LOGARITHMS 1

Simplify Log₂256 - Log₃243

Solution

= Log₂256 - Log₃243

= Log₂2⁸ - Log₃3⁵    [Since 256=2⁸ and 243=3⁵].

= 8Log₂2 - 5Log₃3    [since Log_aa = 1]

= (8 x 1) - (5 x 1)

= 8 - 5

= 3

Hence Log₂256 - Log₃243 = 3

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

Simplify Log₂1024 – Log₅625

ALGEBRA 1

If 4x + 5y -9 = 0; find x-intercept.

Solution

x-intercept is when y=0.

4x + 5y -9 = 0

4x + 5(0) - 9 = 0

4x - 9 = 0

4x = 0+ 9

4x = 9

4      4

x= ⁹/4

Hence x= ⁹/4

TRY THIS………..

If 11x - 5y - 19 = 0; find x-intercept.

MATRIX 3

POLYGONS 1

An interior angle of a regular polygon is 78⁰ greater than an exterior angle. Find the interior angle.

Solution

Let i = interior angle, e = exterior angle.

Now i  + e=180⁰…………………(1)

But i = e+78⁰ …………………(2)

Substitute (2) in (1) above.

e+78⁰   + e=180⁰

e+ e+78⁰   =180⁰

2e+ 78⁰   =180⁰

2e=180⁰ - 78⁰   

2e=102⁰

2e=102⁰          dividing by 2 both sides.

2      2

e = 51⁰

From (1),

i  + e=180⁰

i  + 51=180⁰

i  =180⁰ - 51⁰

i  =129⁰ answer 

TRY THIS………………………   

An interior angle of a regular polygon is 86⁰ greater than an exterior angle. Find the interior angle.

VECTORS 1

SETS 1

If n(A)= 78 , n(B)= 90 and n(AuB)= 130, find n(AnB).

Solution

n(AuB) = n(A) + n(B) - n(AnB)

130 = 78 + 90 - n(AnB)

130 = 168 - n(AnB)

130 - 168 = - n(AnB)

-38 = -n(AnB)

n(AnB) = 38 [after dividing by -1 both sides]

Hence n(AnB) = 38 answer

TRY THIS………….

If n(A)= 71 , n(B)= 88 and n(AuB)= 130, find n(AnB).

MATRIX 2

EXPONENTIALS 1

Simplify 60

              125^-2/3

Solution

=  60

   125^-2/3

= 60 x 1

         125^-2/3

=  60 x 125^2/3        [Since 1/a^-n = aⁿ]

=  60 x (125^1/3)²        [Since 125^1/3 = cube root of 125 = 5]

=  60 x (5)²        

=  60 x 25       since (5)² = 25

= 1500 answer      

          

TRY THIS…..  

Simplify 20

             216^-2/3

MATRIX 1

SIMPLE INTEREST 1

Rayan deposited the amount of 30,000/= in a bank for 4 years and got a profit of 8400/=. Find the interest rate.

Solution

I = 8400/=, P = 30,000/=, T = 4 years, R = ?

I  = PRT

      100

8400  = 30,000 x R x 4

                  100

8400  = 30,000 x R x 4

                   100

8400  = 300 x R x 4

                      

8400  = 1200R

           

⁷8400  = 1200R

1200       1200

Hence the interest rate was  7%

TRY THIS………….

Rayan deposited the amount of 7,000/= in a bank for 3years and got a profit of 1260/=. Find the interest rate?