Wednesday, 21 March 2018

ACCOUNTS 1


Prepare a profit and loss account for the year ended 31ST May, 2015 from the following balances:
Transport     sh. 69,000
Advertising Sh. 60,000
General expenses sh 35,000
Sundry expenses sh 4,000
Interest received sh. 32,000
Carriage sh 42,000
Gross profit  sh 122,000

Solution

Dr      PROFIT AND LOSS ACCOUNT FOR THE YEAR ENDED ON 31TH, MAY-2011               Cr
Particulars
Folio
Amount
Particulars
Folio
Amount
Transport   

69,000
Gross profit
b/d
122,000
Advertising
60,000
Interest received
32,000
General expenses
35,000
Net Loss
56,000
Sundry expenses
4,000


Carriage
42,000




210,000


210,000


TRY THIS………..


Prepare a profit and loss account for the year ended 31ST September, 2016 from the following balances:
Transport -----------------------sh. 76,000
Advertising ---------------------Sh. 58,000
General expenses------------- sh 37,000
Sundry expenses ----------------sh 9,000
Interest received------------- sh. 32,000
Carriage -------------------------sh 23,000

Gross profit--------------------sh 116,000

EARTH AS SPHERE 1


Change 700 nautical miles into kilometers.

Solution

1 nautical mile= 1.852 km
700 nautical mile= ?

 = 1.852 x 700
          1

=1296.4

=1296.4 to 1 d.p

Hence 700 nautical miles= 1296km.

TRY THIS…………….


Change 60 nautical miles into kilometers

PROBABILITY 1


A bag contains 4 red balls and 6 blue balls. Two balls are taken from the bag. What is the probability that they are both red?

Solution

(This is a problem with replacement)

n(R) = 4, n(B) = 6, n(S) = 10

P(R) = n(R)
            n(S)

P(R) = 4
          10

1st pick = 4/10
2nd pick = 4/10 as well.


P(RR) =  4      x    4
             10           10

P(RR) =   16 /100 = 4/25       

Therefore Probability of drawing a red ball is 4/25     


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


A bag contains 9 purple stones and 11 blue stones. Two stones are taken from the bag. What is the probability that they are both purple?

SEQUENCE&SERIES 1


The 1st term of arithmetic progression is 63 and the common difference is 40. Find the nth term

solution

A1=63, d= 40, n=?

An =A1 + (n-1) d

An=63 + (n-1)40 

An=63 + 40n -40

An=40n + 63-40

An=40n + 23

Hence the nth term is An=40n + 23  

TRY THIS………………….. 


The 1st term of arithmetic progression is 144 and the common difference is 77. Find the nth term

LOGARITHMS 5


Evaluate Log1,000,000,000 +  log 0.01 + log3243

Solution

= Log1,000,000,000 +  log 0.01 + log3243

= Log109 +  log 10-2 + log33-5

= 9Log10 +  (-2log 10) + (-5log33)

= (9x1) + (-2x1) + (-5x1)

= 9 + (-2) + (-5)

= 2

Hence Log1,000,000,000 +  log 0.01 + log3243 = 2

TRY THIS……………..



Evaluate Log100,000,000 +  log 0.0001 + log381

EXPONENTIALS 3




Simplify (6a)2 - 3a2. 
 
Solution

= (6a)2 - 11a2    

= 62.a2 - 11a2               Since (mn)2 =m2 . n2

= 36a2 - 11a2   {since the square number of 6 is 36}

= 25a2

TRY THIS………………

Simplify (8m)2 – 45m2.   

WORD PROBLEMS 1


The sum of four consecutive numbers is 1358. Find the 3rd number.

Solution

Let the numbers be as shown in the table below

1st number
2nd number
3rd number
4th number
TOTAL
n
n+1
n+2
n+3
1358

Then, n + (n+1) + (n+2) + (n+3) = 1358

4n + 1+2+3= 1358

4n + 6 = 1358

4n = 1358 – 6

4n = 1352 

4n = 1352
 4        4

n = 338

3rd number = n +2

                   = 338 + 2

                   = 340

Hence the 3rd number is 340

TRY THIS………………….. 


The sum of four consecutive numbers is 426. Find the largest number.  


Sunday, 18 March 2018

EXPAND 3



Expand (y – 4)(y – 11)

Solution

= (y – 4) (y – 11)

= y (y – 11) – 4 (y – 11)

= y2 – 11y – 4y + 44 

= y2 – 15y + 44 answer

TRY THIS………..

Expand (a – 7) (a – 10)


LOGARITHMS 4



If log 2= 0.3010; find the value of log 400,000 without using tables.

solution

log400,000=log(4 x 100,000)

=log4 + log100,000

=log22 + log105

=2log2 + 5log10

=2(0.3010) + (5 x 1)

=(0.6020) +  5

=5. 6020

Hence log400,000=5. 6020


TRY THIS……………

If log 2= 0.3010; find the value of log 4,000,000 without using tables.

Saturday, 17 March 2018

FACTORIZE 1


Factorize 625x- 169y2

Solution

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

625x2- 169y2  = 252x2 - 132y2

                   = (25x)2 - (13y)2

                   = (25x - 13y)(25x + 13y)

Hence 625x2 - 169y2 = (25x - 13y)(25x + 13y)

TRY THIS………………………….



factorize 121c2- 25d2