DIFFERENCE OF 2 SQUARES 1

Evaluate 6657² – 6647²

Solution

6657² – 6647² = (6657 + 6647)( 6657 – 6647)

                     = (13304)( 10)

                     = 133040

Hence 6657² – 6647² = 133040.

TRY THIS…………………

evaluate 1955² – 1945²

TRANSPOSITION OF FORMULAE 2

SIMULTANEOUS EQUATIONS 2

Solve the following equations by substitution method.

x + y = 9

x + 3y = 13

Solution

x + y = 9 ----------- (i)

x + 3y = 13 ---------- (ii)

from equation (i)

x + y = 9

x = 9- y ----------(iii)

substitute equation (iii) in (ii) above,

x + 3y = 13

(9- y)  + 3y = 13

9+2y = 13

2y = 13 - 9

2y = 4

2      2

y = 2

From equation (iii)

x = 9- 2 ----------(iii)

x = 9- 2

 x = 7

Hence x=7 and y=2.

TRY THIS………………………..

4x - y = 20

3x + 2y = 70

SETS 2

If n(A) = 30 , n(AuB) = 60 and n(AnB) =10, find n(B)

Solution

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

  60     = 30 + n(B)  – 10

  60     = 30 -10 + n(B)  

  60     = 20 + n(B)  

  60 - 20        = n(B)

  40        = n(B)

Hence n(B) = 40 answer

TRY THIS…………………………….

If n(A)= 40 , n(AuB) = 70 and n(AnB) = 20, find n(B).

SIMPLE INTEREST 2

Rayan deposited the amount of 6,000/= in a bank for 5 years and got a profit of 2000/=. Find the interest rate?

Solution

I = 2000/=, P = 6,000/=, T = 5 years, R = ?

I  = PRT

      100

2000  = 6,000 x R x 5

                      100

2000  = 6,000 x R x 5

                      100

2000  = 60 x R x 5

                     

2000  = 300R

          

^6.672000  = 300R

     300       300

Hence the interest rate was Tsh 6.67%

TRY THIS……………….

Kibonde deposited the amount of 9,000/= in a bank for 4 years and got a profit of 3000/=. Find the interest rate?

RADIAN INTO DEGREES 1

Change ^∏/90 radians into degrees.

Solution

Ө = 180⁰ x s                but s = ^∏/90

       ∏

Ө = 180⁰  x  ∏              

       ∏     90

Ө =  ² 180   x   ∏ ¹             

          ₁∏     90₁

Hence ^∏/90 radian is equal to 2⁰.

TRY THIS……………

Change ^∏/20 radians into degrees.

PERCENTAGE PROFIT 1

A man got a profit of 500/= after selling an item for 2500/=. Find the percentage profit.

Solution

%’ge profit = Profit   X  100    where B. P. represents Buying Price.

                         B.P

%’ge profit = 500   X  100   

                       2500

%’ge profit = 20%   

                       

Hence Percentage Profit is 20%

TRY THIS……………………………

A man got a profit of 600/= after selling an item for 3000/=. Find the percentage profit.

LENGTH OF AN ARC 1

Find the length of an arc if the radius of the circle is 10cm.

Solution

L = ∏r

      180⁰

L = ∏ x  10

             180⁰

L = ∏ cm

      18

Hence length of an arc is ^∏/18 cm

TRY THIS……………

Find the length of an arc if the radius of the circle is 8cm.

SIMPLE INTEREST 1

Dikshi deposited the amount of 6000/= in a bank which gives an interest rate of 3% for 4 years. Find the simple interest she got?

Solution

I = ?,  P = 6,000/=, T = 4 years, R = 3%

I  = PRT

      100

I  = 6000 x 3 x 4

            100

I  = 6000 x 3 x 4

            100

I  = 60 x 3 x 4

          

I  = 720/=

Hence the simple interest was Tsh 720/=

TRY THIS…………………………

Harshita deposited the amount of 7600/= in a bank which gives an interest rate of 4% for 5 years. Find the simple interest she got?

TRANSPOSITION OF FORMULAE 1

If A = HNE make E the subject of the formula.

Solution

A = HNE

  A   =   HNE

HN      HN

 A   =   E

HN     

Hence   E =      A 

                       HN     

TRY THIS………………………..

If K = WRG make G the subject of the formula.