ACCOUNTS-2

From the following information you are required to prepare a balance sheet of BIBANJA & Co. LTD as at 06.09.2013

Creditors----------------------------120,000/=

Debtors ------------------------------250,000/=

Bank Overdraft---------------------80,000/=

Cash in Hand----------------------130,000/=

Stock------------------------------------57,000/=

Bank loan----------------------------200,000/=

Furniture------------------------------93,000/=

Premises-----------------------------260,000/=

Capital-------------------------------390,000/=

Solution

Balance sheet of BIBANJA & Co. LTD as at 06.09.2013

LIABILITIES	Amount	Amount	ASSETS	Amount	Amount
Capital CURRENT LIABILITIES Creditors Bank Overdraft LONG TERM LIABILITIES Bank loan	120,000    80,000	390,000 200,000 200,000	FIXED  ASSETS Premises Furniture CURRENT  ASSETS Stock Debtors Cash in hand	57,000 250,000  130,000	260,000   93,000 437,000
		790,000			790,000

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

From the following information you are required to prepare a balance sheet of MARUKU & Co. LTD as at 06.04.2015

Creditors----------------------------127,000/=

Debtors ------------------------------260,000/=

Bank Overdraft---------------------85,000/=

Cash in Hand----------------------140,000/=

Stock------------------------------------57,000/=

Bank loan----------------------------200,000/=

Furniture------------------------------93,000/=

Premises-----------------------------262,000/=

Capital-------------------------------400,000/=

LOGARITHMS 6

MIDPOINT-1

Find the midpoint of a line from (1, 14) to (17, 10)

Solution

x₁=1, x₂=17, y₁=14, y₂=10.

Mid point = (x1 + x2, y1 + y2)

                        2             2

Mid point = (1 + 17, 14 + 10)

                       2              2

Mid point = (18, 24)

                     2    2

Hence midpoint = (9, 12)

TRY THIS……………………..

  

Find the midpoint of a line from (6, 2) to (14, 6)

RADICALS 5

ALGEBRA 2

If │2x – 19 │= 21; Find  x

Solution

±(2x – 19 )= 21

2x -19= 21    OR   –(2x-19) = 21

2x – 19 = 21    OR   -2x+19= 21

2x = 21 + 19    OR   -2x= 21-19

2x = 40     OR   -2x  =  2

2      2                2        2

x = 20  OR  x = 1

Hence x = 20 OR x = 1     

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

If │4x – 12 │= 48; Find  x

LOGARITHMS 6

ANGLES 1

If x-7⁰ and 4x + 22⁰ are complementary angles, find the value of x.

Solution

Complementary angles add up to 90⁰.

so,  x-7⁰ + 4x + 22⁰ = 90⁰.

so,  x + 4x + 22⁰ - 7⁰ = 90⁰.

so,  5x + 15⁰ = 90⁰.

so,  5x = 90⁰ -  15⁰

so,  5x = 75⁰

so,  5x = 75¹⁵

      5      5

Hence x = 15⁰

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

If 3x - 4⁰ and 7x + 54⁰ are complementary angles, find the value of x.

NUMBER LINE 2

SETS 2

In Kasanga village the number of people who speak English or French is 300. 150 of them speak English and 170 of them speak French. How many speak both languages?

solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.

Let French=n(F), English= n(E).

n(E)= 180,

n(F)= 170,

n(EuF) = 300,

n(EnF)=?

n(EuF) = n(E) + n(F) - n(EnF)

300  =  150 + 170 – n(EnF)

300  =  320 – n(EnF)

n(EnF) =  320 – 300

n(EnF) =  20

Hence n(EnF)=20 answer

∴  20 speak both languages   .

TRY THIS……..

In Malenda village the number of people who speak English or French is 280. 185 of them speak English and 175 of them speak French. How many speak both languages? 

RADICALS 4

EXPONENTIALS 4

Find x if 64^x = 0.125; find x.

Solution

64^x = 0.125

(2⁶)^x = 0.125          [since 64=2⁶ ]

2^6x = 0.125          

2^6x = ¹²⁵/₁₀₀₀     [converting 0.125 into fraction]       

2^6x = ¹/₈    [after simplifying]       

2^6x = 8^-1           [since ¹/_a=a^-1]

2^6x = (2³)^-1

2^6x = 2^{3 x-1}           

2^6x = 2^-3           [since (a^c)^d =a^cd]

2^6x = 2^-3           [same bases cancel out]

6x = -3         

6x = -3 ^-1        

6      6 ₂

x= ^-1/2

Hence x= ^-1/2  .

TRY THIS…………………….

Find x if 16^2m = 0. 5; find m.

LOGARITHMS 5

FUNCTIONS 1

If f(x) = |x - 24| evaluate f(-50)

solution

f(x) = |x - 24|

f(-50) = |-50- 24|

f(-50) = |-74| = 74 since any number out of absolute signs is +ve.

Hence f(-50) = 74

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

If f(x) = |x - 30| evaluate f(-15)

RADICALS 3

ALGEBRA 1

If  x+4y = 1            find  ^x/y             

    x-3y     4

solution

x+4y = 1           

x-3y     4

1(x-3y) = 4(x+4y)           [after cross multiplying]

x-3y = 4x+16y

x - 4x = 16y + 3y

-3x = 19y

¹-3x =   19y         [dividing by -3 both sides]

₁-3        -3

x =   19y         

        -3

      

x =     19y ¹   [dividing by y both sides]    

y       -3y ₁

x = ^-19/₃

y    

Hence ^x/_y = ^-19/₃answer.          

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

If  x+2y = 1            find  ^x/y             

    x- 2y     6

NUMBER LINE 1

AXIS OF SYMMETRY 1

Find the axis of symmetry for F(x) = 6x² + 48x + 8

Solution

a=6, b=48

Axis of symmetry = -b/2a

                                  =  -(48)

                                       2 x 6

                                 =    -48

                                         12

                                 =   -4

                                       

Hence the axis of symmetry is ^-10/3

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

Find the axis of symmetry for F(x) = 5x² + 40x - 2

MATRIX 3

LOGARITHMS 4

Evaluate Log₂(256 x 64 x 32).

Solution

= Log₂(256 x 64 x 32)

= Log₂256 +  Log₂64 +  Log₂32                   (applying the product rule)

= Log₂2⁸ +  Log₂2⁶    +  Log₂2⁵                      ( 256= 2⁸ and 64=2⁶ ,32=2⁵)

= 8Log₂2 +  6Log₂2    +  5Log₂2         ( remember  Log_aa^c = cLog_aa )

= (8 x 1) +  (6 x 1) +  (5 x 1)                  ( remember  Log_aa = 1 )

= 8 + 6 + 5

= 19

hence Log₂(256 x 64 x 32) = 19

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

Evaluate Log₂(512 x 128 x 32).