Track quiz
Ten quick questions, one for each lesson. Use the table if you get stuck.
| Idea | Remember |
|---|---|
| Break into primes | Divide by primes until you reach 1. The primes are the factors. |
| HCF and LCM | HCF: smallest powers of shared primes. LCM: greatest powers of all. |
| Squares | A perfect square has an even power of every prime. |
| The lemma | If a prime divides n², it divides n. A divisor that is not prime can fail. |
| Proof for √2 and √3 | Suppose, square, lemma, substitute, lemma, contradiction. |
| Proof for √5 | The same steps, with 5 as the prime. |
| What a proof settles | A search tries some fractions. A proof covers all of them. |
| Write it in order | Each line needs the line before it. The lemma here is for a prime. |
| A number joined to a root | Suppose the number is a fraction. Get the root alone. The root would be a fraction. |
| Three numbers | Count a missing prime as power 0. HCF takes the smallest power of each prime. LCM takes the greatest. |
132 = 2 × 2 × 3 × 11. Which box size cannot pack 132 laddus evenly?
What is the HCF of 36 and 60?
72 = 2³ × 3². Which smallest number must you multiply by for a perfect square?
8 divides 4 × 4 = 16, but 8 does not divide 4. Why does the lemma not break?
In the √3 proof, p = 3m turns p² = 3q² into q² = 3m². Which fact then gives "3 divides q"?
Which line of the √5 proof comes first?
A student offers 2.236 for √5. 2.236 × 2.236 = 4.999696. Why is that not a proof?
Why can the √5 steps not prove that √4 is irrational?
Which number is irrational?
What is the LCM of 4, 6 and 10?
Now open Chapter 1, Real Numbers, in your NCERT Maths book. Its exercises use these ideas.
Next: Polynomials. Numbers give way to expressions with letters, and their zeros.