Friday, 28 November 2014

LOGARITHMS 1




Evaluate log32435

Solution

= log32435

= log3(35)5

= log3325

= 25 x log33    [since logaa = 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

Thursday, 27 November 2014

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 – 12t2

Solution

= 3t – 12t

= 3t(1 – 4t2)

= 3t[(1)2 – (2t)2]

= 3t[(1 – 2t)(1 + 2t)]

= 3t (1 – 2t)(1 + 2t)

TRY THIS……………..

Factorize completely 3m – 108m2

Sunday, 23 November 2014

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