LOGARITHMS 1

Evaluate log₃243⁵

Solution

= log₃243⁵

= log₃(3⁵)⁵

= log₃3²⁵

= 25 x log₃3    [since log_aa = 1]

= 25 x 1

= 25

Hence log₃243⁵ = 25

TRY THIS………………

Evaluate log₅3125⁶

FACTORIZE - 2

Factorize 36x²- 81y²

Solution

we use difference of two squares a² – b² = (a - b)(a + b)

36x²- 81y² = 6²x² - 9²y²

                     = (6x)² - (3y)²

                     = (6x - 3y)( 6x + 3y)

Hence 36x² - 81y² = (6x - 3y)(6x + 3y)

TRY THIS………………………….

factorize 49x²- 144y²

COORDINATE GEOMETRY 1

Find the midpoint of a line from (13, 4) to (5, 10).

Solution

x1=13, x2=5, y1=4,y2=10.

Mid point = (x1 + x2, y1 + y2)

                            2             2

Mid point = (13 + 5,  4 + 10)

                          2          2

Mid point = (18, 14)

                      2    2

Hence midpoint = (9, 7)

TRY THIS……………………..

Find the midpoint of a line from (-4, 8) to (1, -2)

FACTORIZATION 1

Factorize completely 3t – 12t³

Solution

= 3t – 12t³ 

= 3t(1 – 4t²)

= 3t[(1)² – (2t)²]

= 3t[(1 – 2t)(1 + 2t)]

= 3t (1 – 2t)(1 + 2t)

TRY THIS……………..

Factorize completely 3m – 108m³

SIMILARITY - 1

Prove that the following triangles are similar

Solution

EF  = 28  = 2 

BC    14

FG  = 70  = 2 

AB     35

<ABC = <EFG = 123⁰

∴ ∆ABC  ᷈  ∆EFG -------- [By SAS similarity theorem]

 TRY THIS............

 Prove that the following triangles are similar