ICSE Class 12 Syllabus for Mathematics

The ISC (Indian School Certificate) Class 12 Mathematics syllabus is designed to provide a thorough understanding of various mathematical concepts, preparing students for higher education and practical applications. Here’s a detailed overview:

ISC Class 12 Mathematics Syllabus

1. Relations and Functions

  • Relations: Definition, types of relations (reflexive, symmetric, transitive, and antisymmetric).
  • Functions: Definition, domain, range, and types of functions (one-to-one, onto, bijective).
  • Inverse of a function: Finding and using inverse functions.
  • Composite functions: Composition of functions and their properties.

2. Algebra

  • Matrices:

    • Definition, types, and operations (addition, subtraction, multiplication).
    • Determinants and their properties.
    • Adjoint and inverse of a matrix.
    • Solution of linear equations using matrices.

  • Determinate:

    • Calculation and properties of determinants.
    • Applications in solving linear systems using determinants.

  • Vectors:

    • Definition, addition, subtraction, and scalar multiplication.
    • Dot product and cross product of vectors.
    • Scalar triple product and its applications.

  • Three-Dimensional Geometry:

    • Coordinates of a point in 3D space.
    • Direction cosines and ratios.
    • Equation of a line and plane in space.
    • Distance between two points, point to plane, and line to plane.

3. Calculus

  • Differentiation:

    • Definition, rules, and applications of differentiation.
    • Derivatives of various functions including polynomial, trigonometric, exponential, and logarithmic functions.
    • Applications in finding maxima and minima of functions.

  • Integration:

    • Indefinite integrals: Basic integration rules, integration by substitution, partial fractions, and by parts.
    • Definite integrals: Fundamental theorem of calculus, properties, and applications.
    • Area under curves and between curves.

  • Differential Equations:

    • Definition and formation of differential equations.
    • Solutions of first-order differential equations: Variable separable, homogeneous, and linear.
    • Applications to growth and decay problems.

4. Differential Equations

  • Formation and Solutions:
    • First-order and higher-order differential equations.
    • Methods of solving differential equations.
    • Applications in various fields such as physics and engineering.

5. Probability

  • Probability Theory:

    • Basic concepts and definitions.
    • Conditional probability and Bayes’ theorem.
    • Random variables and probability distributions.
    • Expected value and variance of random variables.

  • Statistics:

    • Measures of central tendency (mean, median, mode).
    • Measures of dispersion (range, variance, standard deviation).
    • Correlation and regression analysis.

6. Linear Programming

  • Formulation and Solution:
    • Linear programming problems and their graphical solutions.
    • Simplex method and applications.
    • Interpretation of solutions and feasible regions.

7. Mathematical Reasoning

  • Mathematical Induction:
    • Principle of mathematical induction.
    • Proofs and applications of the induction principle.
  • Logical Reasoning:
    • Statements, logical operations, and truth tables.
    • Proofs using logical reasoning and implications.

8. Co-ordinate Geometry

  • Straight Line:

    • Equation of a line, slope, and intercept form.
    • Distance between two points and the angle between two lines.

  • Circle:

    • Equation of a circle and properties.
    • Tangents and normals to a circle.

  • Conic Sections:

    • Parabola, ellipse, and hyperbola: Definitions, equations, and properties.

Practical Work

  • Mathematical Software and Tools:
    • Using software for solving mathematical problems and visualizing concepts.
    • Data analysis and interpretation using mathematical tools.

This syllabus provides a strong foundation in mathematics, emphasizing both theoretical understanding and practical problem-solving skills. It prepares students for various competitive exams and higher studies in fields that require advanced mathematical knowledge.

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