| Applied Mathematics for Class 11th & 12th (Concepts and Questions) | ||
|---|---|---|
| 11th | Concepts | Questions |
| 12th | Concepts | Questions |
Class 12th Applied Mathematics Concepts
Chapter 1: Numbers, Quantification and Numerical Applications
This chapter builds on numerical concepts, focusing on applications like modulo arithmetic, congruence modulo, alligation and mixture problems, numerical inequalities, solving equations, and analyzing data related to boats & streams, pipes & cisterns, races, games, and partnership.
Chapter 2: Matrices
Explore the concept of matrices, their types, and algebraic operations including addition, scalar multiplication, and matrix multiplication. Learn about determinants, finding the inverse of a matrix, and applying matrices to solve systems of linear equations.
Chapter 3: Differentiation and Its Applications
This chapter covers the fundamentals of differentiation, including derivatives of various functions (exponential, logarithmic, parametric forms), higher-order derivatives, and key applications such as determining the rate of change, identifying increasing/decreasing functions, and finding maxima and minima, particularly in cost, revenue, and profit scenarios.
Chapter 4: Integration and Its Application
Learn about integration as the reverse process of differentiation (anti-derivative). This chapter covers indefinite integrals, standard integration formulas, techniques like substitution, and definite integrals. Applications include calculating the area under simple curves and concepts like consumer and producer surplus.
Chapter 5: Differential Equations and Modeling
This chapter introduces differential equations, covering concepts like order and degree. Learn methods for solving first-order, first-degree differential equations (variable separable, potentially homogeneous and linear) and understand their application in modeling real-world scenarios like growth and decay.
Chapter 6: Probability Distribution
Explore the concept of random variables and their probability distributions. This chapter focuses on discrete distributions like the Binomial and Poisson distributions, and introduces the continuous Normal distribution, along with calculating expectation (mean) and variance.
Chapter 7: Inferential Statistics
Dive into the process of drawing conclusions about a population based on sample data. This chapter covers concepts of population and sample, parameter estimation (point and interval estimates like confidence intervals), and the fundamentals of hypothesis testing (null/alternative hypothesis, significance level, p-value).
Chapter 8: Index Numbers and Time Based Data
Learn how to measure relative changes over time using index numbers (price, quantity). This chapter covers methods for constructing index numbers (simple, weighted like Laspeyres, Paasche), tests for adequacy, and introduces time series analysis concepts like components and moving averages.
Chapter 9: Financial Mathematics
This chapter delves deeper into financial calculations, covering perpetuity, sinking funds, methods for calculating Equated Monthly Installments (EMI), valuation of bonds, calculation of investment returns, Compound Annual Growth Rate (CAGR), and basics of stocks, shares, and debentures.
Chapter 10: Linear Programming
Explore optimization techniques through Linear Programming Problems (LPP). This chapter covers formulating LPPs from real-world situations, understanding terminology (objective function, constraints), solving LPPs graphically, and identifying feasible/infeasible and bounded/unbounded solutions.