CBSE

Mathematics (IX-X) (CODE NO. 041) Session 2024-25 The Mathematics syllabus for Session 2024-25 (Code No. 041) has been revised to reflect the evolving needs of society and align with the National Curriculum Framework 2005, as well as guidelines from the Focus Group on Teaching of Mathematics. This updated curriculum is crafted to meet the diverse requirements of all student categories and encourages teachers to connect mathematical concepts with real-life applications and interdisciplinary subjects. At the secondary level, Mathematics aims to enhance students' capacity to address everyday problems using mathematical skills and knowledge. The curriculum includes comprehensive studies of the number system, algebra, geometry, trigonometry, mensuration, statistics, graphs, and coordinate geometry. A core focus is also placed on students learning problem-solving through algebraic methods and utilizing trigonometry to tackle practical problems like height and distance calculations. Experiments involving numbers, geometric forms, hypothesis framing, and observational verification are key components to deepen students' mathematical understanding. Mathematics instruction is to be activity-based, engaging students through concrete materials, models, patterns, charts, games, puzzles, and experiments. This hands-on approach is intended to develop core competencies, stimulate logical reasoning, and cultivate problem-solving skills. Objectives The primary goals for teaching Mathematics at the secondary level are to help learners: Strengthen mathematical knowledge and skills gained in earlier stages; Achieve a strong grasp of basic algebraic skills and enhance their drawing abilities; Acquire foundational knowledge and understanding through motivation, visualization, and logical analysis; Experience reasoning flow when proving results or solving complex problems; Apply mathematical skills creatively, sometimes using multiple methods; Cultivate logical thinking, analytical abilities, and effective articulation; Gain an awareness of social issues such as environmental protection, family planning, national integration, and the elimination of gender biases; Familiarize themselves with modern technology and mathematical software, supporting a connection to the digital world; Appreciate Mathematics as a problem-solving tool and a field with beautiful structures and patterns; Develop respect for renowned Mathematicians and their contributions; Participate actively in Mathematics-related competitions and view the subject as a valuable discipline for study; Recognize the practical applications of Mathematics in daily life. 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 Review of representation of natural numbers, integers, and rational numbers on the number Rational numbers as recurring/ terminating decimals. Operations on real numbers. Examples of non-recurring/non-terminating 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. Definition of nth root of a real 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. 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 ) UNIT II: ALGEBRA 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 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: and their use in factorization of polynomials. 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 + c0.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 (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the (Prove) If two lines intersect, vertically opposite angles are (Motivate) Lines which are parallel to a given line are 3. TRIANGLES (22) Periods (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). (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). (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). (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 (RHS Congruence) (Prove) The angles opposite to equal sides of a triangle are (Motivate) The sides opposite to equal angles of a triangle are 4. QUADRILATERALS (13) Periods (Prove) The diagonal divides a parallelogram into two congruent (Motivate) In a parallelogram opposite sides are equal, and (Motivate) In a parallelogram opposite angles are equal, and (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and (Motivate) In a parallelogram, the diagonals bisect each other and (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 (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse. (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. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely. (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. (Motivate) Angles in the same segment of a circle are equal. (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. (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. UNIT VI: STATISTICS 1. STATISTICS - (15) Periods Bar graphs, histograms (with varying base lengths), and frequency polygons. MATHEMATICS QUESTION PAPER DESIGN CLASS – IX (2024-25) 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 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 ax2 + 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. 4. ARITHMETIC PROGRESSIONS (10) Periods Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems. UNIT III: COORDINATE GEOMETRY 1. Coordinate Geometry - (15) Periods Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). UNIT IV: GEOMETRY 1. TRIANGLES (15) Periods Definitions, examples, counter examples of similar triangles. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are 2. CIRCLES (10) Periods Tangent to a circle at, point of contact (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. (Prove) The lengths of tangents drawn from an external point to a circle are UNIT V: TRIGONOMETRY 1. INTRODUCTION TO TRIGONOMETRY (10) Periods Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios. 2. TRIGONOMETRIC IDENTITIES (15) Periods Proof and applications of the identity sin2A + cos2A 1. Only simple identities to be given. 3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°. UNIT VI: MENSURATION AREAS RELATED TO CIRCLES (12) Periods Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only. SURFACE AREAS AND VOLUMES (12) Periods Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. UNIT VII: STATISTICS AND PROBABILITY STATISTICS (18) Periods Mean, median and mode of grouped data (bimodal situation to be avoided). PROBABILITY (10) Periods Classical definition of probability. Simple problems on finding the probability of an event. MATHEMATICS-Standard QUESTION PAPER DESIGN CLASS – X (2024-25) Time: 3 Hours 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 MATHEMATICS-Basic QUESTION PAPER DESIGN CLASS – X (2024-25) Time: 3Hours 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 60 75 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 12 15 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 8 10 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 Download PDF File : CLick Here Read Also : PRESCRIBED BOOKS: Mathematics - Textbook for class IX - NCERT Publication Mathematics - Textbook for class X - NCERT Publication Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication Laboratory Manual - Mathematics, secondary stage - NCERT Publication Mathematics exemplar problems for class IX, NCERT Mathematics exemplar problems for class X, NCERT