QUADRATIC FORMULA 1

SIMPLE INTEREST 1

Dikshi deposited the amount of 9000/= in a bank which gives an interest rate of 3% for 2 years. Find the simple interest she got?

Solution

I = ?,  P = 9,000/=, T = 2 years, R = 5%

I  = PRT

      100

I  = 9000 x 5 x 2

            100

I  = 9000 x 5 x 2

            100

I  = 90 x 5 x 2

          

I  = 900/=

Hence the simple interest was Tsh 900/=

TRY THIS……………………

Dikshi deposited the amount of 9000/= in a bank which gives an interest rate of 6% for 7 years. Find the simple interest she got?

EXPONENTS 3

Write in expanded form: 5⁷

Solution

5⁷ = 5 x 5 x 5 x 5 x 5 x 5 x 5

TRY THIS……………….

Write in expanded form: 7⁸

PERCENTAGE PROFIT 3

A man got a profit of 200/= after selling an item for 5000/=. Find the percentage profit.

Solution

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

                       B.P

%’ge profit = 200   x  100   

                     5000

%’ge profit = 4%   

                       

Hence Percentage Profit is 4%

TRY THIS………………….

A man got a profit of 500/= after selling an item for 4000/=. Find the percentage profit.

LOGARITHMS 1

Evaluate Log₂(128 x 16).

Solution

= Log₂(128 x 16)

= Log₂128 +  Log₂16          (applying the product rule)

= Log₂2⁷ +  Log₂2⁴             (32= 2⁵ and 16=2⁴ )

= 7Log₂2 +  4Log₂2       ( remember  Log_aa^c = cLog_aa )

= (7 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 7 + 4

= 11

hence Log₂(128 x 16) = 11

TRY THIS………………

Evaluate Log₂(256 x 4). 

INEQUALITIES 1

Solve for x and locate the answer on a number line. 2x – 1 ≤ x + 5 ≤ 6x    

Solution

2x – 1 ≤ x + 5 and  x + 5 ≤ 6x

2x – x ≤ 1+ 5 and  5 ≤ 6x - x

x ≤ 6 and  5 ≤ 5x (divide by 5 both sides)

x ≤ 6 and  1 ≤ x

x ≤ 6 and  x ≥ 1 

the diagram:

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

Solve for x and locate the answer on a number line: 2x – 1 ≤ x + 9 ≤ 4x 

PERCENTAGE PROFIT 2

A man sold an item at 7000/=. Find the profit made if the percentage profit was 2% .

Solution

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

                         B.P

2% =      P         X  100   

            7000

7000  x  2% = P x 100   

14000 = P x 100

                    

14,000 = 100P

14,000  = 100P

  100         100

        

P = 140

                      

Hence the profit was 140/=

TRY THIS…………..

A man sold an item at 12000/=. Find the profit made if the percentage profit was 4% .

LENGTH OF AN ARC 1

Find the length of an arc if the radius of the circle is 80cm.

Solution

r = 80cm

L = ∏r

      180⁰

L = ∏ x  80

             180⁰

L = 4∏ cm

        9

Hence length of an arc is ^4∏/9 cm

TRY THIS………………….

Find the length of an arc if the radius of the circle is 60cm.

EXPONENTS 2

Simplify the following by writing in power form:

4⁵⁰

4¹⁰

Solution

= 4^{50 - 10} 

=4⁴⁰

TRY THIS……………….

Simplify the following by writing in power form:

3⁵⁰

3⁴⁰

AXIS OF SYMMETRY 1

Find the axis of symmetry for F(x) = 3x² - 48x + 5

Solution

a=3, b=-48

Axis of symmetry = -b/2a

                             =  -(-48)

                                 2 x 3

                            =    48

                                  6

Hence the axis of symmetry is 8

TRY THIS……………

Find the axis of symmetry for F(x) = 2x² - 20x + 5.