APPROXIMATIONS - 5

Estimate the value of 2.3  x  0.064

solution

= 2.3  x  0.064

= 2.0 x 0.06      [ 2.3 ≈ 2.0 to ones and 0.064 ≈ 0.06 to hundredths]

= 0.12

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

Estimate the value of 3.2  x  0.083

LOGARITHMIC EQUATIONS - 7

If Log_ax = 46, find Log_a(¹/x)

Solution

= Log_a(¹/x)

= Log_ax^-1

= -1 x Log_ax

= -1 x 46

= -46

TRY THIS………..

If Log_aW= 89, find Log_a(¹/W)

SIMPLE INTEREST-2

Rayan deposited the amount of 80,000/= in a bank for 2 years and got a profit of 1200/=. Find the interest rate?

Solution

I = 1200/=, P = 80,000/=, T = 2 years, R = ?

I  = PRT

      100

1200  = 80,000 x R x 2

                      100

1200  = 80,000 x R x 2

                      100

1200  = 800 x R x 2

                      

1200  = 4000R

           

³1200  = 4000R

  4000      4000

Hence the interest rate was  0.3%

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?

EXPONENTIALS - 1

If a² = 30; find the value of a⁴.

solution

a⁴ = (a²)².

a⁴ = (30)².   [ since a² = 30]

a⁴ = 30 x 30

a⁴ = 900  answer

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

NECTA FORM II - 2012 QN. 8

If a² = 12; find the value of a⁴.

PERCENTAGE PROFIT - 1

A man got a profit of 400/= after selling an item for 8000/=. Find the percentage profit.

Solution

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

                      B.P.

%’ge profit = 400   X  100   

                    8000

%’ge profit = 5%   

                       

Hence Percentage Profit is 5%

TRY THIS……………………………

A man got a profit of 1500/= after selling an item for 600,000/=. Find the percentage profit.

DIFFERENCE OF 2 SQUARES - 4

Factorize 1-B²

Solution

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

1-B² = 1²-B²       

        = (1 - B)(1 + B)

Hence 1 - B² = (1 - B)(1 + B)

TRY THIS…………….

Factorize 16 - W²

APPROXIMATIONS 4

Estimate the value of 4143  ÷ 52.

Solution

= 4123     

     52

= 4000      [ since 4143 ≈ 4000   and   52 ≈ 50 ]

     50

= 80

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

Estimate the value of 7203  ÷ 19

SETS - 2

If n(A)= 60 , n(AuB) = 160 and n(AnB)=10, find n(B)

Solution

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

  160     = 60 + n(B)  – 10

  160     = 60 -10 + n(B) 

  160     = 50 + n(B) 

  160 - 50        = n(B)

  110        = n(B)

Hence n(B) = 110 answer

TRY THIS…………………………….

If n(A)= 63 , n(AuB) = 125 and n(AnB) = 30, find n(B).

SIMPLE INTEREST-1

Priya deposited the amount of 90000/= in a bank which gives an interest rate of 3% for 4 years. Find the simple interest she got.

Solution

I = ?,  P = 90,000/=, T = 4 years, R = 3%

I  = PRT

      100

I  = 90,000 x 3 x 4

            100

I  = 90,000 x 3 x 4

            100

I  = 900 x 3 x 4

          

I  = 10,800/=

Hence the simple interest was Tsh 10,800/=

TRY THIS………………….

Edmund deposited the amount of 70,000/= in a bank which gives an interest rate of 5% for 4 years. Find the simple interest he got?

DIFFERENCE OF 2 SQUARES 3

Evaluate 2794² – 2784²

Solution

2794² – 2784² = (2794 + 2784)( 2794 – 2784)

                     = (5578)( 10)

                     = 55780

Hence 2794² – 2784² = 55780

TRY THIS…………….

Evaluate 931² – 831²