Mathematical thinking is linked to subjects where mathematics can be productively applied. Studying applied mathematics will enhance learning and understanding of Physics, Chemistry, Economics, Accountancy and other Skill based subjects. Through this course students will learn problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing and communicating mathematical thinking.
UNIT 1: SETS, RELATIONS AND FUNCTIONS (10 Marks)
Sets and their representation, Empty set, Equal sets, Subset, Power Set Ordered pair, Cartesian product, Relation, Domain ,Co domain, Range, Equivalence relation, One-One, Onto and Into functions Logarithm as a special function, Interval in which logarithm becomes one-one and onto, Laws of logarithm.
UNIT 2: TRIGONOMETRY (10 Marks)
Trigonometric functions in different quadrants, Trigonometric ratios of allied angles, Trigonometric ratios of sum and difference of 2 angles, Trigonometric ratios of multiple and sub multiple angles, Trigonometric Equations and solutions.
UNIT 3: ALGEBRA (18 Marks)
1. Complex numbers-concept of iota, Imaginary numbers, arithmetic operations on complex numbers(addition, subtraction, multiplication, division) Conjugate and modulus, Standard form a+ib of a complex number, square root of a complex number, Representation of a complex number in geometric form, vector form, polar form.
2. Quadratic equations: Solution of a quadratic equation with non real roots for real number coefficients and complex number as coefficient.
3. Arithmetic Progression - nth term and sum to n terms of an A.P, Arithmetic mean, Applications of A.P
4. Geometric Progression: nth term and sum to n terms of a G.P. Geometric mean, relation between Arithmetic and Geometric mean, Special sums.
5. Partial Fractions - Definition of polynomial fraction proper and improper fraction and definition of partial fraction.
UNIT 4: LINEAR INEQUATIONS AND COORDINATE GEOMETRY (12 Marks)
1. Graphical solution of a linear Inequation in 2 variables, solution set for simultaneous linear in equation.
2. Slope of a line, various forms of equations of a line-, point slope form, slope intercept form, two point form, intercept form and normal form, General Equation of a line.
3. Conic Sections-circle, parabola,. Standard equation of a circle and parabola.
UNIT 5: STATISTICS AND COMMERCIAL MATHEMATICS (20 Marks)
Measures of dispersion-Range, mean deviation from mean, Mean deviation from median for discrete frequency distribution and continuous frequency distribution Variance and standard deviation for discrete and continuous frequency distribution Demographic Statistics-Infant Mortality Rate, Crude Death Rate, Standardized Death Rate, Cost of Living Index Number, Wholesale Price Index Simple and Compound Interest, Profit, Loss, Discount and Percentage, Commission, Brokerage, Ratio Proportion and their properties, Insurance, Annuity
UNIT 6: PERMUTATION, COMBINATION, BINOMIAL THEOREM AND PROBABILITY (10 Marks)
Fundamental Principle of Counting, Factorial n-n!, npr and ncr and their relation. Statement of Binomial theorem for positive integral indices, general and middle terming binomial expansion. Conditional Probability, Multiplication Theorem on Probability, Independent Events.