Saturday 30 January 2016

FACTORIZATION 2


Factorize completely   (3x-2)2 - x2  

solution

= (3x-2)2 - x2 

= [(3x-2) - x][ (3x-2) + x ]  --- since a2 + b2 = (a+b)(a-b) Here a is (x-2) and b is x.

= [3x-2 - x][ 3x-2 + x ] 

= [3x-x-2][ 3x+ x - 2  ] 

= [2x-2][ 4x - 2  ] 

= [2x-2][ 4x - 2  ] 

Hence  (3x-2)2 - x2  = (2x-2)(4x - 2) 

TRY THIS....................


Factorize completely   (4x-1)2 - x2  

ARC LENGTH 1


Find radius if the length of an arc of the circle is /15 cm.

Solution

L= /5  , r = ?

L = r
      180

/5  = r
         180

180  x /5  = r  x   180   
                    180


180  =
     5      
                    
180  =
    15  

180   =  
    15      


r = 36cm

Hence radius is 36 cm


TRY THIS………………..


Find radius if the length of an arc of the circle is /20 cm.

ALGEBRA-1


Express as a single fraction m - 5 + m+1
                                              6          4
solution
= m - 5 + m+1
      6          4

= 2(m – 5) + 3(m+1)
            12         

= 2m - 10 + 3m+3
            12         

= 2m + 3m + 3- 10
          12         

= 5m +  -7
      12         

= 5m - 7
     12         

=  5m - 7                 answer
      12       

TRY THIS...................
Express as a single fraction 4c - 1 + 2d+1

                                              4            2

GEOMETRY 1


If x-50 and 4x + 350 are complementary angles, find the value of x.

Solution

Complementary angles add up to 900.

so,  x-50 + 4x + 350 = 900.
so,  x + 4x + 350 - 50 = 900.
so,  5x + 300 = 900.
so,  5x = 900 -  300
so,  5x = 600

so,  5x = 6012
       5       5

Hence x = 120

TRY THIS...............


If 3x - 120 and 2x + 570 are complementary angles, find the value of x.

LOGARITHMS 1


Evaluate Log2(512 ÷ 8).

Solution

= Log2(512 ÷ 8)

= Log2512 -  Log28          (applying the quotient rule)

= Log229 -  Log223             ( 256= 28 and 8=23 )

= 9Log22 -  3Log22       ( remember  Logaac = cLogaa )

= (9 x 1) - (3 x 1)          ( remember  Logaa = 1 )

= 9 - 3

= 6


hence Log2(128 ÷ 64) = 6

TRY THIS...............


Evaluate Log2(1024 ÷ 32).

DIFFERENCE OF 2 SQUARES 1


Evaluate 27972 – 27872

Solution

27972 – 27872 = (2797 + 2787)( 2797 – 2787)

                     = (5584)( 10)

                     = 55840

Hence 27972 – 27872 = 55840

TRY THIS…………….



Evaluate 9362 – 8362

SIMPLE INTEREST 1


Rayan deposited the amount of 80,000/= in a bank for 2 years and got a profit of 2500/=. Find the interest rate?

Solution

I = 1200/=, P = 80,000/=, T = 2 years, R = ?

I  = PRT
      100

2500  = 80,000 x R x 2
                      100

2500  = 80,000 x R x 2
                      100

2500  = 800 x R x 2
                      
2500  = 4000R
           
52500  = 14000R
84000      14000


Hence the interest rate was  1.6%

TRY THIS........................


Rayan deposited the amount of 8,000/= in a bank for 6 years and got a profit of 2100/=. Find the interest rate?

FACTORIZATION 1


Factorize 6x2 + 7x - 5

Solution

= 6x2 + 7x - 5.  We split the middle term (+7x) to be (-3x + 10x).

= 6x2 - 3x + 10x – 5                (-3x) = -14x + 5x.

= (6x2 -3x) + (10x - 5)   grouping the factors.       

= 3x(2x - 1) + 5(2x - 1)

= (3x + 5) (2x -1)

Hence 6x2 + 7x - 5= (3x + 5) (2x -1)answer.

TRY THIS…..


Factorize 14x2 + 3x – 2.