GEOMETRY J2

 The total interior angles of a regular polygon is 3,960⁰. Find the interior angle.

Solution

(n-2)180⁰= Total interior angles.

(n-2)180⁰ = 3,960⁰

(n-2)180⁰ = 3,960⁰      Dividing by 180⁰ both sides

    180⁰              180⁰

 

(n-2) = 22

 n  = 22+2

n = 24

 

i = (n-2)180⁰

       n            .

i = (24-2)180⁰

        24           

 

i = 22 x180⁰

        24           

 

i = 165⁰

 

Interior angle=165⁰

 

Exterior angle=360⁰ ÷ 18

 

Exterior angle=20⁰

 

 Hence the exterior angle is 20⁰  

 

TRY THIS……………….

 

 

The total interior angles of a regular polygon is 2340⁰. Find the interior angle.

LOGARITHMS J1

Find x if Log_x625 = ¹/2

 

solution

 

Log_x625 = ¹/2

 

625 = x^1/2 .

 

25^1/2 = x^1/2 . [since 625 = 25^1/2 in exponential form]

 

25 = x . [like powers cancels out]

 

So, x = 25

 

Hence x = 25

 

 

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

 

 

Find y if Log_y121 = ¹/2

 

GEOMETRY J1

 

The total interior angles of a regular polygon is 2880⁰. Find the exterior angle.

Solution

(n-2)180⁰= Total interior angles.

(n-2)180⁰ = 2880⁰

(n-2)180⁰ = 2880⁰      Dividing by 180⁰ both sides

    180⁰            180⁰

 

(n-2) = 16

 n  = 16+2

n = 18

 

Exterior angle=360⁰ ÷ n

 

Exterior angle=360⁰ ÷ 18

 

Exterior angle=20⁰

 

 Hence the exterior angle is 20⁰  

 

TRY THIS……………….

 

 

The total interior angles of a regular polygon is 2340⁰. Find the exterior angle.

ALGEBRA J1

 

p*q =(p-q)(3p+q) Find (2*-3)

solution

=(p-q)(3p+q)

=[2-(-3)][(3x2)+(-3)]

=[2+3][6+(-3)]

=(5)(3)

=15

Hence (2*-3) = 15

TRY THIS……………….

  

If p*q =(5p-q)(6p+q) Find (4*-2)

EXPONENTIALS J1

 

If y⁵ = 3, find y¹⁰ - 10y⁵.

 

Solution

 

= y¹⁰- 10y⁵.

 

= (y⁵)²- 10y⁵

 

= (3)¹⁰ – (10 x 3)     remember y⁵ = 3

 

= (59049) – (30)

 

= 59019

 

 

Hence y¹⁰- 10y⁵= 59019.

 

TRY THIS……………….

 

 

If  w⁹ = 3, find w³⁶- 10w⁹.

VARIATIONS J1

 

x is directly proportional to y. x=32 while y=8. Find y when x is 188.

 

Solution

 

x ⍺ y

x = ky

 

32 = k x 8

 

32 = 8k    [dividing by 8 both sides]

8      8

 

k = 4

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

 

k = 4, y= ? x = 188.

 

x = ky

 

188 = 4 x y

 

188 = 4y

4        4

 

Hence y = 47.

 

TRY THIS…………….

 

 

x is directly proportional to y. x=40 while y=4. Find y when x is 270.

FACTORIZE J1

Factorize 121-9m²

 

Solution

 

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

 

121-9m² = 11²-3²m²       

 

            = 11² - (3m)²       

 

            = (11 - 3m)(11 + 3m)

 

Hence 121-9m² = (11 - 3m)(11 + 3m)  answer

 

 

TRY THIS…………….

 

 

 

Factorize 81 – 49p² 

SIMPLE INTEREST J1

 

Kibadeni deposited the amount of 8,000/= in a bank for 5 years and got a profit of 4400/=. Find the interest rate?

 

Solution

 

I = 4400/=, P = 8,000/=, T = 5 years, R = ?

 

I  = PRT

      100

 

Where P=Principal amount

            I = simple Interest

           T= Time

           R=Rate

 

4400  = 8,000 x R x 5

                      100

 

 

4400  = 8,000 x R x 5

                      100

 

4400  = 80 x R x 5

                      

4400  = 400R

          

¹¹4400  = 400R

  400       400

 

Hence the interest rate was Tsh11%

 

 

TRY THIS……………….

 

 

 

Oden deposited the amount of 18,000/= in a bank for 4 years and got a profit of 3000/=. Find the interest rate?