Applied Mathematics – Class XII Student Support Material (2025–26)

1️⃣ Unit 1: Numbers, Quantification and Numerical Applications

This unit focuses on practical mathematical concepts used in daily life and competitive examinations. It includes:

Modulo Arithmetic & Congruence Modulo – Understanding remainders and modular operations.

Alligation and Mixture – Solving problems related to mixing ingredients and mean price.

Boats and Streams – Calculating upstream and downstream speeds.

Pipes and Cisterns – Solving time and work problems involving filling and emptying tanks.

Races and Games – Speed, distance, and time-based competitive problems.

Numerical Inequalities – Comparison of algebraic expressions and AM ≥ GM concept.

This unit builds strong analytical and problem-solving skills.

2️⃣ Unit 2: Algebra

This section covers algebraic techniques and their applications. Topics generally include:

Matrices and determinants

Linear equations

Basic algebraic identities

Application-based algebra problems

It helps students develop logical reasoning and structured problem-solving methods.

3️⃣ Unit 3: Calculus

This unit introduces fundamental concepts of calculus, including:

Functions and their properties

Limits and continuity

Differentiation and its applications

Application of derivatives in real-life problems

Students learn how to analyze rates of change and optimization problems.

4️⃣ Unit 4: Probability Distributions

This unit explains different probability models and distributions. It includes:

Random variables

Mean and variance

Discrete probability distributions

It builds understanding of uncertainty and data-based predictions.

5️⃣ Unit 5: Inferential Statistics

This section focuses on statistical analysis and decision-making. It includes:

Measures of central tendency

Measures of dispersion

Correlation and regression

Hypothesis testing concepts

It helps students interpret real-world data scientifically.

6️⃣ Unit 6: Time-Based Data

This unit deals with statistical analysis of time-related data such as:

Time series

Trend analysis

Moving averages

Forecasting techniques

Students learn how to analyze patterns over time.

7️⃣ Unit 7: Financial Mathematics

This unit covers mathematical concepts used in finance, such as:

Simple and compound interest

Annuities

EMI calculations

Investment and returns

It prepares students for real-world financial decision-making.

8️⃣ Unit 8: Linear Programming

This section introduces optimization techniques. It includes:

Formulation of Linear Programming Problems (LPP)

Graphical method of solving LPP

Feasible region and optimal solution

Students learn how to maximize profit or minimize cost using constraints.

9️⃣ Sample Question Papers (1, 2 & 3)

These sections provide full-length sample papers designed according to the latest CBSE pattern. They help students practice time management and exam strategy.

🔟 Useful Links

The final section includes reference materials and additional resources for further learning and practice.