# Mathematics and Statistics 12th Board Exam HSC Commerce: Marketing and Salesmanship Maharashtra State Board Topics and Syllabus

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

## Syllabus

1 Mathematical Logic
• Statements
• Logical Connectives
• Statement patterns and logical equivalence
• Algebra of statements
• Venn diagrams
1.1 Mathematical Logic
1.2 Matrices
• Determinant of a Matrix
• Introduction
• Meaning
• Definition
• Types of Matrices
• Types of Matrices:
1. Column matrix
2. Row matrix
3. Square matrix
4. Diagonal matrix
5. Scalar matrix
6. Identity matrix
7. Zero matrix
• Algebra of Matrices
• Transpose of a Matrix
• Symmetric Matrix
• Skew-Symmetric Matrix
• Equality 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
1.4 Applications of Derivatives
1.5 Integration
• 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
1. 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
2. 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
3. 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),
1.6 Definite Integration
• 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
1. int_a^a f(x) dx = 0
2. int_a^b f(x) dx = - int_b^a f(x) dx
3. int_a^b f(x) dx = int_a^b f(t) dt
4. 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]
5. int_a^b f(x) dx = int_a^b f(a + b - x) dx
6. int_0^a f(x) dx = int_0^a f(a - x) dx
7. int_0^(2a) f(x) dx = int_0^a f(x) dx + int_0^a f(2a - x) dx
8. 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
1.7 Applications of Definite Integration
2 Matrices
• Definition and types of matrices
• Algebra of matrices
• Inverse of a matrix
• Solution of equations
2.1 Commission, Brokerage and Discount
• 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
2.2 Insurance and Annuity
2.3 Linear Regression
2.4 Time Series
2.5 Index Numbers
2.6 Linear Programming
2.7 Assignment Problem and Sequencing
2.8 Probability Distributions
3 Continuity

Continuity of a function at a point

4 Differentiation
• Derivative of Inverse function
• Logarithmic Differentiation
• Derivative of implicit function
• Derivative of parametric function
• Second order derivative
5 Applications of Derivative
• Increasing and decreasing functions
• Maxima and minima
6 Indefinite Integration
• Definition of an integral
• Integral of standard functions
• Rules of Integration
• Methods of Integration
• Integration by parts
7 Definite Integrals
• Properties of Definite Integrals
1. int_a^a f(x) dx = 0
2. int_a^b f(x) dx = - int_b^a f(x) dx
3. int_a^b f(x) dx = int_a^b f(t) dt
4. 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]
5. int_a^b f(x) dx = int_a^b f(a + b - x) dx
6. int_0^a f(x) dx = int_0^a f(a - x) dx
7. int_0^(2a) f(x) dx = int_0^a f(x) dx + int_0^a f(2a - x) dx
8. 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
8 Ratio, Proportion and Partnership

Ratio, proportion and partnership

9 Commission, Brokerage and Discount
• Commission and Brokerage
• Discount
10 Insurance and Annuity

Insurance and Annuity

11 Demography
• Introduction, Definition
• Uses of vital statistics
• Measurements of Mortality
• Life tables
12 Bivariate Data and Correlation
• Bivariate frequency distribution
• Karl Pearson’s coefficient of correlation
• Rank correlation
13 Regression Analysis Introduction
• Equation of line of regression
• Regression coefficients and their properties
14 Random Variable and 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
15 Management Mathematics
• Inequations
• Linear Programming Problem
• Assignment Problem
• Sequencing