Maharashtra State Board Syllabus For 12th Board Exam Mathematics and Statistics: Knowing the Syllabus is very important for the students of 12th Board Exam. Shaalaa has also provided a list of topics that every student needs to understand.
The Maharashtra State Board 12th Board Exam Mathematics and Statistics syllabus for the academic year 2023-2024 is based on the Board's guidelines. Students should read the 12th Board Exam Mathematics and Statistics Syllabus to learn about the subject's subjects and subtopics.
Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the Maharashtra State Board 12th Board Exam Mathematics and Statistics Syllabus pdf 2023-2024. They will also receive a complete practical syllabus for 12th Board Exam Mathematics and Statistics in addition to this.
Maharashtra State Board 12th Board Exam Mathematics and Statistics Revised Syllabus
Maharashtra State Board 12th Board Exam Mathematics and Statistics and their Unit wise marks distribution
Maharashtra State Board 12th Board Exam Mathematics and Statistics Course Structure 2023-2024 With Marking Scheme
Syllabus
- Mathematical Logic
- Logical Connective, Simple and Compound Statements
- Concept of Statements
- Conjunction (∧)
- Disjunction (∨)
- Conditional statement (Implication) (→)
- Biconditional (Double implication) (↔) or (⇔)
- Negation (∼)
- Statement Patterns and Logical Equivalence
- Algebra of Statements
- Idempotent law
- Associative law
- Commutative law
- Distributive law
- Identity law
- Complement law
- Involution law
- DeMorgan’s laws
- Venn Diagrams
- Statements
- Logical Connectives
- Statement patterns and logical equivalence
- Algebra of statements
- Venn diagrams
- Truth Value of Statement
- Logical Connective, Simple and Compound Statements
- Concept of Statements
- Conjunction (∧)
- Disjunction (∨)
- Conditional statement (Implication) (→)
- Biconditional (Double implication) (↔) or (⇔)
- Negation (∼)
- Quantifier and Quantified Statements in Logic
- Universal quantifier (∀)
- Existential quantifier (∃)
- Statement Patterns and Logical Equivalence
- Algebra of Statements
- Idempotent law
- Associative law
- Commutative law
- Distributive law
- Identity law
- Complement law
- Involution law
- DeMorgan’s laws
- Venn Diagrams
- Determinant of a Matrix
- Introduction
- Meaning
- Definition
- Types of Matrices
- Types of Matrices:
- Column matrix
- Row matrix
- Square matrix
- Diagonal matrix
- Scalar matrix
- Identity matrix
- Zero matrix
- Algebra of Matrices
- Transpose of a Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Equality of Two matrices
- Addition of Two Matrices
- Scalar Multiplication of a Matrix
- Multiplication of Two Matrices
- Properties of Matrices
- Elementary Transformations
- Interchange of any two rows or any two columns
- Multiplication of the elements of any row or column by a non-zero scalar
- Adding the scalar multiples of all the elements of any row (column) to corresponding elements of any other row (column)
- Inverse of Matrix
- Inverse of a nonsingular matrix by elementary transformation
- Inverse of a square matrix by adjoint method
- Application of Matrices
- Method of Inversion
- Method of Reduction
- Introduction of Derivatives
- Increasing and Decreasing Functions
- Maxima and Minima
- First and Second Derivative test
- Determine critical points of the function
- Find the point(s) of local maxima and local minima and corresponding local maximum and local minimum values
- Find the absolute maximum and absolute minimum value of a function
- Application of Derivatives to Economics
- Integration
- Methods of Integration: Integration by Substitution
- ∫ tan x dx = log | sec x | + C
- ∫ cot x dx = log | sin x | + C
- ∫ sec x dx = log | sec x + tan x | + C
- ∫ cosec x dx = log | cosec x – cot x | + C
- Methods of Integration: Integration by Parts
- `int(u.v) dx = u intv dx - int((du)/(dx)).(intvdx) dx`
- Integral of the type ∫ ex [ f(x) + f'(x)] dx = exf(x) + C
- Integrals of some more types
- `I = int sqrt(x^2 - a^2) dx = x/2 sqrt(x^2 - a^2) - a^2/2 log | x + sqrt(x^2 - a^2 )| + C`
- `I = int sqrt(x^2 - a^2) dx = x/2 sqrt(x^2 - a^2) - a^2/2 log | x + sqrt(x^2 - a^2 )| + C`
- `I = int sqrt(x^2 - a^2) dx = x/2 sqrt(x^2 - a^2) - a^2/2 log | x + sqrt(x^2 - a^2 )| + C`
- Methods of Integration: Integration Using Partial Fractions
No From of the rational function Form of the partial fraction 1 `(px + q )/((x-a)(x-b))`a ≠ b `A/(x-a) + B/(x-b)` 2 `(px+q)/(x-a)^2` `A/(x-a) + B/(x-a)^2` 3 `((px)^2 + qx +r)/((x-a)(x-b)(x-c))` `A/(x-a)+B/(x-b) + C /(x-c)` 4 `((px)^2 + qx + r)/((x-a)^2 (x-b))` ` A/(x-a) + B/(x-a)^2 +C/(x-b)` 5 `((px)^2 + qx +r)/((x-a)(x^2 + bx +c))` `A/(x-a) + (Bx + C)/ (x^2 + bx +c)`,
- Fundamental Theorem of Integral Calculus
If ∫ f(x) dx = g(x) + c, then
`int_a^b f(x) dx = [g(x) + c]_a^b = g(b) - g(a)`.
- Properties of Definite Integrals
- `int_a^a f(x) dx = 0`
- `int_a^b f(x) dx = - int_b^a f(x) dx`
- `int_a^b f(x) dx = int_a^b f(t) dt`
- `int_a^b f(x) dx = int_a^c f(x) dx + int_c^b f(x) dx`
where a < c < b, i.e., c ∈ [a, b] - `int_a^b f(x) dx = int_a^b f(a + b - x) dx`
- `int_0^a f(x) dx = int_0^a f(a - x) dx`
- `int_0^(2a) f(x) dx = int_0^a f(x) dx + int_0^a f(2a - x) dx`
- `int_(-a)^a f(x) dx = 2. int_0^a f(x) dx`, if f(x) even function
= 0, if f(x) is odd function
- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves
- Simple curves: lines, parabolas, polynomial functions
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Methods of Solving First Order, First Degree Differential Equations
- Application of Differential Equations
- Population Growth and Growth of bacteria
- Ratio active Decay
- Newton's Law of Cooling
- Surface Area
- Introduction of Matrices
- Algebra of Matrices
- Transpose of a Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Equality of Two matrices
- Addition of Two Matrices
- Scalar Multiplication of a Matrix
- Multiplication of Two Matrices
- Inverse of Matrix
- Inverse of a nonsingular matrix by elementary transformation
- Inverse of a square matrix by adjoint method
- Solution of Equations
- Definition and types of matrices
- Algebra of matrices
- Inverse of a matrix
- Solution of equations
- Commission and Brokerage Agent
- Principal
- Commission
- Commission Agents
- Broker
- Factor
- Del Credere Agent
- Discount
- Drawer and Drawee
- Date of bill and Face value
- Nominal Due Date and Legal Due Date
- Discounting a Bill
- Banker’s Discount, Cash Value, Banker’s Gain
- Concept of Insurance
Meaning of Insurance
Principles of Insurance :
- utmost good faith
- insurable interest
- indemnity
- contribution
- doctrine of subrogation
- causa proxima
- mitigation of loss
- Fire Insurance
- Accident Insurance
- Marine Insurance
- Annuity
- Terminology of Annuity
- Annuity Due
- Sinking Fund
- Regression
- Evolution of Regression
- Difference between Correlation and Regression
- Two Regression lines
- X on Y => X = a + by
- Y on X => Y = a + bx
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Secular Trend
- Seasonal Variation
- Cyclical Variation
- Irregular Variation
- Mathematical Models
- Additive Model
- Multiplicative Model
- Measurement of Secular Trend
- Method of Freehand Curve ( Graphical Method)
- Method of Moving Averages
- Method of Least Squares
- Index Numbers
- Types of Index Numbers
- Price Index Number
- Quantity Index Number
- Value Index Number
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Weighted Aggregate Method
- Laspeyre's Price Index Number
- Paasche’s Price Index Number
- Dorbish-Bowley’s Price Index Number
- Fisher’s Ideal Price Index Number
- Marshall-Edgeworth’s Price Index Number
- Walsh’s Price Index Number
- Weighted Aggregate Method
- Cost of Living Index Number
Steps in Construction of Cost of Living Index Numbers
- Choice of Base Year
- Choice of Commodities
- Collection of Prices
- Choice of Average
- Choice of Weights
- Purpose of Index Numbers
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
- Introduction of Linear Programming
- Definition of related terminology such as constraints, objective function, optimization.
- Linear Programming Problem (L.P.P.)
- Meaning of Linear Programming Problem
- Mathematical formulation of a linear programming problem
- Familiarize with terms related to Linear Programming Problem
- Mathematical Formulation of Linear Programming Problem
- Assignment Problem
- Definition and formulation
- Solution of assignment problems (Hungarian Method)
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Unbalanced assignment problem
- Maximization Problem
- Restricted assignment problem
- Alternative optimal solutions
- Sequencing Problem
- Types of Sequencing Problem
- Sequencing n jobs on Two Machine
- Sequencing n jobs on three machine
- Finding an Optimal Sequence
- Mean of a Random Variable
- Types of Random Variables
- Discrete random variable
- Continuous random variable
- Probability Mass Function
- Cumulative Distribution Function or Distribution Function
- Cumulative Distribution Function from Probability Mass function
- Probability Mass Function from Cumulative Distribution Function
- Random Variables and Its Probability Distributions
- Probability distribution of a random variable
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Probability density function
- Cumulative distribution function
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
- Continuous Function of Point
Continuous left hand limit
Continuous right hand limit
Continuity of a function at a point
- Derivatives of Implicit Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- The Concept of Derivative
- Derivative of Inverse function
- Logarithmic Differentiation
- Derivative of implicit function
- Derivative of parametric function
- Second order derivative
- Increasing and Decreasing Functions
- Maxima and Minima
- Increasing and decreasing functions
- Stationary Value of a function
- Local and Global (Absolute) Maxima and Minima
- Increasing and decreasing functions
- Maxima and minima
- Indefinite Integration
- Methods of Integration
- Decomposition method
- Decomposition by Partial Fractions
- Method of substitution or change of variable
- Important Results
- Integration by parts
- Bernoulli’s formula for Integration by Parts
- Integrals of the form
- Integration of Rational Algebraic Functions
- Integration by Parts
Integral of the types
`int e^x{f(x)+f^'(x)}dx`
`intsqrt(x^2+a^2)dx, intsqrt(x^2-a^2)dx`
`int (px+q) sqrt(ax^2+bx+c)" "dx`
- Methods of Integration
- Definition of an integral
- Integral of standard functions
- Rules of Integration
- Methods of Integration
- Integration by parts
- Properties of Definite Integrals
- `int_a^a f(x) dx = 0`
- `int_a^b f(x) dx = - int_b^a f(x) dx`
- `int_a^b f(x) dx = int_a^b f(t) dt`
- `int_a^b f(x) dx = int_a^c f(x) dx + int_c^b f(x) dx`
where a < c < b, i.e., c ∈ [a, b] - `int_a^b f(x) dx = int_a^b f(a + b - x) dx`
- `int_0^a f(x) dx = int_0^a f(a - x) dx`
- `int_0^(2a) f(x) dx = int_0^a f(x) dx + int_0^a f(2a - x) dx`
- `int_(-a)^a f(x) dx = 2. int_0^a f(x) dx`, if f(x) even function
= 0, if f(x) is odd function
- Applications of Definite Integrals
- Definite Integral
- Properties
- Applications
Ratio, proportion and partnership
- Commission and Brokerage
- Discount
Insurance and Annuity
- Introduction, Definition
- Uses of vital statistics
- Measurements of Mortality
- Life tables
- Statistics (Entrance Exam)
- Bivariate Frequency Distribution
bivariate data, tabulation of bivariate data
- Bivariate Frequency Distribution
- Rank Correlation
- Spearman’s Rank Correlation Coefficient
- Bivariate frequency distribution
- Karl Pearson’s coefficient of correlation
- Rank correlation
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Regression Coefficient of X on Y and Y on X
bxy × byx = r2, 0 ≤ bxy × byx ≤ 1
- Regression Propertise
- Equation of line of regression
- Regression coefficients and their properties
- Random Variables and Its Probability Distributions
- Probability distribution of a random variable
- Binomial Theorem and Binomial Distribution
- Poisson Distribution
- Normal Distribution
- Probability Distribution of a Discrete Random Variable
- Probability Distribution
- Definition and types of random variables
- Probability Distribution of a Discrete Random Variable
- Probability Distribution of a Continuous Random Variable
- Binomial Theorem
- Binomial Distribution
- Poisson Distribution
- Normal Distribution
- Inequations in Management Mathematics
- Linear Programming Problem in Management Mathematics
- Assignment Problem
- Definition and formulation
- Solution of assignment problems (Hungarian Method)
- Sequencing in Management Mathematics
- Inequations
- Linear Programming Problem
- Assignment Problem
- Sequencing