March 3, 2022

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.

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 |

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:

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).

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.

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).

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

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

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.

**x****2****+1****x****2****+3x+1**** =1-(****3x+1****x****2****+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

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.

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

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.

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

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

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.

- 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.

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.

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 |

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/ |

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.

Frequently Asked Questions

What is the question paper pattern for ISC Class 12 Maths Syllabus 2020-21?

The ISC Class 12 Maths Syllabus 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 holds a weightage of 65 marks and consists of six questions. Candidates will be required to attempt all questions.

Candidates will have a choice of attempting questions from either Section B or Section C. Section B / C holds a weightage of 15 Marks.Candidates will be required to attempt all questions EITHER from Section B or Section C.

Is it possible to drop Mathematics in class 12th, if a student is having six subjects in ICSE Board. If yes, what is the procedure?

Yes, it's possible to drop mathematics. Please approach the Head of your School about your request. The Head of the School will then inform the Council that you wish to drop a subject and the reason for doing so. Please note, for the ISC Examination, you have to opt for a minimum of four subjects of which English is compulsory. Please note that the students are however advised to study a minimum of five subjects (English plus four subjects).

What would be more difficult, CBSE Maths Examination or ICSE Maths Examination?

Students do have the impression that ICSE is difficult as opposed to CBSE, It is not true, though. The CBSE syllabus focuses mostly on application-based topics related to competitive exams, whereas the ICSE syllabus is more detailed. Well, all the board tests students ' experience and practice of topics in their way. According to experts, certain topics are taught in a more detailed manner by the ICSE commission. CBSE 12th commerce maths syllabus is structured with an emphasis on competitive test preparations and contains NCERT textbooks which are highly useful in this respect.

Which are the best books to learn Class 12 Maths Syllabus?

The best books for Maths class 12 for the CBSE board are recommended by NCERT, and for the ICSE board, the books are based on the recommendations of ISC and as suggested by your school.

How are sample papers useful in preparing for the Maths Class 12 Board exam?

Sample papers are a perfect tool for exam planning. This lets students assess their readiness for the tests. It also serves to maintain ample preparation and successful revision. The class 12th maths syllabus is vast and, therefore, a comprehensive practice is required. The more you train, the more likely you are to perform well in the board test.

How many chapters/Units are there in ICSE class 12th Maths Syllabus?

There are a total of 10 units in maths class 12 ISC syllabus for the academic session 2020-2021.

Is ISC Class 12 maths Syllabus same for Commerce and Science Students?

Yes, Both the streams follow the same ISC Class 12 Maths Syllabus prescribed by CISCE board.

What are the benefits of taking Maths with Commerce in ICSE Board?

Pursuing Commerce with maths opens up a plethora of graduation course options after 10+2.

Some of them are B.Sc Maths, B.Sc Statistics, B.Sc Honours courses, etc. Pursuing mathematics also helps students prepare for professional courses like CA,CS, etc.

What are the career opportunities after completing 10+2 with Mathematics?

There are a multitude of career opportunities available for both commerce with maths students and PCM/PCMB stream students.

Some of the Career opportunities after studying maths in class 12th are listed below:

accountant

computer programmer

engineering – all fields

investment manager

government research and laboratories

theoretical mathematician

mathematician

numerical analyst

statistician

teacher

market researcher

Which one is better for preparing class 12 ISC maths syllabus 2020, Sample paper, or previous year papers?

Students who aspire to score high marks in their board examination must attempt both sample papers and previous year papers. Sample papers give a summary of the most recent exam trend and question paper type, while the previous year's question papers help to explain the critical topics most likely to be addressed.

Updated On : March 3, 2022

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.

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 |

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:

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).

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.

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).

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

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

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.

**x****2****+1****x****2****+3x+1**** =1-(****3x+1****x****2****+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

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.

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

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.

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

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

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.

- 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.

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.

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 |

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/ |

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.

Frequently Asked Questions

What is the question paper pattern for ISC Class 12 Maths Syllabus 2020-21?

The ISC Class 12 Maths Syllabus 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 holds a weightage of 65 marks and consists of six questions. Candidates will be required to attempt all questions.

Candidates will have a choice of attempting questions from either Section B or Section C. Section B / C holds a weightage of 15 Marks.Candidates will be required to attempt all questions EITHER from Section B or Section C.

Is it possible to drop Mathematics in class 12th, if a student is having six subjects in ICSE Board. If yes, what is the procedure?

Yes, it's possible to drop mathematics. Please approach the Head of your School about your request. The Head of the School will then inform the Council that you wish to drop a subject and the reason for doing so. Please note, for the ISC Examination, you have to opt for a minimum of four subjects of which English is compulsory. Please note that the students are however advised to study a minimum of five subjects (English plus four subjects).

What would be more difficult, CBSE Maths Examination or ICSE Maths Examination?

Students do have the impression that ICSE is difficult as opposed to CBSE, It is not true, though. The CBSE syllabus focuses mostly on application-based topics related to competitive exams, whereas the ICSE syllabus is more detailed. Well, all the board tests students ' experience and practice of topics in their way. According to experts, certain topics are taught in a more detailed manner by the ICSE commission. CBSE 12th commerce maths syllabus is structured with an emphasis on competitive test preparations and contains NCERT textbooks which are highly useful in this respect.

Which are the best books to learn Class 12 Maths Syllabus?

The best books for Maths class 12 for the CBSE board are recommended by NCERT, and for the ICSE board, the books are based on the recommendations of ISC and as suggested by your school.

How are sample papers useful in preparing for the Maths Class 12 Board exam?

Sample papers are a perfect tool for exam planning. This lets students assess their readiness for the tests. It also serves to maintain ample preparation and successful revision. The class 12th maths syllabus is vast and, therefore, a comprehensive practice is required. The more you train, the more likely you are to perform well in the board test.

How many chapters/Units are there in ICSE class 12th Maths Syllabus?

There are a total of 10 units in maths class 12 ISC syllabus for the academic session 2020-2021.

Is ISC Class 12 maths Syllabus same for Commerce and Science Students?

Yes, Both the streams follow the same ISC Class 12 Maths Syllabus prescribed by CISCE board.

What are the benefits of taking Maths with Commerce in ICSE Board?

Pursuing Commerce with maths opens up a plethora of graduation course options after 10+2.

Some of them are B.Sc Maths, B.Sc Statistics, B.Sc Honours courses, etc. Pursuing mathematics also helps students prepare for professional courses like CA,CS, etc.

What are the career opportunities after completing 10+2 with Mathematics?

There are a multitude of career opportunities available for both commerce with maths students and PCM/PCMB stream students.

Some of the Career opportunities after studying maths in class 12th are listed below:

accountant

computer programmer

engineering – all fields

investment manager

government research and laboratories

theoretical mathematician

mathematician

numerical analyst

statistician

teacher

market researcher

Which one is better for preparing class 12 ISC maths syllabus 2020, Sample paper, or previous year papers?

Students who aspire to score high marks in their board examination must attempt both sample papers and previous year papers. Sample papers give a summary of the most recent exam trend and question paper type, while the previous year's question papers help to explain the critical topics most likely to be addressed.