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Concept Maps

Real Numbers — Concept Maps

Jammu & Kashmir Board · Class 10 · Mathematics

4 concept maps of Real Numbers for Jammu & Kashmir Board Class 10 Mathematics, each also written out as a text outline.

116 questions50 flashcards11 formulas & key relations5 concepts

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A Venn diagram illustrating the classification of real numbers into rational and irrational numbers, with further subdivisions for rational numbers (integers, whole numbers, natural numbers).
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One of 6 illustrations for Real Numbers in Super Tutor — alongside flashcards, concept maps and practice questions.

4 Concept Maps

How to Correctly Identify Rational vs Irrational Numbers

How to Correctly Identify Rational vs Irrational Numbers

The map in words

  • Given a number
    • Is it a fraction p divided by q where q is not 0?
      • Yes: Are p and q integers?
        • Yes: RATIONAL
        • No: Check further
          • Does it involve a square root?
            • Square root of a perfect square: RATIONAL - e.g. root 9 equals 3
            • Square root of a non-perfect-square: IRRATIONAL - e.g. root 2
      • No - it is a decimal: Is the decimal terminating or repeating?
        • Terminating like 0.25: RATIONAL
        • Non-terminating AND repeating like 0.333...: RATIONAL
        • Non-terminating AND non-repeating like pi: IRRATIONAL

Real Numbers Chapter — Complete Concept Map

Real Numbers Chapter — Complete Concept Map

The map in words

  • Real Numbers
    • Fundamental Theorem
      • Every composite has prime factors
      • Factorisation is UNIQUE
      • Like a fingerprint
      • Gauss proved it
    • Prime Factorisation
      • Factor Tree Method
      • Ascending order of primes
      • Powers of primes
      • Examples 32760 and 123456789
    • HCF Calculation
      • Euclid Division Algorithm
      • Prime Factorisation Method
      • Lowest powers of common primes
      • DRAW steps to find HCF
    • LCM Calculation
      • Prime Factorisation Method
      • Highest powers of all primes
      • HCF times LCM equals a times b
      • Only for two numbers
    • Irrational Numbers
      • Cannot write as p over q
      • RATIO hidden in iRRATIOnal
      • Square root of any prime
      • Proof by contradiction
    • Key Theorems
      • Theorem 1.1 FTA
      • Theorem 1.2 prime divides a squared
      • Theorem 1.3 root 2 irrational
      • Extends to all prime roots

Real Numbers — Complete Chapter Overview

Real Numbers — Complete Chapter Overview

The map in words

  • Real Numbers
    • Fundamental Theorem
      • Prime Factorisation
        • Unique for each number
        • Factor Tree Method
      • HCF
        • Common primes
        • Minimum powers
      • LCM
        • All primes
        • Maximum powers
      • HCF x LCM = a x b
        • Only for 2 numbers
    • Irrational Numbers
      • Cannot write as p over q
      • Root 2 Root 3 Root 5
      • Pi is irrational
      • Proof by Contradiction
        • Assume rational
        • Derive contradiction
        • Conclude irrational
    • Decimal Expansions
      • Terminating
        • q = 2^m x 5^n only
        • Finite digits
      • Non-terminating Repeating
        • Other prime factors in q
        • Rational numbers
      • Non-terminating Non-repeating
        • Irrational numbers

Real Numbers

Real Numbers

The map in words

  • Real Numbers
    • Euclid's Division Algorithm
    • Fundamental Theorem of Arithmetic
    • Prime Factorisation
    • HCF and LCM
    • Irrational Numbers
    • Proof by Contradiction
    • Decimal Expansion of Rational Numbers
    • Square Root Irrationality Results

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Frequently Asked Questions

What are the important topics in Real Numbers for Jammu & Kashmir Board Class 10 Mathematics?
Key topics in Real Numbers include Euclid's Division Algorithm, Fundamental Theorem of Arithmetic, HCF and LCM by Prime Factorisation, Irrational Numbers and Irrationality Proofs. Study these first, then practise questions on each for the Jammu & Kashmir Board Class 10 board exam.
What do the concept maps for Real Numbers show?
The 4 maps show how the ideas in Real Numbers connect: How to Correctly Identify Rational vs Irrational Numbers; Real Numbers Chapter — Complete Concept Map. Each map is also written out as an outline on this page.
How should I revise Real Numbers for the Jammu & Kashmir Board Class 10 board exam?
Learn the core ideas first, then work through the 116 practice questions on Real Numbers. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Jammu & Kashmir Board Class 10 Mathematics Concept Maps

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