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ISC Class 12 syllabus is a detailed set of content that covers all the topics taught in previous classes in a deeper way, which also makes it more extensive and tougher to cover for some students. The first step for any student to prepare for ISC Board exams is to have a clear understanding of the syllabus.

ISC Syllabus for Class 12 Mathematics is designed by CISCE to provide students with a comprehensive understanding of fundamental mathematical concepts, preparing them for real-world applications and further studies. With a focus on both theoretical principles and practical problem-solving skills, Class 12 ISC Maths Syllabus 2025 aims to develop critical thinking and analytical abilities among students.

Through topics such as Calculus, Algebra, Probability, and Vector, students will explore the beauty and utility of mathematics in various contexts.

Physics and **Mathematics** are among the most difficult subjects and require maximum time for preparation. Since students have to complete the syllabus on time, they can either club it with ISC Class 12 English or ISC Class 12 Hindi using the syllabus.

So download the **ISC Class 12 Mathematics Syllabus PDF** for the 2024-25 session from the link provided below and start preparing for your ISC Maths Board Exam.

**2024-25 Latest Syllabus**

**ISC Class 12 MATHEMATICS 2024-25 SYLLABUS**

Let’s discuss some changes made in the Mathematics ISC 12 Class Syllabus 2024-25, which include some newly added topics as well as some major reductions in the units and chapters. To find out about new changes, look at the table below:

**Section A **

**Determinants (Algebra):**consistency, inconsistency, and number of solutions of the system of linear equations by examples

Note: The conditions for consistency of equations in two and three variables, using matrices are to be covered.

**Calculus:**Derivatives of composite functions using the chain rule**Differential Equations Calculus:**Formation of differential equations by eliminating arbitrary constant(s).

**Three-dimensional Geometry:**coplanar and skew lines, the shortest distance between two lines; Lines (coplanar skew lines); the shortest distance between two lines

**Section B **

**Probability:**variance of a random variable

**Project Work - Paper II**

**Section A**

- Construct a composition table using a binary function addition/multiplication modulo upto 5 and verify the existence of the properties of the binary operation.
- For a given function, give the geometrical interpretation of Mean Value theorems. Explain the significance of closed and open intervals for continuity and differentiability properties of the theorems.
- Explain the geometrical significance of the point of inflexion with examples and illustrate it using graphs.
- Illustrate the concept of definite integral ∫
^{a}_{b }f(x) dx, expressing as the limit of a sum and verify it by actual integration.

**Section B**

- Describe the geometrical interpretation of the scaler triple product and for a given data, find the scaler triple product.

**Section C**

- Using any suitable data, find the minimum cost by applying the concept of Transportation concept.

**Section A **

**Relations and Functions:**sin^{-1}x, cos^{-1}x,tan^{-1}x etc. graphs

**Section B **

**Probability:**variance of a random variable

**Applications of Integrals:**only standard form

**Linear Programming**: Note: Transportation problem is excluded

There will be two papers of Mathematics for Class 12

**Paper I:** Theory (3 hours): 80 marks

**Paper II**: Project Work: 20 marks

This is a written paper and the syllabus is divided into three sections A, B, and C. While Section A is compulsory for all candidates, they still have a choice to attempt questions either from Section B or Section C.

Candidates will have to complete two projects, one from Section A and one from either Section B or Section C. Paper II -Project Work will be evaluated by the subject teacher and a Visiting Examiner appointed locally and approved by CISCE.

**Section A**

1. Using a graph, demonstrate a function which is one-one but not onto.

2. Using a graph demonstrate a function which is invertible.

3. Construct a composition table using a binary function addition/multiplication modulo upto 5 and verify the existence of the properties of binary operation.

4. Draw the graph of y = sin-1 x (or any other inverse trigonometric function), using the graph of y = sin x (or any other relevant trigonometric function). Demonstrate the concept of mirror line (about y = x) and find its domain and range.

5. Explore the principal value of the function sin-1 x (or any other inverse trigonometric function) using a unit circle.

6. Find the derivatives of a determinant of the order of 3 x 3 and verify the same by other methods.

7. Verify the consistency of the system of three linear equations of two variables and verify the same graphically. Give its geometrical interpretation.

8. For a dependent system (non-homogeneous) of three linear equations of three variables, identify an infinite number of solutions.

9. For a given function, give the geometrical interpretation of Mean Value theorems. Explain the significance of closed and open intervals for continuity and differentiability properties of the theorems.

10. Explain the concepts of increasing and decreasing functions, using the geometrical significance of dy/dx. Illustrate with proper examples.

11. Explain the geometrical significance of point of inflexion with examples and illustrate it using graphs.

12. Explain and illustrate (with suitable examples) the concept of local maxima and local minima using graph.

13. Explain and illustrate (with suitable examples) the concept of absolute maxima and absolute minima using graph.

14. Illustrate the concept of definite integral, expressing as the limit of a sum, and verify it by actual integration.

15. Demonstrate application of differential equations to solve a given problem (for example, population increase or decrease, bacteria count in a culture, etc.).

16. Explain the conditional probability, the theorem of total probability, and the concept of Bayes’ theorem with suitable examples.

17. Explain the types of probability distributions and derive mean and variance of binomial probability distribution for a given function.

**Section B**

18. Using vector algebra, find the area of a parallelogram/triangle. Also, derive the area analytically and verify the same.

19. Using Vector algebra, prove the formulae of properties of triangles (sine/cosine rule, etc.)

20. Using Vector algebra, prove the formulae of compound angles, e.g. sin (A + B) = Sin A Cos B + Sin B Cos A, etc.

21. Describe the geometrical interpretation of scalar triple product and for a given data, find the scalar triple product.

22. Find the image of a line with respect to a given plane.

23. Find the distance of a point from a given plane measured parallel to a given line.

24. Find the distance of a point from a line measured parallel to a given plane.

25. Find the area bounded by a parabola and an oblique line.

26. Find the area bounded by a circle and an oblique line.

27. Find the area bounded by an ellipse and an oblique line.

28. Find the area bounded by a circle and a circle.

29. Find the area bounded by a parabola and a parabola.

30. Find the area bounded by a circle and a parabola. (Any other pair of curves which are specified in the syllabus may also be taken.)

**Section C**

31. Draw a rough sketch of Cost (C), Average Cost(AC) and Marginal Cost (MC)

**Or **

Revenue (R), Average Revenue (AR) and Marginal Revenue (MR).

Give their mathematical interpretation using the concept of increasing-decreasing functions and maxima-minima.

32. For a given data, find regression equations by the method of least squares. Also, find angles between regression lines.

33. Draw the scatter diagram for a given data. Use it to draw the lines of best fit and estimate the value of Y when X is given and vice-versa.

34. Using any suitable data, find the minimum cost by applying the concept of Transportation problem.

35. Using any suitable data, find the minimum cost and maximum nutritional value by applying the concept of Diet problem.

36. Using any suitable data, find the Optimum cost in the manufacturing problem by formulating a linear programming problem (LPP).

**NOTE:** *No question paper for Project Work will be set by CISCE and VIVA-VOCE (3 Marks) for each Project is to be conducted only by the Visiting Examiner, and should be based on the Project only*

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