Laws of Indices
(i) am × an = am+n
(ii) am ÷ an = am-n
(iii) (am)n = am×n
(iv) (a × b)m = am × bm
(v) (a ÷ b)m = am ÷ bm
(vi) a-m = 1\over a^m
(vii) (a)o = 1
(viii) \sqrt[n]{a} = (a) 1/n
(ix) If am = an, then m = n
Basic Expansion Formula
| (i) (a + b)2 | = | a2 + 2ab + b2 |
| = | (a – b)2 + 2ab | |
| (ii) (a – b)2 | = | a2 – 2ab + b2 |
| = | (a + b)2 – 2ab | |
| (iii) a2 – b2 | = | (a + b)(a – b) |
| (iv) (a + b)3 | = | a3 + 3a2b + 3ab2 + b3 |
| (v) (a – b)3 | = | a3 – 3a2b + 3ab2 – b3 |
| (vi) a3 + b3 | = | (a + b)(a2 – ab + b2) |
| = | (a + b)3 – 3ab (a + b) | |
| (vii) a3 – b3 | = | (a – b)(a2 + ab + b2) |
| = | (a – b)3 + 3ab (a – b) |
Simple Interest
(i) Simple Interest (SI) = \text{P × r × t}\over 100
- P = principal
- r = rate of interest
- t = time (in year)
(ii) Amount (A) = SI + P
Other formulae
(iii) P = \text{SI} × 100\over \text{r × t} (iv) t = \text{SI} × 100\over \text{P × r} (iii) r = \text{SI} × 100\over \text{P × t}
Profit and Loss
1. SP = CP + P
2. P = SP – CP
3. % P = \text{P}\over \text{CP}×100
4. SP = ({100+\text{\%P}\over 100}) × CP
5. CP = ({100\over 100+\text{\%P}}) × SP
6. SP = CP – L
7. L = CP – SP
8. % L = \text{L}\over \text{CP}×100
9. SP = ({100-\text{\%L}\over 100}) × CP
10. CP = ({100\over 100-\text{\%L}}) × SP
11. Discount (d) = MP – SP
12. % discount = d\over MP × 100
13. SP = ({100 – \text{\%d}\over 100}) × MP
14. MP = ({100 \over 100 – \text{\%d}}) × SP
15. d = [1 – ({1 – {d_1\over 100}})({1 – {d_2\over 100}})] × 100
- SP = Selling Price
- CP = Cost Price
- L = Loss
- %L = Percent Loss
- P = Profit
- %P = Percent Profit
- MP = Marked and Listed Price