ISC Class 12 Mathematics Marking Scheme

Do you know what it takes to get admission in the most elite institutions of our country? It’s the 12 board result, doesn’t matter whether you are medical, non-medical, commerce, or art student. Class 12 is the last year of schooling education, and your overall schooling performance is judged based on your 12th exam marks. It won’t be wrong if we call class 12 as the base of your future.

ICSE Class 12 Mathematics Scheme

The two boards ICSE and CBSE are the one, were in, and requires the student to remember a lot. Both CBSE and ICSE have slightly different focus regarding course content. CBSE is extremely focused on Science and Math, but ICSE is more balanced with an equal focus on Language, Arts and Science.

When it comes to Class 12 Mathematics Scheme, it requires a systematic and well-organized preparation. Here we have some useful and effective tips on how to crack Mathematics paper of your final year of schooling and achieve best score.

The Marking Scheme of Mathematics consists of 6 topics and accordingly allotted marks to each in the following way:

Sl no Topics Marks
1 Relations and Functions 10
2 Algebra 13
3 Calculus 44
4 Vector and three-dimensional Geometry 17
5 Linear programming 6
6 Probability 10

As we can see, maximum marks are carried by Calculus, then Geometry and then Algebra. So let’s concentrate more on Calculus first since it seems scoring and important.

Calculus (44 Marks)

Calculus consists of five sections namely:

Continuity and Differentiability

Under Continuity and Differentiability, you need to be clear on concepts like derivatives of composite functions, inverse trigonometric functions and implicit functions.

Applications of Derivatives

Applications of Derivative consist of increasing and decreasing functions, use of derivatives in approximation, maxima and minima and simple problems that illustrate basic principles and understanding of the subject.


Integration is an inverse process of differentiation. Integration of a variety of functions by substitution, by a partial fraction and by parts.

Applications of the Integrals

Applications of integrals cover Applications in finding the area under simple curves, especially lines/circles/parabola/ellipses only in standard form.

Differential Equations

Definition of a differential equation, order and degree, general and particular solutions of a differential equation. For instance:

by/dx + py=q where p and q are functions of x or constants.

Vectors and Three-Dimensional Geometry (17 Marks)

It consists of two sections namely:


It represents Vectors and Scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector.

Three-dimensional Geometry

Three-dimensional geometry consists of direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line.

Algebra (13 Marks)

Algebra also consists of two sections namely:


The matrix is all about notation, order, types of matrices and skew -symmetric matrices. Operation on Matrices: Addition and multiplication.


This involves determinant of a square matrix up to 3X3 matrices, properties of determinants and minor cofactors in finding the area of a triangle.

Relations and functions (10 Marks)

Relations and Functions consist of types of relative: symmetric, transitive and equivalence relations. One to one and onto functions.

Linear programming (6 Marks)

Introduction to linear programming, its terminologies such as constraints, objective functions and Optimization.

Probability (10 Marks)

It consists of conditional probability, multiplication theorem on probability. Bayes’ theorem, Bernoulli trials and Binomial distribution.

After knowing all the marking scheme and distribution of ISC class 12 Mathematics and the concepts and topics, you need to be prepared. Start working from the start and give more importance according to the marks distribution and pattern of the question paper.

Practise This Question

There are 3 apples, 4 mangoes and 1 watermelon available in a fruit shop. What is the ratio of apples to total fruits?