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NCERT Solutions For Class 9 Maths 2021 - Updates Here

New Update on 30-06-2021: NCERT Solutions for Class 9 Maths - NCERT Solutions for Class 9 Maths is released by the NCERT Authority. The National Council of Educational Research and Training releases the NCERT Class 9 Maths Books which are known for their Quality Syllabus and high standard Maths. As students have to focus on Mathematics as it is the fundamental Main subject, many students find it hard to understand the NCERT Class 9 Maths. Hereby, students are provided with the NCERT Solutions for Standard 9 along with the Maths Text book questions and answers. Candidates can get a clear view and idea if they initially try all the Mathematics questions on their own and then refer to the Solutions for checking answers and to have a look through of how the answers are handled in the Solutions. Candidates have to prepare their learning with respect to the Syllabus that is prescribed for the Subject. Candidates will have to necessarily have a look over the Solutions to get a clarity from NCERT Class 9 maths Chapter 1.

The official link to check the NCERT Solutions for Class 9 Maths is activated and is released officially.

Check here - NCERT Solutions for Class 9 Maths

CHAPTER 1: NUMBER SYSTEMS

Representation of terminating/non-terminating recurring decimals on the number line (and successive magnification method). Presentation of square roots of 2, 3 and other non-rational numbers. Rationalization of real numbers, laws of integral powers and rational exponents with positive real bases in Number Systems.

• Study Online (English/Hindi)
• Exercise 1.1
• Exercise 1.2
• Exercise 1.3
• Exercise 1.4
• Exercise 1.5
• Exercise 1.6
• Assignment based on Chapter 1 in English
• NCERT Books for Class 9
• प्रश्नावली 1.1
• प्रश्नावली 1.2
• प्रश्नावली 1.3
• प्रश्नावली 1.4
• प्रश्नावली 1.5
• प्रश्नावली 1.6
• Assignment based on Chapter 1 in Hindi

CHAPTER 2: POLYNOMIALS

Examples and definition of a polynomial, coefficient, degrees, zeroes and terms of a polynomial. Constant, linear, quadratic and cubic polynomials, monomials, binomials, trinomials. Factors and multiples, Remainder and factor theorems, factorization of a polynomials using factor theorem.

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• Exercise 2.1

• Exercise 2.2

• Exercise 2.3

• Exercise 2.4

• Exercise 2.5

• Assignment based on Chapter 2 in English

• प्रश्नावली 2.1

• प्रश्नावली 2.2

• प्रश्नावली 2.3

• प्रश्नावली 2.4

• प्रश्नावली 2.5

• Assignment based on Chapter 2 in Hindi

CHAPTER 3: COORDINATE GEOMETRY

In this chapter Coordinate Geometry we will study the concept of cartesian plane, coordinates of a point in this xy – plane, name, terms, notations and other terms associated with the coordinate plane. Abscissa and ordinate of a points. Plotting a point in xy – plane and naming it.

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• Exercise 3.1

• Exercise 3.2

• Exercise 3.3

• Assignment based on Chapter 3 in English

• प्रश्नावली 3.1

• प्रश्नावली 3.2

• प्रश्नावली 3.3

• Assignment based on Chapter 3 in Hindi

CHAPTER 4: LINEAR EQUATIONS IN TWO VARIABLES

This chapter provides the introduction to the equation in two variables of the type ax + by + c = 0. Proving a linear equation has infinite number of solutions. Plotting a linear equation on graph and justification of any point on line. Problems based on Linear Equations in Two Variables in daily life.

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• Exercise 4.1

• Exercise 4.2

• Exercise 4.3

• Exercise 4.4

• Assignment based on Chapter 4 in English

• NCERT books

• प्रश्नावली 4.1

• प्रश्नावली 4.2

• प्रश्नावली 4.3

• प्रश्नावली 4.4

• Assignment based on Chapter 4 in Hindi

CHAPTER 5: INTRODUCTION TO EUCLID’S GEOMETRY

Euclid’s geometry and history of Indian geometry. Introduction to Euclid’s Geometry provides a way of defining the common geometrical shapes and terms. Euclid’s five postulates and redefining (equivalent versions) the fifth postulates. Relationship between axiom, postulates and theorems.

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• Exercise 5.1

• Exercise 5.2

• Assignment based on Chapter 5 in English

• प्रश्नावली 5.1

• प्रश्नावली 5.2

• Assignment based on Chapter 5 in Hindi

CHAPTER 6: LINES AND ANGLES

There are two theorems in Lines and Angles chapter which may be asked for proof. First is “If two lines intersect, vertically opposite angles are equal” and second is “The sum of the angles of a triangle is 180.”. Rest theorems are given for motivations and questions will be asked on the basis of all these theorems (Motivate/Prove).

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• Exercise 6.1

• Exercise 6.2

• Exercise 6.3

• Assignment based on Chapter 6 in English

• प्रश्नावली 6.1

• प्रश्नावली 6.2

• प्रश्नावली 6.3

• Assignment based on Chapter 6 in Hindi

CHAPTER 7: TRIANGLES

In this chapter Triangles, two theorems (“Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence)” and “The angles opposite to equal sides of a triangle are equal.”) are given for proof and the rest will be asked in the form of applications/problems.

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• Exercise 7.1

• Exercise 7.2

• Exercise 7.3

• Exercise 7.4

• Exercise 7.5

• Assignment based on Chapter 7 in English

• प्रश्नावली 7.1

• प्रश्नावली 7.2

• प्रश्नावली 7.3

• प्रश्नावली 7.4

• प्रश्नावली 7.5

• Assignment based on Chapter 7 in Hindi

CHAPTER 8: QUADRILATERALS

The chapter Quadrilaterals contains only one theorem( “The diagonal divides a parallelogram into two congruent triangles”) for proof. Other will be asked in the form of application and conceptual questions. Questions are on the basis of properties of quadrilaterals and combinations of it with triangles.

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• Exercise 8.1

• Exercise 8.2

• Assignment based on Chapter 8 in English

• प्रश्नावली 8.1

• प्रश्नावली 8.2

• Assignment based on Chapter 8 in Hindi

CHAPTER 9: AREAS OF PARALLELOGRAMS AND TRIANGLES

The combinations of areas of parallelograms and triangles are given to prove in most of the question. Proof and questions based on “Parallelograms on the same base and between the same parallels have the same area” will be asked. Example of median may be used as theorem in most of the questions.

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• Exercise 9.1

• Exercise 9.2

• Exercise 9.3

• Exercise 9.4

• Assignment based on Chapter 9 in English

• प्रश्नावली 9.1

• प्रश्नावली 9.2

• प्रश्नावली 9.3

• प्रश्नावली 9.4

• Assignment based on Chapter 9 in Hindi

CHAPTER 10: CIRCLES

“Equal chords of a circle subtend equal angles at the center” and “The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle” are given for proof in Circles. The other theorems are important for solving questions based on triangle, quadrilateral and circles.

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• Exercise 10.1

• Exercise 10.2

• Exercise 10.3

• Exercise 10.4

• Exercise 10.5

• Exercise 10.6

• Assignment based on Chapter 10 in English

• प्रश्नावली 10.1

• प्रश्नावली 10.2

• प्रश्नावली 10.3

• प्रश्नावली 10.4

• प्रश्नावली 10.5

• प्रश्नावली 10.6

• Assignment based on Chapter 10 in Hindi

CHAPTER 11: CONSTRUCTIONS

There are two categories of constructions. One is Construction of bisectors of line segments and angles of measure 60, 90, 45 etc. The other is construction of a triangle given its base, sum/difference of the other two sides and one base angle & given perimeter and base angles.

• Study Online (English/Hindi)

• Exercise 11.1

• Exercise 11.2

• Assignment based on Chapter 11 in English

• प्रश्नावली 11.1

• प्रश्नावली 11.2

• Assignment based on Chapter 11 in Hindi

CHAPTER 12: HERON’S FORMULA

Use of Heron’s formula to find the area of triangles, quadrilaterals (dividing it into two triangles) and other polygons. Knowledge of formulae of plane figures will also help in doing questions.

• Study Online (English/Hindi)
• Exercise 12.1
• Exercise 12.2
• Assignment based on Chapter 12 in English
• NCERT books
• प्रश्नावली 12.1
• प्रश्नावली 12.2
• Assignment based on Chapter 12 in Hindi

CHAPTER 13: SURFACE AREAS AND VOLUMES

Students are familiar with surface areas and volumes as they have already studies mensuration in earlier classes. This chapter also contains problems based on surface areas and volumes of cube, cuboids, cylinders, cones, spheres and hemispheres. Conversion of one figure into the other comparing volumes is also given as an application of mensuration.

• Exercise 13.1

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  • Hindi Medium

• Exercise 13.2

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• Exercise 13.3

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• Exercise 13.4

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• Exercise 13.5

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  • Hindi Medium

• Exercise 13.6

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  • Hindi Medium

• Exercise 13.7

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  • Hindi Medium

• Exercise 13.8

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  • Hindi Medium

• Exercise 13.9

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  • English Medium

  • Hindi Medium

• Assignment based on Chapter 13 in English

• Assignment based on Chapter 13 in Hindi

CHAPTER 14: STATISTICS

Introduction to statistics includes the presentation of data collected in raw form. Presentation of data in tabular form by grouping them in proper intervals, drawing a bar graph, histogram or polygon. Finding the measure of central tendency mean, mode and median of raw data.

• Exercise 14.1

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  • Hindi Medium

• Exercise 14.2

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  • Hindi Medium

• Exercise 14.3

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  • Hindi Medium

• Exercise 14.4
  • Study Online (English/Hindi)
  • English Medium
  • Hindi Medium
• Assignment based on Chapter 14 in English
• Assignment based on Chapter 14 in Hindi

CHAPTER 15: PROBABILITY

Probability based on observation or frequency approach. Questions based on real life or day to day incidents. Toss of a coin, throwing a dice, based on deck of cards, etc. questions based on simple events.

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• Exercise 15.1

• प्रश्नावली 15.1

• Assignment based on Chapter 15 in English

• Assignment based on Chapter 15 in Hindi

• NCERT books

NCERT Solutions For Class 9 Maths Chapter 10: Circles

CBSE Class 9 Maths Chapter 10: Chapter Summary

Students will study about circles, associated words, and the attributes of a circle in this chapter. A circle is a group of points on a plane that are all equidistant from one another. The locus of points equidistant from a particular point is called a circle. The fixed point is referred to as the centre, while the fixed distance is referred to as the radius.

The plane is divided into three portions by a circle: inside the circle, on the circle, and outside the circle. Students will study about the centre of a circle, radius, diameter, arcs and their types – major arc and minor arc, semicircle, chords, cyclic quadrilaterals, segments and their two sorts – major segment and minor segment, and other concepts connected to circles in this chapter.

CBSE Class 9 Maths Chapter 10 Important Questions

1. Bisectors of angles A, B, and C of a triangle ABC intersect its circumcircle at D, E, and F respectively. Prove that the angles of the triangle DEF are 90° – (½)A, 90° – (½)B and 90° – (½)C.

2. In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

3. Prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.

4. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lies on the third side.

5. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6, find the radius of the circle.

6. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

7. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.

8. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed, and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.

9. Prove that if chords of congruent circles subtend equal angles at their centers, then the chords are equal.

10. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the center.

11. AC and BD are chords of a circle which bisect each other. Prove that
    (i) AC and BD are diameters
    (ii) ABCD is a rectangle.

12. Prove that a cyclic parallelogram is a rectangle.