# Maths and Stats HSC Science (General) 12th Standard Board Exam Maharashtra State Board Syllabus 2024-25

## Maharashtra State Board 12th Standard Board Exam Maths and Stats Syllabus - Free PDF Download

Maharashtra State Board Syllabus 2024-25 12th Standard Board Exam: The Maharashtra State Board 12th Standard Board Exam Maths and Stats Syllabus for the examination year 2024-25 has been released by the MSBSHSE, Maharashtra State Board. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2024-25 Maharashtra State Board 12th Standard Board Exam Maths and Stats Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new Maharashtra State Board syllabus to prepare for their annual exam properly.

The detailed Maharashtra State Board 12th Standard Board Exam Maths and Stats Syllabus for 2024-25 is below.

Academic year:

## Maharashtra State Board 12th Standard Board Exam Mathematics and Statistics Revised Syllabus

Maharashtra State Board 12th Standard Board Exam Mathematics and Statistics and their Unit wise marks distribution

## Syllabus

1 Mathematical Logic
1.1 Mathematical Logic
1.2 Matrics
• Elementry Transformations
• 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
• Applications of Determinants and Matrices
• Consistent System
• Inconsistent System
• Solution of a system of linear equations using the inverse of a matrix
1.3 Trigonometric Functions
• Trigonometric Equations and Their Solutions
• Trigonometric equation
• Solution of Trigonometric equation
• Principal Solutions
• The General Solution
• Solutions of Triangle
• Polar co-ordinates
• Relation between the polar co-ordinates and the Cartesian co-ordinates
• Solving a Triangle
• The Sine rule
• The Projection rule
• Applications of the Sine rule, the Cosine rule and the Projection rule
• Inverse Trigonometric Functions
• Introduction of Inverse Trigonometric Functions
1.4 Pair of Straight Lines
• Combined Equation of a Pair Lines
• Homogeneous Equation of Degree Two
• Degree of a term
• Homogeneous Equation
• Angle between lines represented by ax2 + 2hxy + by2 = 0
• General Second Degree Equation in x and y
• The necessary conditions for a general second degree equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
1. abc + 2fgh - af2 - bg2 - ch2 = 0
2. h2 - ab ≥ 0
• Equation of a Line in Space
• Equation of a line through a given point and parallel to a given vector vec b
• Equation of a line passing through two given points
1.5 Vectors
• Representation of Vector
• Magnitude of a Vector
• Vectors and Their Types
• Zero Vector
• Unit Vector
• Co-initial and Co-terminus Vectors
• Equal Vectors
• Negative of a Vector
• Collinear Vectors
• Free Vectors
• Localised Vectors
• Algebra of Vectors
• Addition of Two Vectors
- Parallelogram Law
- Triangle Law of addition of two vectors
• Subtraction of two vectors
• Scalar multiplication of a vector
• Coplaner Vector
• Vector in Two Dimensions (2-D)
• Three Dimensional (3-D) Coordinate System
• Co-ordinates of a point in space
• Co-ordinates of points on co-ordinate axes
• Co-ordinates of points on co-ordinate planes
• Distance of P(x, y, z) from co-ordinate planes
• Distance of any point from origin
• Distance between any two points in space
• Distance of a point P(x, y, z) from coordinate axes
• Components of Vector
• Vector addition using components
• Components of a vector in two dimensions space
• Components of a vector in three-dimensional space
• Position Vector of a Point P(X, Y, Z) in Space
• Component Form of a Position Vector
• Vector Joining Two Points
• Section Formula
• Section formula for internal division
• Midpoint formula
• Section formula for external division
• Scalar Product of Vectors (Dot)
• Finding angle between two vectors
• Projections
• Direction Angles and Direction Cosine
• Direction ratios
• Relation between direction ratios and direction cosines
• Vector Product of Vectors (Cross)
• Angle between two vectors
• Geometrical meaning of vector product
• Scalar Triple Product of Vectors
• Vector Triple Product
• Addition of Vectors
1.6 Line and Plane
• Vector and Cartesian Equations of a Line
• Equation of a line passing through a given point and parallel to given vector
• Equation of a line passing through given two points
• Distance of a Point from a Line
• Introduction of Distance of a Point from a Line
• Distance between two parallel lines
• Distance Between Skew Lines and Parallel Lines
• Distance between skew lines
• Distance between parallel lines
• Equation of a Plane
• Passing through a point and perpendicular to a vector
• Passing through a point and parallel to two vectors
• Passing through three non-collinear points
• In normal form
• Passing through the intersection of two planes
• Angle Between Planes
• Coplanarity of Two Lines
• Distance of a Point from a Plane
1.7 Linear Programming
2 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)
• Matrices
• Inverse by Elementary Transformation
• Elementary Transformation of a Matrix Revision of Cofactor and Minor
• Inverse of a Matrix Existance
• Solving System of Linear Equations in Two Or Three Variables Using Reduction of a Matrix Or Reduction Method
• Determinants
• Adjoint Method
• Algebraic Operations on Matrices
• Addition of Matrices
• Solution of System of Linear Equations by – Inversion Method
2.1 Differentiation
2.2 Applications of Derivatives
• Applications of Derivatives in Geometry
• Derivatives as a Rate Measure
• Velocity
• Acceleration
• Jerk
• Approximations
• Rolle's Theorem
• Lagrange's Mean Value Theorem (LMVT)
• 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
2.3 Indefinite Integration
• Indefinite 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),
2.4 Definite Integration
• Definite Integral as Limit of Sum
• 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).

• Methods of Evaluation and Properties of Definite Integral
2.5 Application of Definite Integration
2.6 Differential Equations
• Differential Equations
• Order and Degree of a Differential Equation
• Formation of Differential Equations
• Formation of Differential equations from Physical Situations
• Formation of Differential Equations from Geometrical Problems
• Methods of Solving First Order, First Degree Differential Equations
• Homogeneous Differential Equations
• Linear Differential Equations
• Application of Differential Equations
• Population Growth and Growth of bacteria
• Ratio active Decay
• Newton's Law of Cooling
• Surface Area
• Solution of a Differential Equation
2.7 Probability Distributions
• Random Variables and Its Probability Distributions
• Probability distribution 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
• Probability Distribution of Discrete Random Variables
• Probability Distribution of a Continuous Random Variable
• Probability density function
• Cumulative distribution function
• Variance of a Random Variable
• Expected Value and Variance of a Random Variable
2.8 Binomial Distribution
3 Trigonometric Functions
• Trigonometric Functions
• Trigonometric equations
• General Solution of Trigonometric Equation of the Type

sinθ, = 0, cosθ = 0, tanθ = 0, sinθ = sinα, cosθ = cosα, tanθ = tanα, sin2 θ = sin2 α, cos2 θ = cos2 α, tan2 θ = tan2 α, acosθ + bsinθ = C

• Hero’s Formula in Trigonometric Functions
• Napier Analogues in Trigonometric Functions
• Solutions of Triangle
• Polar co-ordinates
• Relation between the polar co-ordinates and the Cartesian co-ordinates
• Solving a Triangle
• The Sine rule
• The Projection rule
• Applications of the Sine rule, the Cosine rule and the Projection rule
• Inverse Trigonometric Functions
• Introduction of Inverse Trigonometric Functions
• Inverse Trigonometric Functions - Principal Value Branch
• Graphs of Inverse Trigonometric Functions
• Properties of Inverse Trigonometric Functions

Inverse of Sin, Inverse of cosin, Inverse of tan, Inverse of cot, Inverse of Sec, Inverse of Cosec

4 Pair of Straight Lines
• Pair of Straight Lines
• Pair of Lines Passing Through Origin - Combined Equation
• Pair of Lines Passing Through Origin - Homogenous Equation
• Theorem - the Joint Equation of a Pair of Lines Passing Through Origin and Its Converse
• Condition for Parallel Lines
• Condition for Perpendicular Lines
• Pair of Lines Not Passing Through Origin-combined Equation of Any Two Lines
• Point of Intersection of Two Lines
• Acute Angle Between the Lines

Acute Angle Between the Lines represented by ax2+2hxy+by2=0

5 Circle
• Circle
• Tangent of a Circle - Equation of a Tangent at a Point to Standard Circle
• Tangent of a Circle - Equation of a Tangent at a Point to General Circle
• Condition of tangency

only for line y = mx + c to the circle x2 + y2 = a2

• Tangents to a Circle from a Point Outside the Circle
• Director circle
• Length of Tangent Segments to Circle
• Normal to a Circle - Equation of Normal at a Point
6 Conics
• Conics
• Tangents and normals - equations of tangent and normal at a point

for parabola, ellipse, hyperbola

• Condition of tangency

for parabola, ellipse, hyperbola

• Tangents in terms of slope

for parabola, ellipse, hyperbola

• Tangents from a Point Outside Conics
• Locus of Points from Which Two Tangents Are Mutually Perpendicular
• Properties of Tangents and Normals to Conics

without proof

7 Vectors
• Vector and Cartesian Equations of a Line
• Vectors Revision
• Linear Combination of Vectors
• Condition of collinearity of two vectors
• Conditions of Coplanarity of Three Vectors
• Midpoint Formula for Vector
• Centroid Formula for Vector
• Application of Vectors to Geometry
• Medians of a Triangle Are Concurrent
• Altitudes of a Triangle Are Concurrent
• Angle Bisectors of a Triangle Are Concurrent
• Diagonals of a Parallelogram Bisect Each Other and Converse
• Median of Trapezium is Parallel to the Parallel Sides and Its Length is Half the Sum of Parallel Sides
• Angle Subtended on a Semicircle is Right Angle
• Collinearity and Coplanarity of Vectors
• Section Formula
• Section formula for internal division
• Midpoint formula
• Section formula for external division
• Basic Concepts of Vector Algebra
• Position Vector
• Direction Cosines and Direction Ratios of a Vector
• Scalar Triple Product of Vectors
• Geometrical Interpretation of Scalar Triple Product
8 Three Dimensional Geometry
9 Line
10 Plane
11 Linear Programming Problems
12 Continuity
• Introduction of Continuity
• Definition of Continuity
• Continuity of a Function at a Point

left hand limit, right hand limit

• Condition 1: If f (x) is to be continuous at x = a then f (a) must be defined.
• Condition 2: If f(x) is to be continuous at  x = a then limxa→f (x) must exist.
• Condition 3: If f(x) is to be continuous at  x = a then limxa→f (x) = f (a).
• Defination of Continuity of a Function at a Point
• Discontinuity of a Function
• Types of Discontinuity
• Jump Discontinuity
• Removable Discontinuity
• Infinite Discontinuity
• Continuity in Interval - Definition
• The intermediate value theorem for continuous functions
• Concept of Continuity
• Algebra of Continuous Functions
• Exponential and Logarithmic Functions
• Continuity of Some Standard Functions - Polynomial Function
• Continuity of Some Standard Functions - Rational Function
• Continuity of Some Standard Functions - Trigonometric Function
• Continuity - Problems
13 Differentiation
14 Applications of Derivative
15 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 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),
• 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
• Definite Integral as the Limit of a Sum
• Fundamental Theorem of Calculus

Area function, First fundamental theorem of integral calculus and Second fundamental theorem of integral calculus

• 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
• Evaluation of Definite Integrals by Substitution
• Integration
• Integration by Non-repeated Quadratic Factors
16 Applications of Definite Integral
• Area of the Region Bounded by a Curve and a Line
• Area of the Region Bounded by a Curve & X-axis Between two Ordinates
• Area of the Region Bounded by a Curve & Y-axis Between two Abscissa
• Circle-line, elipse-line, parabola-line
• Area Between Two Curves
• Applications of Integrations
• Volume of Solid of Revolution

volume of solid obtained by revolving the area under the curve about the axis (simple problems)

17 Differential Equation
18 Statistics
• Statistics (Entrance Exam)
• Bivariate Frequency Distribution

bivariate data, tabulation of bivariate data

• Scatter Diagram

(I) a) Perfect positive correlation, b) Positive correlation with high degree, c) Positive correlation with low degree
(II) a) Perfect negative correlation, b) Negative correlation with high degree, c) Negative correlation with low degree
(III) No correlation (Zero correlation)

• Covariance of Ungrouped Data
• Covariance for Bivariate Frequency Distribution
• Karl Pearson’s Coefficient of Correlation
19 Probability Distribution
• Conditional Probability
• Independent Events
• Random Variables and Its Probability Distributions
• Probability distribution of a random variable
• Probability Distribution
• Discrete and Continuous Random Variable
• Probability Mass Function (P.M.F.)
• Cumulative Probability Distribution of a Discrete Random Variable
• Expected Value, Variance and Standard Deviation of a Discrete Random Variable
• Apply arithmetic mean of frequency distribution to find the expected value of a random variable
• Calculate the Variance and S.D. of a random variable
• Probability Density Function (P.D.F.)
• Distribution Function of a Continuous Random Variable
• Probability Distribution of a Discrete Random Variable
20 Bernoulli Trials and Binomial Distribution
• Bernoulli Trials and Binomial Distribution
• Bernoulli Trial
• Conditions for Binomial Distribution
• Calculation of Probabilities
• Normal Distribution (P.D.F)

mean, variance and standard deviation, standard normal variable, simple problems

• Mean of Binomial Distribution (P.M.F.)
• Variance of Binomial Distribution (P.M.F.)
• Standard Deviation of Binomial Distribution (P.M.F.)

Share
Notifications