Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Syllabus: Mathematics for Class 9

Syllabus: Mathematics for Class 9 | Mathematics (Maths) Class 9 PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


 
2 
 
COURSE STRUCTURE CLASS –IX 
 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 10 
II ALGEBRA  20 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 27 
V MENSURATION  13 
VI STATISTICS  06 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS       (18) Periods 
 
1.  Review of representation of natural numbers, integers, and rational numbers on the number 
line. 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 ,  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. Rationalization (with precise meaning) of real numbers of the type 
  and  (and their combinations) where x and y are natural number and a and b are 
integers. 
 
5.  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               (26) 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 2


 
2 
 
COURSE STRUCTURE CLASS –IX 
 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 10 
II ALGEBRA  20 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 27 
V MENSURATION  13 
VI STATISTICS  06 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS       (18) Periods 
 
1.  Review of representation of natural numbers, integers, and rational numbers on the number 
line. 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 ,  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. Rationalization (with precise meaning) of real numbers of the type 
  and  (and their combinations) where x and y are natural number and a and b are 
integers. 
 
5.  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               (26) 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. 
 
3 
 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (16) 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.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.  
 
UNIT III: COORDINATE GEOMETRY 
  
     COORDINATE GEOMETRY            (7) Periods 
 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations. 
 
UNIT IV: GEOMETRY 
    
1.   INTRODUCTION TO EUCLID'S GEOMETRY                                              (7) 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. 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    (15) 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) Lines which are parallel to a given line are parallel. 
 
 
3. TRIANGLES (22) 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). 
 
Page 3


 
2 
 
COURSE STRUCTURE CLASS –IX 
 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 10 
II ALGEBRA  20 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 27 
V MENSURATION  13 
VI STATISTICS  06 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS       (18) Periods 
 
1.  Review of representation of natural numbers, integers, and rational numbers on the number 
line. 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 ,  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. Rationalization (with precise meaning) of real numbers of the type 
  and  (and their combinations) where x and y are natural number and a and b are 
integers. 
 
5.  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               (26) 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. 
 
3 
 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (16) 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.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.  
 
UNIT III: COORDINATE GEOMETRY 
  
     COORDINATE GEOMETRY            (7) Periods 
 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations. 
 
UNIT IV: GEOMETRY 
    
1.   INTRODUCTION TO EUCLID'S GEOMETRY                                              (7) 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. 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    (15) 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) Lines which are parallel to a given line are parallel. 
 
 
3. TRIANGLES (22) 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). 
 
 
4 
 
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. 
 
 
4. QUADRILATERALS       (13) 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. CIRCLES    (17) Periods 
 
 
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) Equal chords of a circle (or of congruent circles) are equidistant from the center 
(or their respective centers) and conversely. 
4.(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. 
5.(Motivate) Angles in the same segment of a circle are equal. 
6.(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. 
7.(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° 
and its converse. 
 
 
UNIT V: MENSURATION 
 
 
1. AREAS      (5) Periods 
 
Area of a triangle using Heron's formula (without proof)  
 
 
 
2. SURFACE AREAS AND VOLUMES      (17) Periods 
 
Surface areas and volumes of spheres (including hemispheres) and right circular cones. 
 
 
 
Page 4


 
2 
 
COURSE STRUCTURE CLASS –IX 
 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 10 
II ALGEBRA  20 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 27 
V MENSURATION  13 
VI STATISTICS  06 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS       (18) Periods 
 
1.  Review of representation of natural numbers, integers, and rational numbers on the number 
line. 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 ,  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. Rationalization (with precise meaning) of real numbers of the type 
  and  (and their combinations) where x and y are natural number and a and b are 
integers. 
 
5.  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               (26) 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. 
 
3 
 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (16) 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.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.  
 
UNIT III: COORDINATE GEOMETRY 
  
     COORDINATE GEOMETRY            (7) Periods 
 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations. 
 
UNIT IV: GEOMETRY 
    
1.   INTRODUCTION TO EUCLID'S GEOMETRY                                              (7) 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. 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    (15) 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) Lines which are parallel to a given line are parallel. 
 
 
3. TRIANGLES (22) 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). 
 
 
4 
 
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. 
 
 
4. QUADRILATERALS       (13) 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. CIRCLES    (17) Periods 
 
 
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) Equal chords of a circle (or of congruent circles) are equidistant from the center 
(or their respective centers) and conversely. 
4.(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. 
5.(Motivate) Angles in the same segment of a circle are equal. 
6.(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. 
7.(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° 
and its converse. 
 
 
UNIT V: MENSURATION 
 
 
1. AREAS      (5) Periods 
 
Area of a triangle using Heron's formula (without proof)  
 
 
 
2. SURFACE AREAS AND VOLUMES      (17) Periods 
 
Surface areas and volumes of spheres (including hemispheres) and right circular cones. 
 
 
 
 
5 
 
 
UNIT VI: STATISTICS  
 
          STATISTICS                 (15) Periods 
 
Bar graphs, histograms (with varying base lengths), and frequency polygons.  
 
 
 
MATHEMATICS  
QUESTION PAPER DESIGN 
CLASS – IX (2023-24) 
 
Time: 3 Hrs.                                                                                                                                        Max. Marks: 80 
 
                               
S. 
No. 
Typology of Questions 
Total 
Marks 
% 
Weightage 
(approx.) 
1 
Remembering: Exhibit memory of previously learned material by 
recalling facts, terms, basic concepts, and answers. 
Understanding: Demonstrate understanding of facts and ideas by 
organizing, comparing, translating, interpreting, giving descriptions, 
and stating main ideas 
43 54 
2 
Applying: Solve problems to new situations by applying acquired 
knowledge, facts, techniques and rules in a different way. 
19 24 
3 
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 
18 22 
 Total  
80 100 
 
 
 
 
 
INTERNAL ASSESSMENT         20 MARKS 
Pen Paper Test and Multiple Assessment  (5+5)                                                                    10 Marks 
Portfolio                                                                                                      05 Marks 
Lab Practical (Lab activities to be done from the prescribed books)                             05 Marks 
Page 5


 
2 
 
COURSE STRUCTURE CLASS –IX 
 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 10 
II ALGEBRA  20 
III COORDINATE GEOMETRY 04 
IV GEOMETRY 27 
V MENSURATION  13 
VI STATISTICS  06 
 Total  80 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBERS       (18) Periods 
 
1.  Review of representation of natural numbers, integers, and rational numbers on the number 
line. 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 ,  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. Rationalization (with precise meaning) of real numbers of the type 
  and  (and their combinations) where x and y are natural number and a and b are 
integers. 
 
5.  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               (26) 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. 
 
3 
 
 
2.   LINEAR EQUATIONS IN TWO VARIABLES (16) 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.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.  
 
UNIT III: COORDINATE GEOMETRY 
  
     COORDINATE GEOMETRY            (7) Periods 
 
The Cartesian plane, coordinates of a point, names and terms associated with the 
coordinate plane, notations. 
 
UNIT IV: GEOMETRY 
    
1.   INTRODUCTION TO EUCLID'S GEOMETRY                                              (7) 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. 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    (15) 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) Lines which are parallel to a given line are parallel. 
 
 
3. TRIANGLES (22) 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). 
 
 
4 
 
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. 
 
 
4. QUADRILATERALS       (13) 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. CIRCLES    (17) Periods 
 
 
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) Equal chords of a circle (or of congruent circles) are equidistant from the center 
(or their respective centers) and conversely. 
4.(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. 
5.(Motivate) Angles in the same segment of a circle are equal. 
6.(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. 
7.(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° 
and its converse. 
 
 
UNIT V: MENSURATION 
 
 
1. AREAS      (5) Periods 
 
Area of a triangle using Heron's formula (without proof)  
 
 
 
2. SURFACE AREAS AND VOLUMES      (17) Periods 
 
Surface areas and volumes of spheres (including hemispheres) and right circular cones. 
 
 
 
 
5 
 
 
UNIT VI: STATISTICS  
 
          STATISTICS                 (15) Periods 
 
Bar graphs, histograms (with varying base lengths), and frequency polygons.  
 
 
 
MATHEMATICS  
QUESTION PAPER DESIGN 
CLASS – IX (2023-24) 
 
Time: 3 Hrs.                                                                                                                                        Max. Marks: 80 
 
                               
S. 
No. 
Typology of Questions 
Total 
Marks 
% 
Weightage 
(approx.) 
1 
Remembering: Exhibit memory of previously learned material by 
recalling facts, terms, basic concepts, and answers. 
Understanding: Demonstrate understanding of facts and ideas by 
organizing, comparing, translating, interpreting, giving descriptions, 
and stating main ideas 
43 54 
2 
Applying: Solve problems to new situations by applying acquired 
knowledge, facts, techniques and rules in a different way. 
19 24 
3 
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 
18 22 
 Total  
80 100 
 
 
 
 
 
INTERNAL ASSESSMENT         20 MARKS 
Pen Paper Test and Multiple Assessment  (5+5)                                                                    10 Marks 
Portfolio                                                                                                      05 Marks 
Lab Practical (Lab activities to be done from the prescribed books)                             05 Marks 
 
6 
 
 
 
COURSE STRUCTURE CLASS –X 
 
Units Unit Name Marks 
I NUMBER SYSTEMS 06 
II ALGEBRA  20 
III COORDINATE GEOMETRY 06 
IV GEOMETRY 15 
V TRIGONOMETRY 12 
VI MENSURATION 10 
VII STATISTICS & PROBABILTY 11 
 Total  80 
 
 
UNIT I: NUMBER SYSTEMS 
 
1. REAL NUMBER          (15) Periods 
 
Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and 
after illustrating and motivating through examples, Proofs of irrationality of   
 
 
UNIT II: ALGEBRA 
 
 
1. POLYNOMIALS                                                                                (8) Periods 
 
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic 
polynomials.  
 
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES                                      (15) Periods 
 
Pair of linear equations in two variables and graphical method of their 
solution, consistency/inconsistency. 
 
Algebraic conditions for number of solutions. Solution of a pair of linear equations in two 
variables algebraically - by substitution, by elimination. Simple situational problems.  
 
 
3. QUADRATIC EQUATIONS                                                                                          (15) Periods 
 
Standard form of a quadratic equation ax
2
 + bx + c = 0, (a ? 0). Solutions of quadratic 
equations (only real roots) by factorization, and by using quadratic formula. Relationship 
between discriminant and nature of roots. 
 
Situational problems based on quadratic equations related to day to day activities to be 
incorporated. 
Read More
44 videos|412 docs|54 tests

Top Courses for Class 9

44 videos|412 docs|54 tests
Download as PDF
Explore Courses for Class 9 exam

Top Courses for Class 9

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Syllabus: Mathematics for Class 9 | Mathematics (Maths) Class 9

,

MCQs

,

Syllabus: Mathematics for Class 9 | Mathematics (Maths) Class 9

,

ppt

,

Summary

,

Semester Notes

,

practice quizzes

,

Objective type Questions

,

Viva Questions

,

Exam

,

past year papers

,

Syllabus: Mathematics for Class 9 | Mathematics (Maths) Class 9

,

video lectures

,

pdf

,

Previous Year Questions with Solutions

,

Free

,

mock tests for examination

,

Extra Questions

,

Important questions

,

shortcuts and tricks

,

Sample Paper

,

study material

;