*Page counts are approximate and vary by edition.
1. Overview | Item | Details | |------|---------| | Title | Pure Mathematics (often referred to as “HKale Pure Maths”) | | Author / Compiler | H. K. Alam (commonly abbreviated as H. K. A. L. E.) – a well‑known author of school‑level mathematics textbooks in India. | | Publisher | Usually published by S. Chand (or occasionally by S. Chand & Co. ). | | Edition | Most widely circulated editions are the 5th and 6th editions (the 6th is the latest as of 2023). | | Target Audience | Indian CBSE/NCERT Class 11 & 12 students preparing for board exams and competitive exams (JEE, NEET, etc.). | | Subject Focus | Pure mathematics topics: Algebra, Trigonometry, Calculus, Vectors, Matrices, Complex Numbers, Probability & Statistics, etc. | 2. Structure & Content | Chapter | Major Topics Covered | Typical Page Count* | |---------|----------------------|---------------------| | 1. Sets, Relations & Functions | Set theory, Venn diagrams, types of relations, functions & their properties | ~12 | | 2. Complex Numbers | Algebraic & polar forms, De‑Moivre’s theorem, roots of unity | ~16 | | 3. Quadratic Equations & Functions | Roots, discriminant, nature of roots, graphical representation | ~14 | | 4. Sequences & Series | Arithmetic & geometric progressions, sum to n terms, binomial theorem | ~18 | | 5. Permutations & Combinations | Counting principles, binomial coefficients, probability basics | ~12 | | 6. Matrices & Determinants | Operations, inverses, Cramer's rule, applications to linear equations | ~22 | | 7. Trigonometry | Identities, equations, inverse functions, area of triangle, heights | ~20 | | 8. Limits & Continuity | Formal ε‑δ definition, one‑sided limits, continuity criteria | ~12 | | 9. Differentiation | Rules, applications, maxima/minima, curve sketching, related rates | ~30 | |10. Integration | Indefinite integrals, definite integrals, applications (area, volume) | ~28 | |11. Vectors & Three‑Dimensional Geometry | Vector algebra, scalar & vector products, line & plane equations | ~24 | |12. Probability | Conditional probability, Bayes theorem, random variables | ~12 | |13. Statistics | Measures of central tendency, dispersion, regression, correlation | ~14 | hkale pure maths textbook pdf
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