## TS PSC TRT SGT 2017 Mathematics Syllabus

TS PSC TRT Secondary Grade Teacher (SGT) 2017 Mathematics subject Syllabus for Telugu, Hindi, English, Urdu, Bengali, Marathi, Tamil, Kannada Medium.

### TS PSC TRT SGT 2017 Mathematics Syllabus

** Part – V
Mathematics (Marks: 09)**

**1. Number System (Elementary Number Theory):** Number system (N,W,Z,Q,R) Numeration and Notation, Representation of numbers on Number Line, place value and four fundamental operations , properties of numbers, squares, cubes, square roots (R) and their extraction square roots of real numbers and cube roots, factorization method, types of surds conjugation and rationalization of surds, Prime and composite numbers, types of prime numbers (co, twin, relative etc.),Fermat number, even and odd numbers, prime factors, LCM, GCD and Theorem of Gauss on relative primes, Roman Numerals, Test of divisibility.

International System, Concepts and types of fractions, decimal fractions, rational and irrational numbers, decimal

representation, writing pure recurring decimal / mix recurring decimal with integral part their fundamental operations and their use in daily life.

**2. Arithmetic:** Length, weight, capacity, Time and Money their standard unit and Relation between them, and their use in daily life. Unitary method, Ratio and proportion, Inverse Proportion, Percentages, trade discount, Average, profit – loss, Simple interest, compound interest, Partnership, time-distance and work. Problems pertaining to Clocks and calendar.

**3. Simple Equations:** Properties of Equality, Equations, Solving in-equation using their properties, Linear in-equations and their graphs, System of inequations. Linear equations in two variables, System of linear equations and

their graphs, Simultaneous equation in two variables, Dependant equations, System of equations, Linear functions.

**4. Algebra:** Basic Concepts of Algebra, Algebraic expressions and their Fundamental operations, Degree of a monomial, polynomial, Zero of a polynomial, Fundamental operations of polynomials, Value of expression, Solving Equations. Properties of Polynomials (Commutative etc) and fundamental operations of polynomials.

Factorization, Polynomials over integers, Simplification of polynomials, Some special products, Square roots of algebraic expressions, Equations with rational and decimal coefficients, Set – concept – types – Set building form, roster’s form, equality, cardinal and ordinal number, Representation of sets with Venn diagrams , Basic set

operations ,Compliment of a Set, Laws of set operations, principal of duality, Relations, Cartesian product of two sets, Applications of set theory, inverse relation, types of relation, Multiplication of a multinomial by a monomial,

Binomial expansions, Identities, Division Rule (Remainder Theorem) Factorization GCF/HCF, Factors of multinomial, Common binomial factor, Division of a monomial by a monomial, Factorization of quadratic expression, Exponents and powers, Laws of indices, powers with exponent zero, Formula and their uses, Changing the subject of the formulae, Remainder theorem, Horner’s method of synthetic division, The problem leading to quadratic equations, Laws of rational indices, Modulus of a real number.

**5. Geometry:** Structure of geometry and Historical back ground, Geometry in Real Life, Fundamentals in Geometry, Method of proof, concept of converse, Rotation of an angle, Types of angles, Construction and measurement of angles, Line, axis, shapes, reflections. Symmetry – line of symmetry, point of symmetry, reflection, image of an angle.

Construction of Different Angles, line segments, midpoint, etc. Triangles, its properties, Inequalities in a triangle,

Types of Triangles, Parts of triangle, special cases like unique triangle, concurrency, Similar triangle and their properties, Theorems on similar triangle Congruency of triangles, SAS/ASA/SSA Axioms , Some theorems,

Construction of triangles, harder cases, different types, concurrent lines in triangles (some theorems) Median, altitudes of a triangle the circum centre, in centre, the ex-centres, the centroid, orthocenter (Concurrency of

triangles).

Circles and its parts, Locus, Congruency of Circles, Cyclic Quadrilaterals, Axioms, Straight line, basic axioms parallel lines, Some theorem based on Parallel lines, Angles of a polygon, theorems based on polygons, Similar polygons Parallelogram and its properties, Geometric inequalities, Quadrilaterals , exterior and interior and convex and their constructions, Elements of Three dimensional Objects, Nets of 3 Dim diagrams, Some theorems and their Converse.

**6. Mensuration:** Perimeter and Area of Triangle, Quadrilateral, Sector, Circle, different types of paths and polygons. Perimeter and Area of four walls of room, Surface Area and Volumes of Cubes and Cuboids. Tan diagrams,

conversion of units.

**7. Data Handling and Statistics:** Introduction to data, data presentation, diagrammatic presentation of data, Guidelines for constructing a diagram, Constructions of Pictographs, Bar-graphs, Pie diagram, Frequency distribution table, frequency graphs (curves, polygon), Ogive curves, Average, Median, Mode.

TS PSC TRT Secondary Grade Teacher (SGT) 2017 Mathematics subject Syllabus for Telugu, Hindi, English, Urdu, Bengali, Marathi, Tamil, Kannada Medium.