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AP DSC SA Maths Syllabus

PART - I

I. General Knowledge And Current Affairs (Marks: 10)

PART - II

II. Perspectives In Education (Marks: 05)

1. History of Education :

· The Education in Ancient India - Pre-Vedic and Post-Vedic period, Medieval Education.

· Education in Pre Independent era - Woods Despatch (1854), Hunter Commission (1882), Hartog Committee (1929), Sargent Committee (1944).

· Education in Post Independent era - Mudaliar Commission (1952-53), Kothari Commission (1964-66), Ishwarbhai Patel committee (1977), NPE-1986, POA- 1992

2. Teacher Empowerment:

· Need, interventions for empowerment, Professional code of conduct for teachers, Teacher motivation, Professional development of Teachers and Teacher organizations, National / State Level Organizations for Teacher Education, Maintenance of Records and Registers in Schools.

3. Educational Concerns in Contemporary India:

· Democracy and Education, Equality, Equity, Quality in Education, Equality of Educational opportunities.

· Economics of Education, Education as Human Capital, Education and Human Resource Development, Literacy - Saakshar Bharat Mission.

· Population Education, Gender - Equality, Equity and Empowerment of Women, Urbanization and migration, Life skills.

· Adolescence Education

· Value Education – Morel Value and Professional Eathics in Education.

· Health and Physical Education

· Inclusive Education - Classroom Management in Inclusive Education

· Role of Education in view of Liberalization, Privatization and Globalization

· Programmes and Projects – APPEP, DPEP, Sarva Siksha Abhiyan, National Programme for Education of Girls at Elementary Level (NPEGEL), Rashtriya Madhyamika Siksha Abhiyan(RMSA), Rashtriya Aveshekar Abhiyan (RAA), KGBVs, Model Schools.

· Incentives and special provisions – Mid Day Meals, Free Books, Scholarship, Awards, Welfare Hostels, Transportation.

· Current Trends in Education – Badi pelusthondi, Badi ki Vasta, Mavuru – Mana Badi, Vidyanjali, Swacha Patasala, Inspire, Kalavutsav.

4. Acts / Rights:

· Right of Children to Free and Compulsory Education Act - 2009

· Right to Information Act - 2005

· Child Rights

· Human Rights.

5. National Curriculum - Framework, 2005: Perspective, Guiding Principles, Learning and Knowledge, Teaching Learning Process, Assessment, Systemic Reforms.

PART - III

III. Classroom implications of Educational Psychology – 05Marks

1. Individual differences: Inter and intra individual differences, meaning, nature and

theories of intelligence with special emphasis to multiple intelligence, IQ, assessment

of intelligence, EQ, Creativity. Attitude, Aptitude, Interest, Habit and its Influence on

Intelligence – Class room implementation.

2. Learning: Theories and approaches of learning, learning curves, Factors, Phases,

Dimensions of learning, Types of learning, Transfer of learning. Memory, Forgetting,

Learning and assessment– Class room implementation.

3. Personality: Nature, characteristics and theories of personality, factors of

Personality, Assessment of Personality, Mental health, Adjustment, Stress – nature,

Symptoms and management. Emotional intelligence, Management of emotions –

Class room implementation.

PART - IV

IV. Maths – Content (Class-VI to Intermediate Present syllabus) (40 Marks)

1. Arithmetic

Ratio and Proportion - Applications of Ratio- Comparing Quantities using proportion -

Direct and Inverse proportion

2. Number System

Knowing Our Numbers –rounding of numbers - Whole Numbers- predecessor – successor

– number line -Playing With Numbers – divisibility rules -LCM & HCF -Integers -

Fractions - Decimals -Rational Numbers -Squares, cubes Square roots, Cube roots

Real numbers -Representing irrational numbers on Number line – representing real

numbers on the number line through successive magnification – rationalisation –Real

numbers- operations on real numbers- law of exponents for real numbers- surds(

exponential form & radical form )

Euclid’s division lemma & its application in finding HCF – fundamental theorem of

Arithmetic & its application (HCF & LCM, decimal representation of rational numbers

(terminating or non-terminating recurring and vice versa))

Non-terminating & non recurring decimals as irrationals – irrationality of√2, √3 etc.-

properties of irrational numbers

Logarithm - exponential & logarithmic forms-Properties & Laws of logarithms-standard

base of logarithm- use of logarithms in daily life situation-

Sets –& its representation (Roster form& set builder form)-examples- classification of

sets(empty, finite, infinite, subset& super set, universal set, disjoint sets, power set of a

set, equality of sets) Venn diagram – operations on sets ( union, intersection, difference,

cardinal number of a set

3. Geometry

Measures of Lines and Angles - Symmetry - -Understanding 3D, 2D Shapes -

Representing 3D in 2D-Lines and Angles -Triangle and Its Properties -Congruency of

Triangles- -Quadrilaterals - Practical Geometry -Construction of Triangles Construction

of Quadrilaterals - Exploring Geometrical Figures-

The Elements of Geometry -Area –Circles

Similar Triangles & Tangents and secants to a circle

Proofs in Mathematics

4. Mensuration

Perimeter and Area - Area of Plane Figures -Surface areas and Volumes

5. Algebra

Introduction to Algebra- Simple Equations- Exponents - Algebraic Expressions

- Exponents & Powers - Linear Equations in one variable – Factorisation Polynomials &

Factorisation - Linear Equations in Two Variables - Pair of Linear Equations in Two

Variables - Quadratic Equations- Progressions- Arithmetic Progression- properties of

A.P.- Arithmetic mean –Geometric Progression –nth term–properties of AP,G.P.

Functions :

· Ordered pair- Cartesian product of sets – Relation - Function & its types - image &

pre-image – Definitions.

· Inverse functions and Theorems.

· Domain, Range, Inverse of real valued functions.

Mathematical Induction

· Principle of Mathematical Induction & Theorems.

· Applications of Mathematical Induction.

· Problems on divisibility.

Matrices:

· Types of matrices

· Scalar multiple of a matrix and multiplication of matrices

· Transpose of a matrix

· Determinants

· Adjoint and Inverse of a matrix

· Consistency and inconsistency of Equations- Rank of a matrix

· Solution of simultaneous linear equations

Complex Numbers:

· Complex number as an ordered pair of real numbers- fundamental operations

· Representation of complex numbers in the form a + ib.

· Modulus and amplitude of complex numbers –Illustrations.

· Geometrical and Polar Representation of complex numbers in Argand plane- Argand

diagram.

De Moivre’s Theorem:

· De Moivre’s theorem- Integral and Rational indices.

· nth roots of unity- Geometrical Interpretations – Illustrations.

Quadratic Expressions:

· Quadratic expressions, equations in one variable

· Sign of quadratic expressions – Change in signs – Maximum and minimum values

· Quadratic in-equations

Theory of Equations:

· The relation between the roots and coefficients in an equation

· Solving the equations when two or more roots of it are connected by certain relation

· Equation with real coefficients, occurrence of complex roots in conjugate pairs and its

consequences

· Transformation of equations – Reciprocal Equations.

Permutations and Combinations:

· Fundamental Principle of counting – linear and circular permutations

· Permutations of ‘n’ dissimilar things taken ‘r’ at a time

· Permutations when repetitions allowed

· Circular permutations

· Permutations with constraint repetitions.

· Combinations-definitions and certain theorems

Binomial Theorem:

· Binomial theorem for positive integral index

· Binomial theorem for rational Index (without proof).

· Approximations using Binomial theorem

Partial fractions:

· Partial fractions of f(x)/g(x) when g(x) contains non –repeated linear factors.

· Partial fractions of f(x)/g(x) when g(x) contains repeated and/or non-repeated linear

factors.

· Partial fractions of f(x)/g(x) when g(x) contains irreducible factors.

6. Statistics

DATA HANDLING - Frequency Distribution Tables and Graphs- Grouped dataungrouped

data – Measrues of Central Tendency -Mean, median & mode of grouped and

ungrouped data – ogive curves –MEASURES OF DISPERSION -Range - Mean deviation

-Variance and standard deviation of ungrouped/grouped data. -Coefficient of variation and

analysis of frequency distribution with equal means but different variances.

7. Probability

Probability - Random experiment and outcomes - Equally likely outcomes - Trail and

Events - Linking the chance to Probability - uses of probability in real life

Probability-a theoretical approach – probability & modelling –equally likely events -

mutually exclusive events –finding probability – elementary event –exhaustive events -

complementary events & probability – impossible & certain events – deck of cars &

Probability –use & applications of probability - Probability

· Random experiments and events

· Classical definition of probability, Axiomatic approach and addition theorem of

probability.

· Independent and dependent events conditional probability- multiplication theorem and

Bayee’s theorem.

Random Variables and Probability Distributions:

· Random Variables

· Theoretical discrete distributions – Binomial and Poisson Distributions

8. Coordinate Geometry

Cartesian system-Plotting a point in a plane if its co-ordinates are given.

Distance between two points - Section formula (internal division of a line segment in the

ratio m : n) – centroid of a triangle – trisectional points of a line segment -Area of triangle

on coordinate plane- collinearity –straight lines -Slope of a line joining two points

Locus :

· Definition of locus – Illustrations.

· To find equations of locus - Problems connected to it.

Transformation of Axes :

· Transformation of axes - Rules, Derivations and Illustrations.

· Rotation of axes - Derivations – Illustrations.

The Straight Line :

· Revision of fundamental results.

· Straight line - Normal form – Illustrations.

· Straight line - Symmetric form.

· Straight line - Reduction into various forms.

· Intersection of two Straight Lines.

· Family of straight lines - Concurrent lines.

· Condition for Concurrent lines.

· Angle between two lines.

· Length of perpendicular from a point to a Line.

· Distance between two parallel lines.

· Concurrent lines - properties related to a triangle.

Pair of Straight lines:

· Equations of pair of lines passing through origin, angle between a pair of lines.

· Condition for perpendicular and coincident lines, bisectors of angles.

· Pair of bisectors of angles.

· Pair of lines - second degree general equation.

· Conditions for parallel lines - distance between them, Point of intersection of pair of

lines.

· Homogenizing a second degree equation with a first degree equation in X and Y.

Circle :

· Equation of circle -standard form-centre and radius of a circle with a given line

segment as diameter & equation of circle through three non collinear points -

parametric equations of a circle.

· Position of a point in the plane of a circle – power of a point-definition of tangentlength

of tangent

· Position of a straight line in the plane of circle-conditions for a line to be tangent –

chord joining two points on a circle – equation of the tangent at a point on the circlepoint

of contact-equation of normal.

· Chord of contact - pole and polar-conjugate points and conjugate lines - equation of

chord with given middle point.

· Relative position of two circles- circles touching each other externally, internally

common tangents-centres of similitude- equation of pair of tangents from an external

point.

System of circles:

· Angle between two intersecting circles.

· Radical axis of two circles- properties- Common chord and common tangent of two

circles – radical centre.

· Intersection of a line and a Circle.

Parabola:

· Conic sections –Parabola- equation of parabola in standard form-different forms of

parabola- parametric equations.

· Equations of tangent and normal at a point on the parabola (Cartesian and parametric)

- conditions for straight line to be a tangent.

Ellipse:

· Equation of ellipse in standard form- Parametric equations.

· Equation of tangent and normal at a point on the ellipse (Cartesian and parametric) -

condition for a straight line to be a tangent.

Hyperbola:

· Equation of hyperbola in standard form- Parametric equations.

· Equations of tangent and normal at a point on the hyperbola (Cartesian and

parametric) - conditions for a straight line to be a tangent- Asymptotes.

Three Dimensional Coordinates :

· Coordinates.

· Section formulas - Centroid of a triangle and tetrahedron.

Direction Cosines and Direction Ratios :

· Direction Cosines.

· Direction Ratios.

Plane :

· Cartesian equation of Plane - Simple Illustrations.

9. Trigonometry

Trigonometry - Naming the side in a right triangle-trigonometric ratios – defining

trigonometric ratios –trigonometric ratios of some specific angles ( 450,300 &600, 00 &900 )

–trigonometric ratios of complementary angles – trigonometric identities – Applications of

Trigonometry - Line of sight & horizontal -Angle of elevation & depression -Drawing

figures to solve problems – solution for two triangles

Trigonometric Ratios up to Transformations:

· Graphs and Periodicity of Trigonometric functions.

· Trigonometric ratios and Compound angles.

· Trigonometric ratios of multiple and sub- multiple angles.

· Transformations - Sum and Product rules.

Trigonometric Equations:

· General Solution of Trigonometric Equations.

· Simple Trigonometric Equations – Solutions.

Inverse Trigonometric Functions:

· To reduce a Trigonometric Function into a bijection.

· Graphs of Inverse Trigonometric Functions.

· Properties of Inverse Trigonometric Functions.

Hyperbolic Functions:

· Definition of Hyperbolic Function – Graphs.

· Definition of Inverse Hyperbolic Functions – Graphs.

· Addition formulas of Hyperbolic Functions.

Properties of Triangles:

· Relation between sides and angles of a Triangle

· Sine, Cosine, Tangent and Projection rules.

· Half angle formulae and areas of a triangle

· In-circle and Ex-circle of a Triangle.

10. Vector Algebra

Addition of Vectors:

· Vectors as a triad of real numbers.

· Classification of vectors.

· Addition of vectors.

· Scalar multiplication.

· Angle between two non-zero vectors.

· Linear combination of vectors.

· Component of a vector in three dimensions.

· Vector equations of line and plane including their Cartesian equivalent forms.

Product of Vectors:

· Scalar Product - Geometrical Interpretations - orthogonal projections.

· Properties of dot product.

· Expression of dot product in i, j, k system – Angle between two vectors.

· Geometrical Vector methods.

· Vector equations of plane in normal form.

· Angle between two planes.

· Vector product of two vectors and properties.

· Vector product in i, j, k system.

· Vector Areas.

· Scalar Triple Product.

· Vector equations of plane in different forms, skew lines, shortest distance and their

Cartesian equivalents. Plane through the line of intersection of two planes, condition

for coplanarity of two lines, perpendicular distance of a point from a plane, Angle

between line and a plane. Cartesian equivalents of all these results

· Vector Triple Product – Results

11. Calculus

Limits and Continuity:

· Intervals and neighbourhoods.

· Limits.

· Standard Limits.

· Continuity.

Differentiation:

· Derivative of a function.

· Elementary Properties.

· Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function -

Derivatives.

· Methods of Differentiation.

· Second Order Derivatives.

Applications of Derivatives:

· Errors and approximations.

· Geometrical Interpretation of a derivative.

· Equations of tangents and normal’s.

· Lengths of tangent, normal, sub tangent and sub normal.

· Angles between two curves and condition for orthogonality of curves.

· Derivative as Rate of change.

· Rolle’s Theorem and Lagrange’s Mean value theorem without proofs and their

geometrical interpretation.

· Increasing and decreasing functions.

· Maxima and Minima.

Integration:

· Integration as the inverse process of differentiation- Standard forms –properties of

integrals.

· Method of substitution- integration of Algebraic, exponential, logarithmic,

trigonometric and inverse trigonometric functions. Integration by parts.

· Integration- Partial fractions method.

· Reduction formulae.

Definite Integrals:

· Definite Integral as the limit of sum

· Interpretation of Definite Integral as an area.

· Fundamental theorem of Integral Calculus.

· Properties.

· Reduction formulae.

· Application of Definite integral to areas.

Differential equations:

· Formation of differential equation-Degree and order of an ordinary differential

equation.

· Solving differential equation by

a) Variables separable method.

b) Homogeneous differential equation.

c) Non - Homogeneous differential equation.

d) Linear differential equations.

V. Methodology (20 Marks)

1. Meaning and Nature of Mathematics, History of Mathematics.

2. Contributions of Great Mathematicians - Aryabhatta, Bhaskaracharya, Srinivasa

Ramanujan, Euclid, Pythagoras, George cantor.

3. Aims and Values of teaching Mathematics, Instructional objectives (Blooms

taxonomy)

4. Mathematics curriculum: Principles, approaches of curriculum construction, -Logical

and Psychological, Topical and Concentric, Spiral approaches. Qualities of a good

Mathematics text book.

5. Methods of teaching mathematics- Heuristic method, Laboratory method, Inductive

and Deductive methods, Analytic and Synthetic methods, Project method and Problem

Solving method.

6. Unit Plan, Year Plan, Lesson Planning in Mathematics.

7. Instructional materials, Edgar Dale's Cone of Experience.

8. Evolving strategies for the gifted students and slow learners,

9. Techniques of teaching mathematics like Oral work, written work, Drilling,

Assignment, Project, Speed and Accuracy.

10.Mathematics club, Mathematics structure, Mathematics order and pattern sequence.

11. Evaluation - Types, Tools and Techniques of Evaluation, Preparation of SAT

Analysis, Characteristics of a good test.