Introduction
Mathematics is an important subject in the commerce stream, as it helps students develop analytical and problem-solving skills. The curriculum for mathematics in class 12 commerce is more advanced compared to class 10. In class 12, students delve deeper into concepts like calculus, statistics, and financial mathematics.

Difference in Syllabus
- Algebra: In class 12, the algebra syllabus includes topics like matrices, determinants, and inverse trigonometric functions. These topics are not covered in class 10.
- Calculus: Calculus is a major addition to the class 12 syllabus. Students learn about differentiation, integration, and their applications. Class 10 mathematics does not include any calculus topics.
- Probability and Statistics: While class 10 covers basic concepts of probability, class 12 goes into more depth. Students learn about conditional probability, Bayes' theorem, and probability distributions. Statistics topics like correlation and regression are also introduced in class 12.
- Financial Mathematics: Class 12 commerce introduces financial mathematics, which involves concepts like compound interest, annuities, and depreciation. These topics are not covered in class 10.
- Coordinate Geometry: While both class 10 and class 12 cover coordinate geometry, the complexity of topics increases in class 12. Students learn about the equation of a line, circle, parabola, and ellipse.
- Trigonometry: Trigonometry is a common topic in both class 10 and class 12. However, in class 12, students study trigonometric functions, inverse trigonometric functions, and their properties in more detail.

Increased Complexity
Class 12 mathematics is more challenging compared to class 10. The concepts are presented in a more abstract and analytical manner. Students are expected to understand and apply mathematical principles to solve complex problems. The use of formulas and theorems becomes more prevalent in class 12.

Application in Commerce
Mathematics in class 12 commerce is specifically tailored to suit the requirements of commerce students. The syllabus includes topics like financial mathematics, which directly relate to commerce and economics. Students learn how to calculate interest, depreciation, and other financial quantities, which are essential for business and finance.

Conclusion
Mathematics in class 12 commerce builds upon the foundation laid in class 10. The syllabus becomes more advanced, covering topics like calculus, financial mathematics, and probability. The increased complexity of the subject challenges students to think analytically and apply mathematical principles to real-life scenarios. Understanding mathematics is crucial for commerce students as it equips them with the necessary skills for business and finance.