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Real Numbers — Study Plan

Madhya Pradesh Board · Class 10 · Mathematics

A step-by-step study plan for Real Numbers, Madhya Pradesh Board Class 10 Mathematics: what to learn first, what to practise and when to revise.

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.

Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas and key ideas. Focus on: Euclid's Division Algorithm, Fundamental Theorem of Arithmetic, HCF and LCM by Prime Factorisation.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 116 questions available for this chapter.

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Real Numbers after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • Any positive integer can be divided by another positive integer with remainder smaller than the divisor.
  • It is mainly used to find the HCF of two positive integers.
  • It is different from the Fundamental Theorem of Arithmetic, which is about multiplication and factorisation.
  • Every composite number has a prime factorisation.
  • The factorisation is unique except for the order of the primes.
  • Prime factors are usually written in ascending order.
  • For two numbers, HCF x LCM = product of the numbers.
  • HCF is the product of the smallest powers of common prime factors.
  • LCM is the product of the greatest powers of all prime factors involved.

Common Mistakes to Avoid

Euclid's division algorithm is the same as the Fundamental Theorem of Arithmetic.

Any composite number can be written as a product of primes in many different correct ways.

If a number ends in 0, then any power of 4 can also end in 0 for some value of n.

Memory Tips

Euclid's division algorithm

Fundamental Theorem of Arithmetic

Uniqueness apart from order

Prime factor tree for 32760

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Frequently Asked Questions

What are the important topics in Real Numbers for Madhya Pradesh 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 Madhya Pradesh Board Class 10 board exam.
How should I revise Real Numbers for the Madhya Pradesh 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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