## Unit 1 - Numbers, Quantification and Numerical Applications

Prime Numbers, Encryptions using Prime Numbers

Binary Numbers

Complex Numbers (Preliminary idea only)

Indices, Logarithm and Antilogarithm

Laws and  properties of logarithms

Simple applications of logarithm and antilogarithm

Numerical problems on averages, calendar, clock, time, work and distance, mensuration, seating arrangement

## Unit 2 - Algebra

Sets

Types of sets

Venn diagram

De Morgan's laws

Problem solving using Venn diagram

Relations and types of relations

Introduction of Sequences, Series

Arithmetic and  Geometric progression

Relationship between AM and GM

Basic concepts of Permutations and Combinations

Permutations, Circular Permutations, Permutations with restrictions

Combinations with standard results

## Unit 3 - Mathematical & Logical Reasoning

Mathematically acceptable statements

Connecting words/ phrases in Mathematical statement consolidating the understanding of "if and  only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and  their use through variety of examples related to real life and  Mathematics

Problems based on logical reasoning  (coding-decoding, odd man out, blood relation, syllogism etc)

## Unit 4 - Calculus

Introducing functions

Domain and  Range of a function

Types of functions (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function)

Graphical representation of functions

Concept of limits and  continuity of a function

Instantaneous rates of change

Differentiation as a process of finding derivative

Derivatives of algebraic functions using Chain rule

Tangent line and  equations of tangents

## Unit 5 - Probability

Random experiment, sample space, events, mutually exclusive events

Independent and Dependent Events

Law of Total Probability

Bayes’ Theorem

## Unit 6 - Descriptive Statistics

Types of data  (raw data, univariate data, bivariate and multi-variate data)

Data  on various scales (nominal, ordinal, interval and  ratio scale)

Data  representation and visualization

Data  interpretation (central tendency, dispersion, deviation, variance, skewness and  kurtosis)

Percentile rank and quartile rank

Correlation (Pearson and  Spearman method of correlation)

Applications of descriptive statistics using real time data

## Unit 7 - Basics of Financial Mathematics

Interest and interest rate

Accumulation with simple and  compound interest

Simple and  compound interest rates with equivalency

Effective rate of interest

Present value, net present value and future value

Annuities, calculating value of regular annuity

Simple applications of regular annuities (up to 3 period)

Tax, calculation of tax and  simple applications of tax calculation in Goods and service tax, Income Tax

Bills, tariff rates, fixed charge, surcharge, service charge

Calculation and  interpretation of electricity bill, water  supply bill and other supply bills

(Comparing interest rates on various types of savings; calculating income tax; electricity bills, water  bill; service surcharge using realistic data)

## Unit 8 - Coordinate Geometry

Straight Line

Circles

Parabola

(Only standard forms and  graphical representation on two-dimensional plane)

PRACTICALS

Calculating average, interest (simple and  compound), creating pictographs, drawing pie chart,  bar graphs, calculating central tendency; visualizing graphs (straight line, circles and  parabola using real time data)

Suggestion :

Plot the graph  of functions on excel; study the nature of function at various points, drawing lines of tangents;

Create budget of income and spending;

Create compare sheet of price, features to buy a product;

Prepare best option plan to buy a product  by comparing cost, shipping charges, tax and other hidden cost;