Class 12 is an important step in a student's academic life because their career depends on the results of the board exam. The ISC Class 12 Syllabus contains several important subjects that are a key part of higher education, from which mathematics is a very important subject and a significant part of competitive examinations. Therefore students should have an idea of the ISC Class 12 Maths Syllabus.
 Having a strong grasp on mathematics often forms the foundation for many essential topics involving the application of formulas and concepts.
 ISC Class 12 Maths Syllabus includes chapters such as differentiation, integration, matrix, among others.
 CISCE has decided to reduce the ISC Class 12 Syllabus for the academic year 20202021 as a onetime measure. The aim is to reduce stress related to the current health emergency and to eliminate learning gaps.
 The syllabus allows the students to understand the objectives of the course and help them plan the test optimally. The syllabus includes chapters and concepts.
This article is intended to provide you with a detailed overview of the class 12th Maths syllabus, weightage of each topic, and the best Books.
ISC Class 12th Mathematics Syllabus (Unitwise)
The Maths theory exam holds a weightage of 80 marks and 20 marks are allotted to Project Work. These two sums up the final calculations for the Board exam. ICSE class 12th Maths syllabus is divided into three sections A, B, and C.
 Section A is compulsory for all candidates. Section A (65 marks) will consist of six questions. Candidates will be required to attempt all questions. The internal choice will be provided in two questions of two marks, two questions of four marks and two questions of six marks each.
 Candidates will have a choice of attempting questions from either Section B or Section C. Section B / C (15 marks), Candidates will be required to attempt all questions EITHER from Section B or Section C. Internal, choice will be provided in one question of two marks and one question of four marks.
The unit wise marking scheme as per the updated ISC Class 12th Maths syllabus is listed below:
S.No 
UNIT 
TOTAL 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 
ISC Class 12 Maths Syllabus 202021
To compensate for the loss of instructional hours during the current 20202021 session, the CISCE has worked with its subject experts to reduce the ISC Class 12 Maths Syllabus at ICSE and ISC level. The syllabus has been reduced, keeping in mind the linear progression across classes, while ensuring that core concepts related to the subject are retained.
 Heads of CISCE affiliated schools have been asked to ensure that the relevant subject teachers at ICSE and ISC level conduct the syllabus strictly on the basis of the sequence of topics set out in the syllabus;
 To facilitate a further reduction in the syllabus, if required, depending on the situation of the pandemic in the country,
Detailed ISC Class 12 Maths Syllabus comprising of units and subunits is mentioned below:
Unit 1. Relations and Functions (Section A)
(i) Types of relations:
reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions, composite functions, the inverse of a function.
 Relations as:
 Relation on a set A
 Identity relation, empty relation, universal relation.
 Types of Relations: reflexive, symmetric, transitive, and equivalence relation.
 Functions:
 Conditions of invertibility.
 Composite functions and invertible functions (algebraic functions only).
(ii) Inverse Trigonometric Functions
Definition, domain, range, principal value branch. Elementary properties of inverse trigonometric functions.
Principal values
sin1x, cos1x, tan1x , etc. and their graphs.
Sin1x=cos11 x;sin1x+cos1x=2 and similar relations for cot1x, tan1x, etc.
sin1x+siny=sin1(x1y2 y1x2)
sin1xsiny=sin1(x1y2 +y1x2)
cos1x+cos1y=cos1(xy1y2 1x2)
cos1xcos1y=cos1(xy+1y2 1x2)
Similarly, tan1x+tan`1y=tan1xy1+xy, xy>1
Formulae for 2sin1x, 2cos1x, 2tan1x, 3tan1x etc, and application of these formulae.
Unit 2. Algebra Matrices and Determinants (Section A)
(i) Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skewsymmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Non Commutativity of multiplication of matrices and existence of nonzero matrices whose product is the zero matrices (restricted to square matrices of order up to 3). Invertible matrices and proof of the uniqueness of inverse, if it exists (Here all matrices will have real entries).
(ii) Determinants
The determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors. Adjoint and inverse of a square matrix. Solving a system of linear equations in two or three variables (having unique solutions) using the inverse of a matrix.
 Types of matrices (m × n; m, n ≤ 3), order; Identity matrix, Diagonal matrix.
 Symmetric, Skew symmetric.
 Operation – addition, subtraction, multiplication of a matrix with scalar, multiplication of two matrices (the compatibility).
 Above =AB(say) but BA is not possible.
 Singular and nonsingular matrices.
 Existence of two nonzero matrices whose product is a zero matrix.
 Inverse
(22, 33)A1= AdjAA
 Martin’s Rule (i.e. using matrices)
a1x+b1y+c1z=d1
a2x+b2y+c2z=d2
a3x+b3y+c3z=d3
Problems based on the above equations.
 Determinants
 Order
 Minors
 Cofactors
 Expansion
 Properties of determinants
 Problems based on the properties of determinants
Unit 3. Calculus (Section A)
(i) Differentiation
The 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. Secondorder derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
 Differentiation
 Derivatives of trigonometric functions
 Derivatives of exponential functions
 Derivatives of logarithmic functions
 Derivatives of inverse trigonometric functions
 Differentiation by means of substitution
 Derivatives of implicit functions and chain rule
 e for composite functions.
 Derivatives of Parametric functions.
 Differentiation of a function with respect to another function e.g. differentiation of Sinx3 with respect to x3
 Logarithmic Differentiation
 Finding dy/dx when y=xxx
 Successive differentiation up to 2nd order
Note: Derivatives of composite functions using the chain rule.
00 form and ∞∞ form
(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 is given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).
 Equation of Tangent and Normal
 Increasing and decreasing functions
 Maxima and minima
 Stationary/turning points
 Absolute maxima/minima
 Local maxima/minima
 First derivatives test and second derivatives test
 Application problems based on maxima and minima
(iii) Integrals
Integration as the 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.
 Indefinite integral
 Integration as the inverse of differentiation
 Antiderivatives of polynomials and functions (ax+b)n, sinx, cosx, sec2x, cosec2x, etc
 Integrals of the type sin2x, cos2x, cos3x, cos4x
 Integration of 1x, ex, etc.
 Integration by substitution
 Integrals of the type f' (x) [f(x)]n, f('x)f(x),
 Integration of tanx, cotx, secx, cosec x
 Integration by parts.
When degree of f (x) ≥ degree of g(x), e.g.
x2+1x2+3x+1 =1(3x+1x2+3x+2)
 Definite Integral
 The fundamental theorem of calculus (without proof)
 Properties of definite integrals.
 Problems based on the following properties of definite integrals are to be covered.
abf(x)dx= abf(t)dt
abf(x)dx= abf(x)dx
abf(x)dx= acf(x)dx+bcf(x)dx, where a<c<b
abf(x)dx= abf(a+bx)dx
0af(x)dx= 0af(ax)dx
aaf(x)dx= 20af(x)dx, if f is an even function
0, if f is an odd function
(iv) Differential Equations
Definition, order, and degree, general, and particular solutions of a differential equation. Formation of differential equations whose general solution is given. The solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of the first order and first degree. Solutions of linear differential equations of the type: dydx +py=q, where p and q are functions of x or constants.
dxdy +px=q, where p and q are functions of y or constants.
 Differential equations, order, and degree
 Formation of differential equations by eliminating arbitrary constant(s)
 The solution of differential equations
 Variable separable
 Homogeneous equations
 Linear form Py Q dx dy + = where P and Q are functions of x only. Similarly, for dx/dy
NOTE 1: Equations reducible to variable separable type are included.
NOTE 2: The secondorder differential equations are excluded.
Unit 4. Probability (Section A)
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem.
 Independent and dependent events conditional events
 Laws of Probability, addition theorem, multiplication theorem, conditional probability
 The theorem of Total Probability
 Bayes theorem
Unit 5. Vectors (Section B)
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, the addition of vectors, multiplication of a vector by a scalar. Definition, Geometrical Interpretation, properties, and application of scalar (dot) product of vectors, vector (cross) product of vectors, the scalar triple product of vectors.
As directed line segments.
 Magnitude and direction of a vector
 Types: equal vectors, unit vectors, zero vectors
 Position vector.  Components of a vector
 Vectors in two and three dimensions. i, j, k as unit vectors along the x, y, and the zaxes; expressing a vector in terms of the unit vectors
 Operations: Sum and Difference of vectors; scalar multiplication of a vector
 Scalar (dot) product of vectors and its geometrical significance
 Cross product  its properties
 area of a triangle, area of the parallelogram, collinear vectors
 Scalar triple product
 The volume of a parallelepiped, coplanarity
NOTE: Proofs of geometrical theorems by using Vector algebra are excluded.
Unit 6. Three  Dimensional Geometry (Section B)
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. The distance of a point from a plane.
 Equation of xaxis, yaxis, zaxis and lines parallel to them
 Equation of xy  plane, yz – plane, zx – plane.  Direction cosines, direction ratios
 The angle between two lines in terms of direction cosines /direction ratios
 Condition for lines to be perpendicular/ parallel
Lines
 Cartesian and vector equations of a line through one and two points
 Coplanar and skew lines
 Conditions for the intersection of two lines
 The distance of a point from a line
Planes
 Cartesian and vector equation of a plane
 Direction ratios of the normal to the plane
 One point form
 Normal form
 Intercept form
 The distance of a point from a plane
 The intersection of the line and plane
 The angle between two planes, a line, and a plane
Unit 7. Application of Integrals (Section B)
Application in finding the area bounded by simple curves and coordinate axes. The area enclosed between two curves.
 Application of definite integrals
 The area bounded by curves, lines, and coordinate axes is required to be covered
 Simple curves: lines, parabolas, and polynomial functions
Unit 8. Application of Calculus (Section C)
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
 increasingdecreasing functions
NOTE: Application involving differentiation, increasing, and decreasing function to be covered.
Unit 9. Linear Regression (Section C)
 Lines of regression of x on y and y on x.
 Lines of best fit.
 The regression coefficient of x on y and y on x.
 bxy byx=r2, 0 bxy byx 1
 Identification of regression equations
 Estimation of the value of one variable using the value of another variable from the appropriate line of regression.
Unit 10. Linear Programming (Section C)
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, the 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 nontrivial constraints).
Introduction, the definition of related terminology such as constraints, objective function, optimization, advantages of linear programming; limitations of linear programming; application areas of linear programming; different types of linear programming (L.P.) problems, the mathematical formulation of L.P problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimum feasible solution.
ISC Class 12 Maths Blueprint 202021
The number of questions of different types in each part is mentioned below:
Section 
Topics 
Question Type 
Marking 
Number of Questions 
Total Marks 
Section A 
Relation and functions, Algebra, Calculus, and Probability 
MCQ & Question with oneliner Answers 
1 marks 
15 questions 
15 marks 
Questions with the short answer I 
2 marks 
5 questions 
10 marks 
Questions with short answer II 
4 marks 
4 questions 
16 marks 
Questions with Long answers 
6 marks 
4 questions 
24 marks 
Total 

65 marks 
Section B 
Vectors, Three dimensional Geometry, and application of integrals 
MCQ & Question with oneliner Answers 
1 marks 
5 questions 
5 marks 
Questions with the short answer I 
2 marks 
1 questions 
2 marks 
Questions with short answer II 
4 marks 
2 questions 
10 marks 
Total 

15 Marks 
OR 
Section C 
Application of Calculus, Linear Programming, and Linear regression 
MCQ & Question with oneliner Answers 
1 marks 
5 questions 
5 marks 
Questions with the short answer I 
2 marks 
1 questions 
2 marks 
Questions with short answer II 
4 marks 
2 questions 
10 marks 
Total 

15 Marks 
Total 

80 Marks 
Best Books for ISC Class 12 Maths Syllabus
The table below shows the best Preparation Books for ISC Class 12 Maths Syllabus prescribed by the ICSE Board.
Author 
12th Maths books 
12th Maths books price 
O.P. Malhotra, S.K. Gupta, Anubhuti Gangal 
S. Chand's ISC Mathematics Book II for Class XII Paperback 
Rs. 1125/ 
M.L. Aggarwal 
Understanding I.S.C. Mathematics (Vol. I & II) Class XII Paperback 
Rs. 895/ 
C.B. Gupta 
S. Chand's ISC Commerce for Class XII Paperback – 
Rs. 630/ 
Arihant Experts 
All In One ISC Mathematics Class 12 Paperback – 
Rs.375/ 
R.D Sharma 
Mathematics for Class 12 by R D Sharma (set of 2 volumes) 
Rs. 580/ 
R.S. Aggarwal 
Senior Secondary School Mathematics for Class 12 Examination 
Rs. 500/ 
Oswaal 
Oswaal Sample Question Paper Class 12 Mathematics 
Rs. 199/ 
Mathematics Board Exam Preparation Tips
Here are a few crucial tips and tricks that will help you prepare for your ISC Maths Board Exam:
 First of all, take a thorough look at the detailed ISC Class 12 Maths Syllabus and exam pattern. Study each topic of the Ncert book thoroughly for CBSE Boards and from books recommended by school for ICSE Board.
 Make sure you make notes which include important points during your study. Those notes will help during the revision period.
 Strategize and then prepare, the long form questions (56 marks), which are the most feared, usually come from the Calculus or Probability section, so try to gain perfection in them by practicing them regularly.
 Try as many mock tests as you can. Practice until you have perfected that part.
 After completing each section, attempt the sectionwise tests to evaluate your preparation.
 Make a list of your mistakes and try to improvise on the same thing.
 Make sure you follow up on your study plan regularly, consistency and perseverance are of the utmost importance to excel in boards.