LOGARITHMS-10

If log₅(3x + 101)=3; find x

   Solution

log₅(3x + 92)=3

 (3x + 92)=5³   

                      

 3x + 92=125

3x = 125 – 92

3x =  33

3x =  33   

3        3

X = 11

Hence x = 11

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

If log₂(2x - 22)=5; find x

APPROXIMATIONS-4

Estimate the value of 2.3  x  0.034

solution

= 2.3  x  0.034

= 2.0 x 0.03      [ 2.3 ≈ 2.0 to ones and 0.034 ≈ 0.03 to hundredths]

= 0.06

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

Estimate the value of 6.2  x  0.083

FUNCTIONS - 2

If F(x) = 12x + 6; Find F^-1(x).

Solution

HINT: F^-1(x) means inverse.

PROCEDURE:

Make x the subject and then interchange x and y variables.

Let y=F(x)

So,  y= 12x + 6

y – 6 = 12x

y – 6  = 12x

 12        12

y – 6   = x

   12

x  =   y – 6     after rearranging

            12

 y^-1 = x – 6     after interchanging x and y variables.

            12

F^-1(x) = x – 6     after interchanging x and y variables.

               12

Hence, F^-1(x) = x – 6     

                           12

TRY THIS……………………………

If F(x) = 5x + 28; Find F^-1(x).

LOGARITHMS-9

Evaluate Log₂(512 ÷ 8).

Solution

= Log₂(512 ÷ 8)

= Log₂512 -  Log₂8          (applying the quotient rule)

= Log₂2⁹ -  Log₂2³             ( 512= 2⁸ and 8=2³ )

= 9Log₂2 -  3Log₂2       ( remember  Log_aa^c = cLog_aa )

= (9 x 1) - (3 x 1)          ( remember  Log_aa = 1 )

= 9 - 3

= 6

hence Log₂(512 ÷ 8) = 6

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

Evaluate Log₂(1024 ÷ 32). 

MATOKEO YA FORM IV - 2015

 BOFYA HAPA KUPATA MATOKEO YA 

KIDATO CHA NNE 2015

Chagua Herufi Ya Shule Yako.
A	B	C	D	E	F
G	H	I	J	K	L
M	N	O	P	Q	R
S	T	U	V	W	X
Y			Z

FRACTIONS - 2

Express as a single fraction m - 5 + m+1

                                               6          4

solution

= m - 5 + m+1

      6          4

= 2(m – 5) + 3(m+1)

            12         

= 2m - 10 + 3m+3

            12          

= 2m + 3m + 3- 10

            12         

= 5m +  -7

       12         

= 5m - 7

     12         

=  5m - 7                 answer

       12       

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

Express as a single fraction 4c - 1 + 2d+1

                                              4           2

RELATIONS - 2

Let R={(5,3), (6,1), (-2,-6), (14,-20)}. Find the domain and range of R.

solution

For domain we check on the values of x in each point.

Domain={5, 6, -2, 14}

For range we check on the values of y in each point.

Range={3, 1, -6, -20}

Hence Domain={5, 5, -2, 14} and Range = {3, 1, -6, -20}

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

Let R={(7,1), (-13,5), (-1,-2), (14, -9)}. Find the domain and range of R.

DIFFERENCE OF 2 SQUARES - 2

Evaluate 2797² – 2787²

Solution

2797² – 2787² = (2797 + 2787)( 2797 – 2787)

                     = (5584)( 10)

                     = 55840

Hence 2797² – 2787² = 55840

TRY THIS…………….

Evaluate 936² – 836²

SETS - 4

If n(A)= 176 , n(B)= 160 and n(AnB)=150, find n(AuB).

Solution

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

             = 176 + 160 – 150

             = 336 – 150

             = 186

Hence n(AuB) = 186 answer

TRY THIS…………………………….

If n(A)= 146 , n(B)= 164 and n(AnB)=100, find n(AuB).

SIMPLE INTEREST-3

Rayan deposited the amount of 80,000/= in a bank for 2 years and got a profit of 2500/=. Find the interest rate?

Solution

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

I  = PRT

      100

2500  = 80,000 x R x 2

                      100

2500  = 80,000 x R x 2

                      100

2500  = 800 x R x 2

                      

2500  = 4000R

           

⁵2500  = ¹4000R

₈4000      ₁4000

Hence the interest rate was  1.6%

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?