Hello,

The UP Board Class 12 Mathematics syllabus is structured into six units, each covering specific topics. Here's a breakdown:

1. Relations and Functions(10 Marks):

• Relations and Functions: Types of relations—reflexive, symmetric, transitive, and equivalence relations.
• Inverse Trigonometric Functions: Definition, range, domain, and properties.

2. Algebra(15 Marks):

• Matrices: Concept, notation, equality, types (zero, identity, symmetric, skew-symmetric), and operations (addition, multiplication).
• Determinants: Properties, minors, cofactors, applications, and inverse of matrices.

3. Calculus (44 Marks):

• Continuity and Differentiability: Differentiation of composite functions, inverse trigonometric functions, and implicit functions.
• Applications of Derivatives: Rate of change, tangents, normals, maxima, and minima.
• Integrals: Integration as the inverse of differentiation, methods of integration, and applications in finding areas.
• Differential Equations: Formation, order, degree, and solutions of differential equations.

4. Vectors and Three-Dimensional Geometry (18 Marks):

• Vectors: Magnitude, direction, types, addition, scalar multiplication, and dot and cross products.
• Three-Dimensional Geometry: Direction cosines/ratios, equations of lines and planes, and angles between them.

5. Linear Programming (5 Marks):

• Linear Programming Problems: Formulation and graphical solutions.

6. Probability (8 Marks):

• Conditional Probability: Multiplication rule, independent events, Bayes' theorem.
• Random Variables: Probability distributions, mean, variance, and binomial distribution.