CBSE Class 9 Maths Sample Question Papers and Worksheets

If you are looking for Class 9 Mathematics model papers, periodic test papers, Important Questions, MCQ Questions, Sample Papers, Study Notes, Hot Questions, Worksheets, Class Assignments, Practice Exercises, Word Problems, Previous Year question papers, Solved papers, Unit tests and other related study material for exam preparation then you are at the right place.

Total Papers : 104

Total Papers : 104

Worksheets of Class 9

CBSE Worksheets for Class 9 Mathematics contains all the important questions on Mathematics as per NCERT syllabus. These Worksheets for Class 9 Mathematics or 9th grade Mathematics worksheets help students to practice, improve knowledge as they are an effective tool in understanding the subject in totality. Also Multiple Choice Questions based Worksheets help students in learning in depth concepts while out of the class.

Worksheets of Class 9 Mathematics

Question bank of Class 9

On Ribblu one can get immense collections of CBSE Question Bank for Class 9 Mathematics which includes important questions 9th Class Chapter wise as per NCERT syllabus. Students while preparing for final exams must practice all the important questions of 9th grade Mathematics. All these Important Questions chapter wise have been uploaded by various registered users.

Question bank of Class 9 Mathematics

Sample Papers of Class 9

By Solving CBSE Sample Papers for Class 9 Mathematics, immensely helps students in preparing for the final exams. These Class 9 sample papers and 9th grade sample question papers are prepared in accordance with the latest syllabus and guidelines that are issued by the central board. If one wants to have a clear idea of how the final exam papers would be in terms of level of difficulty, time and other aspects then, all students must make sure that they do sample papers once their course revision is finished.

Sample Papers of Class 9 Mathematics

Revision Notes of Class 9

CBSE Revision Notes For Class 9 Mathematics are very important for quick revision to recall all that has been learned throughout the year. On Ribblu.com one can find Study Key Notes or Revision notes for all subjects of 9th Class STD and which includes Mathematics as per CBSE and NCERT syllabus. Notes make this process of recall easy. One can easily revise the precise notes in a day or two. Once they get the hint, the students are quick to recall the entire material.

Revision Notes of Class 9 Mathematics

Question Papers of Class 9

If you are looking for CBSE Question Papers for Class 9 Mathematics then you are at the right place. On Ribblu you will find Class 9 Mathematics Question Papers, 9th class previous year board question papers and MCQs Paper for Class 9 Mathematics, as per NCERT Syllabus. Solving them gives students the clear idea of how the final exam papers would be in terms of level of difficulty, time and other aspects, so all students must attempt as many Mathematics Question Papers as possible once their course revision is finished so as to get the best score in final exams

Question Papers of Class 9 Mathematics

Test Papers of Class 9

CBSE Test Papers from Class 9 Mathematics are very important for exam preparations. Students need to practice these practice test papers of class 9th and periodic and assessment unit tests of grade 9th while preparing for final exams. Practicing these Test Papers will enable students to identify important topics of chapters for preparing final exams. As per CBSE Guidelines schools need to conduct weekly tests and periodic tests. So these Previous Class Test papers, periodic and Unit Test Papers of Mathematics gives students the clear idea of what are the important aspects in a particular topic and thereby increase their fundamental concepts and knowledge and prepare them for Final Exams.

Test Papers of Class 9 Mathematics

Supplementary Helping Aids For CBSE Exams Preparation.

Indian Education system primarily consists of two parts one being studying the subjects and the other one is appearing for exams and tests. All these exams are conducted by schools for various classes to gauge how much the students have understood , learned and what is their capability score in any particular subject. But sometimes even after understanding the topics fully there are chances the students don’t do well in exams because of lack of preparation from the examination perspective. The reason being that one needs to prepare for exams in a particular way and for that previous question papers, sample papers, worksheets and unit test papers play a major role.

The important factors in performing well in the exams, apart from, studying day & night, grasping everything and retaining everything, is, to be able to study smart and in a proper disciplined manner, so that all the efforts translate into performance.

When preparing for your exams every expert recommends that students should invest more time and effort into solving question papers and worksheets from previous year

This practice not only will familiarise the students with the format of the question paper, it will also teach them the discipline of answering the entire question paper within the time allotted to you at the examination. The more one solves these, the more confidence will be gained towards achievement of highest score. Often it happens that in the exams the children know the solution of every question but due to lack of time they miss some portions. So it is imperative to practice before hand so that everything is attempted on time in main exams

Class 9 Mathematics Term Wise Syllabus

Number Systems (8 Marks)

Algebra (17 Marks)

Coordinate Geometry (4 Marks)

Geometry (28 Marks)

Mensuration (13 Marks)

Statistics & Probability (10 Marks)

Term I

Chapter 1 : Real Numbers

Review of representation of natural numbers, integers and rational numbers on the number line. Representation of terminating / non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

Definition of nth root of a real number.

Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/(√x+√y) (and their combinations) where x and y are natural number and a and b are integers.

Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

Chapter 2 : Polynomials

Definition of a polynomial in one variable with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zeroes of polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeroes of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.

Recall of algebraic expressions and identities. Verification of identities:

(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx, (x ± y)3 = x3 ± y3 ± 3xy (x ± y), x3 ± y3 = (x ± y) (x2 ± xy + y2), x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

and their use in factorization of polynomials.

Chapter 3: Coordinate Geometry

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

Chapter 4: Linear Equations in Two Variables

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

Chapter 5: Introduction to Euclid's Geometry

History - Geometry in India and Euclid's geometry. Euclid's method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example:

(Axiom) 1. Given two distinct points, there exists one and only one line through them.

(Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

Chapter 6: Lines and Angles

  1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 1800and the converse.
  2. (Prove) If two lines intersect, vertically opposite angles are equal.
  3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
  4. (Motivate) Lines which are parallel to a given line are parallel.
  5. (Prove) The sum of the angles of a triangle is 1800.
  6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

Chapter 7: Triangles

  1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
  2. (Prove) 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).
  3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
  4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)
  5. (Prove) The angles opposite to equal sides of a triangle are equal.
  6. (Motivate) The sides opposite to equal angles of a triangle are equal.
  7. (Motivate) Triangle inequalities and relation between ‘angle and facing side' inequalities in triangles.

Chapter 12: Heron’s Formula

Area of a triangle using Heron's formula (without proof) and its application in finding the area of a quadrilateral.

Chapter 14: Statistics

Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency polygons, Mean, median and mode of ungrouped data.

Chapter 15: Probability

History, repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on statistics).

Term II

Chapter 8: Quadrilaterals

  1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
  2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
  3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
  4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
  5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
  6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and is half of it and (motivate) its converse.

Chapter 9: Area of Parallelogram and Triangles

Review concept of Area, Recall area of a rectangle.

  1. (Prove) Parallelograms on the same base and between the same parallels have the equal area.
  2. (Motivate) Triangles on the same base (or equal base) and between the same parallels are equal in area.

Chapter 10: Circles

Through examples, arrive at definition of circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.

  1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse.
  2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
  3. (Motivate) There is one and only one circle passing through three given non-collinear points.
  4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centre) and conversely.
  5. (Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  6. (Motivate) Angles in the same segment of a circle are equal.
  7. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
  8. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

Chapter 11: Constructions

Construction of bisectors of line segments and angles of measure 60o, 90o, 45o etc., equilateral triangles.

Construction of a triangle given its base, sum/difference of the other two sides and one base angle. Construction of a triangle of given perimeter and base angles.

Chapter 13: Surface Areas and Volumes

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

Suggested Mathematics Question Paper Design - Class 9

Typology of Questions

Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.

Number of Questions Asked that are Objective type Questions = 6

Number of Questions Asked that are Short Answer Type Questions = 4

Number of Questions Asked that are Long Answer Type Questions = 1

Total Marks = 20

Total Weightage = 25%

Typology of Questions

Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions and stating main ideas

Number of Questions Asked that are Objective type Questions = 6

Number of Questions Asked that are Short Answer Type Questions = 2

Number of Questions Asked that are Long Answer Type Questions = 3

Total Marks = 23

Total Weightage = 29%

Typology of Questions

Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.

Number of Questions Asked that are Objective type Questions = 5

Number of Questions Asked that are Short Answer Type Questions = 4

Number of Questions Asked that are Long Answer Type Questions = 1

Total Marks = 19

Total Weightage = 24%

Typology of Questions

Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations

Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.

Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions

Number of Questions Asked that are Objective type Questions = 3

Number of Questions Asked that are Short Answer Type Questions = 4

Number of Questions Asked that are Long Answer Type Questions = 1

Total Marks = 18

Total Weightage = 22%

Internal Assessmen = 20 Marks

Pen Paper Test and Multiple Assessment (5+5) = 10 Marks

Portfolio = 5 Marks

Lab Practical (Lab activities to be done from the prescribed books) = 5 Marks

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