ACCOUNTS-1

Prepare a profit and loss account for the year ended 31^ST May, 2011 from the following balances:

Transport     sh. 64,000

Advertising Sh. 55,000

General expenses sh 35,000

Sundry expenses sh 4,000

Interest received sh. 32,000

Carriage sh 32,000

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    Advertising General expenses Sundry expenses Carriage		64,000 55,000 35,000 4,000 32,000	Gross profit Interest received Net Loss	b/d	122,000 32,000 36,000
		190,000			190,000

TRY THIS………..

Prepare a profit and loss account for the year ended 31^ST July, 2015 from the following balances:

Transport     sh. 70,000

Advertising Sh. 55,000

General expenses sh 36,000

Sundry expenses sh 7,000

Interest received sh. 32,000

Carriage sh 22,000

Gross profit  sh 130,000

MATRIX 2

RATIOS 1

The areas of two circles are in the ratio of 25:4 . Calculate the radius of the smaller circle when the radius of larger circle is 40 cm. 

solution

let R = radius of larger circle

let r = radius of smaller circle

R= 40cm, r = ? Ratio = 25:4.

For larger circle

A1 = ∏R² …………(i)

For smaller circle

A2 = ∏r² …………(ii)

A1 = ∏R²

A2    ∏r²

A1 = R²

A2     r²

A1 = (R/r)² 

A2

√(^A1/A2) =  (R/r)

√(²⁵/4) =  (40/r)

5 = 40                 

2     r

(2 x 40) = (5 x r)     after cross multiply.

80 = 5r

80 = 5r

5      5

r = 16

∴ radius of smaller circle is 16cm.

TRY THIS………..

NECTA 1997 QN 5(c)

The areas of two circles are in the ratio of 16:9 . Calculate the radius of the smaller circle when the radius of larger circle is 24 cm. 

EXPONENTIALS 3

LOGARITHMS 3

Simplify Log₂128 – Log₅15625

Solution

= Log₂128 – Log₅15625

= Log₂2⁷ – Log₅5⁶ 

= 7Log₂2 – 6Log₅5   because Log_aaⁿ =  nLog_aa

= (7 x 1) – (6 x 1)  

= 7 – 6

= 1

Hence Log₂128 – Log₅15625 = 1 

TRY THIS…………..

NECTA 1995 QN 24b

Simplify Log₂32 – Log₃9.

MATRIX 1

EXPONENTIALS 2

If (2^x-17)(7^y+8) = (2²⁰)(7²⁸) find 2x+y.

solution

2^x-17 = 2²⁰

x – 17 = 20

x = 20+17

x = 37

…………………………

7^y+8 = 7²⁸

y + 8 = 28

y = 28 - 8

y = 20

……………………

2x + y = 2(37) + 20 = 74 + 20=94.

TRY THIS………….

 NECTA F-IV,2008 QN. 3a

If (2^x-7)(7^y+8) = (2²⁰)(7²⁸) find (i)x+y.      (ii) y/x

RADICALS 2

PROBABILITY 1

A number is chosen at random from 21 – 32 inclusive. Find the probability that it is a prime or a multiple of 3.

Solution

THIS IS A MUTUALLY EXCLUSIVE EVENT

Let n(S) represent sample space

P(M) = probability of a multiple of 3

P(R) = probability of prime number

n(S) = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32} = 12

n(M) = {21, 24, 27, 30} = 4

n(R) = {23, 29, 31} = 3

P(M) = ⁴/12

P(R) = ³/12

………………………….

P(MuR) = P(M) + P(R)

P(MuR) = ⁴/12 + ³/12

              = ⁷/12

              = ⁷/12

P(MuR) = ⁷/12 answer

TRY THIS…………………

A number is chosen at random from 17 – 30 inclusive. Find the probability that it is a prime number or a multiple of 4.

SIMPLIFY 1

Simplify the expression

m² + t²/ (s + t)

solution

from difference of two squares p² - q² = (p - q)(p + q)

= m² + t²/ (s + t)

= (m + t)(m - t)

      m + t

= (m + t)(m - t)

      m + t

=  m - t    answer

      

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

NECTA FORM II - 2012 QN. 12

Simplify the expression

a² + b²/ (a + b)