Chapter - Sets

1. Sets and their Representations

2. The Empty Set, Finite and Infinite Sets, Equal Sets

3. Subsets, Power Set, Universal Set

4. Venn Diagrams, Operations on Sets

5. Complement of a Set

6. Union and Intersection of Two Sets

Set: A set is a well-defined collection of objects.

Representaiton of sets:

(i) Roster or Tabular form, (ii) Rule method or set builder form.

 

Chapter - Surds

Surds:

(i) The surd conjugate of √a + √b (or a + √b) is √a - √b (or a - √b) and conversely. 

(ii) If a is rational, √b is a surd and a + √b (or, a - √b) = 0 then a = 0 and b = 0. 

(iii) If a and x are rational, √b and √y are surds and a + √b = x + √y then a = x and b = y.

Chapter - Law of Indices

Laws of Indices:

(i) aᵐ ∙ aⁿ = aᵐ + ⁿ 

(ii) aᵐ/aⁿ = aᵐ - ⁿ 

(iii) (aᵐ)ⁿ = aᵐⁿ 

(iv) a = 1 (a ≠ 0). 

(v) a-ⁿ = 1/aⁿ 

(vi) ⁿ√aᵐ = aᵐ/ⁿ 

(vii) (ab)ᵐ = aᵐ ∙ bⁿ. 

(viii) (a/b)ᵐ = aᵐ/bⁿ 

(ix) If aᵐ = bᵐ (m ≠ 0), then a = b. 

(x) If aᵐ = aⁿ then m = n.