Chapter Summaries›Class 12 Applied Mathematics

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Class 12 Applied MathematicsChapter Summaries

8 chapters · Quick revision in under 3 minutes per chapter

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

More resources for Class 12 Applied Mathematics

NCERT Solutions →Important Questions →Deleted Topics →Revision Checklist →

Class 12 Applied MathematicsChapter Summaries

Numbers, Quantification and Numerical Applications

Algebra

Calculus

Probability Distributions

Index Numbers and Time-Based Data

Financial Mathematics

Linear Programming

Inferential Statistics

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