CBSE Class 9 Mathematics Latest Syllabus for 2015

Scroll down to download pdf file

Maths Course Structure - Class IX

 

UNITS

 

MARKS

I

NUMBER SYSTEMS

06

II

ALGEBRA

20

III

COORDINATE GEOMETRY

06

IV

GEOMETRY

22

V

MENSURATION

14

VI

STATISTICS AND PROBABILITY

12

 

TOTAL

80

 

UNIT I : NUMBER SYSTEMS

(20) Periods

 

1. REAL NUMBERS

 

 

Review of representation of natural numbers, integers, 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.

 

 

Examples of nonrecurring / non terminating decimals such as v2, v3, v5 etc. Existence of non-rational numbers (irrational numbers) such as v2, v3 and their representation on the number line.

 

 

Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.

 

 

Existence of vx for a given positive real number x (visual proof to be emphasized).

 

 

Definition of nth root of a real number.

 

 

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.)

 

 

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

 

 

 

 

 

UNIT II : ALGEBRA

 

 

1. POLYNOMIALS

(25) Periods

 

Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial / equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization

 

 

of ax2 + bx + c, a1 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.

 

 

Recall of algebraic expressions and identities. Further identities of the type (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx, (x y)3 = x3 y3 3xy (x y).

 

 

x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2-xy - yz - zx) and their use in factorization of. polymonials. Simple
expressions reducible to these polynomials.

 

 

2.LINEAR EQUATIONS IN TWO VARIABLES

(12) Periods

 

Recall of linear equations in one variable. Introduction to the equation in two variables. Prove 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 seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

 

 

UNIT III : COORDINATE GEOMETRY

 

 

1.COORDINATE GEOMETRY

(9) Periods

 

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate
plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y = mx + c and linking with the chapter on linear equations in two variables.

 

 

UNIT IV : GEOMETRY

 

 

1. INTRODUCTION TO EUCLID'S GEOMETRY

(6) Periods

 

History - Euclid and geometry in India. 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.

 

 

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

 

 

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

 

 

2. LINES AND ANGLES

(10) Periods

 

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the converse.

 

 

2. (Prove) If two lines intersect, the 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 180o.

 

 

6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interiors opposite angles.

 

 

3. TRIANGLES

(20) Periods

 

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 Congruene).

 

 

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.

 

 

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.

 

 

4. QUADRILATERALS

(10) Periods

 

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 (motivate) its converse.

 

 

5. AREA

 

 

Review concept of area, recall area of a rectangle.

 

 

1. (Prove) Parallelograms on the same base and between the same parallels have the same area.

 

 

2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.

 

 

6. CIRCLES

(15) Periods

 

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, subtended angle.

 

 

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

 

 

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center 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 center(s) and conversely.

 

 

5. (Prove) 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.

 

 

6. (Motivate) Angles in the same segment of a circle are equal.

 

 

7. (Motivate) If a line segment joining two points subtendes 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 the either pair of the opposite angles of a cyclic quadrilateral is 180o and its converse

 

 

7. CONSTRUCTIONS

(10) Periods

 

1. Construction of bisectors of line segments & angles, 60o, 90o, 45o angles etc., equilateral triangles.

 

 

2. Construction of a trangle given its base, sum/difference of the other two sides and one base angle.

 

 

3. Construction of a triangle of given perimeter and base angles.

 

 

UNIT V :MENSURATION

 

 

1.AREAS

(4) Periods

 

Area of a triangle using Heros formula(without proof) and its application in finding the area of a quadrilateral

 

 

2.SURFACE AREAS AND VOLUMES

(10) Periods

 

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

 

 

UNIT VI : STATISTICS AND PROBABILITY

 

 

1.STATISTICS

(13) Periods

 

Introduction to statistics: Collection of data, Presentation of data- tabular form, ungrouped / grouped, bar graphs, histograms(with varying base lengths), frequency polygons,
qualitative analysis of data to choose the correct form of presentation for the
collected data. Mean, median, mode of ungrouped data.

 

 

2.PROBABILITY

(12) Periods

 

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

 

 

 

 

 

INTERNAL ASSESSMENT

20 MARKS

Evaluation of activities

10 Marks

Project Work

05 Marks

Continuous Evaluation

05 Marks

 

Click on the text For more study material for Class IX please click here - Class IX

Latest CBSE News

  • CBSE has issued a notification to all schools regarding re-conduct of Class 12 Economics Paper and class 10 Mathematics paper Exams to be re-conducted Class 12 – Economics (Code 030) Class 10 – Mathematics (Code 041) There were reports that the examination papers for the above mentioned subjects were leaked prior to the exam. Also it has come to notice post investigation that hand written paper...
  • In line with governments initiative to improve health and fitness amongst youngsters and also to improve state of physical, mental, emotional, social and spiritual well-being and not merely the absence of disease or infirmity CBSE will be introducing Health and Physical Education classes as mainstream education for classes 9 to 12. This will help the students to understand the benefits of being...
  • CBSE board is in the process of making major changes in the syllabus for all classes according to which NCERT books will be revised. The new NCERT Books will be applicable from next year. In continuation to the changes being made, it has now been decided that QR codes will be printed on new set of NCERT Textbooks which will be issued in 2019. Students will be able to scan the QR code using their...
  • The problems faced by CBSE board during the current ongoing board exams for class 10 and class 12 doesn’t seems to end. The investigations for the major paper leak for class 12 is still going on with students agitating and filing cases in SC against the re-conduct of examinations. Now due to Bharat Bandh organized in Punjab by various Dalit Organizations all schools and public transport systems...
  • The Board's Class  X/XII Examinations scheduled on 02.04.2018 could not be conducted in the State of Punjab due to Bharat Bandh and had to be cancelled. It has now been decided to conduct the above said cancelled examinations  on 27'" April 2018 (Friday) for candidates of the State of Punjab for Class X/XII. 2018. Following is the schedule for conduct of Examination : Friday, 27'" April,2018 - 10...
  • NCERT has again made clear that as per the syllabus and guidelines issued by them, no homework must be given to students upto class 2. The CBSE schools have already been directed to follow the instructions but the schools are still giving homework to students in order to show that they are making the child study or to display to society about their education standards. Also clarification came on...
  • Read the statement by CBSE below- Subsequent to the false news circulated on various media platforms on 11.04.2018 alleging that some questions in JEE (Main) 2018 Exam were identical to 2016 mock test of Narayana Coaching Academy, CBSE issued a detailed clarification yesterday (11.04.2018) itself to all media debunking the false news after thorough enquiry into the matter. While it is established...