Number
Systems
Complete chapter resources for CBSE Class 9 Maths — topic breakdown, key concepts, sample questions, previous year board questions, and instant AI question paper generation.
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- Rational number: p/q, q ≠ 0; decimal terminates or repeats
- Irrational number: non-terminating, non-repeating decimal (e.g. √2, π)
- Rationalise: 1/(√a+√b) × (√a−√b)/(√a−√b)
- Surds law: √a × √b = √(ab), a,b ≥ 0
- Exponent law: aᵐ × aⁿ = aᵐ⁺ⁿ (a > 0)
- Rational exponent: a^(p/q) = (a^(1/q))^p
What this chapter covers
Chapter 1 of NCERT Class 9 Mathematics introduces students to the full hierarchy of the real number system. Beginning with natural numbers and integers, the chapter builds up through rational numbers — those expressible as p/q with q ≠ 0 — to the landmark concept of irrational numbers: quantities like √2, √3, and π whose decimal expansions never terminate and never repeat. Together, rationals and irrationals constitute the set of all real numbers, which can be mapped one-to-one onto every point of the number line.
A large portion of the chapter focuses on working with surds — expressions of the form ∜a where a is a positive rational. Students learn to locate irrational numbers on the number line using the geometrical construction of right triangles (successive hypotenuses √2, √3, √5, …), and to simplify and compare surd expressions. The technique of rationalising the denominator — multiplying by a conjugate surd to remove irrationals from the bottom of a fraction — is a high-frequency board skill introduced here.
The chapter closes with laws of exponents for real numbers, extending the familiar integer-power rules (product, quotient, power-of-a-power) to rational exponents such as a^(1/2) = √a and a^(p/q) = (ᵍ√a)ᵖ. These laws underpin simplification questions across all higher classes and are regularly tested in CBSE Class 9 unit tests and annual exams.
What's inside Chapter 1
As per NCERT Class 9 Mathematics (CBSE syllabus)
How this chapter fits in
Useful for setting question difficulty and cross-chapter papers.
Systems
Marks & question-type breakdown
Typical pattern based on CBSE Class 9 Maths school and board papers from the last five years.
| Question type | Marks | Typical count | What's usually tested |
|---|---|---|---|
| MCQ / Objective | 1 | 1–2 | Classify a number (rational/irrational), evaluate a simple exponent |
| Very Short Answer | 2 | 1 | Rationalise a denominator or simplify a surd expression |
| Short Answer | 3 | 1 | Locate √n on the number line or prove a number is irrational |
| Long Answer | 4–5 | 0–1 | Multi-step simplification using exponent and surd laws together |
| Total (approximate) | 4–6 | 3–5 | Weightage varies across school papers and term structure |
8 sample questions — generated by MarksZen AI
Aligned to CBSE Class 9 Maths Chapter 1. Covers all question types across Easy, Medium, and Hard difficulty.
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From CBSE board examinations
Actual questions from past Class 9 Maths school and board papers — Number Systems chapter.
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- All 4 topics of this chapter
- MCQ + short answer + proof questions
- Answer key included
- PDF export ready