Numbers & Quantification 
1.2 
Binary Numbers 
 Express decimal numbers in binary system
 Express binary numbers in decimal system

 Definition of number system (decimal and binary)
 Conversion from decimal to binary system and vice  versa

1.4 
Indices, Logarithm and Antilogarithm 
 Relate indices and logarithm /antilogarithm
 Find logarithm and antilogarithms of given number

 Applications of rules of indices
 Introduction of logarithm and antilogarithm
 Common and Natural logarithm

1.5 
Laws and properties of logarithms 
 Enlist the laws and properties of logarithms
 Apply laws of logarithm

 Fundamental laws of logarithm

1.6 
Simple applications of logarithm and antilogarithm 
 Use logarithm in different applications

 Express the problem in the form of an equation and apply logarithm/ antilogarithm

Numerical Applications 
1.7 
Averages 
 Determine average for a given data

 Definition and meaning
 Problems on average, weighted average

1.8 
Clock 
 Evaluate the angular value of a minute
 Calculate the angle formed between two hands of clock at given time
 Calculate the time for which hands of clock meet

 Number of rotations of minute hand / hour hand of a clock in a day
 Number of times minute hand and hour hand coincides in a day

1.9 
Calendar 
 Determine Odd days in a month/ year/ century
 Decode the day for the given date

 Definition of odd days
 Odd days in a year/ century.
 Day corresponding to a given date

1.10 
Time, Work and Distance 
 Establish the relationship between work and time
 Compare the work done by the individual / group w.r.t. time
 Calculate the time taken/ distance covered/ Work done from the given data

 Basic concept of time and work
 Problems on time taken / distance covered / work done

1.11 
Mensuration 
 Solve problems based on surface area and volume of 2D and 3D shapes
 Calculate the volume/ surface area for solid formed using two or more shapes

 Comparison between 2D and 3D shapes
 Combination of solids
 Transforming one solid shape to another

1.12 
Seating arrangement 
 Create suitable seating plan/ draft as per given conditions (Linear/circular)
 Locate the position of a person in a seating arrangement

 Linear and circular seating arrangement
 Position of a person in a seating arrangement

Unit – 2 Algebra 
Sets 
2.1 
Introduction to sets – definition 
 Define set as welldefined collection of objects

 Definition of a Set
 Examples and Nonexamples of Set

2.2 
Representation of sets 
 Represent a set in Roster form and Set builder form

 Write elements of a set in Set Builder form and Roster Form
 Convert a set given in Roster form into Set builder form and viceversa

2.3 
Types of sets and their notations 
 Identify different types of sets on the basis of number of elements in the set
 Differentiate between equal set and equivalence set

 Types of Sets: Finite Set, Infinite Set, Empty Set, Singleton Set

2.4 
Subsets 
 Enlist all subsets of a set
 Find number of subsets of a given set
 Find number of elements of a power set

 Subset of a given set
 Familiarity with terms like Superset, Improper subset, Universal set, Power set

2.5 
Intervals 
 Express subset of real numbers as intervals

 Open interval, closed interval, semi open interval and semi closed interval

2.6 
Venn diagrams 
 Apply the concept of Venn diagram to understand the relationship between sets
 Solve problems using Venn diagram

 Venn diagrams as the pictorial representation of relationship between sets
 Practical Problems based on Venn Diagrams

2.7 
Operations on sets 
 Perform operations on sets to solve practical problems

 Operations on sets include
i) Union of sets
ii) Intersection of sets
iii) Difference of sets
iv) Complement of a set
v) De Morgan’s Laws

Relations 
2.8 
Ordered pairs
Cartesian product of two sets 
 Explain the significance of specific arrangement of elements in a pair
 Write Cartesian product of two sets
 Find the number of elements in a Cartesian product of two sets

 Ordered pair, order of elements in an ordered pair and equality of ordered pairs
 Cartesian product of two nonempty sets

2.9 
Relations 
 Express relation as a subset of Cartesian product
 Find domain and range of a relation

 Definition of Relation, examples pertaining to relations in the real number system

Sequences and Series 
2.11 
Sequence and Series 
 Differentiate between sequence and series

 Sequence:𝑎_{1},𝑎_{2},𝑎_{3},…,𝑎_{𝑛}
 Series: 𝑎_{1}+𝑎_{2}+𝑎_{3}+⋯+𝑎_{𝑛}

2.12 
Arithmetic Progression 
 Identify Arithmetic Progression (AP)
 Establish the formulae of finding 𝑛^{𝑡ℎ}term and sum of n terms
 Solve application problems based on AP
 Find arithmetic mean (AM) of two positive numbers

 General term of AP:
𝑡_{𝑛}=𝑎+(𝑛−1)𝑑
 Sum of n terms of AP :
S_{n}=$$\frac{n}{2}[2a+(n1)d]$$
AM of 𝑎 𝑎𝑛𝑑 𝑏=$$\frac{a+b}{2}$$

2.13 
Geometric Progression 
 Identify Geometric Progression (GP)
 Derive the 𝑛^{𝑡ℎ}term and sum of n terms of a given GP
 Solve problems based on applications of GP
 Find geometric mean (GM) of two positive numbers
 Solve problems based on relation between AM and GM

 General term of GP:
𝑡_{𝑛}= 𝑎𝑟^{𝑛−1}
 Sum of n terms of a GP:
S_{n}=$$\frac{a(r^{n1})}{r1}$$
 Sum of infinite term of GP =$$\frac{a}{1r},$$ where −1 < 𝑟 < 1
 Geometric mean of a and b = $$\sqrt{ab}$$
 For two positive numbers a and b, AM ≥GM i.e., $$\frac{a+b}{2}\ge\sqrt{ab}$$

2.14 
Applications of AP and GP 
 Apply appropriate formulas of AP and GP to solve application problems

Applications based on
 Economy Stimulation
 The Virus spread etc.

Permutations and Combinations 
2.15 
Factorial 
 Define factorial of a number
 Calculate factorial of a number

Definition of factorial: n! = n(n1)(n2)…3.2.1
Usage of factorial in counting principles 
2.16 
Fundamental Principle of Counting 
 Appreciate how to count without counting

Fundamental Principle of Addition
Fundamental Principle of Multiplication 
2.17 
Permutations 
 Define permutation
 Apply the concept of permutation to solve simple problems

Permutation as arrangement of objects in a definite order taken some or all at a time
Theorems under different conditions resulting in $$^{n}\text{P}_r=\frac{n!}{(nr)!}\text{or}\space n^{r}\space\text{or}\\\frac{n!}{n_1!n_2!...n_k!}$$ arrangements 
2.20 
Combinations 
 Define combination
 Differentiate between permutation and combination
 Apply the formula of combination to solve the related problems

The number of combinations of n different objects taken r at a time is given by $$^{n}\text{C}_r=\frac{n!}{r!.(nr)!}$$ Some results on combinations:
^{n}C_{0 }= 1 = ^{n}C_{n}
^{n}C_{a} = ^{n}C_{b} ⇒ a=b or a+ b=n
^{n}C_{r} = ^{n}C_{nr}
^{n}C_{r} + ^{n}C_{r1} = ^{n+1}C_{r}

Unit 3 Mathematical Reasoning 
3.2 
Logical reasoning 
 Solve logical problems involving odd man out, syllogism, blood relation and coding decoding

 Odd man out
 Syllogism
 Blood relations
 Coding Decoding

Unit – 4 Calculus 
4.1 
Functions 
 Identify dependent and independent variables
 Define a function using dependent and independent variable

 Dependent variable and independent variable
 Function as a rule or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)

4.2 
Domain and Range of a function 
 Define domain, range and codomain of a given function

 Domain as a set of all values of independent variable
 Codomain as a set of all values of dependent variable
 Range of a function as set of all possible resulting values of dependent variable

4.3 
Types of functions 
 Define various types of functions
 Identify domain, codomain and range of the function

 Following types of functions with definitions and characteristics
Constant function, Identity function, Polynomial function, Rational function, Composite function, Logarithm function, Exponential function, Modulus function, Greatest integer function, Signum function, Algebraic function

4.4 
Graphical representation of functions 
 Representation of function graphically

 Graph of some polynomial functions, Logarithm function, Exponential Function, Modulus function, Greatest integer function, Signum function

4.5 
Concepts of limits and continuity of a function 
 Define limit of a function
 Solve problems based on the algebra of limits
 Define continuity of a function

 Left hand limit, Right hand limit, Limit of a function, Continuity of a function

4.6 
Instantaneous rate of change 
 Define instantaneous rate of change

 The ratio $$\frac{\Delta y}{\Delta x}=\frac{f(x+\Delta x)f(x)}{\Delta x}$$ as instantaneous rate of change, where Δ𝑦 is change in 𝑦 and Δ𝑥 is change in 𝑥 at any instant

4.7 
Differentiation as a process of finding derivative 
 Find the derivative of the functions

 Derivatives of functions (non trigonometric only)

4.8 
Derivatives of algebraic functions using Chain Rule 
 Find the derivative of function of a function

 If 𝑦=𝑓(𝑢) where 𝑢=𝑔(𝑥) then differential coefficient of 𝑦 w.r.t x is $$\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}$$

Unit – 5 Probability 
5.1 
Introduction 
 Appreciate the use of probability in daily life situations

 Probability as quantitative measure of uncertainty
 Use of probability in determining the insurance premium, weather forecasts etc.

5.2 
Random experiment and sample space 
 Define random experiment and sample space with suitable examples

 Sample space as set of all possible outcomes

5.3 
Event 
 Define an event
 Recognize and differentiate different types of events and find their probabilities

 Types of Event:
Impossible and sure event, Independent and dependent event, mutually exclusive and exhaustive event

5.4 
Conditional Probability 
 Define the concept of conditional probability
 Apply reasoning skills to solve problems based on conditional probability

 Conditional Probability of event E given that F has occurred is: $$\text{𝑃(𝐸𝐹)=}\frac{P(E∩F)}{P(F)},\space𝑃(𝐹)≠0$$

5.5 
Total Probability 
 Interpret mathematical information and identify situations when to apply total probability
 Solve problems based on application of total probability

 Total Probability:
Let 𝐸_{1},𝐸_{2} , …,𝐸_{𝑛} be a partition of the sample space S, then probability of an event A associated with S is:$$\text{𝑃(𝐴) =}\Sigma^{n}_{j=1}P(E_j)P(AE_J)$$

5.6 
Bayes’ Theorem 
 State Bayes’ theorem
 Solve practical problems based on Bayes’ Theorem

 Bayes’ Theorem:
If 𝐸1,𝐸2,…,𝐸𝑛 be n non empty events which constitute a partition of a sample space 𝑆 and 𝐴 be any event with non zero probability, then: $$\text{𝑃(𝐸}_𝑖\text{𝐴) =}\frac{𝑃(𝐸_𝑖)𝑃(𝐴𝐸_𝑖)}{\Sigma^{n}_{j=1}𝑃(𝐸_𝑗)𝑃(𝐴𝐸_𝑗)}$$

Unit 6 Descriptive Statistics 
6.4 
Data Interpretation 
Measure of Dispersion 
 Understand meaning of dispersion in a data set
 Differentiate between range, quartile deviation, mean deviation and standard deviation
 Calculate range, quartile deviation, mean deviation and standard deviation for ungrouped and grouped data set
 Choose appropriate measure of dispersion to calculate spread of data

 Mean deviation around mean and median
 Standard deviation and variance
 Examples of different kinds of data helping students to choose and compare different measures of dispersion


Skewness and Kurtosis 
 Define Skewness and Kurtosis using graphical representation of a data set
 Interpret Skewness and Kurtosis of a frequency distribution by plotting the graph
 Calculate coefficient of Skewness and interpret the results

 Examples of symmetrical and asymmetrical data
 Visualization of graphical representation of data using Excel Spreadsheet or any other computer assisted tool

6.5 
Percentile rank and Quartile rank 
 Define Percentile rank and Quartile rank
 Calculate and interpret Percentile and Quartile rank of scores in a given data set

 Emphasis on visualizing, analysing and interpreting percentile and quartile rank scores

6.6 
Correlation 
 Define correlation in values of two data sets
 Calculate Product moment correlation for ungrouped and grouped data
 Calculate Karl Pearson’s coefficient of correlation
 Calculate Spearman’s rank correlation
 Interpret the coefficient of correlation

 Emphasis on application, analysis and interpreting the results of coefficient of correlation using practical examples

Unit – 7 Financial Mathematics 
7.1 
Interest and Interest Rates 
 Define the concept of Interest Rates
 Compare the difference between Nominal Interest Rate, Effective Rate and Real Interest Rate
 Solve Practical applications of interest rate

 Impact of high interest rates and low interest rates on the business

7.2 
Accumulation with simple and compound interest 
 Interpret the concept of simple and compound interest
 Calculate Simple Interest and Compound Interest

 Meaning and significance of simple and compound interest
 Compound interest rates applications on various financial products

7.3 
Simple and compound interest rates with equivalency 
 Explain the meaning, nature and concept of equivalency
 Analyze various examples for understanding annual equivalency rate

 Concept of Equivalency
 Annual Equivalency Rate

7.4 
Effective rate of interest 
 Define with examples the concept of effective rate of interest

 Effective Annual Interest Rate
= (1 + i/n)^{n} – 1
where:
i = Nominal Interest Rate
n = No. of Periods

7.5 
Present value, net present value and future value 
 Interpret the concept of compounding and discounting along with practical applications
 Compute net present value
 Apply net present value in capital budgeting decisions

 Formula for Present Value:
PV = CF/(1 + r)^{n}
Where:
CF = Cash Flow in Future Period
r = Periodic Rate of return or Interest (also called the discount rate or the required rate of return)
n = no. of periods
 Use of PVAF, FVAF tables for practical purposes
 Solve problems based on Application of net present value

7.6 
Annuities, Calculating value of Regular Annuity 
 Explain the concept of Immediate Annuity, Annuity due and Deferred Annuity
 Calculate General Annuity

 Definition, Formulae and Examples

7.7 
Simple applications of regular annuities (upto 3 period) 
 Calculate the future value of regular annuity, annuity due
 Apply the concept of Annuity in real life situations

 Examples of regular annuity:
Mortgage Payment, Car Loan Payments, Leases, Rent Payment, Insurance payouts etc.

7.8 
Tax, calculation of tax, simple applications of tax calculation in Goods and service tax, Income Tax 
 Explain fundamentals of taxation
 Differentiate between Direct and indirect tax
 Define and explain GST
 Calculate GST
 Explain rules under State Goods and Services Tax (SGST) Central Goods and Services Tax (CGST) and Union Territory Goods and Services Tax (UTGST)

 Computation of income tax
Add Income from
Salary, house property, business or profession, capital gain, other sources, etc.
Less deductions
PF, PPF, LIC, Housing loan, FD, NSC etc.
 Assess the Individuals under Income Tax Act
 Formula for GST
Different Tax heads under GST

7.9 
Bills, tariff rates, fixed charge, surcharge, service charge 
 Describe the meaning of bills and its various types
 Analyze the meaning and rules determining tariff rates
 Explain the concept of fixed charge

 Tariff rates its basis of determination
 Concept of fixed charge service charge and their applications in various sectors of Indian economy

7.10 
Calculation and interpretation of electricity bill, water supply bill and other supply bills 
 To interpret and analyze electricity bills, water bills and other supply bills
 Evaluate how to calculate units consumed under electricity bills/water bill

 Components of electricity bill/water supply and other supply bills:
i) overcharging of electricity
ii) water supply bills
iii) units consumed in electricity bills

Unit – 8 Coordinate Geometry 
8.1 
Straight line 
 Find the slope and equation of line in various form
 Find angle between the two lines
 Find the perpendicular from a given point on a line
 Find the distance between two parallel lines

 Gradient of a line
 Equation of line:
Parallel to axes, pointslope form, twopoints form, slope intercept form, intercept form
 Application of the straight line in demand curve related to economics problems

8.2 
Circle 
 Define a circle
 Find different form of equations of a circle
 Solve problems based on applications of circle

 Circle as a locus of a point in a plane
 Equation of a circle in standard form, central form, diameter form and general form

8.3 
Parabola 
 Define parabola and related terms
 Define eccentricity of a parabola
 Derive the equation of parabola

 Parabola as a locus of a point in a plane.
 Equation of a parabola in standard form:
 Focus, Directrix, Axis, Latus rectum, Eccentricity
 Application in parabolic reflector, beam supported by wires at the end of the support, girder of a railway bridge, etc.
