# ISC class 12 Maths Syllabus

## ISC Class 12 Maths Syllabus For Semester (1 & 2) 2023-2024

Class 12 is a significant turning point in a student’s academic career because the Board test results determine their career path. Maths is a crucial subject and a substantial element of competitive Examinations, according to the ISC Class 12 Maths Syllabus, which includes several required courses that are an essential part of higher education. As a result, students should read thoroughly and carefully understand the ISC Class 12 Maths Syllabus.

This page will give you a comprehensive overview of the ISC Class 12th Maths Syllabus, including the weightage of each topic, along with some recommended books to provide further assistance.

## ISC Class 12 Maths Syllabus 2023-24 – Semester (1 & 2)

The following is the unit-by-unit marking scheme for the new ISC Class 12th Maths Syllabus:

 S.No Units Weightage Section A – 65 Marks 1. Relations and Functions 10 Marks 2. Algebra 10 Marks 3. Calculus 32 Marks 4. Probability 13 Marks Section B – 15 Marks 5. Vectors 5 Marks 6. Three-Dimensional Geometry 6 Marks 7. Applications of Integrals 4 Marks (OR) Section C – 15 Marks 8. Application of Calculus 5 Marks 9. Linear Regression 6 Marks 10. Linear Programming 4 Marks Total 80 Marks

To compensate for the loss of academic hours throughout this 2023-2024 session, the CISCE has worked with its subject specialists to modify and recreate the ISC Class 12 Maths Syllabus. The curriculum has been shortened while preserving the subject’s fundamental principles and maintaining a logical progression between Classes.

## Access ISC Class 12 Maths Syllabus & Study Materials 2023-24

Many vital areas involving the application of formulas and concepts are built on a firm foundation of Maths. Differentiation, integration, and matrix are among the topics covered in the ISC Class 12 Maths Syllabus. As a one-time measure, CISCE has decided to shorten the ISC Class 12 Maths Syllabus for 2023-2024. The goal is to relieve stress caused by the present health crisis and close learning gaps. The Syllabus enables students to comprehend the course objectives and aids in the optimal planning of the test. Chapters and concepts are included in the Syllabus.

The complete Syllabus for the year 2023-24 session, along with a few other relevant links important for preparation purposes:

ISC Class 12 Maths – Syllabus

ISC Class 12 Maths – Textbooks

ISC Class 12 Maths – Study Notes

ISC Class 12 Maths – Sample papers

ICSE Sample Question Papers

ICSE Revision Notes

ICSE Important Questions

ICSE Question Papers

## ISC Class 12 Maths Paper Pattern

The Maths theoretical test is of 80 marks, while Project Work is of 20 marks. These two sum up the final computations for the Board.

The ISC Maths Syllabus for Class 12 is divided into three sections: A, B, and C.

All candidates must complete Section A as it is compulsory. There are six questions in Section A (65 marks). The candidates must answer all questions. The internal choice will be divided into two two-mark questions, two four-mark questions, and two six-mark questions.

Candidates will be able to choose whether to attempt questions from Section B or Section C. Section B / C (15 marks): Candidates must answer ALL questions from either Section B or Section C. Internally, there will be an option in one two-mark Question and one four-mark Question.

## ISC Class 12 Maths Blueprint 2023-24

The number of different sorts of questions in each part is listed below:

 Section Topics Question Type Marking Number of Questions Total Marks Section A Relation and Functions, Algebra, Calculus, and Probability MCQ & Question with one-liner Answers   Questions with the short answer I   Questions with short answers II   Questions with Long answers 1 mark         2 marks       4 marks       6 marks 15 questions         5 questions       4 questions       4 questions 15 marks         10 marks       16 marks       24 marks Total 65 marks Section B Vectors, Three-dimensional Geometry, and application of integrals MCQ & Question with one-liner Answers   Questions with the short answer I   Questions with short answers II 1 mark         2 marks       4 marks 5 questions         1 question       2 questions 5 marks         2 marks       10 marks Total 15 Marks (OR) Section C Application of Calculus, Linear Programming, and Linear regression MCQ & Question with one-liner Answers   Questions with the short answer I   Questions with short answers II 1 mark         2 marks       4 marks 5 questions         1 question       2 questions 5 marks         2 marks       10 marks Total 15 Marks Total 80 Marks

## Best Books for ISC Class 12 Maths Syllabus

The table below lists the best ISC Class 12 Maths Syllabus Preparation Books recommended by the ICSE Board –

 Author 12th Maths books O.P. Malhotra, S.K. Gupta, Anubhuti Gangal S. Chand’s ISC Maths Book II for Class XII Paperback M.L. Aggarwal Understanding ISC Maths (Vol. I & II) Class- XII Paperback C.B. Gupta S. Chand’s ISC Commerce for Class XII Paperback Arihant Experts All In One ISC Maths Class 12 Paperback R.D Sharma Maths for Class 12 by R D Sharma (set of 2 volumes) R.S. Aggarwal Senior Secondary School Maths for Class 12 Examination Oswaal Oswaal Sample Question Paper Class 12 Maths

## Maths Examination Preparation Tips

Here are a few key pointers to remember as you prepare for your ISC Maths Board Examination:

• First and foremost, review the ISC Class 12 Maths Syllabus and Examination Pattern. Thoroughly study each topic in the books recommended by the school for the ICSE Board.
• Make sure you take notes that incorporate important facts during your study.
• Plan ahead of time for the most challenging and time-consuming long-form questions (5-6 marks) that are often asked from the Calculus or Probability sections. As a result, strive to refine them by practising them regularly.
• Take as many practise tests as possible. Practise until you’ve mastered that section.
• Take the section-by-section Examination after you’ve completed each part to assess how well you’ve prepared and monitor the time as well.

## ISC Mathematics Class 12 Syllabus

The syllabus is divided into three sections: A, B and C. Section A is compulsory for all candidates. You have a choice of attempting questions from either Section B or Section C. There is one paper of three hours duration of 80 marks.

Section A is of 65 marks and Section B or C is of 15 marks.

### 1. Relations and Functions

(i) Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, inverse of a function.

(ii) Inverse Trigonometric Functions

Definition, domain, range, principal value branch. Elementary properties of inverse trigonometric functions.

### 2. Algebra

Matrices and Determinants

(i) Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order upto 3). Invertible matrices and proof of the uniqueness of inverse, if it exists (here all matrices will have real entries).

(ii) Determinants

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

### 3. Calculus

(i) Continuity, Differentiability and Differentiation.

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

(ii) Applications of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

(iii) Integrals

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

(iv) Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree.

Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants. dx/dy + px = q, where p and q are functions of y or constants.

### 4. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable.

### 5. Vectors

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio.

Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

### 6. Three – dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

### 7. Application of Integrals

Application in finding the area bounded by simple curves and coordinate axes. Area enclosed between two curves.

### 8. Application of Calculus

Application of Calculus in Commerce and Economics in the following:

• Cost function,
• average cost,
• marginal cost and its interpretation
• demand function,
• revenue function,
• marginal revenue function and its interpretation,
• Profit function and breakeven point.
• Rough sketching of the following curves: AR, MR, R, C, AC, MC and their mathematical interpretation using the concept of maxima & minima and increasing- decreasing functions.

### 9. Linear Regression

• Lines of regression of x on y and y on x.
• Scatter diagrams
• The method of least squares.
• Lines of best fit.
• Regression coefficient of x on y and y on x.
• bxy × byx = r2
• Identification of regression equations
• Properties of regression lines.
• Estimation of the value of one variable using the value of other variable from appropriate line of regression.

### 10. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).