New Syllabus Maths

8/4/2019 New Syllabus Maths

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New

Revised syllabus

From Class VI to X

Mathematics


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Table-3

Subject: MathsSyllabus Distribution of Major themes / topics & themes wise concepts across classes from VI to X of A.P.

Distribution of class wiseS.No.

Majorthemes /topics

units

Class VI Class VII Class VIII Class IX C

1 NumberSystem:

Number System:i) Knowing out numbers:

Prime, Composite, Co-primes

Sieve of EratosthenesFactors, divisors and

Multiples,Prime Factorization

L.C.M., H.C.F. andproperties

Problem solving usingL.C.M. &

H.C.F.ii) Playing with numbers:-Simplification of bracketsBasic patterns of Divisibility

Tests divisibility of ( 4,7,8,9 &11)

iii) Whole numbers:Properties of 0 & 1Number line, seeing

patterns

Real numbers

Concept of set, set language.

Notation: Roster form (mistingnumbers, elements)

Candidates will be extended tobe familiar with the terms andsymbols connected with sets.

Set of numbers: N,W,I, or Z, Qand R.

Subsets: Concept of subset.Rational numbers:

Properties of rational numbers.(including identities). Usinggeneral form of expression todescribe properties.

Consolidation of operations on

rational numbers. Rational numbers of all

properties (closure,associating, commutative,identity, inverse) for alloperations in brief

Table showing all properties

Real numbers

Introduction of irrational Nos.

Representation of rational andirrational Nos. on number line,

Real numbers: union of rationaland irrational numbers

Group, abelian group, field, orderedfield

Introduction of surds:Types of surdsConjugate surdsRationalization of a surd

i. Powers:Integers as exponents

Laws of exponents with integralpowerii. Square and square rootssquare roots:

a. factor methodb. Division method (not more

than 2 decimals places)

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iv) Integers :The need of integers,

representing on number line.Ordering of numbers,

comparison,additions, subtraction,

multiplicationand division of integers

(Rational numbers) Simplefractions,

Comparison of RationalNumbers.Four fundamental operations,decimal fractions, Terminatingand non terminating Decimals.Conversion of proper fractions

into decimal fractions and viceversa.Properties of Rationalnumbers through patternsRepresenting rational numberon the number lineWord problems involvingdecimal fractions ( two

operations ( together onmoney mass and temperature)

Representation of rational

numbers on the number line. Between any two rational

numbers there lies anotherrational number (Makingchildren see that if we take tworational numbers then unlikefor whole numbers, is this caseyou can keep finding more and

more numbers that lie betweenthem).

Verbal problems of daily lifesituations.

Def. of rational numbers,properties, table of propertiesof n,w,z,q.

Order properties of rationals

Examples for someterminating, non-terminating

Ex: 17/5 = 3.4, 2/3 = 0.6.1/11=0.09

Problems and examplesEg: 0.12=3/25, 0.3=1/3 etc.

Notation, trail and error offinding z, properties of squareroots with examples

Factorization method of findingsquare roots

Definition of cube

Method for finding the cuberoot of a number (primefactorization)

Perfect cubes

Cubes and cube roots: Only factor

method ( not more than 3 digits)estimating square roots and cuberoots

Introducing Pythagorean triplets

iii. Playing with numbers: Finding themissing numerals

represented by alphabet in sumsinvolving any of the four operationsnumber puzzles and games numberpatterns


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2 ARITHEM

ETIC

ARITHEMETIC

RATIO-PROPORTION:Ratio as a form of comparison,terms of ratio, antecedent andconsequent. Expression ofratio in least terms.Proportion as equality of tworatios concept of meanproportion, third and fourth

proportions.Unitary methodDirect & Inverse proportionsSimple word problems onDirect and Inverse proportions( on time and work)

PERCENTAGES:Concept of % and simple

applications conversion offractions and decimals into %and vice-versa.Finding what percent of onenumber is of another number.

Commercial Mathematics

Revision of ratio Terms of ratio

Definition of compound rationwith examples

Definition of proportion

Terms of proportion Rule of proportion

Finding unknown term of aproportion

Definition of direct proportionsymbolic notation, constant

Problems related to real lifesituations

Same as for indirect and mixedproportions

Percentages(Profit / loss, discount)

Percentage on introduction Understanding percentage as

a fraction with denominator100

Converting fractions anddecimals into percentage andvice-versa

Application to profit and loss(single transaction only)

How percentage of profit / lossin business

How percentage is describedin discount

Compound interest

Difference between SI & CI(Compounded yearly up to 3years or half yearly up to 3 steps)

Extension of profit and loss,discount partnership, continuing ofinverse proportion, time and workand application.

Clock mathematics Relative speed, angular speed

Arithmetic:

Time & DistanceProblems on RelativeSpeed(related to trains&steamers)Loans Repaymentsin installments.

Sales Tax, VAT

ARITHME

Income Tstocks, shbrokerage


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Simple interest

Application to simple interest(time period in completeyears).

Definition of simple interest Describing P,T,R

Calculation of S.I using I =PTR / 100

Finding amount on S.I as

A = P (1 + TR /100)3 Algebra Algebra Introduction:

Constants, Variables, terms,Coefficients, Powers,Algebraic expressions.Degree of expression.Like terms & unlike terms.Monomial and binomial.Addition of algebraicexpression vertically &horizontally.Subtraction of algebraicexpression.Multiplication of monomial bymonomial.Multiplication of binomial bymonomial.

Use of Brackets &Parenthesis.Value of expression.Exponents & powers.(Simple problems)(Basis, Power, Index)

Algebraic expressions

Definition of Algebraicexpression terms, coefficients

Value of expression:

Values for monomials,binomials and multinomialswith examples

Degree of monomial / polynomial: Definitions with examples

Zero of polynomial:

Distinguish between zero of apolynomial / zero polynomialwith examples

Simplest form of an expression: Simplification of terms by

adding like terms andarrangement by degree ofterms

SetsIntroduction of sets concept of a setdifferent representations of a set finiteand infinite sets, universal setcomplementary set, single ton emptysetCardinal numberEquivalent sets, Equal setsPower sets

Exponents and powersa. Meaning of x in ax (x Z)b. Laws of positive integral

exponents am x an = am+n(m,nZ)

am / an = am-n (m>n) = 1/ an-m (m


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Defining an exponent, base

power with examples

Laws of exponents:

Expanded form and short formof a power

Laws of exponents withexamples

Idea of how a = 1 ?

Special productsReview of simple algebraicproducts: Rules of multiplications

Horizontal / vertical methods ofmultiplication

Product of monomial withmonomial, binomial, multinomial:Product of a binomial with anotherbinomial: Expanding products using

special products

Special products of (a+b)2,

(a-b)2 , (a+b) (a-b):

Geometrical proofs for specialproducts

Application of special productsin daily life problems ( ifpossible) with good no. of

and expression of the

form(x+p)(x+q)(x+r)(x+s)+tand reciprocalpolynomials solvingax4+bx3+dx2+bx+a,which are reducibleinto quadraticpolynomials.

d) Solution of quadraticequation by formulamethod

x= -b (b2-4ac)1/2/ 2a

Sum of the rootsProduct of the rootsDiscriminantFraming quadratic

equations when rootsare given (, )

SetsI. Revision ofi) A Set- Set language.

ii) Representation of

setRoster form andset builder formiii) Finite and infinitesets, empty set.Iv) Subjects and equalsets. Listing outsubsets in every dayset.

AUA' =A,

7. De Mor(AUB) = AA U B-------------

RelationsfunctionsRelations

Ordered pordered pproduct by graphicPropertiesA X (BUC

U(AXC)A x (BC

(AXC)Through eRelations everyday of a relatioof Cartesirelation exbuilder foDomain ra

relation, urelation - relations symmetricsymmetricrelation a


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exercises.

Factorization

Definition of algebraic factor

Definition of HCF of algebraicterm

Rule of common factor withexamples

Taking common term by

changing signs Taking common by shifting the

terms

Definition of perfect squareterms, square roots withexamples

Factorization with specialproducts (perfect squares)

Eg: x2 + 2x+1 = x2+2(x)-(1)+(1)2= (x+1)2= (x+1) (x+1)

Equations and inequations

Review of simple equations Properties of equalities with

examples

Method of transposition forsolving equation

Solution of equations withinvolving different models

Verbal problems (daily lifesituation)

Ineequalities with examples

v) Cardinal number of

a set. Equivalence,Super set, power set ofa set.vi) Set operations-union and intersection ,disjoint setsvii) Universal set-complement of set-

II). (i) difference of twosets.(ii) Venn diagram.

(iii) Operation on setsand their properties,AUB= BUA,AB= BA

(AUB)UC=AU(BUC)(AB) C = A (BC)

1 =U, U1 = , (A1)1=A

(iv) Transpose conceptand its properties.

n( AUB)+n (AB) =n(A) +n(B)where n(A) is thenumber of elements ina finite set A andformulae for n(AUBUC),n (ABC) and

Function

IntroductioTypes of fCompoun

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POLYNO

PolynomIntegers 1. Roots oand their by Inspecunder whroots.

1.1. Rema

factor the

1.2. Factopolynomiafourth degtheorem adivision m

1.3. Factoexpressio

1.4. Quaddiscriminaroots relroots andGraphical


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Inequal relations with number

lines

problems there of.

Problems onapplication of sets.

quadratics

1.5. Binom-------------

PROGRE

ArithmetProgress

Introductiodifferent ty

MotivationA.P.

Derivation

results of term and

terms in An, n2, MotivationG.P.

Derivationresults of and sum o

G.P.

Introductio4 Geometry Basic Geometrical Ideas( 2 D)

Introduction to geometry, itslinkage with daily life.Point, Line , Line segment,

Triangles

Definition of triangle, interior

Sides and angles Types of triangles acc. To

Coordinate geometryCo-ordinates of pointPlotting of points in co-ordinate axes(Cartesian place)

Coordinate geometryi) Distance formulaFrom originBetween two points

CoordinaReview thCo-ordinadone earl


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On the line

Outside the line8. A line parallel to a given

line.

formed is equal to the sum of the two

interiors opposite angles of all

Circles:Through examples, arrive atdefinitions of circle related concepts,radius, circumference, diameter,chord, are subtended angle.

1. (Motivate) (Prove) Equal chords ofa circle subtend equal angles atthe center and its converse.

2. (Motivate) The perpendicular fromthe center of a circle to a cordbisects the chord and conversely,the line drawn through the centerof a circle to bisect a chord isperpendicular to the chord.

3. (Motivate) There is one and onlyone circle passing through threegiven non-collinear points.

4. (Motivate) Equal chords of a circle(or of congruent circles) areequidistant from the center(s) andconversely.

5. (Prove) The angle subtended byan arc at the center is double theangle subtended by it at any pointon the remaining part of the circle.

6. (Motivate) Angles in the samesegment of a circle are equal.

7. (Motivate) If a line segment joiningtwo points subtends equal angleat two other points lying on the

3. (Motivate) Angles inthe same segment of acircle are equal.

4. (Motivate)An anglein a semicircle is aright angle.

5.(Motivate) If a linesegment joining twopoints subtended equalangles at two otherpoints lying on thesame side of the linecontaining thesegment, the fourpoints lie on a circle.

6. (Prove) The sum ofeither pair of theopposite angles ofcyclic quadrilateral is1800 and its converse.

V. CONSTRUCTIONS

1. Construction ofbisectors of angles,600, 900, 450 angleetc., and alsoequilateral triangles.

perpendic

radius throf contact

2. (Prove)tangents dexternal pequal.

3. (Motivachords of intersect iof the circproducedformed bysegments

4. (Prove)

drawn throf a contato a circleangles whmakes wittangent arespectiveformed incorresponsegmentsconverse.5. (Motivatouch eac(internallythe point oon the line


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same side of the line containing

the segment, the four points lie ona circle.

8. (Motivate) The sum of the eitherpair of the opposite angles of acyclic quadrilateral is 1800 and itsconverse.

ConstructionsCircum circle, in circle excircle,medium, orthocenter, centroide of atriangles

2. Construction of a

triangle given its base,sum/difference of theother two sides andone base angle.

3. Construction of atriangle of givenperimeter and baseangles.

4. Construction of atriangle equal in areato a given convexquadrilateral.

5. Construction of atriangle equal in area

to that of a givenpentagon.

centers.

III. CONS

1. Divisionsegment both interexternally2. Tangenfrom a po3. Construtriangle sitriangle.

4. Construof direct ctangents tcircles. (D

Tangent, common T

5. Construquadrilatealternate theorem

5 Mensuration

CONCEPT OF PERIMETERAND AREA:

1Introduction and generalunderstanding of perimeterusing many shapes.Shapes of different kinds with

Areas

Area of four walls of a room

Areas of rectangular paths

Surface areas of cube, cuboid Area of triangle

Area of quadrilateral,

Areas1. Area of triangle using Heronsformula (without proof) and its2. Relation between sides and anglesof a triangle (300, 600, 900)(450, 450, 900)

MensurationSurface area andvolume of prism,pyramid, right circularcylinder, Cone, sphereand Hemisphere.

MensuraSurface AVolumes.i) Problemsurface avolumes oof any two


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Frequency Distribution,

Greater thanCumulative FrequencyDistribution,

Frequency Graphs Histogram, FrequencyPolygon,Frequency Curve,CumulativeFrequency Curves,Less than CumulativefrequencyDistribution curve,Greater thanCumulative frequencydistribution curve.

ProbabilityHistoryRandom experimentsAn event, Experiment,TrialSample spaceMutually exclusiveeventsDependent eventsIndependent events

Mode for

Mode for Empirical Arithmeticand Mode

Probabilii. RevisionExperimeAn EventSample sMutually EDependenIndepend

ii. TheoreProbabilit

Addition rMultiplica

Classical Probabilit

Empirical Probabilit

Probabilityconditiona

Some coutechnique

PermutaCombin


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n! (Fa

ProbabilitBinomial, (only Pas

7 TRIGONOMETRY

----- ----- ------ TRIGONOMETRY:Introduction (History)Units of Measurementof angles.Sexagesimal system.ii) Centesimal systemiii) Radian (Circular)measure.

FundamentalTrigonometrical Ratios.(Sin, Cos, Tan

etc. 0/2

Behaviour ofTrigonometric Ratios

(Table for 00,300,450,600,900)

TRIGONO

i. RevisionFundameTrigonom(Sin, Co

0/2BehaviouTrigonom(Table for300,450,60ii. Trigono

complemeand suppangles (AA,B 2)Sin (90-Cos (90- ii. Proof aof TrigonoIdentities.Sin2 + coSin2 = 1Cosec2iii. Heights(8)Simple anproblems


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Distances

(Problemsinvolve mright triangElevation/should be

8 Matrices ----- ------ ----- ------ MatricesDefinitionmatrix, typtypes of oinverse mof SystemEquationsmethod arule.

LIST OF FORMULAE: (Probability X class)

Relative probability (PA) = m/n Where A is an event getting head, m is total number of times the event occurs and n is the number of times the experiment is perform

P(A or B) = P(A)+P(R) probability of either of the two exclusive events is the sum of the probability.

P (A or B) = P (A)+ P( R ) - P(AB) when the events are not mutually exclusive and probability of either A or B is the same of the two probability me m is the probabB hyper ting together.

P (AB) = P(A) x P(B) where P (AB) is the J unit probability of the event A and P (B) is the marginal probability of the event B. Thus the J runt probability of the two eoccurring together or incussassic is the product of the marginal probability.


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P (B/A) = P (B) in are of independent events, the conditional probability event B, give the occurrence of event A is simply the probability event (B).

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New Syllabus Maths