Friday 28 March 2014

LOGARITHMS B15



If Logax = 13, find Loga(1/x)

Solution

= Loga(1/x)

= Logax-1

= -1 x Logax

= -1 x 13

= -13


TRY THIS………..

If LogaW= 26, find Loga(1/W)

ARITHMETIC PROGRESSION C3



The 1st term of an A.P. is 80 and the common difference is 24. Find the 10th term.

Solution

A1= 80, d = 24

An = A1 + (n-1)d

A10 = A1 + (10-1)d

A10 = A1 + 9d

A10 = 80 + (9x24) [ after substituting A1= 80, d = 24 as given above]

A10 = 80 + 216

A10 = 296

Hence the 10th term is 296.



TRY THIS……………

The 1st term of an A.P. is 17 and the common difference is 33. Find the 8th term.

FUNCTIONS B13



If F(x) = 8x + 10; 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= 8x + 10

y – 10 = 8x

y – 10  = 8x
   8          8

y – 10   = x
   8

x  =   y – 10     after rearranging
           8

 y-1 = x – 10     after interchanging x and y variables.
             8

F-1(x) = x – 10     after interchanging x and y variables.
                8

Hence, F-1(x) = x – 10     
                              8


TRY THIS……………………………

If F(x) = 7x + 20; Find F-1(x).

LOGARITHMS B14



If log 2= 0.3010; find the value of log 25 without using tables.

solution

log25=log(100÷ 4)

=log100 - log4

=log102 – log22

=2log10 – 2log2

=(2x1) – 2(0.3010)

=2– 2(0.3010)

=2 – 0.6020

=1.398

Hence log25=1.398


TRY THIS……………

If log 2= 0.3010; find the value of log 25 without using tables.

Tuesday 25 March 2014

CIRCLES C11



Find the value of <PRN in the figure below.



Solution

<PMR = <PNR ( angles subtended by the same arc are equal)

<PMR = 680

so, <PMN = 680 + 360

                = 1040

<PMN + <PRN = 1800 (opposite angles in a cyclic quadrilateral add up to 180)

1040 + <PRN = 1800

  <PRN = 1800 - 1040

  <PRN = 760