Applied Mathematics ❤️ School Directory

By Anand

October 30, 2020

Exam Structure

There are eight units - (i) Numbers, Quantification and Numerical Applications, (ii) Algebra, (iii) Mathematical Reasoning, (iv) Calculus, (v) Probability, (vi) Descriptive Statistics, (vii) Basics of Financial Mathematics, and (viii) Coordinate Geometry.

Course Structure

S.No.	Unit	Marks
I	Numbers, Quantification and Numerical Applications	9
II	Algebra	10
III	Mathematical Reasoning	6
IV	Calculus	10
V	Probability	10
VI	Descriptive Statistics	12
VII	Basics of Financial Mathematics	18
VIII	Coordinate Geometry	5
	Total	80

Unit I: 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 II: 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 III: Mathematical and 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 IV: 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 V: Probability

Random experiment, sample space, events, mutually exclusive events
Independent and Dependent Events
Law of Total Probability
Bayes’ Theorem

Unit VI: 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 VII: 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)