Class 12 Applied MathematicsChapter Summaries

8 chapters · Quick revision in under 3 minutes per chapter · Updated 2025-26

Ch 1

Numbers, Quantification and Numerical Applications

Covers modular arithmetic, successive discounts, partnership, time and work, time and distance, and Boats and Streams — all in the context of applied numericals.

Topics covered

Modular arithmetic and clock arithmeticSuccessive discounts and profit-loss calculationsPartnership — ratio of profit sharing based on capital and timeTime-Work-Distance numericalsMixture and alligation problems

Ch 2

Algebra

Covers matrices (addition, scalar multiplication, multiplication, transpose) and determinants (calculation, properties, inverse of 2×2 and 3×3 matrices, solving linear equations using Cramer's rule).

Topics covered

Matrix operations: addition, multiplication, scalar multiplicationDeterminant calculation (2×2 and 3×3)Inverse of a matrix using cofactorsSystem of linear equations: Cramer's rule and matrix methodProperties of determinants

Ch 3

Calculus

Covers limits (standard results), continuity, differentiation of log and exponential functions, and applications of derivatives in business — marginal cost, marginal revenue, maxima and minima of cost and profit functions.

Topics covered

Limits: standard results and evaluationContinuity at a pointDifferentiation: log x, eˣ, product and quotient rulesApplication: marginal cost, marginal revenue, elasticity of demandMaxima and minima: business problems with second derivative test

Ch 4

Probability Distributions

Covers random variables, expected value and variance, Bernoulli trials, Binomial distribution (mean = np, variance = npq), and introduction to normal distribution.

Topics covered

Random variable: discrete and continuousExpected value E(X) and variance Var(X)Bernoulli trial: n trials, p probability of successBinomial distribution formula P(X=r) = nCr · pʳ · qⁿ⁻ʳNormal distribution: shape, properties, standard normal variable z

Ch 5

Index Numbers and Time-Based Data

Covers construction of index numbers (Laspeyre's, Paasche's, Fisher's), Consumer Price Index, time series analysis, and trend by moving averages.

Topics covered

Simple and weighted index numbersLaspeyre's Price Index = Σ(p₁q₀)/Σ(p₀q₀) × 100Paasche's Price Index = Σ(p₁q₁)/Σ(p₀q₁) × 100Fisher's Ideal Index = √(L × P)Consumer Price Index (CPI) and its usesTime series: trend, seasonal, cyclical, irregular componentsMoving averages (3-year and 5-year) for trend calculation

Ch 6

Financial Mathematics

Covers compound interest, effective rate of interest, EMI calculation, annuities (present value and future value), sinking funds, linear depreciation, and reducing balance method.

Topics covered

Compound interest: A = P(1 + r/n)^(nt)Effective rate of interest vs nominal rateEMI = P·r(1+r)ⁿ / [(1+r)ⁿ − 1]Annuity: present value and future value formulasSinking fund calculationStraight line depreciation vs reducing balance depreciation

Ch 7

Linear Programming

Covers formulation of linear programming problems, graphical method (feasible region, corner points), and application to maximisation (profit) and minimisation (cost) problems in business.

Topics covered

LPP: objective function, constraints, non-negativity restrictionGraphical method: plot constraint lines, identify feasible regionCorner point theorem: optimal value at a vertex of feasible regionTypes: maximise (profit, revenue) and minimise (cost, time)Unbounded and infeasible cases

Ch 8

Inferential Statistics

Covers population vs sample, types of sampling (random, stratified, systematic), sampling distributions, Central Limit Theorem, confidence intervals, and basic hypothesis testing (z-test, t-test).

Topics covered

Population vs sample: census vs sample surveyTypes of sampling: simple random, stratified, systematic, clusterSampling distribution of mean: propertiesCentral Limit Theorem: large samples approximate normalConfidence intervals: 95% and 99%Hypothesis testing: null and alternative hypothesis, z-test

Frequently Asked Questions

Can I revise Class 12 Applied Mathematics in one day using summaries?

Yes. Each chapter summary here takes under 3 minutes to read. With 8 chapters, you can cover all of Class 12 Applied Mathematics in a focused 2–3 hour session. Use these summaries to identify gaps — then revisit only those chapters in detail.

Are chapter summaries enough for CBSE Class 12 Applied Mathematics board exam?

Summaries are for revision, not first learning. Use them after you've already studied the chapter — they quickly confirm what you remember and flag what you don't. For first-time study, read the NCERT textbook and work through important questions chapter-by-chapter.

What is covered in Class 12 Applied Mathematics chapter summaries?

Each summary here covers the main concepts of the chapter, key topics that CBSE tests, and important points for the board exam. Deleted topics (removed from the 2025-26 CBSE syllabus) are clearly marked so you don't waste time on content that won't be tested.

What is the fastest way to revise Class 12 Applied Mathematics for CBSE boards?

Read the chapter summary, then immediately close it and try to recall the key topics listed — without looking. Anything you miss, mark for one more read. This active recall method is proven to be 3× more effective than re-reading the textbook, and takes a fraction of the time.

Complete Study Pack — Class 12 Applied Mathematics

NCERT Solutions →Important Questions →CBQ Practice →Sample Papers 2025-26 →Previous Year Papers →Last Minute Revision →Revision Checklist →Deleted Topics →