Class-9-10-Curriculum-2018-2019-Maths Class 10 Notes | EduRev

Class 10 : Class-9-10-Curriculum-2018-2019-Maths Class 10 Notes | EduRev

 Page 1


MATHEMATICS (IX-X) 
 
(CODE NO. 041) 
Session 2018-19 
 
The Syllabus in the subject of Mathematics has undergone changes from time to time in 
accordance with growth of the subject and emerging needs of the society. The present revised 
syllabus has been designed in accordance with National Curriculum Framework 
 
2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to 
meet the emerging needs of all categories of students. For motivating the teacher to relate the 
topics to real life problems and other subject areas, greater emphasis has been laid on 
applications of various concepts. 
 
The curriculum at Secondary stage primarily aims at enhancing the capacity of students to 
employ Mathematics in solving day-to-day life problems and studying the subject as a separate 
discipline. It is expected that students should acquire the ability to solve problems using 
algebraic methods and apply the knowledge of simple trigonometry to solve problems of height 
and distances. Carrying out experiments with numbers and forms of geometry, framing 
hypothesis and verifying these with further observations form inherent part of Mathematics 
learning at this stage. The proposed curriculum includes the study of number system, algebra, 
geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. 
 
The teaching of Mathematics should be imparted through activities which may involve the use of 
concrete materials, models, patterns, charts, pictures, posters, games, puzzles and 
experiments. 
 
Objectives 
 
The broad objectives of teaching of Mathematics at secondary stage are to help the learners to: 
 
? consolidate the Mathematical knowledge and skills acquired at the upper primary stage; ?
? acquire knowledge and understanding, particularly by way of motivation and visualization, 
of basic concepts, terms, principles and symbols and underlying processes and skills; ?
? develop mastery of basic algebraic skills; ?
? develop drawing skills; ?
? feel the flow of reason while proving a result or solving a problem; ?
? apply the knowledge and skills acquired to solve problems and wherever possible, by more 
than one method; ?
? to develop ability to think, analyze and articulate logically; ?
? to develop awareness of the need for national integration, protection of environment, 
observance of small family norms, removal of social barriers, elimination of gender 
biases; ?
? to develop necessary skills to work with modern technological devices and mathematical 
softwares. ?
? to develop interest in mathematics as a problem-solving tool in various fields for its 
beautiful structures and patterns, etc. ?
? to develop reverence and respect towards great Mathematicians for their contributions to 
the field of Mathematics; ?
? to develop interest in the subject by participating in related competitions; ?
? to acquaint students with different aspects of Mathematics used in daily life; ?
? to develop an interest in students to study Mathematics as a discipline. ?
 
 
 
Page 2


MATHEMATICS (IX-X) 
 
(CODE NO. 041) 
Session 2018-19 
 
The Syllabus in the subject of Mathematics has undergone changes from time to time in 
accordance with growth of the subject and emerging needs of the society. The present revised 
syllabus has been designed in accordance with National Curriculum Framework 
 
2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to 
meet the emerging needs of all categories of students. For motivating the teacher to relate the 
topics to real life problems and other subject areas, greater emphasis has been laid on 
applications of various concepts. 
 
The curriculum at Secondary stage primarily aims at enhancing the capacity of students to 
employ Mathematics in solving day-to-day life problems and studying the subject as a separate 
discipline. It is expected that students should acquire the ability to solve problems using 
algebraic methods and apply the knowledge of simple trigonometry to solve problems of height 
and distances. Carrying out experiments with numbers and forms of geometry, framing 
hypothesis and verifying these with further observations form inherent part of Mathematics 
learning at this stage. The proposed curriculum includes the study of number system, algebra, 
geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. 
 
The teaching of Mathematics should be imparted through activities which may involve the use of 
concrete materials, models, patterns, charts, pictures, posters, games, puzzles and 
experiments. 
 
Objectives 
 
The broad objectives of teaching of Mathematics at secondary stage are to help the learners to: 
 
? consolidate the Mathematical knowledge and skills acquired at the upper primary stage; ?
? acquire knowledge and understanding, particularly by way of motivation and visualization, 
of basic concepts, terms, principles and symbols and underlying processes and skills; ?
? develop mastery of basic algebraic skills; ?
? develop drawing skills; ?
? feel the flow of reason while proving a result or solving a problem; ?
? apply the knowledge and skills acquired to solve problems and wherever possible, by more 
than one method; ?
? to develop ability to think, analyze and articulate logically; ?
? to develop awareness of the need for national integration, protection of environment, 
observance of small family norms, removal of social barriers, elimination of gender 
biases; ?
? to develop necessary skills to work with modern technological devices and mathematical 
softwares. ?
? to develop interest in mathematics as a problem-solving tool in various fields for its 
beautiful structures and patterns, etc. ?
? to develop reverence and respect towards great Mathematicians for their contributions to 
the field of Mathematics; ?
? to develop interest in the subject by participating in related competitions; ?
? to acquaint students with different aspects of Mathematics used in daily life; ?
? to develop an interest in students to study Mathematics as a discipline. ?
 
 
 
 
COURSE STRUCTURE CLASS -IX 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 08 
II ALGEBRA  17 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 28 
V MENSURATION  13 
VI STATISTICS & PROBABILITY 10 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS (18 Periods) 
1. 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. 
Operations on real numbers. 
 
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers 
(irrational numbers) such as v , v  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. 
 
3. Definition of nth root of a real number.  
4. Existence of v  
 
for a given positive real number x and its representation on the number line 
with geometric proof. 
 
5. Rationalization (with precise meaning) of real numbers of the type 
 
 
    v 
  and  
 
 v  
v
 
 (and their combinations) where x and y are natural number and a and 
b are integers. 
6. 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.) 
 
 
UNIT II: ALGEBRA 
 
1.  POLYNOMIALS            (23) Periods 
Definition of a polynomial in one variable, with examples and counter examples. 
Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a 
polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, 
trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the 
Remainder Theorem with examples. Statement and proof of the Factor Theorem. 
Factorization of ax
2
 + 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:  
(     )
  
   
 
 + 
 
   
 
              
(   )
  
  
 
    
  
      (   ) 
 
  
  
 
 (    ) ( 
 
       
 
 
 
 
   
 
   
 
      (     ) ( 
 
   
 
   
 
         ) 
and their use in factorization of polynomials. 
Page 3


MATHEMATICS (IX-X) 
 
(CODE NO. 041) 
Session 2018-19 
 
The Syllabus in the subject of Mathematics has undergone changes from time to time in 
accordance with growth of the subject and emerging needs of the society. The present revised 
syllabus has been designed in accordance with National Curriculum Framework 
 
2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to 
meet the emerging needs of all categories of students. For motivating the teacher to relate the 
topics to real life problems and other subject areas, greater emphasis has been laid on 
applications of various concepts. 
 
The curriculum at Secondary stage primarily aims at enhancing the capacity of students to 
employ Mathematics in solving day-to-day life problems and studying the subject as a separate 
discipline. It is expected that students should acquire the ability to solve problems using 
algebraic methods and apply the knowledge of simple trigonometry to solve problems of height 
and distances. Carrying out experiments with numbers and forms of geometry, framing 
hypothesis and verifying these with further observations form inherent part of Mathematics 
learning at this stage. The proposed curriculum includes the study of number system, algebra, 
geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. 
 
The teaching of Mathematics should be imparted through activities which may involve the use of 
concrete materials, models, patterns, charts, pictures, posters, games, puzzles and 
experiments. 
 
Objectives 
 
The broad objectives of teaching of Mathematics at secondary stage are to help the learners to: 
 
? consolidate the Mathematical knowledge and skills acquired at the upper primary stage; ?
? acquire knowledge and understanding, particularly by way of motivation and visualization, 
of basic concepts, terms, principles and symbols and underlying processes and skills; ?
? develop mastery of basic algebraic skills; ?
? develop drawing skills; ?
? feel the flow of reason while proving a result or solving a problem; ?
? apply the knowledge and skills acquired to solve problems and wherever possible, by more 
than one method; ?
? to develop ability to think, analyze and articulate logically; ?
? to develop awareness of the need for national integration, protection of environment, 
observance of small family norms, removal of social barriers, elimination of gender 
biases; ?
? to develop necessary skills to work with modern technological devices and mathematical 
softwares. ?
? to develop interest in mathematics as a problem-solving tool in various fields for its 
beautiful structures and patterns, etc. ?
? to develop reverence and respect towards great Mathematicians for their contributions to 
the field of Mathematics; ?
? to develop interest in the subject by participating in related competitions; ?
? to acquaint students with different aspects of Mathematics used in daily life; ?
? to develop an interest in students to study Mathematics as a discipline. ?
 
 
 
 
COURSE STRUCTURE CLASS -IX 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 08 
II ALGEBRA  17 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 28 
V MENSURATION  13 
VI STATISTICS & PROBABILITY 10 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS (18 Periods) 
1. 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. 
Operations on real numbers. 
 
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers 
(irrational numbers) such as v , v  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. 
 
3. Definition of nth root of a real number.  
4. Existence of v  
 
for a given positive real number x and its representation on the number line 
with geometric proof. 
 
5. Rationalization (with precise meaning) of real numbers of the type 
 
 
    v 
  and  
 
 v  
v
 
 (and their combinations) where x and y are natural number and a and 
b are integers. 
6. 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.) 
 
 
UNIT II: ALGEBRA 
 
1.  POLYNOMIALS            (23) Periods 
Definition of a polynomial in one variable, with examples and counter examples. 
Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a 
polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, 
trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the 
Remainder Theorem with examples. Statement and proof of the Factor Theorem. 
Factorization of ax
2
 + 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:  
(     )
  
   
 
 + 
 
   
 
              
(   )
  
  
 
    
  
      (   ) 
 
  
  
 
 (    ) ( 
 
       
 
 
 
 
   
 
   
 
      (     ) ( 
 
   
 
   
 
         ) 
and their use in factorization of polynomials. 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (14) Periods 
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. 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 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. 
 
UNIT III: COORDINATE GEOMETRY 
 COORDINATE GEOMETRY           (6) Periods 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations, plotting points in the plane. 
 
UNIT IV: GEOMETRY    
1.   INTRODUCTION TO EUCLID'S GEOMETRY   (6) Periods 
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. 
 
 
2. LINES AND ANGLES (13) Periods 
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 
180
O
 and 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 180
O
. 
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. 
 
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 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. 
 
Page 4


MATHEMATICS (IX-X) 
 
(CODE NO. 041) 
Session 2018-19 
 
The Syllabus in the subject of Mathematics has undergone changes from time to time in 
accordance with growth of the subject and emerging needs of the society. The present revised 
syllabus has been designed in accordance with National Curriculum Framework 
 
2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to 
meet the emerging needs of all categories of students. For motivating the teacher to relate the 
topics to real life problems and other subject areas, greater emphasis has been laid on 
applications of various concepts. 
 
The curriculum at Secondary stage primarily aims at enhancing the capacity of students to 
employ Mathematics in solving day-to-day life problems and studying the subject as a separate 
discipline. It is expected that students should acquire the ability to solve problems using 
algebraic methods and apply the knowledge of simple trigonometry to solve problems of height 
and distances. Carrying out experiments with numbers and forms of geometry, framing 
hypothesis and verifying these with further observations form inherent part of Mathematics 
learning at this stage. The proposed curriculum includes the study of number system, algebra, 
geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. 
 
The teaching of Mathematics should be imparted through activities which may involve the use of 
concrete materials, models, patterns, charts, pictures, posters, games, puzzles and 
experiments. 
 
Objectives 
 
The broad objectives of teaching of Mathematics at secondary stage are to help the learners to: 
 
? consolidate the Mathematical knowledge and skills acquired at the upper primary stage; ?
? acquire knowledge and understanding, particularly by way of motivation and visualization, 
of basic concepts, terms, principles and symbols and underlying processes and skills; ?
? develop mastery of basic algebraic skills; ?
? develop drawing skills; ?
? feel the flow of reason while proving a result or solving a problem; ?
? apply the knowledge and skills acquired to solve problems and wherever possible, by more 
than one method; ?
? to develop ability to think, analyze and articulate logically; ?
? to develop awareness of the need for national integration, protection of environment, 
observance of small family norms, removal of social barriers, elimination of gender 
biases; ?
? to develop necessary skills to work with modern technological devices and mathematical 
softwares. ?
? to develop interest in mathematics as a problem-solving tool in various fields for its 
beautiful structures and patterns, etc. ?
? to develop reverence and respect towards great Mathematicians for their contributions to 
the field of Mathematics; ?
? to develop interest in the subject by participating in related competitions; ?
? to acquaint students with different aspects of Mathematics used in daily life; ?
? to develop an interest in students to study Mathematics as a discipline. ?
 
 
 
 
COURSE STRUCTURE CLASS -IX 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 08 
II ALGEBRA  17 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 28 
V MENSURATION  13 
VI STATISTICS & PROBABILITY 10 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS (18 Periods) 
1. 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. 
Operations on real numbers. 
 
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers 
(irrational numbers) such as v , v  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. 
 
3. Definition of nth root of a real number.  
4. Existence of v  
 
for a given positive real number x and its representation on the number line 
with geometric proof. 
 
5. Rationalization (with precise meaning) of real numbers of the type 
 
 
    v 
  and  
 
 v  
v
 
 (and their combinations) where x and y are natural number and a and 
b are integers. 
6. 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.) 
 
 
UNIT II: ALGEBRA 
 
1.  POLYNOMIALS            (23) Periods 
Definition of a polynomial in one variable, with examples and counter examples. 
Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a 
polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, 
trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the 
Remainder Theorem with examples. Statement and proof of the Factor Theorem. 
Factorization of ax
2
 + 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:  
(     )
  
   
 
 + 
 
   
 
              
(   )
  
  
 
    
  
      (   ) 
 
  
  
 
 (    ) ( 
 
       
 
 
 
 
   
 
   
 
      (     ) ( 
 
   
 
   
 
         ) 
and their use in factorization of polynomials. 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (14) Periods 
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. 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 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. 
 
UNIT III: COORDINATE GEOMETRY 
 COORDINATE GEOMETRY           (6) Periods 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations, plotting points in the plane. 
 
UNIT IV: GEOMETRY    
1.   INTRODUCTION TO EUCLID'S GEOMETRY   (6) Periods 
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. 
 
 
2. LINES AND ANGLES (13) Periods 
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 
180
O
 and 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 180
O
. 
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. 
 
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 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. 
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 in half of it and (motivate) its converse. 
 
 
5. AREA           (7) Periods  
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 (or equal base) base and between the same parallels are 
equal in area. 
 
6. CIRCLES (15) Periods 
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 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 (or their respective centers) 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 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. 
 
7. CONSTRUCTIONS (10) Periods 
1. Construction of bisectors of line segments and angles of measure 60
o
, 90
o
, 45
o
 etc., 
equilateral triangles. 
2. Construction of a triangle 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. 
Page 5


MATHEMATICS (IX-X) 
 
(CODE NO. 041) 
Session 2018-19 
 
The Syllabus in the subject of Mathematics has undergone changes from time to time in 
accordance with growth of the subject and emerging needs of the society. The present revised 
syllabus has been designed in accordance with National Curriculum Framework 
 
2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to 
meet the emerging needs of all categories of students. For motivating the teacher to relate the 
topics to real life problems and other subject areas, greater emphasis has been laid on 
applications of various concepts. 
 
The curriculum at Secondary stage primarily aims at enhancing the capacity of students to 
employ Mathematics in solving day-to-day life problems and studying the subject as a separate 
discipline. It is expected that students should acquire the ability to solve problems using 
algebraic methods and apply the knowledge of simple trigonometry to solve problems of height 
and distances. Carrying out experiments with numbers and forms of geometry, framing 
hypothesis and verifying these with further observations form inherent part of Mathematics 
learning at this stage. The proposed curriculum includes the study of number system, algebra, 
geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. 
 
The teaching of Mathematics should be imparted through activities which may involve the use of 
concrete materials, models, patterns, charts, pictures, posters, games, puzzles and 
experiments. 
 
Objectives 
 
The broad objectives of teaching of Mathematics at secondary stage are to help the learners to: 
 
? consolidate the Mathematical knowledge and skills acquired at the upper primary stage; ?
? acquire knowledge and understanding, particularly by way of motivation and visualization, 
of basic concepts, terms, principles and symbols and underlying processes and skills; ?
? develop mastery of basic algebraic skills; ?
? develop drawing skills; ?
? feel the flow of reason while proving a result or solving a problem; ?
? apply the knowledge and skills acquired to solve problems and wherever possible, by more 
than one method; ?
? to develop ability to think, analyze and articulate logically; ?
? to develop awareness of the need for national integration, protection of environment, 
observance of small family norms, removal of social barriers, elimination of gender 
biases; ?
? to develop necessary skills to work with modern technological devices and mathematical 
softwares. ?
? to develop interest in mathematics as a problem-solving tool in various fields for its 
beautiful structures and patterns, etc. ?
? to develop reverence and respect towards great Mathematicians for their contributions to 
the field of Mathematics; ?
? to develop interest in the subject by participating in related competitions; ?
? to acquaint students with different aspects of Mathematics used in daily life; ?
? to develop an interest in students to study Mathematics as a discipline. ?
 
 
 
 
COURSE STRUCTURE CLASS -IX 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 08 
II ALGEBRA  17 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 28 
V MENSURATION  13 
VI STATISTICS & PROBABILITY 10 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS (18 Periods) 
1. 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. 
Operations on real numbers. 
 
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers 
(irrational numbers) such as v , v  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. 
 
3. Definition of nth root of a real number.  
4. Existence of v  
 
for a given positive real number x and its representation on the number line 
with geometric proof. 
 
5. Rationalization (with precise meaning) of real numbers of the type 
 
 
    v 
  and  
 
 v  
v
 
 (and their combinations) where x and y are natural number and a and 
b are integers. 
6. 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.) 
 
 
UNIT II: ALGEBRA 
 
1.  POLYNOMIALS            (23) Periods 
Definition of a polynomial in one variable, with examples and counter examples. 
Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a 
polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, 
trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the 
Remainder Theorem with examples. Statement and proof of the Factor Theorem. 
Factorization of ax
2
 + 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:  
(     )
  
   
 
 + 
 
   
 
              
(   )
  
  
 
    
  
      (   ) 
 
  
  
 
 (    ) ( 
 
       
 
 
 
 
   
 
   
 
      (     ) ( 
 
   
 
   
 
         ) 
and their use in factorization of polynomials. 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (14) Periods 
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. 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 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. 
 
UNIT III: COORDINATE GEOMETRY 
 COORDINATE GEOMETRY           (6) Periods 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations, plotting points in the plane. 
 
UNIT IV: GEOMETRY    
1.   INTRODUCTION TO EUCLID'S GEOMETRY   (6) Periods 
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. 
 
 
2. LINES AND ANGLES (13) Periods 
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 
180
O
 and 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 180
O
. 
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. 
 
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 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. 
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 in half of it and (motivate) its converse. 
 
 
5. AREA           (7) Periods  
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 (or equal base) base and between the same parallels are 
equal in area. 
 
6. CIRCLES (15) Periods 
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 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 (or their respective centers) 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 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. 
 
7. CONSTRUCTIONS (10) Periods 
1. Construction of bisectors of line segments and angles of measure 60
o
, 90
o
, 45
o
 etc., 
equilateral triangles. 
2. Construction of a triangle 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 Heron's formula (without proof) and its application in finding the 
area of a quadrilateral. 
 
 
 
2. SURFACE AREAS AND VOLUMES (12) Periods 
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right 
circular cylinders/cones. 
 
 
UNIT VI: STATISTICS & 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. Mean, median and mode of ungrouped data. 
 
2.     PROBABILITY     (9) Periods 
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). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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