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 2020-2021 as a one-time 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 (Unit-wise)

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 2020-21

To compensate for the loss of instructional hours during the current 2020-2021 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

sin-1x, cos-1x, tan-1x , etc. and their graphs.

Sin-1x=cos-11 x;sin-1x+cos-1x=2 and similar relations for cot-1x, tan-1x, etc.

sin-1x+sin-y=sin-1(x1-y2 -y1-x2)

sin-1x-sin-y=sin-1(x1-y2 +y1-x2)

cos-1x+cos-1y=cos-1(xy-1-y2 1-x2)

cos-1x-cos-1y=cos-1(xy+1-y2 1-x2)

Similarly, tan-1x+tan`-1y=tan-1x-y1+xy, xy>-1

Formulae for 2sin-1x, 2cos-1x, 2tan-1x, 3tan-1x 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 skew-symmetric 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 non-zero 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, co-factors. 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 non-singular matrices.
• Existence of two non-zero matrices whose product is a zero matrix.
• Inverse

(22, 33)A-1= 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. Second-order 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.

• L' Hospital's theorem.

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 real-life 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
• Anti-derivatives 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+b-x)dx

0af(x)dx= 0af(a-x)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 second-order 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 z-axes; 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 x-axis, y-axis, z-axis 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 break-even point
• increasing-decreasing 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 non-trivial 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 2020-21

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 one-liner 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 one-liner 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 one-liner 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 (5-6 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 section-wise 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.