| UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS |
| Numbers & Quantification |
| 1.1 | Numbers in Indian Knowledge System and Binary Numbers | - Introduction to Numbers in Indian Knowledge System
- Conversion of decimal numbers to binary system and vice-versa and its applications.
| Students will be able to - Gain acquaintance with traditional way of expressing numbers
- Understand the relation between decimal and binary number system.
- Able to convert from one system to another.
- Understand the application of Binary number system in programming, coding, machine learning etc.
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| 1.2 | Indices, Logarithm and Antilogarithm | - Indices and its properties
- Common and Natural logarithm
- Laws of logarithms
- Logarithm and exponential as inverse operations
- Procedure of finding logarithm and antilogarithms of given number
- Applications of logarithms
| Students will be able to - Apply rules of indices
- define logarithms and antilogarithms as inverse operations
- distinguish between common logarithms and natural logarithms
- apply logarithmic and antilogarithmic techniques to simplify complex calculations, and solve practical problems
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| Numbers in day-to-day Life |
| 1.3 | Clocks | - Evaluate the angular value of a minute
- Measure of angle formed between two hands of clock at given time
- Calculation of the time for which hands of clock meet
| Students will be able to - Calculate the angular displacement of hour and minute hands
- Find the exact time when clock hands coincide, are opposite, or form a specific angle
- Understand the practical utility of calendar
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| 1.4 | Calendar | - Odd days in a month/ year/ century
- Decode the day for the given date
| Students will be able to - Calculate odd days in any given month, year, or century
- Find the day of the week for any given date
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| 1.5 | Time and Work | - Relationship between work and time
- Comparison of the work done by the individual / group w.r.t. time
| Students will be able to - Solve time-work problems
- Represent time-work relationship graphically
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| 1.6 | Speed, Distance and Time | - The time taken/ distance covered from the given data.
| Students will be able to - Represent distance-time relationship graphically
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| 1.7 | Seating arrangement | - Creation of seating plan/ draft as per given conditions (Linear/circular).
- Locating the position of a person in a seating arrangement.
| Students will be able to - Design and create seating plans in linear and circular arrangements
- Determine the exact position of any person in a seating arrangement by analysing the given conditions and applying logical reasoning
- Apply seating arrangement concepts to real-life situations
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| UNIT – 2 ALGEBRA |
| Sets |
| 2.1 | Introduction to Sets – Sets and their representation | - Set as well-defined collection of objects.
- Representation of a set in Roster form and Set builder form
- Different types of sets on the basis of number of elements in the set
- Differentiate between equal set and equivalent set
| Students will be able to - understand the systematic development of set theory.
- represent sets accurately using both roster form and set-builder form
- differentiate between the two methods of expressing the same set.
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| 2.2 | Subsets, Intervals as subsets | - Subsets
- Power set and its elements
- Universal Set
- Subset of real numbers as intervals
| Students will be able to - list all possible subsets of a given set, calculate the total number of subsets
- justify why the empty set is a subset of every set through logical reasoning.
- define power sets, construct the power set of a given set by identifying all its subsets
- Get an idea about the special sets i.e., intervals which have wide utility in the study of analysis.
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| 2.3 | Venn Diagrams and Operations on Sets | - Concept of Venn diagram to understand the relationship between sets
- Problems using Venn diagram
- Operations on sets
| Students will be able to - Use set operations to solve problems in various fields, such as probability, and data analysis.
- Develop problem-solving skills using set theory and Venn diagrams.
- Perform operations on sets to solve practical problems
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| Relations |
| 2.4 | Ordered pairs
Cartesian product of two sets | - Significance of specific arrangement of elements in a pair
- Cartesian product of two sets
| Students will be able to - Understand the concept of ordered pairs
- Find the Cartesian product of two finite sets
- Calculate the number of elements in a Cartesian product
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| 2.5 | Relations | - Expressing relation as a subset of Cartesian product
- Domain and range of a relation
| Students will be able to - Identify and express relations as subsets of Cartesian products
- Determine the domain and range of any relation
- Create and analyse custom relations from everyday situations
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| Mathematical Logic |
| 2.6 | Mathematical Logic | - Logical problems involving odd man out, syllogism, blood relation and coding-decoding
| Students will be able to - Identify patterns and solve odd man out problems
- Draw valid conclusions using syllogism
- Decode blood relations and solve coding-decoding problems
- Apply logical reasoning skills to real-life decision-making situations
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| Sequences and Series |
| 2.7 | Sequence and Series | - Differentiate between sequence and series
| Students will be able to - Distinguish between sequences and series
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| 2.8 | Arithmetic Progression | - Arithmetic mean (AM) of two positive numbers
| Students will be able to - Calculate and apply arithmetic mean (AM) of two positive numbers to find average values in real-life situations
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| 2.9 | Geometric Progression | - Introduction of Geometric Progression (GP)
- n th term of a GP
- sum of n terms and sum of infinite terms of a GP
- Problems based on applications of GP
- Geometric mean (GM) of two positive numbers
- Relation between AM and GM and related problems
- Application problems based on AP and GP
| Students will be able to - Identify and construct geometric progressions
- Calculate geometric mean (GM) of two positive numbers
- Analyse and prove the AM-GM inequality relationship
- Apply formulas of arithmetic and geometric progressions strategically to solve real-world problems
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| UNIT – 3 CALCULUS |
| Functions |
| 3.1 | Functions and their graphs | - Dependent and independent variables
- Definition of function using dependent and independent variable
- Domain, range and co-domain of a given function
- Types of functions
- Graphical representation of function
| Students will be able to - Define dependent and independent variables
- Define and differentiate between domain, co-domain, and range of functions
- Classify and define various types of functions
- Determ
- ine domain, co-domain, and range of given functions
- Represent functions graphically on coordinate planes
- Apply function concepts to solve real-life problems involving mapping relationships like student enrollments systems, profit-loss calculations, and designing input-output models for business.
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| Limits, Continuity and Derivatives |
| 3.2 | Limits and continuity of functions | - Limit of a function
- Continuity of a function
| Students will be able to - Define and understand the concept of limit of a function by analysing the behaviour of functions.
- Solve problems based on the algebra of limits.
- Define continuity of a function at a point and over an interval
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| 3.3 | Differentiation | - Instantaneous rate of change
- Finding the derivative of the functions
| Students will be able to - Define the derivative of a function and relate it to the slope of the tangent to a curve.
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| 3.4 | Algebra of derivatives | - Differentiation of addition, subtraction, multiplication and division of two or more functions
- Differentiation of a function of a function
| Students will be able to - state and apply the fundamental rules of differentiation for sum, difference, product, and quotient of two or more functions
- understand the chain rule as the method for differentiating composite functions.
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| UNIT – 4 PERMUTATIONS & COMBINATIONS & PROBABILITY |
| Combinatorics |
| 4.1 | Combinatorics | - Factorial of a number
- Fundamental Principle of Counting
- Concept of Permutation
- Simple problems based on permutations
| Students will be able to - Understand and calculate factorials of numbers
- Appreciate how to count without counting
- Define permutation and apply the concept in problem solving
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| | - Define combination
- Difference between permutation and combination
- Problems based on Combinations
| - Define combination and differentiate it from permutation
- Apply permutation and combination formulas strategically
- Model complex counting situations using permutation and combination concepts
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| Probability |
| 4.2 | Probability | - Random experiment and sample space with suitable examples
- Event and its Types
- Concept of Probability
- Problems based on calculating probabilities in real life situations
- Concept of conditional probability
| Students will be able to - Define random experiment and sample space with suitable examples
- Recognize and differentiate different types of events and find their probabilities
- Appreciate the use of probability in daily life situations
- Apply reasoning skills to solve problems based on conditional probability
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| UNIT-5 DESCRIPTIVE STATISTICS |
| Measures of Dispersion and Percentiles |
| 6.1 | Measures of Dispersion | - Meaning of dispersion in a data set
- Range, mean deviation, standard deviation and variance
| Students will be able to - Understand the meaning of dispersion in a data set
- Differentiate between range, mean deviation and standard deviation
- Calculate range, range standard deviation and variance, and standard deviation for ungrouped and grouped data set
- Choose appropriate measure of dispersion to calculate spread of data
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| 6.2 | Percentiles | - Concept of Percentile rank
- Calculate and interpret Percentile rank of scores in a given ungrouped data set.
| Students will be able to - Calculate, analyze and interpret Percentile rank of scores in a given ungrouped data set.
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| Correlation |
| 6.3 | Correlation | - Concept of Correlation
- Karl Pearson’s coefficient of Correlation for ungrouped data
- Spearman’s Rank Correlation for ungrouped data
| Students will be able to - Analyze relationships between variables by calculating and interpreting Karl Pearson's coefficient of correlation and Spearman's rank correlation coefficient for ungrouped data.
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| Regression |
| 6.4 | Regression | - Concept of Regression analysis
- Dependent and independent variables Independent variables
- Regression Coefficients
- Regression Equations
- Properties of Regression Equations
| Students will be able to - Distinguish between correlation and regression analysis.
- Compute regression coefficients.
- Solve real-world problems by selecting and applying appropriate correlation or regression techniques.
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| UNIT – 6 FINANCIAL MATHEMATICS |
| Interests and Annuities |
| 6.1 | Interest and Interest Rates | - Concept of Interest Rates
- Comparison of the difference between Nominal Interest Rate, Effective Rate and Real Interest Rate
- Practical applications of interest rate w.r.t simple and compound interest
- Concept of effective rate of interest
| Students will be able to - Understand the concept of interest rates
- Differentiate between nominal interest rate, effective rate, and real interest rate
- Calculate and compare simple and compound interest
- Apply interest rate concepts to solve real-life financial problems
- Define and explain the concept of effective rate of interest
- Analyze and evaluate financial products and investment schemes
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| 6.2 | Annuities | - Meaning of Immediate Annuity, Annuity due and Deferred Annuity
- Future and present value of ordinary annuity, annuity due (up to 3 period)
- Concept of Annuity in real life situations
| Students will be able to - Understand and differentiate between immediate annuity, annuity due, and deferred annuity
- Calculate the future and present value of regular annuity and annuity due
- Apply annuity concepts to real-life financial situations
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| Tax and Utility Bills |
| 6.3 | Taxes and Utility Bills | - Concept of Income tax and GST w.r.t. tax new guidelines
- Utility bills and its various types – Electricity, Water and PNG Bills
| Students will be able to - Understand the concept of income tax and GST
- Calculate income tax and GST liabilities using applicable tax brackets
- Analyse and calculate types of utility bills – Electricity and Water Bills
- Apply taxation and utility billing concepts to real-life situations.
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| UNIT – 7 COORDINATE GEOMETRY |
| Straight Lines |
| 7.1 | Straight lines | - Concept of slope of a line
- Various forms of equation of line
| Students will be able to - Understand the gradient as the measure of steepness and calculate it using coordinates
- Derive and apply various algebraic forms to represent lines in a Cartesian plane.
- Apply linear equations to model real- world scenarios like demand and supply curves in economics.
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| Circles and Parabola |
| 7.2 | Circles and Parabola | - Determination of equations of circle and parabola as a locus of a point in a plane under certain conditions
- Different form of equations of a circle
- Solve problems based on applications of circle
| Students will be able to - Define circles and parabolas as sets of points satisfying specific geometric conditions in a plane.
- Formulate and solve equations of circles in standard, central, diameter, and general forms.
- Identify the properties of a parabola and express its standard form equation based on its focus and directrix.
- Utilize the properties of circles to solve practical and coordinate-based mathematical problems.
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