Updated On : September 8, 2023

**Reader's Digest: **Wondering what the term '*Applied Mathematics***' **means? Read this blog to learn the concepts, weightage, syllabus, project topics, prep tips & more!

Gone are the days when mathematics was seen as a core subject with vast abstract equations and theories, mainly serving students from a pure science background.

Recognizing the ever-growing demand for mathematical proficiency in diverse fields, especially Commerce and Social Sciences, the Central Board of Secondary Education (CBSE) has brought a game-changer - the **Applied Mathematics** subject for Class 12.

Launched as an elective in the commerce stream, this subject aims to bridge the gap observed in the existing mathematics syllabus, seemingly falling short in catering to the practical needs of commerce and social science streams.

Here are the points to be discussed:

**Basic Intro of CBSE Class 12 Applied Mathematics:**An introduction to the subject and its significance in the CBSE Class 12 curriculum.**CBSE Applied Mathematics****Class 12****Weightage:**A breakdown of the subject's weightage across different units to help students prioritize their study.**Assessment Plan for CBSE Applied Mathematics 2024:**Examining this subject's evaluation methods and assessment criteria.**Core Maths v/s Applied Maths:**A comparison between traditional core mathematics and applied mathematics, highlighting their distinctive features.**Projects Topics for CBSE Applied Mathematics**: A compilation of engaging project ideas that allow students to apply their mathematical knowledge practically.**CBSE Applied Mathematics Class 12 Preparation Tips:**Practical tips and strategies to excel in CBSE Class 12 Applied Mathematics, including recommended study resources and time management techniques.

CBSE Class 12 Applied Mathematics is a branch of mathematics that deals with mathematical methods and techniques widely used in practical applications. It is introduced at the senior secondary level to equip students with mathematical knowledge and skills that can be applied to various fields and everyday scenarios.

Since this is a new subject, it is evident that everyone wonders **what Applied Mathematics is**. Applied Mathematics, a combination of mathematical science and specialized knowledge, is used to apply mathematical methods in different fields like physics, medicine, biology, engineering, computer science, business, and industry.

Most of the problems require the application of mathematics, i.e., real-time usage of maths. The problems come from subjects like Chemistry, Biology, Physics, etc.

These problems require the application of mathematics and knowledge of various branches of mathematics, like analysis, differential equations, and stochastics, utilizing analytical and numerical methods.

As per the notice, the applied mathematics CBSE class 12 circular helps students explore future career options. It also helps students to reinforce mathematical communication by formulating conjectures, verifying logical arguments, and testing hypotheses.

*Imagine playing a video game where you must build bridges and roads or even predict how much money you'll earn from a virtual lemonade stand. *

*Applied Mathematics is like the magic tool in this game that helps you make these decisions using math! Instead of just learning numbers and formulas, you learn how to use this math in real-life situations. *

According to experts, opting for applied mathematics helps students in their future careers. With the help of the **CBSE Class 12 Commerce Syllabus**, you will get an idea about important topics from the exam point of view and plan your preparation accordingly.

Let us have a look at the table below to know all the topics and weightage of CBSE class 12 applied mathematics:

Unit Name |
No. of Periods |
Marks |

Numbers, Quantification and Numerical Applications | 30 | 11 |

Algebra | 20 | 10 |

Calculus | 50 | 15 |

Probability Distributions | 35 | 10 |

Inferential Statistics | 10 | 05 |

Index Numbers and Time-based data | 30 | 06 |

Financial Mathematics | 50 | 15 |

Linear Programming | 15 | 08 |

Total | 240 | 80 |

Internal Assessment | - | 20 |

Total Marks | - | 100 |

**Explore More: CBSE Class 12 Applied Maths Algebra**

Studying CBSE Class 12 Applied Mathematics is beneficial for several reasons:

**Understanding Mathematical and Statistical Tools**: It helps students understand fundamental mathematical and statistical tools and how they are applied in the fields of commerce, business, finance, economics, and social sciences.**Modelling Real-World Problems**: Applied Mathematics teaches students to translate real-world experiences and problems into mathematical expressions using numerical, algebraic, and graphical representations. This skill is essential for problem-solving in various practical contexts.**Data Analysis and Interpretation**: The course enables students to make sense of data by organizing, representing, interpreting, and analyzing it. They can draw meaningful inferences from real-world situations, which is valuable in decision-making and research.**Logical Reasoning**: Applied Mathematics helps students develop logical reasoning skills essential for problem-solving in both mathematical and real-life scenarios. These skills can be applied to tackle a wide range of challenges.**Mathematical Communication**: It reinforces mathematical communication by encouraging students to formulate conjectures, validate logical arguments, and test hypotheses. This enhances their ability to communicate their findings and reasoning.**Interdisciplinary Connections**: The course fosters connections between Mathematics and other disciplines. This interdisciplinary approach allows students to apply mathematical concepts and techniques to various fields of study, broadening their knowledge and skills.

**Read More: CBSE Class 12 Applied Maths Probability**

The assessment plan for CBSE Applied Mathematics is as follows:

**Total Marks**: The overall assessment of the course is out of 100 marks.**Components**: The assessment plan consists of two main components: External Exam and Internal Assessment.**External Exam**: The external exam will be a written test of 3 hours duration and will consist of 80 marks.**Internal Assessment**: The internal assessment carries a weightage of 20 marks and includes various activities spread throughout the semester or academic year.

- The internal assessment activities encompass projects and practical work, including Excel-based practicals.
- Teachers can select activities from the suggested list of practicals or plan similar activities.
- Teachers are encouraged to use local data sources for data-based practicals to make them more relevant for students.

Refer to the table summarizing the weightage for each area of internal assessment for CBSE Class 12 Applied Mathematics:

Sl. No. | Area and Weightage | Assessment Area | Marks Allocated |
---|---|---|---|

1 | Project Work (10 marks) | Project Work and Record | 5 |

Year-end Presentation/Viva of the Project | 5 | ||

2 | Practical Work (10 marks) | Performance of Practical and Record | 5 |

Year-end Test of Any One Practical | 5 | ||

Total |
20 |
20 |

Applied mathematics involves quantities such as numerical values and units of measurement, and it is used in practical applications in day-to-day life. CBSE applied mathematics is used in the following applications.

- Information Theory
- Engineering
- Game Theory
- Operations Research
- Statistics
- Signal Processing
- Wavelets
- Numerical Analysis
- Cryptography

Here's a table summarizing the key differences between CBSE Class 12 **Core Mathematics and Applied Mathematics**:

Aspect | Core Mathematics (Regular) | Applied Mathematics |
---|---|---|

Nature of the Course | Traditional Mathematics curriculum with a focus on pure mathematical concepts and theory. | Emphasis on applying mathematical concepts and tools to real-world problems in commerce, economics, and social sciences. |

Subject Matter | Algebra, Geometry, Calculus, Probability, Statistics, etc. | Mathematical tools and techniques relevant to business, finance, economics, data analysis, and social sciences. |

Application Focus | Primarily theoretical, with less emphasis on practical applications. | Strong focus on practical applications and problem-solving in real-world scenarios. |

Relevance to Career Paths | Suitable for students pursuing careers in mathematics, engineering, and other technical fields. | Particularly beneficial for students interested in careers in commerce, business, finance, economics, or social sciences. |

Problem-Solving | More abstract and theoretical problem-solving. | Practical problem-solving skills applied to real-world situations. |

Mathematical Communication | Focused on theoretical proofs and mathematical reasoning. | Emphasis on clear communication of mathematical concepts and findings in applied contexts. |

Interdisciplinary Connections | Limited interdisciplinary connections. | Encourages interdisciplinary connections with business, economics, and social sciences. |

Curriculum Content | Traditional mathematics topics without specific application contexts. | Application-oriented topics related to commerce, economics, and social sciences. |

Exam Pattern and Assessment | Typically assesses theoretical knowledge and mathematical rigour. | Includes real-world problem-solving tasks, data analysis, and practical applications in assessments. |

Career Opportunities and Further Study | Provides a strong foundation for technical and mathematical careers. | Equips students with skills relevant to careers in commerce, finance, economics, data analysis, and social sciences. |

**Check Out: CBSE Class 12 Applied Maths Basic Financial with Mathematics**

Here are some topics on practicals for Class 12 CBSE Applied Mathematics topics that you can work on using Excel and other tools:

**i) Finding Maxima/Minima on Excel Graphs:**

- Choose a mathematical function (e.g., quadratic, cubic) and create its graph in Excel.
- Use Excel's tools to find and label the maxima and minima points on the graph.

**ii) Probability and Dice Roll Simulation:**

- Create a simulation in Excel to model the probability of different outcomes when rolling dice.
- Analyze the results and compare them to theoretical probabilities.

**iii) Matrix Multiplication and Inverse:**

- Implement matrix multiplication and inverse operations in Excel.
- Verify the correctness of your calculations and explore their applications in solving systems of linear equations.

**iv) Stock Market Data Analysis on Excel:**

- Collect historical stock market data for a specific company or index.
- Use Excel to visualise trends, moving averages, and stock performance.

**v) Data Analysis on Weather, Price, Inflation, and Pollution:**

- Collect data on these topics and organize it in Excel.
- Use Excel's data analysis tools to perform statistical analysis, calculate correlations, and visualize trends.

**vi) Data Analysis from Newspapers:**

- Collect data from newspapers or online sources on traffic congestion, sports activities, or market trends.
- Use Excel to create trendlines, analyze data patterns, and make predictions based on historical data.

**Find Out: CBSE Class 12 Applied Maths Numerical Applications**

These are excellent project ideas for Class 12 Applied Mathematics. Here's a brief description of each project:

Project Topics | Description |
---|---|

Use of Prime Numbers in Coding and Decoding Messages | Explore prime numbers' role in cryptography and develop coding and decoding algorithms using these principles. |

Prime Numbers and Divisibility Rules | Investigate the properties of prime numbers and their divisibility rules, delving into their unique mathematical characteristics. |

Logarithms for Financial Calculations | Apply logarithmic functions to financial calculations, including interest, present value, future value, and profit/loss, especially when dealing with large values. |

Cardinality of Sets and Orders of Infinity | Study set cardinality and orders of infinity in set theory, exploring the mathematical concepts that underpin these abstract notions. |

Comparing Sets of Numbers | Analyze and compare various numbers, including natural, rational, and real numbers, examining their properties and relationships. |

Venn Diagrams in Problem Solving | Utilize Venn diagrams as problem-solving tools to address practical issues involving set relationships, showcasing their effectiveness in visualizing complex scenarios. |

Fibonacci Sequence and Its Applications | Explore the Fibonacci sequence's historical significance and mathematical properties, uncovering its presence in nature and diverse applications. |

Validating Mathematical Statements | Test the validity of mathematical statements through logical reasoning and create truth tables to demonstrate the logical relationships between different propositions. |

Investigating Graphs of Functions | Analyze the properties and behaviours of various mathematical functions through graphical representations, enhancing your understanding of mathematical concepts. |

Census Data Visualization | Collect data from census sources and create visual representations to convey demographic information effectively, concluding the findings from the data. |

Questionnaire for Money Spending | Design and administer a questionnaire to collect data on spending habits, allowing you to draw insightful conclusions and analyze spending patterns based on the responses. |

Newspaper Graph Analysis | Gather and analyze data depicted by graphs in local newspapers, comparing your analysis with the provided data to identify trends and potential discrepancies. |

Population Migration Data Analysis | Investigate the impact of population migration on urbanization using relevant data sources, enabling you to conclude migration patterns and urban development. |

Weather Data Comparison | Collect and graphically represent weather data, comparing it with historical data to identify trends and variations in weather patterns over time. |

Career Graph of Athletes | Analyze the career trajectories of athletes, such as cricketers or tennis players, based on their performance statistics, helping you uncover trends and patterns in their sporting journeys. |

Vehicle Registration and Accidents | Correlate vehicle registration data with pollution levels and accident rates to draw meaningful conclusions about the relationship between vehicle numbers, pollution, and accidents. |

Crop Data Analysis | Collect crop-related data from a specific region, including temperature and rainfall, to determine their impact on crop yields and agricultural productivity. |

Rainfall Prediction | Predict rainfall for a specific week using historical weather data, employing mathematical models and statistical methods to make informed forecasts. |

Weather Prediction | Explore weather prediction by analyzing past data related to monsoon patterns and developing predictive models to forecast weather conditions accurately. |

Kirana Shop Sales Optimization | Analyze sales data from local shops to optimize stock levels and maximize profits, utilizing mathematical techniques to enhance decision-making in retail operations. |

Stock Price Movement | Study the movement of stock prices over time, identifying trends and patterns in stock market data to make informed investment decisions. |

Insurance Risk Assessment | Analyze data to assess risk for insurance companies, using mathematical models and statistical analysis to evaluate and manage insurance-related risks. |

Stock Market Crash Prediction | Investigate factors contributing to stock market crashes and develop predictive models to anticipate potential market downturns, aiding in risk management strategies. |

Election Outcome Prediction | Predict election outcomes through exit polls and data analysis, utilizing statistical methods and data interpretation to accurately forecast electoral results. |

Infant Mortality Prediction | Use data analysis to predict infant mortality rates based on various influencing factors, facilitating proactive measures to address healthcare and societal challenges. |

You can go through some simple tips and tricks mentioned below to know how to better prepare for class 12 Applied Mathematics CBSE:

**Practice Real-World Applications**: Focus on practical applications of mathematical concepts. Practice solving problems related to commerce, economics, finance, and data analysis to strengthen your applied mathematics skills.**Data Analysis Skills**: Develop strong data analysis skills. Learn how to collect, organize, and analyze data, a key aspect of the course.**Conceptual Clarity**: Build a strong foundation in fundamental mathematical concepts such as calculus, algebra, and statistics. A deep understanding of these topics is essential for tackling applied problems.**Problem-Solving Strategies**: Develop effective problem-solving strategies, especially for real-world scenarios. Learn to model problems mathematically and apply appropriate techniques to solve them.**Interdisciplinary Connections**: Explore connections between applied mathematics and other disciplines like economics, finance, and business studies. This will help you apply mathematical concepts more effectively.**Practical Applications**: Work on practical projects or case studies related to commerce and economics. This hands-on experience will enhance your understanding of how mathematics is used in real-world situations.**Regular Practice**: Practice regularly, focusing on both theoretical and practical aspects. Solve sample papers, previous years' question papers, and exercises from your textbook. Refer to some of the best**CBSE 12th Commerce Books**that explain all the concepts with examples.**Effective Time Management**: Create a study schedule that allocates sufficient time to each topic. Prioritize areas where you need more practice or improvement.**Clear Mathematical Communication**: Practice presenting your mathematical solutions clearly and concisely. Ensure your answers are well-structured and include relevant explanations.

In the evolving education landscape, CBSE Class 12 Applied Mathematics is a beacon of change, steering students away from traditional mathematical abstractions towards real-world applications.

**Key Takeaways:**

*Applied Mathematics bridges the gap between theoretical math and practical usage, catering to Commerce and Social Sciences.**The subject's unit-wise weightage empowers students to streamline their study efforts effectively.**Practical skills, data analysis, and logical reasoning are key strengths honed through CBSE Class 12 Applied Mathematics.**It differs significantly from traditional Core Mathematics, focusing on real-world problem-solving.**Project ideas provide hands-on experience, translating theory into practice.**Effective preparation involves regular practice, interdisciplinary exploration, and practical application of mathematical concepts.*

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