Real Numbers · Class 10 Maths · Chapter 1
Real Numbers
CBSE Class 10 · Mathematics · Chapter 1 — Foundation of Number Theory
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Six free PDFs covering every angle of this chapter — read the deck, drill the MCQs, sit the full board paper, then check against the marking scheme.
Full lecture deck — FTA, irrationality proofs, decimal expansions. Misconception red-boxes + Hindi glossary throughout. Read first.
Download PDF →PYQ-tagged warm-up. Each question carries year + set + marks + per-Q time budget. Score yourself, identify weak topics, then jump to the board paper.
Download PDF →Full CBSE-pattern paper — 4 sections, closed-book. Matches current blueprint. Sit it under timer before checking the marking scheme.
Download PDF →Model answers + the exact step-by-step structures CBSE markers reward with full credit. Memorise the FORMAT, not just the content.
Download PDF →Exam-day revision card — every formula, every PYQ pattern, a 90-minute revision flow. Print and stick on your desk.
Download PDF →Plain-language guide for parents — what's being learned, what to ask your child, weak-spot indicators, expected marks, time to master.
Download PDF →Top PYQ patterns · 10-year aggregate
| 95% | Prove √p is irrational (p ∈ {2, 3, 5, 7}) — use the 3-step template above. Co-prime → Theorem 1.3 → contradiction. | 3 MARKS |
| 85% | Find HCF / LCM by prime factorisation — set up tables, pick smallest powers for HCF, greatest for LCM. | 2 MARKS |
| 60% | Decimal expansion classification — terminating iff denominator (lowest form) = 2ⁿ · 5ᵐ. | 2 MARKS |
| 40% | Word problem: bells ringing at intervals / soldiers marching in columns — LCM application. | 3 MARKS |
| 30% | Case-study or HOTS on the FTA — usually combines factorisation + verification. | 4 MARKS |