Paper-3 | Discipline Knowledge in Mathematics
Subject Contents – Mathematics
1. Number System-I: Counting of Numbers; Fundamental Operations; Types of Numbers; Real Numbers; Mathematical Units and Conversions; Utility of Euclid division lemma, Problems on surds; Divisibility rules their possible remainders, Pythagorean triplets; Using alphabet in place of digit in divisibility rules, missing numbers; Prime and composite, even and odd numbers, need and applications of fundamental theorem of arithmetic, difference between factors and multiples and prime factors-LCM and HCF; Characteristics and importance in finding solutions to daily life situations (e.g.p).
2. Number System-II: Patterns of numbers; Progressions- A.P. and G.P- relating to daily life situations; Building the relation between numbers and graphical representations; Squares – Square root, Cube-Cube root; Ratio, Golden Ratio, Compound Ratio, Inverse Ratio, Addition and Subtraction of equal Ratios; Proportion – Direct and inverse; Fractions (Numerator and denominator); Applications on the above.
3. Percentages in daily life situations and SETS :Profit and loss, Discount ; Simple interest and Compound interest, VAT and their applications ; Sets-Concept in building a set and rationale; types of sets; Operations on sets Venn Diagrams and related daily life problems. Sets- Compliment, properties on operations and cardinalitySeries; Complex numbers and its fundamental operations; Conjugates;Fundamental principle of counting (Linear and Circular) Combinations and related to daily life problems.Modulus of a Real Number and absolute value.Types of statements and proofs, quantifiers; Tautology and contradictions.
4. Fundamentals of Algebra; Linear expressions and equations in one & two variables Pairs linear equations in two variables; Basic Operations on Algebraic expressions –Laws and properties of exponents; Factorization; Special products; Operations on Polynomials and Factorization; Quadratic expressions and equations. Logarithms and their use. Graphical Representations Mathematical Induction/ Quadratic Expressions/ Linear Programming / Determinants/ Matrices :Relation between two variables and there graphical representation, basic ideas related to function and respective theorems, types of functions ; Mathematical induction, problems on divisibility using principle of Mathematical Induction; Quadratic expressions – change in sign, maxima and minima values; Basis concepts of linear programming problems; Binomial theorem and approximations. Order of Matrix; Properties of Determinants of Matrices and solving of equations.
5. Geometry: Fundamental concepts; Contextual situations, basic ideas like point , line, ray, lines segment, angle, plane , curve, circle etc., and related terminology; Relations between lines and angles; Lines of a plane and their properties; Axioms , postulates, Euclid axioms, historical back ground, non-Euclidean geometry; Types and Properties of Geometrical figures; Types and Properties of triangle, quadrilateral,
Polygon etc.,; Properties of Circle and Parts of Circles; Comparison of Geometrical figures – Congruency, Similarity etc.,; BPT, Pythagoras, Theorems applications; Relations between Circles and Lines; Areas of Geometrical Figures – Related theorems; Practical Geometry; Basic constructions, Constructions of Triangles, Quadrilaterals, Circles, Similar triangles, Tangents to Circles and related problems.
6. Co-ordinate Geometry: Basic concepts, dividing a line segment in the given ratio and its usage in different situations, slope of a line, distance between two points, area of triangles, Quadrilaterals and Collinearity of points.
7. Concept of locus; Straight line – different forms of straight line and conversions; Angle between two lines; Length of perpendicular from a point to a line; Distance between two parallel lines; Circle Equation – standard form, center and radius; Position of a point in plane of circle; Relative positions of two circles –Transformation of Axes- 3-D Geometry-DR’s and DC’s and Cartesian equation of a plane. Conic Section.
8. Mensuration: Plane figures; Need and importance of Area and Perimeter of different
triangles, quadrilaterals, polygons , circles, ring etc., in daily life; Solid
Need and importance of CSA, TSA and volume of prism, cube, cuboids, pyramid,
cylinder, cone, sphere, hemisphere; Conversions from one solid to another;
Problems with combination of solids (not more than three) in daily life; Conversions- 3- D figures and 2-D figures.
9. Statistics and Probability :Data handling : Types and representation of data; Measure of central tendency of ungrouped and grouped data specific usages; Presentation of data – different graphs and related problems ; Probability Basic concepts, outcomes
and chances; Events – mutually exclusive,
possible and impossible, complementary; Applications of probability Measures of dispersions – Range, Q.D, M.D, S.D. ; Coefficient of variation; Probability- Random experiments and events (Independent and Dependent); Addition and multiplication theorems of probability;
Random variables. Axiomatic approach.
10. Trigonometry : Basic concepts; Trigonometric ratios; Trigonometric values for specific angles; Complementary angles; Trigonometric Identities; Conversions of Trigonometric ratios – Trigonometric transformations – Heights and distances; Trigonometric ratios of compound angles; Properties of triangles – relation between sides and angles of a triangles – Inverse trigonometric functions. Multiples and submultiples –Trigonometric expansions.