March 3, 2022

The Central Board of Secondary Education (CBSE) has introduced Applied Mathematics as a new academic elective for Class 11 Commerce Stream. Calculus is one of the topics included in the Applied Maths syllabus for class 11.

The calculus syllabus might look similar to regular Maths subject but in Applied Maths, you need to use applications of Mathematical methods for solving problems.

To help you better understand the calculus topic, we have provided the detailed syllabus, weightage, the pattern of questions asked, preparation tips, sample papers, and sample questions in this post.

Calculus is a division of mathematics that allows you to consider changes in values associated with a function. It plays a vital role in taxes, profit, and revenue calculations which are very important for any business.

For example, given a formula that shows how much money you get every day, the calculus will help you understand the related formulas, such as how much money you has in total, and whether you get more or less money than before.

The calculus branch of mathematics is made up of two fields- differential calculus and integral calculus.

Differential calculus divides things into small (different) pieces and tells us how they change from one moment to the next. Also, it plays a valuable role in management and business for decision-making in production (e.g. supply of raw material, wage rates, and taxes).

Integral calculus joins (integrates) the small pieces together, and tells us how much of something is made, overall, by a series of changes.

Calculus finds applications in a lot of daily life problems such as weather prediction, bridge designing, surveying huge data, etc. Calculus is used in many different areas such as physics, astronomy, biology, engineering, economics, medicine, and sociology.

According to the CBSE Class 11 Applied Mathematics Syllabus, there are various topics included in calculus topic and those are as listed below.

Topics In Calculus |

Introducing functions |

Domain and Range of a function |

Types of functions (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function) |

Graphical representation of functions |

Concept of limits and continuity of a function |

Instantaneous rates of change |

Differentiation as a process of finding derivative |

Derivatives of algebraic functions using the Chain rule |

Tangent line and equations of tangents |

The calculus unit holds a weightage of 10 marks out of 80 marks in the **CBSE Class 11 Applied Mathematics** theory exam, which means it holds a 12.5% weightage of Class 11 CBSE Maths Board Paper.

Topic |
No. of Periods |
Total Marks |

Calculus | 30 | 10 |

Calculus is an easy and scoring topic if studied with the correct approach and methodology. You can refer to some of the below-mentioned preparation tips to become more confident, and successful in calculus. Algebra is also an important topic under Maths subject which requires equal preparation.

Develop an effective and time-efficient schedule for practicing problems regularly. Go through with the conceptual meaning of the definition before starting practicing questions of Limits, Derivatives, Integrals, continuity, etc.

- Firstly, understand limits and continuity, then start derivatives as many concepts of previous topics are used in solving questions of the next topic.
- Revise trigonometry and algebra to excel in calculus, you will be able to grasp new concepts of calculus only if your basics of algebra and Trigonometry are clear.
- Try to understand the meaning of the definition, like derivative is just the instantaneous rate of change at a specific time.
- Attempt solved examples and then solve the exercise questions to evaluate your knowledge about the concept.

Calculus is used in almost every branch of fields like social sciences, actuarial sciences, computer sciences, stats, aerospace, economics, business, medicine, demographic shifts, etc, or wherever a problem can be mathematically modeled and an optimal solution is desired.

You can understand the importance of Calculus by reviewing these daily life problems which are solved using calculus concepts like derivatives, integrals, etc.

- A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
- The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x^2+ 36x + 5. Find the marginal revenue, when x = 5, whereby marginal revenue we mean the rate of change of total revenue for the number of items sold at an instant.
- The total cost C(x) in Rupees, associated with the production of x units of an item is given by

C(x) = 0.005 x^3– 0.02 x^2+ 30x + 5000

Find the marginal cost when 3 units are produced, whereby marginal cost means the instantaneous rate of change of total cost at any level of output.

Frequently Asked Questions

What is the difference in the Calculus syllabus of Applied Mathematics and Mathematics?

CBSE class 11th Mathematics Calculus unit holds a weightage of seven marks and comprises of Limits and Derivatives whereas CBSE class 11 Applied Maths Calculus holds a weightage of 10 Marks and comprises of Functions, Limits, Continuity, Derivatives, and tangents.

How to prepare for CBSE Class 11th Applied Mathematics Calculus Unit?

Calculus is a simple and insightful subject if learned with the right approach and technique. First, go through the definitions, then try to solve examples, and after that practice unsolved exercise questions to excel in calculus.

How to download CBSE Class 11 Applied Maths Calculus Study Material PDF?

Candidates can download the CBSE Class 11 Applied Maths Calculus Study Material PDF and applied maths calculus notes class 11 pdf directly by clicking on the download links mentioned above.

How is the CBSE class 11th applied maths calculus useful for commerce students?

Calculus plays a vital role in taxes, profit, and revenue calculations which are very important for Commerce students, For example, given a formula that shows how much money one gets every day, the calculus will help one understand the related formulas, such as how much money one has in total, and whether one gets more or less money than before.

What is the difference between the subjects 'Mathematics' and 'Applied Mathematics'?

Existing mathematics for senior secondary school is a course designed for students to pursue pure mathematics / physical science/engineering at the university level. However, many students want to learn mathematics which is useful for better performance in their chosen subjects; 'Applied Mathematics' is intended for these students and the curriculum focuses on the application of mathematics.

Can a student opt for both ‘Mathematics ’ and ‘Applied Mathematics’?

No. There is only one option, either Mathematics or Applied Mathematics.

Updated On : March 3, 2022

The Central Board of Secondary Education (CBSE) has introduced Applied Mathematics as a new academic elective for Class 11 Commerce Stream. Calculus is one of the topics included in the Applied Maths syllabus for class 11.

The calculus syllabus might look similar to regular Maths subject but in Applied Maths, you need to use applications of Mathematical methods for solving problems.

To help you better understand the calculus topic, we have provided the detailed syllabus, weightage, the pattern of questions asked, preparation tips, sample papers, and sample questions in this post.

Calculus is a division of mathematics that allows you to consider changes in values associated with a function. It plays a vital role in taxes, profit, and revenue calculations which are very important for any business.

For example, given a formula that shows how much money you get every day, the calculus will help you understand the related formulas, such as how much money you has in total, and whether you get more or less money than before.

The calculus branch of mathematics is made up of two fields- differential calculus and integral calculus.

Differential calculus divides things into small (different) pieces and tells us how they change from one moment to the next. Also, it plays a valuable role in management and business for decision-making in production (e.g. supply of raw material, wage rates, and taxes).

Integral calculus joins (integrates) the small pieces together, and tells us how much of something is made, overall, by a series of changes.

Calculus finds applications in a lot of daily life problems such as weather prediction, bridge designing, surveying huge data, etc. Calculus is used in many different areas such as physics, astronomy, biology, engineering, economics, medicine, and sociology.

According to the CBSE Class 11 Applied Mathematics Syllabus, there are various topics included in calculus topic and those are as listed below.

Topics In Calculus |

Introducing functions |

Domain and Range of a function |

Types of functions (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function) |

Graphical representation of functions |

Concept of limits and continuity of a function |

Instantaneous rates of change |

Differentiation as a process of finding derivative |

Derivatives of algebraic functions using the Chain rule |

Tangent line and equations of tangents |

The calculus unit holds a weightage of 10 marks out of 80 marks in the **CBSE Class 11 Applied Mathematics** theory exam, which means it holds a 12.5% weightage of Class 11 CBSE Maths Board Paper.

Topic |
No. of Periods |
Total Marks |

Calculus | 30 | 10 |

Calculus is an easy and scoring topic if studied with the correct approach and methodology. You can refer to some of the below-mentioned preparation tips to become more confident, and successful in calculus. Algebra is also an important topic under Maths subject which requires equal preparation.

Develop an effective and time-efficient schedule for practicing problems regularly. Go through with the conceptual meaning of the definition before starting practicing questions of Limits, Derivatives, Integrals, continuity, etc.

- Firstly, understand limits and continuity, then start derivatives as many concepts of previous topics are used in solving questions of the next topic.
- Revise trigonometry and algebra to excel in calculus, you will be able to grasp new concepts of calculus only if your basics of algebra and Trigonometry are clear.
- Try to understand the meaning of the definition, like derivative is just the instantaneous rate of change at a specific time.
- Attempt solved examples and then solve the exercise questions to evaluate your knowledge about the concept.

Calculus is used in almost every branch of fields like social sciences, actuarial sciences, computer sciences, stats, aerospace, economics, business, medicine, demographic shifts, etc, or wherever a problem can be mathematically modeled and an optimal solution is desired.

You can understand the importance of Calculus by reviewing these daily life problems which are solved using calculus concepts like derivatives, integrals, etc.

- A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
- The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x^2+ 36x + 5. Find the marginal revenue, when x = 5, whereby marginal revenue we mean the rate of change of total revenue for the number of items sold at an instant.
- The total cost C(x) in Rupees, associated with the production of x units of an item is given by

C(x) = 0.005 x^3– 0.02 x^2+ 30x + 5000

Find the marginal cost when 3 units are produced, whereby marginal cost means the instantaneous rate of change of total cost at any level of output.

Frequently Asked Questions

What is the difference in the Calculus syllabus of Applied Mathematics and Mathematics?

CBSE class 11th Mathematics Calculus unit holds a weightage of seven marks and comprises of Limits and Derivatives whereas CBSE class 11 Applied Maths Calculus holds a weightage of 10 Marks and comprises of Functions, Limits, Continuity, Derivatives, and tangents.

How to prepare for CBSE Class 11th Applied Mathematics Calculus Unit?

Calculus is a simple and insightful subject if learned with the right approach and technique. First, go through the definitions, then try to solve examples, and after that practice unsolved exercise questions to excel in calculus.

How to download CBSE Class 11 Applied Maths Calculus Study Material PDF?

Candidates can download the CBSE Class 11 Applied Maths Calculus Study Material PDF and applied maths calculus notes class 11 pdf directly by clicking on the download links mentioned above.

How is the CBSE class 11th applied maths calculus useful for commerce students?

Calculus plays a vital role in taxes, profit, and revenue calculations which are very important for Commerce students, For example, given a formula that shows how much money one gets every day, the calculus will help one understand the related formulas, such as how much money one has in total, and whether one gets more or less money than before.

What is the difference between the subjects 'Mathematics' and 'Applied Mathematics'?

Existing mathematics for senior secondary school is a course designed for students to pursue pure mathematics / physical science/engineering at the university level. However, many students want to learn mathematics which is useful for better performance in their chosen subjects; 'Applied Mathematics' is intended for these students and the curriculum focuses on the application of mathematics.

Can a student opt for both ‘Mathematics ’ and ‘Applied Mathematics’?

No. There is only one option, either Mathematics or Applied Mathematics.