AP TET Paper 1 – MATHEMATICS (30 Marks)
Content (24 Marks)
| NUMBERS | Numbers – Four fundamental operations (Addition, Subtraction, Multiplication, Division) – Knowing about Numbers – Hindu-Arabic system of numeration (Indian system of numeration) – International system of numeration (British system of numeration) – Place value and Face values of a digit in a number – Comparing and Ordering of Numbers – Whole Numbers – Factors and Multiples – Prime and Composite numbers – Even and Odd numbers – Tests for Divisibility of Numbers – Common Factors and Common Multiples – Prime factorization – Highest Common Factor (G.C.D) – Lowest Common Multiple – Integers – properties and fundamental operations – Fractions and decimals – Types of fractions – comparison – Applications of fractions in daily life – four fundamental operations on fractions and decimals – Rational Numbers – Properties of Rational Numbers – Rational Numbers between two rational numbers – Four fundamental Operations on Rational Numbers – Product of reciprocals – Squares – Square roots (Numbers and Decimals) – Properties of Square Numbers – Cubes – Cube roots of Numbers – Playing with Numbers – Games with Numbers – Letters for Digits. |
| ARITHMETIC | BODMAS rule – Ratios and Proportions (Direct, Inverse) – comparing quantities using ratios, proportion, percentage and their applications – Profit and Loss – Discount – Sales Tax/Value Added Tax/Goods and Services Tax – Simple, Compound Interest and their applications. |
| GEOMETRY | Basic geometrical concepts (Point, Line, Line segment, Ray, Curves, Polygons, Angles) – Measuring of Lines – Pairs of Lines – Elements of Angles – Measuring of Angles – Types of Angles – Naming of the given 2D figures of Triangles, Square and Rectangle – The Triangle – Types of Triangles and its Properties – Classification of Polygons – Angle sum property – Kinds of Quadrilaterals (Trapezium, Kite, Parallelogram) – Some special parallelograms (Rhombus, Rectangle, Square) – Constructing different types of Quadrilaterals – Views of 3D-Shapes – Identification of Edges, Vertices and Faces of 3D figures (Euler’s Rule) – Nets for building 3D shapes. |
| DATA HANDLING | Reading and interpreting and analysing the Data (pictograph, tally marks, bar graphs, double bar graph, pie charts) – Arithmetic Mean – Mode – Median of un-grouped data – Chance and Probability. |
| ALGEBRA | Patterns – making rules – The idea of variables – formation of algebraic expressions -Terms, Factors and Coefficients – Linear equations in one variable – terms and types of algebraic expressions – finding the value of an expression – Addition, Subtraction and Multiplication of Algebraic Expressions – Multiplying a Monomial by a Monomial and polynomial – Multiplying a Polynomial by a Polynomial – Standard Identities and their applications – Applications of simple equations to practical situations – Exponents and Powers – Negative exponents – Laws of exponents – Expressing large numbers in the standard form – Factorisation – Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial) – Linear Graphs |
| MENSURATION | Measuring Length, Weight, Capacity, Time-Seasons, Calendar, Money, Area – Symmetry (Line and Rotational) – Perimeter of Triangle, Square, Rectangle, Rhombus, Trapezium, Parallelogram, Circle and Polygon), Area of a Quadrilateral, Surface Area and Volume of Cube, Cuboid and Cylinder – Volume and capacity. |
Methodology (6 Marks)
- Nature and Definitions of Mathematics
- Aims, values and instructional objectives ofteaching Mathematics
- Methods ofTeaching & Remedial measures in Mathematics
- Instructional Material, TLM and Resource Utilization in Mathematics
- Curriculum, Text Book & Instructional Planning.
- Evaluation and Continuous Comprehensive Evaluation
AP TET Paper 2 – MATHEMATICS (30 Marks)
Content (24 Marks)
NUMBER SYSTEM
Numbers – Four fundamental operations (Addition, Subtraction, Multiplication, Division) – Knowing about Numbers – Hindu-Arabic system of numeration (Indian system of numeration) – International system of numeration (British system of numeration) – Place value and Face values of a digit in a number – Comparing and Ordering of Numbers – Whole Numbers – Factors and Multiples – Prime and Composite numbers – Even and Odd numbers – Tests for Divisibility of Numbers – Common Factors and Common Multiples – Prime factorisation – Highest Common Factor (G.C.D) – Lowest Common Multiple – Integers – properties and fundamental operations – Fractions and decimals – Types of fractions – comparison – Applications of fractions in daily life – four fundamental operations on fractions and decimals – Euclid’s Division Lemma and its application – Rational Numbers – Properties of Rational Numbers – Representation of Rational Numbers on the Number line – Rational Numbers between two rational numbers – Four fundamental Operations on Rational Numbers – Rational numbers and their decimal expansions – Non-terminating, recurring decimals in rational numbers – Product of reciprocals – Squares – Square roots (Numbers and Decimals) – Properties of Square Numbers – Cubes – Cube roots of Numbers – Playing with Numbers – Games with Numbers – Letters for Digits – Irrational numbers – Real Numbers and their Decimal Expansions – Operations on Real Numbers – Laws of Exponents for Real Numbers – Properties & Laws of logarithms. Sets and their representation (Roster form and Set builder form) – Classification of sets (Empty, Universal, subset, Finite & Infinite, disjoint sets) – difference of sets – Equal sets – Using diagrams to represent sets – Venn diagrams and cardinality of sets – Basic operations on sets (Union, Intersection).
ARITHMETIC
BODMAS rule – Ratios and Proportions (Direct, Inverse) – comparing quantities using ratios, proportion, percentage and their applications – Profit and Loss – Discount – Sales Tax/Value Added Tax/Goods and Services Tax – Simple, Compound Interest and their applications.
GEOMETRY
Basic geometrical concepts (Point, Line, Line segment, Ray, Curves, Polygons, Angles) – Measuring of Lines – Pairs of Lines – Intersecting Lines and Non-intersecting Lines – Lines parallel to the same line – Elements of Angles – Measuring of Angles – Types of Angles – Pairs of Angles – Naming of the given 2D figures of Triangles, Square and Rectangle – The Triangle – Types of Triangles and its Properties – Congruence and some properties of Triangles – Some more criteria for Congruence of Triangles – Criteria for similarity of triangles – Areas of similar triangles – Pythagoras theorem – Classification of Polygons – Angle sum property – Kinds of Quadrilaterals (Trapezium, Kite, Parallelogram) – Some special parallelograms (Rhombus, Rectangle, Square) – Constructing different types of Quadrilaterals – Views of 3D-Shapes – Identification of Edges, Vertices and Faces of 3D figures (Euler’s Rule) – Nets for building 3D shapes – Introduction to Euclid’s geometry – Euclid’s definitions, axioms and postulates – Angle Subtended by a Chord at a Point – Perpendicular from the Centre to a Chord – Equal Chords and Their Distances from the Centre – Angle Subtended by an Arc of a Circle – Cyclic Quadrilaterals – Tangents of a circle – Number of Tangent to a Circle from any point – Segment of a circle formed by a Secant.
STATISTICS
Reading and interpreting and analysing the Data (pictograph, tally marks, bar graphs, double bar graph, pie charts) – Graphical Representation of Data (Bar graphs, Histogram, Frequency polygons) Measures of Central tendency – Arithmetic Mean – Mode – Median of un-grouped, grouped data Graphical representation of cumulative frequency distribution – Ogive curves.
ALGEBRA
Patterns – making rules – The idea of variables – formation of algebraic expressions -Terms, Factors and Coefficients – Linear equations in one variable – Linear equations in two variables – Solutions of Pair of Linear Equations in Two Variables – Algebraic methods of finding the solutions for a pair of linear equations -Equations reducible to a pair of linear equations in two variables -Solution of a quadratic equation by factorisation & by completing the square – Nature of roots – terms and types of algebraic expressions – finding the value of an expression – Addition, Subtraction and Multiplication of Algebraic Expressions – Multiplying a Monomial by a Monomial and polynomial – Multiplying a Polynomial by a Polynomial – Standard Identities and their applications – Applications of simple equations to practical situations – Exponents and Powers – Negative exponents – Laws of exponents – Expressing large numbers in the standard form – Factorisation – Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial) – Linear Graphs – Polynomials in one variable – Degree, Value, zeroes of a polynomial – Geometrical meaning of the Zeroes of a Polynomial – Graphical representation of linear, Quadratic and Cubic Polynomials – Factorisation of Polynomials – Algebraic Identities – Working with Polynomials – Division algorithm for polynomials – Arithmetic progressions – Parameters of Arithmetic progressions – nth term of an Arithmetic progression – Sum of first n terms in Arithmetic progression – Geometric progressions – nth term of a GP.
MENSURATION
Measuring Length, Weight, Capacity, Time-Seasons, Calendar, Money, Area – Symmetry (Line and Rotational) – Perimeter of Triangle, Square, Rectangle, Rhombus, Trapezium, Parallelogram, Circle and Polygon, Properties of a Parallelogram – The Mid-point Theorem – Area of a Quadrilateral, Surface Area and Volume of Cube, Cuboid and Cylinder -Volume and capacity – Surface Area and volume of a Sphere – Volume of a Right Circular Cone – Surface area of the combination of Solids, Volume of a combination of solids – Conversion of solid from one shape to another
PROBABILITY
Probability – Linking chances to probability – Chance and probability related to real life – Probability – a theoretical approach – Mutually exclusive events – Finding probability – Complementary events and probability – Impossible and certain events – Deck of Cards and Probability – Use and Applications of probability.
CO-ORDINATE GEOMETRY
Cartesian System – Distance between two points – distance between two points on a line parallel to the co-ordinate axis – Distance between any two points on a line in the x-y plane – Section formula – centroid of a triangle – Tri-sectional points of a line – Area of the triangle – Heron’s formula- Collinearity – Straight lines – Slope of the straight line – slope of a line joining two points.
TRIGONOMETRY
Trigonometry – Naming the sides in a Right triangle – Trigonometric Ratios – Defining Trigonometric Ratios – Trigonometric ratios of some specific and complementary angles – Trigonometric identities – Applications of Trigonometry – Drawing figures to solve problems – solutions for two triangles.
Methodology (6 Marks)
- Meaning and Nature of Mathematics, History of Mathematics.
- Contributions of Great Mathematicians – Aryabhatta, Bhaskaracharya, Srinivasa Ramanujan, Euclid, Pythagoras, George cantor.
- 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 book.
- Methods of teaching mathematics- Heuristic method, Laboratory method, Inductive and Deductive
- methods, Analytic and Synthetic methods, Project method and Problem Solving method.
- Unit Plan, Year Plan, Lesson Planning in Mathematics.
- Instructional materials, Edgar Dale’s Cone of Experience.
- Evolving strategies for the gifted students and slow learners
- Techniques of teaching mathematics like Oral work, Written work, Drilling, Assignment, Project, Speed and Accuracy.
- Mathematics club, Mathematics structure, Mathematics order and pattern sequence.
- Evaluation – Types, Tools and Techniques of Evaluation, Preparation of SAT Analysis, Characteristics of a good test
