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CBSE Class 12 Applied Mathematics aims to teach students how to use mathematics in real-world situations. Students understand how to use mathematical techniques to solve problems in various contexts in Applied Mathematics. They approach problems in the actual world by utilising ideas like analysis, differential equations, and stochastics.

For students to comprehend and apply mathematical concepts in a variety of contexts, this applied maths class 12 syllabus 2024-25 serves to bridge the gap between theoretical and applied mathematics. The 2024-25 academic year syllabus was released, and we were prompt about the prediction of the changes. Below, we have provided you with a simple analysis of the Class 12 Applied Mathematics Syllabus, along with:

**PDF download ->**2024-25 (latest) and past year syllabus**Detailed analysis ->**blueprint of all units & chapters

**Class 12 Applied Mathematics Syllabus**

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**2023-24 Class 12 Applied Mathematics Syllabus**

(for reference purposes)

CBSE Class 12 Mathematics might seem similar to Applied Mathematics given the same subject code but both are different. If students want to focus on practical applications then they can study using the syllabus for Class 12 Applied Mathematics otherwise they can study using Class 12 Mathematics.

Simple arithmetic functions

- Solution of simultaneous linear equations using elimination method (up to 3 variables)
- Simple applications of matrices and determinants including the Leontiff input-output model for two variable

Integration of simple algebraic functions (primitive, by substitution, by parts)

Basic applications and inferences

- Index numbers
- uses of index numbers
- Construction of index numbers (simple and weighted)
- Tests of adequacy of index numbers (unit test and time reversal test)
- Trend analysis by moving average method
- Trend analysis by fitting of linear trend line using least squares

Stock, shares and debentures

In the opinion of professionals, understanding applied mathematics can help students in future careers. Students can plan their study by determining the key topics for the test and referring to the CBSE Class 12 Applied Maths Syllabus 2024-25.

The topic "Numbers, Quantification, and Numerical Applications" in CBSE Class 12 Applied Mathematics addresses an array of fundamental concepts about numbers and how they are used in everyday situations.

**Unit 1: Numbers, Quantification and Numerical Applications**

**Number System**

- Different number systems, including hexadecimal, binary, octal, and decimal.
- Conversion of one number system to another.
- Characteristics and operations in many number systems (addition, subtraction, multiplication, and division).

**Number Representation**

- Understanding conventional form and scientific notation.
- Rounding off numbers and significant figures.
- Three different forms of errors exist percentage, relative, and absolute errors.
- Measurement of the spread of errors in computational mathematics.

**Practical Uses**

- Applying mathematical ideas to practical situations in fields including science, engineering, finance, and economics.
- Calculating interest rates, stock prices, data analysis in experiments, and optimisation problem solving are a few examples.

**Quantitative Techniques**

- Introduction to numerical techniques for resolving mathematical problems and equations that are not amenable to analytical solutions.
- Numerical integration and differentiation, approximation, interpolation, and iteration are some possible methods.
- Recognising the benefits and drawbacks of numerical vs analytical approaches.

**Statistical Indicators**

- An overview of fundamental statistical metrics, including variance, standard deviation, mean, median, mode, and range.
- Recognising the importance of these metrics for data analysis and conclusion-making.
- Statistical measurements applied to decision-making and data interpretation.

**Probability**

- Sample space, occurrences, and probability distributions are among the fundamental ideas of probability.
- Recognising the many forms of probability, including experimental, theoretical, and subjective.
- Use of probability ideas to solve issues with risk assessment, decision-making, and games of chance.

**Programming in Linear Form:**

- Overview of linear programming as a mathematical technique for resource allocation optimisation.
- Understanding the ideas behind feasible regions, constraints, objective functions, and optimum solutions.
- Utilising linear programming to address practical optimisation issues in transportation, resource allocation, and production planning, among other domains.

**Unit 2: Algebra**

**Matrices**

- There are several sorts of matrices, including square, diagonal, row, column, scalar, and identity.
- Matrix operations include Addition, subtraction, scalar multiplication, and matrix multiplication.
- Characteristics of matrices distributive, associative, and commutative qualities.
- An inverse matrix Conditions of existence, inverse matrix attributes, and the inverse discovery procedure.
- Using matrices in applications solving Markov chains, geometric object manipulation, systems of linear equations, etc.

**Determinants**

- Properties and Definitions
- Assessment of determinants using a range of techniques: expansion along minors, cofactors, rows or columns, and determinant characteristics.
- Determinant properties include row or column addition or subtraction, scalar multiplication, and row or column switching.
- Define and compute minors and cofactors.
- Use determinants to get the inverse and adjoint of a matrix.

**Programming in Linear Form**

- Creating problems for linear programming: An introduction to the subject.
- The best solution can be found by the graphic technique, which involves representing the restrictions, feasible region, and goal function on a graph.
- Simplex method: An overview of the linear programming problem-solving simplex technique.
- Real-world applications of linear programming include transportation, resource allocation, production scheduling, and diet planning.

**Vectors Algebra**

- Definitions and differences between vectors and scalars.
- Vector types include unit, position, collinear, coplanar, and other types.
- Vector addition and subtraction: The vector addition laws of triangles and parallelograms.
- Definition, characteristics, and geometric meaning of the scalar (dot) product of vectors.
- Vector (cross) product of vectors: Meaning, characteristics, and uses.
- Three vector and scalar products.

**Probability (Optional)**

- Sample space, events, event categories, and probability axioms are the fundamental ideas of probability.
- Probability addition and multiplication theorems.
- Probability with conditions and independent events.
- The Bayes theorem and its uses.

**Unit 3: Calculus**

**Calculus Differential:**

**Limits and Continuity:**This section covers the ideas of limits and continuity of functions, as well as how to evaluate limits using L'Hôpital's Rule and algebraic methods.- Introduction to derivatives as
**rates of change**; first-principles computation of derivatives; and differentiation strategies, including the quotient rule, product rule, chain rule, and implicit differentiation. **Using Derivatives in Applications:**Use of derivatives in a variety of situations, such as tangent and normal determination, change rates, and optimisation issues.

**Calculus of Integrals:**

**Integration:**An introduction to integration as the opposite of differentiation, with integrals calculated by applying fundamental principles and techniques like substitution and integration by parts.**Definite Integrals:**Defined as the limit of a sum, definite integrals can be evaluated in some ways, including by using the Fundamental Theorem of Calculus and integral properties.**Applications of Integrals:**Integrals are used in volume calculations, area calculations, and the resolution of accumulation-related issues.

**Differential Equations**

**Fundamental Ideas:**A description of differential equations, covering the notions of degree and order, as well as how to solve a differential equation.**Formation and Solutions:**creation of ordinary differential equations from specified parameters and their solutions using the variables separable approach and direct integration technique.

**Calculus as Applied to Optimisation:**

**Maxima and Minima:**Utilising derivatives to solve optimisation issues in a variety of real-world circumstances, as well as comprehending the notions of local and global maxima and minima.

**Unit 4: Probability Distributions**

**Functions for Probability Distributions**

- A probability distribution function gives a random variable's potential outcomes probabilities.
- The normal distribution, Poisson distribution, and binomial distribution are examples of common probability distributions.

**Binomial Distribution:**

- The likelihood of a specific number of wins in a set number of independent Bernoulli trials is described by the binomial distribution.
- P(X = k) = C(n, k) * p^k * (1 - p)^(n - k) is the probability mass function for it. Here, n represents the number of trials, k is the number of successes, p is the probability of success in a single trial, and C(n, k) stands for the binomial coefficient "n choose k."

**Poisson Distribution**

- Given a certain average rate of occurrence, the Poisson distribution describes the number of events that take place in a given period or space.
- P(X = k) = (λ^k * e^(-λ)) / k! is its probability mass function, where λ (lambda) is the average rate of occurrence and k is the total number of occurrences.

**Normal Distribution**

- The bell-shaped curve of the normal distribution, also referred to as the Gaussian distribution, represents a continuous probability distribution.
- The two parameters that completely characterise it are the mean (μ) and standard deviation (σ).
- One of the most commonly used distributions in statistics is the normal distribution, which is shown by many natural events.

**Properties and Uses**

- The mean, variance, and standard deviation of probability distributions are among their many characteristics, and they shed light on the data's distribution and central tendency.
- These distributions are used to simulate and analyse random occurrences in a variety of disciplines, including economics, engineering, biology, and the social sciences.

**Calculates and Interpretations**

- Plotting probabilities, anticipated values, variances, and other pertinent statistics related to various probability distributions are among the topics covered in the course.
- Students are assisted in understanding the practical consequences of their calculations by emphasising the interpretation of findings in real-world scenarios.

**Techniques for Solving Problems**

- By using principles from a probability distribution to tackle real-world issues like risk assessment, dependability analysis, and decision-making scenarios, students may hone their problem-solving abilities.

**Unit 5: Inferential Statistics: **Unit 5: Inferential Statistics of the CBSE Class 12 Applied Mathematics curriculum, Inferential Statistics focuses on sophisticated statistical methods for inferring characteristics of populations from sample data.

**Unit 6: Index Numbers and Time-based Data (Continued): **Comprehending index numbers and time series analysis is crucial for making well-informed judgements across several domains, such as business, finance, and economics. The concepts and methods taught in this section can help students gain analytical abilities that are useful in both academic and professional contexts.

**Unit 7: Financial Mathematics:** All things considered, Unit 7: Financial Mathematics gives students the mathematical instruments and methods required to examine financial dealings, investments, and decision-making procedures. It offers a hands-on comprehension of financial ideas and how they are used in actual situations, setting the groundwork for future research or employment in finance, economics, and related professions.

**Unit 8: Linear Programming: **For students pursuing applied mathematics, mastering linear programming is essential since it offers strong tools for decision-making and optimisation in a variety of real-world situations. Gaining an understanding of the ideas, methods, and applications discussed in this subject can assist students in developing transferable analytical and problem-solving skills across a variety of fields.

There are multiple pros of pursuing Applied Mathematics in CBSE Class 12:

**Understanding Tools:** The ability to comprehend basic mathematical and statistical techniques is crucial for students studying business, economics, finance, trade, and social sciences.

**Solving Real-World Issues:** Applied mathematics trains students to use algebra, numbers, and graphs to transform real-world issues into mathematical equations, which simplifies practical solutions.

**Analysing Data:** By learning how to organise, portray, understand, and analyse data, students are better equipped to make insightful decisions and carry out research.

**Developing Logical thinking: **The course helps students develop the logical thinking abilities that are essential for efficiently resolving daily and mathematics problems.

**Boosting Communication:** Students' ability to clearly express discoveries is improved by applying mathematics to support arguments, test hypotheses, and articulate concepts.

**Creating Connections: **Students may apply mathematical principles across a variety of sectors, expanding their knowledge and abilities, by integrating maths with other topics.

Using Excel and additional resources, here are some applications in real life for Class 12 CBSE Applied Mathematics:

**Excel Graphs:** Use Excel to plot different mathematical functions, such as cubic or quadratic equations, and identify the greatest and lowest points of each.

**Probability Simulation:** To simulate and examine the likelihood of various events, use an Excel dice-rolling simulation. Compute the outcomes using theoretical probability to have a deeper understanding of unpredictability.

**Matrix Operations:** To precisely solve systems of linear equations, use Excel's matrix multiplication and inversion functions. Examine the practical applications of these processes.

**Stock Market Analysis:** Apply Excel to see patterns and performance over time by compiling previous stock market information for a certain firm or index. Make wise investing selections by analysing the data to find trends.

**Analyse data: **Use Excel to arrange information on the climate, costs, inflation, and pollution. To improve decision-making, make use of Excel's built-in data analysis features to do statistical analysis, compute correlations, and visualise trends.

**Analyse data from newspapers: **The Internet sources about subjects such as market trends, sporting events, and traffic jams. For a variety of purposes, use Excel to construct trendlines, examine data trends, and forecast using past data.

These hands-on activities improve comprehension of applied mathematical ideas while also honing your ability to solve problems in the real world with Excel and other tools. Students can start preparing for the board exams 2025 using the Class 12 Applied Mathematics Syllabus.

It takes an organised method to prepare for the CBSE Class 12 Applied Mathematics examination, covering both academic knowledge and real-world problem-solving techniques.

**Understand the Syllabus: **Get familiar with the CBSE Class 12 Applied Mathematics syllabus. Evaluate the subjects presented and the relative importance of each topic.

**Get Study Materials:** Get reference books, textbooks, and study aids created especially for CBSE Class 12 Applied Mathematics. You may also get experience by gathering question papers from prior years and sample papers.

**Make a Study Schedule:** Make a study plan that allows enough time for every subject according to its significance and your degree of expertise. you prevent burnout, be sure you incorporate regular pauses.

**Emphasis on Conceptual Understanding:** Pay attention to comprehending each topic's basic ideas rather than reciting facts by heart. Take note of definitions, formulae, theorems, and applications.

**Practice Often:** To improve your problem-solving abilities, practice solving numerical problems frequently. Work through the examples found in reference books and textbooks, and try the exercises after each chapter.

**Solve Past Year Papers and Sample Papers:** To become more used to the examination format and to enhance time management skills, practise solving past year papers and sample papers within the allotted time. Examine your performance and note any areas that still need work.

To perform well on the Applied Mathematics examination using the CBSE class 12 applied mathematics syllabus is to prepare consistently and deliberately. You may increase the likelihood of success by adhering to these guidelines and maintaining your commitment to your studies.

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