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 ∏  = ∏r 

     5      

                    

180 ∏  = ∏r 

    15∏  ∏

180   =  r 

    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  Log_aa^c = cLog_aa )

= (9 x 1) - (3 x 1)          ( remember  Log_aa = 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.