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Contents

**AP DSC SA Maths 2024 Syllabus PDF**

Name of the Organization | Commissioner of School Education, Government of Andhra Pradesh |

Post Name | School Assistants, Language Pandits, Secondary Grade Teachers, Physical Education Teachers |

Category | Syllabus |

Selection Process | Written Test |

Location | Andhra Pradesh |

Official Site | aptet.apcfss.in |

**AP DSC SA Maths Exam Pattern PDF**

Candidates can download the AP DSC Syllabus on this page. AP DSC examination to fill the vacancies, the government is going to conduct a written examination to select the Candidates for these posts. So here on this page, the candidates can get the AP DSC Written Examination Syllabus Completely. Candidates also refer to our website jobsbadi.com to get complete information about AP DSC’s latest Notification Updates.

Sl.no | Name of the Subject | Marks |

1 | Gk and Current Affairs | 10 Marks |

2 | Perspectives of Education | 05 Marks |

3 | Classroom implications Educational Psychology | 05 Marks |

4 | Content | 44 Marks |

5 | Methodology | 16 Marks |

6 | Total | 80 Marks |

**AP DSC SA Maths Syllabus 2024 PDF Download Here**

**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 –
- Inverse functions and
- Domain, Range, Inverse of real valued functions. Mathematical Induction
- Principle of Mathematical Induction &
- Applications of Mathematical
- Problems on 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 +
- Modulus and amplitude of complex numbers –Illustrations.
- Geometrical and Polar Representation of complex numbers in Argand plane- Argand

De Moivre’s Theorem:

- De Moivre’s theorem- Integral and Rational
- n
^{th}roots of unity- Geometrical Interpretations – 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 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
- 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
- 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

### 6. Statistics

DATA HANDLING – Frequency Distribution Tables and Graphs- Grouped data- ungrouped 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
- Independent and dependent events conditional probability- multiplication theorem and Bayee’s

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 –
- To find equations of locus – Problems connected to Transformation of Axes :
- Transformation of axes – Rules, Derivations and
- Rotation of axes – Derivations – The Straight Line :
- Revision of fundamental
- Straight line – Normal form –
- Straight line – Symmetric
- Straight line – Reduction into various
- Intersection of two Straight
- Family of straight lines – Concurrent
- Condition for Concurrent
- Angle between two
- Length of perpendicular from a point to a
- Distance between two parallel
- Concurrent lines – properties related to a Pair of Straight lines:
- Equations of pair of lines passing through origin, angle between a pair of
- Condition for perpendicular and coincident lines, bisectors of
- Pair of bisectors of
- Pair of lines – second degree general
- Conditions for parallel lines – distance between them, Point of intersection of pair of
- Homogenizing a second degree equation with a first degree equation in X and 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
- Position of a point in the plane of a circle – power of a point-definition of tangent- length 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 circle- point of contact-equation of
- Chord of contact – pole and polar-conjugate points and conjugate lines – equation of chord with given middle
- 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
- Intersection of a line and a

Parabola:

- Conic sections –Parabola- equation of parabola in standard form-different forms of parabola- parametric
- 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
- Equation of tangent and normal at a point on the ellipse (Cartesian and parametric) – condition for a straight line to be a

Hyperbola:

- Equation of hyperbola in standard form- Parametric
- Equations of tangent and normal at a point on the hyperbola (Cartesian and parametric) – conditions for a straight line to be a tangent-

Three Dimensional Coordinates :

- Section formulas – Centroid of a triangle and Direction Cosines and Direction Ratios :
- Direction
- Direction Ratios. Plane :
- Cartesian equation of Plane – Simple

### 9. Trigonometry

Trigonometry – Naming the side in a right triangle-trigonometric ratios – defining trigonometric ratios –trigonometric ratios of some specific angles ( 45^{0},30^{0} &60^{0}, 0^{0} &90^{0} )

–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
- Trigonometric ratios and Compound
- Trigonometric ratios of multiple and sub- multiple
- Transformations – Sum and Product rules. Trigonometric Equations:
- General Solution of Trigonometric
- Simple Trigonometric Equations – Inverse Trigonometric Functions:
- To reduce a Trigonometric Function into a
- Graphs of Inverse Trigonometric
- Properties of Inverse Trigonometric Hyperbolic Functions:
- Definition of Hyperbolic Function –
- Definition of Inverse Hyperbolic Functions –
- Addition formulas of Hyperbolic Properties of Triangles:
- Relation between sides and angles of a Triangle
- Sine, Cosine, Tangent and Projection
- Half angle formulae and areas of a triangle
- In-circle and Ex-circle of a

### 10. Vector Algebra

Addition of Vectors:

- Vectors as a triad of real
- Classification of
- Addition of
- Scalar
- Angle between two non-zero vectors.
- Linear combination of
- 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
- Properties of dot
- Expression of dot product in i, j, k system – Angle between two
- Geometrical Vector
- Vector equations of plane in normal
- Angle between two
- Vector product of two vectors and
- Vector product in i, j, k
- Vector
- Scalar Triple
- 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
- Standard
- Differentiation:
- Derivative of a
- Elementary
- Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function – Derivatives.
- Methods of
- Second Order Applications of Derivatives:
- Errors and
- Geometrical Interpretation of a
- Equations of tangents and normal’s.
- Lengths of tangent, normal, sub tangent and sub
- Angles between two curves and condition for orthogonality of
- Derivative as Rate of
- Rolle’s Theorem and Lagrange’s Mean value theorem without proofs and their geometrical
- Increasing and decreasing
- Maxima and

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
- Integration- Partial fractions
- Reduction Definite Integrals:
- Definite Integral as the limit of sum
- Interpretation of Definite Integral as an
- Fundamental theorem of Integral
- Reduction
- Application of Definite integral to Differential equations:
- Formation of differential equation-Degree and order of an ordinary differential equation.
- Solving differential equation by

- Variables separable
- Homogeneous differential
- Non – Homogeneous differential
- Linear differential

### V. Methodology (Present B.Ed. syllabus) (16 Marks)

- Meaning and Nature of Mathematics, History of
- Contributions of Great Mathematicians – Aryabhatta, Bhaskaracharya, Srinivasa Ramanujan, Euclid, Pythagoras, George
- Aims and Values of teaching Mathematics, Instructional objectives (Blooms taxonomy)
- Mathematics curriculum: Principles, approaches of curriculum construction, -Logical and Psychological, Topical and Concentric, Spiral approaches. Qualities of a good Mathematics text
- Methods of teaching mathematics- Heuristic method, Laboratory method, Inductive and Deductive methods, Analytic and Synthetic methods, Project method and Problem Solving
- Unit Plan, Year Plan, Lesson Planning in
- Instructional materials, Edgar Dale’s Cone of
- Evolving strategies for the gifted students and slow learners,
- Techniques of teaching mathematics like Oral work, Written work, Drilling, Assignment, Project, Speed and
- Mathematics club, Mathematics structure, Mathematics order and pattern
- Evaluation – Types, Tools and Techniques of Evaluation, Preparation of SAT Analysis, Characteristics of a good.