REDUCED SYLLABUS

Strictly as per the Reduced CBSE Syllabus released

(CBSE Cir.No.Acad-47/2020)on 7th July 2020

MATHEMATICSSTANDARD

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SYLLABUS MATHEMATICS Class - X (Code No. 041)

Reduced Syllabus issued by CBSE for Academic Year 2020-213 Hours COURSE STRUCTURE CLASS –X Marks 80

Unit No. 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 & Probability 11

Total 80

UNIT I: NUMBER SYSTEMS1. REAL NUMBERS (8) Periods Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating

and motivating through examples, Proofs of irrationality of Decimal representation of rational numbers interms of terminating/non-terminating recurring decimals.

UNIT II: ALGEBRA

1. POLYNOMIALS (4) Periods Zerosofapolynomial.Relationshipbetweenzerosandcoefficientsofquadraticpolynomials.2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (11) Periods Pairoflinearequationsintwovariablesandgraphicalmethodoftheirsolution,consistency/inconsistency. Algebraicconditionsfornumberofsolutions.Solutionofapairof linearequations intwovariables

algebraically - by substitution, by elimination. Simple situational problems. Simpleproblemsonequationsreducibletolinearequations.3. QUADRATIC EQUATIONS (10) Periods Standardformofaquadraticequationax2 + bx + c = 0, (a ≠ 0).Solutionsofquadraticequations(only

real roots)by factorization,andbyusingquadratic formula.Relationshipbetweendiscriminantandnature of roots.

4. ARITHMETIC PROGRESSIONS (4) Periods Motivation for studying Arithmetic Progression Derivation of the nthtermandsumofthefirstnterms

of A.P.

UNIT III: COORDINATE GEOMETRY1. LINES (In two dimensions) (10) Periods Review:Conceptsofcoordinategeometry,graphsoflinearequations.Distanceformula.Sectionformula

(internaldivision).

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UNIT IV: GEOMETRY1. TRIANGLES (10) Periods Definitions, examples, counter examples of similar triangles. 1. (Prove)Ifalineisdrawnparalleltoonesideofatriangletointersecttheothertwosidesindistinct

points, the other two sides are divided in the same ratio. 2. (Motivate)Ifalinedividestwosidesofatriangleinthesameratio,thelineisparalleltothethird

side. 3. (Motivate) If in twotriangles, thecorrespondinganglesareequal, theircorrespondingsidesare

proportional and the triangles are similar. 4. (Motivate)Ifthecorrespondingsidesoftwotrianglesareproportional,theircorrespondingangles

areequalandthetwotrianglesaresimilar. 5. (Motivate)Ifoneangleofatriangleisequaltooneangleofanothertriangleandthesidesincluding

these angles are proportional, the two triangles are similar. 6. (Motivate)Ifaperpendicularisdrawnfromthevertexoftherightangleofarighttriangletothe

hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.

7. (Prove)Inarighttriangle,thesquareonthehypotenuseisequaltothesumofthesquaresontheother two sides.

2. CIRCLES (8) Periods Tangent to a circle at, point of contact. 1. (Prove)The tangentatanypointofacircle isperpendicular to the radius through thepointof

contact. 2. (Prove)Thelengthsoftangentsdrawnfromanexternalpointtoacircleareequal.

3. CONSTRUCTIONS (4) Periods 1. Divisionofalinesegmentinagivenratio(internally). 2. Tangents to a circle from a point outside it.

UNIT V: TRIGONOMETRY1. INTRODUCTION TO TRIGONOMETRY (8) Periods Trigonometricratiosofanacuteangleofaright-angledtriangle.Proofoftheirexistence(welldefined).

Values of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.2. TRIGONOMETRIC IDENTITIES (10) 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 (8) 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°, 60°.

UNIT VI : MENSURATION1. AREAS RELATED TO CIRCLES (10) Periods Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and

perimeter/circumferenceoftheabovesaidplanefigures.(Incalculatingareaofsegmentofacircle,problemsshouldberestrictedtocentralangleof60°and90°only.Planefigures involvingtriangles,simplequadrilateralsandcircleshouldbetaken.)

2. SURFACE AREAS AND VOLUMES (8) Periods 1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres,

hemispheres and right circular cylinders/cones.

...contd. Syllabus

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2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problemswithcombinationofnotmorethantwodifferentsolidsbetaken).

UNIT VII : STATISTICS AND PROBABILITY1. STATISTICS (10) Periods Mean,medianandmodeofgroupeddata(bimodalsituationandstepdeviationmethodforfindingthe

mean to be avoided).2. PROBABILITY (10) Periods Classicaldefinitionofprobability.Simpleproblemsonfindingtheprobabilityofanevent.

Deducted Portion :Chapter Topics Removed

Unit I- Number SystemsReal Numbers Euclid’s division lemmaUnit II- AlgebraPolynomials Statement and simple problems on division algorithm for polyno-

mials with real coefficients.Pair Of Linear Equations In Two Variables

Cross multiplication method

Quadratic Equations Situational problems based on equations reducible to quadratic equations

Arithmetic Progressions Application in solving daily life problems based on sum to n termsUnit III- Coordinate GeometryCoordinate Geometry Area of a triangle.Triangles Proof of the following theorems are deleted

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

Circles No deletionConstructions Construction of a triangle similar to a given triangle.Unit V- TrigonometryIntroduction To Trigonometry Motivate the ratios whichever are defined at 0° and 90°Trigonometric Identities Trigonometric ratios of complementary angles.Heights And Distances No deletionUnit VI- MensurationAreas Related To Circles Problems on central angle of 120°Surface Areas And Volumes Frustum of a cone.Unit VI- Statistics & ProbabilityStatistics Step deviation Method for finding the mean

Cumulative Frequency graphProbability No deletion

...contd. Syllabus

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MATHEMATICS (Standard)QUESTION PAPER DESIGN

CLASS – X (2020-21)Time : 3 hrs Marks : 80

S. No. Typology of QuestionsTotal

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, inter-preting, giving descriptions, and stating main ideas

43 54%

2. Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in adifferentway.

19 24%

3. Analyzing : Examine and break information into parts by identifying motives or causes. Make inferences and findevidencetosupportgeneralizations

Evaluating: Present and defend opinions by making judgmentsaboutinformation,validityofideas,orqual-ity of work based on a set of criteria.

Creating: Compile information together inadifferentway by combining elements in a new pattern or propos-ing alternative solutions

18 22%

Total 80 100

INTERNAL ASSESSMENT 20 Marks

PenPaperTestandMultipleAssessment(5+5) 10Marks Portfolio 05 Marks LabPractical(Labactivitiestobedonefromtheprescribedbooks) 05Marks

...contd. Syllabus