MATHEMATICS MATHEMATICS-Standard QUESTION PAPER DESIGN QUESTION PAPER DESIGN., Lecture notes of Educational Mathematics

Download MATHEMATICS MATHEMATICS-Standard QUESTION PAPER DESIGN QUESTION PAPER DESIGN. and more Lecture notes Educational Mathematics in PDF only on Docsity! 1 MATHEMATICS (IX-X) (CODE NO. 041) Session 2022-23 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 software's.  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. 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 & PROBABILITY 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 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. 5 UNIT VI: STATISTICS & PROBABILITY STATISTICS (15) Periods Bar graphs, histograms (with varying base lengths), and frequency polygons. MATHEMATICS QUESTION PAPER DESIGN CLASS – IX (2022-23) 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 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. 7 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 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. 1. (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 ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5. (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 similar. 2. CIRCLES (10) Periods Tangent to a circle at, point of contact 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.