Real Numbers — Class 10 CBSE Mathematics revision notes
A 4-page visual revision sheet for Real Numbers, written for Class 10 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Real Numbers sheet covers
- Prime factorisation
- The Fundamental Theorem of Arithmetic
- every composite number
- primes collected as powers
- and 12, 18 the same way
- Turning a number into primes
- Prime factors hanging from the number
- HCF
- LCM
- HCF and LCM from the factorisation
- smallest power of each shared prime
- largest power of every prime seen
- the product law, two numbers only
- check it
- HCF and LCM of 24 and 90, by factorising
- Where HCF and LCM actually turn up
- Three numbers at once
- factorise all three
- and the product law is no help
- Two bells, one meeting
- Why a power of 6 can never end in 0
- ending in 0 means a multiple of
- but 6^n splits into 2s and 3s only
- so no 5 ever joins the list
- 4^n is shut out for the same reason
- Numbers that share nothing
- Checking the two answers you wrote
- Symbols
- Revisiting Irrational Numbers
- Rational and irrational numbers
- Why √2 is irrational
- Mixing rational with irrational
- The same proof, dressed differently
- The one line both proofs lean on
- Primes worth knowing by sight
- There is no last prime
- suppose the primes stopped at p
- now look one place further up
- each prime on the list leaves remainder
- so a prime outside the list must exist
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Real Numbers the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.