arc of a circle, and cyclic quadrilaterals. There are 2 theorems in this chapter related to chords. Go through these theorems and learn how to prove them. Refer our solved book in case you face any difficulty.
Chapter 11: Construction
In previous chapters, you came across triangles. But those triangles were not made with precision. As those were for your understanding purpose only. Now in this chapter, students will learn about the basics of construction, and work with some construction on triangles. Know how to measure angle with protector, how to draw perpendicular and how to use the compass. You may find this chapter interesting, if you get the correct knowledge of construction. Solve the exercises at the end.
Chapter 12: Heron’s formula
From previous chapters you have an understanding of squares, triangles, rectangles and quadrilaterals. You know how to calculate perimeters and area. Now in this chapter calculate the area with a different formula. Here, students will learn about the area of a triangle as per Heron’s formula, application of heron’s formula while finding the area of a quadrilateral. Solve the exercise and take a grasp on this new formula.
Chapter 13: Surface Area and Volumes
Through previous chapters you became aware of the area and perimeter of figures. Now learn about new shapes and sizes in this chapter and how to calculate their volume and surface area. Here students will learn about calculating the surface area of a cuboid, and cube, right circular cylinder, right circular cone, the surface area of a sphere, Volume of a cuboid, the volume of a cylinder. Moreover, students will come to know about the volume of the right circular cone, and volume of a sphere.
Chapter 14: Statistics
In your day-to-day life, you may come across various data in newspapers, or magazines. You can also take example of polling results. All this data, when kept in a meaningful manner, is called statistics. Here, in this chapter students will learn about data collection, data presentation, representing data graphically, measurement of central tendency. Solve exercises and learn about the calculation of mean,median and mode. As these three are important from a statistics point of view.
Chapter 15: Probability
In this chapter, students will become familiar with the concept of probability and its experimental approach. Probability is nothing but the uncertainty of any circ*mstances. And in mathematics it is possible to calculate probability. The chapter contains activities which you need to do by yourself. It also contains examples along with the exercises. Understand examples and solve exercises for achieving mastery in probability.
Chapter-wise important theorems, proofs and axioms:
Introduction To Euclid's Geometry:-
(Axiom) There is only one line that connects two different points.
(Theorem) There can't be more than one point in common between two unique lines.
Angles and lines:
(Prove) If a ray is parallel to a line, the total of the two adjacent angles formed is 180°, and vice versa.
(Theorem) Vertically opposite angles are equal when two lines intersect.
(Theorem) Vertically opposite angles are equal when two lines intersect.
(Prove)When a transversal connects two parallel lines, it produces comparable angles, alternate angles, and inner angles.
(Prove) Parallel lines are those that are parallel to a given line.
(Theorem) The sum of a triangle's angles is 180°.
(Prove) When a triangle's side is formed, the outside angle is equal to the sum of the two inside opposite angles.
Triangles-
(Prove) Two triangles are congruent if any two of their sides and included angles are equivalent to any two of their sides and included angles (SAS Congruence).
(Theorem) Two triangles are congruent if any two angles and one triangle included side are equal to any two angles and one triangle's included side (ASA Congruence).
(Prove) Two triangles are congruent if the three sides of one are the same as the three sides of the other (SSS Congruence).
(Prove) Two right triangles are congruent if the hypotenuse and one of their sides are equal to the hypotenuse and one of their sides, respectively.
(Theorem) A triangle's angles opposite equal sides are equal.
(Prove) In a triangle, the sides opposite equal angles are equal.
(Prove)Triangle inequalities and the relationship between 'angle and facing side' inequalities in triangles .
Quadrilaterals-
(Theorem) A parallelogram is divided into two congruent triangles by the diagonal.
(Prove) The opposing sides of a parallelogram are equal, and vice versa.
(Prove) The opposing angles in a parallelogram are equal, and vice versa.
(Prove) A parallelogram is formed when two opposite sides of a quadrilateral are parallel and equal.
(Prove) The diagonals of a parallelogram bisect each other and vice versa.
(Prove)Any line segment linking the midpoints of two triangle sides is parallel to the third side, and vice versa.
Area-
(Theorem) The area of parallelograms with the same base and parallels is the same.
(Prove) Triangles with the same (or equal base) base and parallels have the same area.
Circles-
(Prove)Equal chords of a circle subtend equal angles at the centre, and vice versa.
(Prove) A perpendicular drawn through the centre of a circle to bisect a chord bisects the chord, while a line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
(Prove) There is only one circle that passes across three non-collinear locations.
(Prove)Equidistant chords of a circle (or congruent circles) are equidistant from the centre (or their respective centres), and vice versa.
(Theorem) The angle subtended by an arc at its centre is twice the angle subtended by it at any other point on the circle.
(Prove)Angles within a circle segment are all the same.
(Prove) A circle is formed when a line segment connecting two places subtends an equal angle at two other points on the same side of the line containing the segment.
(Prove) The sum of either of a cyclic quadrilateral's pair of opposite angles equals 180°, and vice versa.
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Other Free CBSE Class 9 Maths Study Material
S. no | CBSE Maths Material for Class 9 |
1 | NCERT Solutions Class 9 Maths |
2 | NCERT Solutions for Class 9 Maths Exercises |
3 | CBSE Class 9 Maths Chapter Wise Revision Notes |
4 | Important Questions for CBSE Class 9 Maths |
5 | Class 9 Math NCERT Exemplar Chapter wise Solutions |
6 | CBSE Sample Papers for Class 9 Maths |
Other Free Study CBSE Material for Class 9
S.No | Free Study Material PDFs |
1 | NCERT Solutions for Class 9 |
2 | CBSE/ NCERT Syllabus for Class 9 |
3 | CBSE Revision Notes for Class 9 |
4 | CBSE Important Questions for Class 9 |
5 | CBSE Sample Papers for Class 9 |
6 | CBSE Previous Year Question for Class 9 |
7 | NCERT Exemplar for Class 9 |
