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.
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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