CBSE 9 Math · U1
Number System
CBSE Class 9 Mathematics Unit I: rational numbers, number-line representation, density of rational numbers, decimal representation, irrational numbers, proofs of irrationality of square roots, and the square root spiral.
Test yourself
A focused, distraction-free run through 30 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 1.1
Rational Numbers and Decimal Representation
Recognising rational numbers, simplifying them, and interpreting terminating and recurring decimals.
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Topic 1.2
Number-Line Representation and Density
Representing rational numbers and finding rational numbers between two given rational numbers.
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Topic 1.3
Irrational Numbers and Real Numbers
Identifying irrational numbers and explaining how rational and irrational numbers sit inside the real number system.
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Topic 1.4
Proofs of Irrationality
Understanding and writing contradiction proofs for the irrationality of square roots.
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Topic 1.5
Square Root Spiral and Exact Representation
Constructing and interpreting exact square-root lengths on the number line.
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