Wednesday 16 December 2015

APPROXIMATIONS - 5


Estimate the value of 2.3  x  0.064

solution

= 2.3  x  0.064

= 2.0 x 0.06      [ 2.3 ≈ 2.0 to ones and 0.064 ≈ 0.06 to hundredths]

= 0.12

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



Estimate the value of 3.2  x  0.083

LOGARITHMIC EQUATIONS - 7


If Logax = 46, find Loga(1/x)

Solution

= Loga(1/x)

= Logax-1

= -1 x Logax

= -1 x 46

= -46


TRY THIS………..


If LogaW= 89, find Loga(1/W)

SIMPLE INTEREST-2


Rayan deposited the amount of 80,000/= in a bank for 2 years and got a profit of 1200/=. Find the interest rate?

Solution

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

I  = PRT
      100

1200  = 80,000 x R x 2
                      100

1200  = 80,000 x R x 2
                      100

1200  = 800 x R x 2
                      
1200  = 4000R
           
31200  = 4000R
  4000      4000


Hence the interest rate was  0.3%

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?

EXPONENTIALS - 1


If a2 = 30; find the value of a4.

solution

a4 = (a2)2.

a4 = (30)2.   [ since a2 = 30]

a4 = 30 x 30

a4 = 900  answer


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


NECTA FORM II - 2012 QN. 8


If a2 = 12; find the value of a4.

PERCENTAGE PROFIT - 1


A man got a profit of 400/= after selling an item for 8000/=. Find the percentage profit.

Solution

%’ge profit = Profit   X  100    [where B. P. represents Buying Price.]
                      B.P.

%’ge profit = 400   X  100   
                    8000

%’ge profit = 5%   
                       
Hence Percentage Profit is 5%

TRY THIS……………………………



A man got a profit of 1500/= after selling an item for 600,000/=. Find the percentage profit.

DIFFERENCE OF 2 SQUARES - 4


Factorize 1-B2

Solution

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

1-B2 = 12-B2       

        = (1 - B)(1 + B)

Hence 1 - B2 = (1 - B)(1 + B)

TRY THIS…………….



Factorize 16 - W2

APPROXIMATIONS 4


Estimate the value of 4143  ÷ 52.

Solution

= 4123     
     52

= 4000      [ since 4143 ≈ 4000   and   52 ≈ 50 ]
     50

= 80

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


Estimate the value of 7203  ÷ 19

SETS - 2


If n(A)= 60 , n(AuB) = 160 and n(AnB)=10, find n(B)

Solution

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

  160     = 60 + n(B)  – 10

  160     = 60 -10 + n(B) 

  160     = 50 + n(B) 

  160 - 50        = n(B)

  110        = n(B)

Hence n(B) = 110 answer



TRY THIS…………………………….



If n(A)= 63 , n(AuB) = 125 and n(AnB) = 30, find n(B).

SIMPLE INTEREST-1


Priya deposited the amount of 90000/= in a bank which gives an interest rate of 3% for 4 years. Find the simple interest she got.

Solution

I = ?,  P = 90,000/=, T = 4 years, R = 3%

I  = PRT
      100

I  = 90,000 x 3 x 4
            100

I  = 90,000 x 3 x 4
            100

I  = 900 x 3 x 4
          
I  = 10,800/=

Hence the simple interest was Tsh 10,800/=

TRY THIS………………….


Edmund deposited the amount of 70,000/= in a bank which gives an interest rate of 5% for 4 years. Find the simple interest he got?

DIFFERENCE OF 2 SQUARES 3


Evaluate 27942 – 27842

Solution

27942 – 27842 = (2794 + 2784)( 2794 – 2784)

                     = (5578)( 10)

                     = 55780

Hence 27942 – 27842 = 55780

TRY THIS…………….



Evaluate 9312 – 8312

INEQUALITIES - 2


If 3x – 17  x + 5  21x; find x

solution

3x – 17  x + 5 and  x + 5  21x

3x – x  17+ 5 and  5  21x - x

2x  22(divide by 2 both sides) and  5  20x (divide by 20 both sides)

x  11 and  1/4  x


x  11 and  x  1/4 

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


If 13x – 11  x + 25  6x; find x

MID POINT 1


Find the midpoint of a line from (11, 4) to (7, 10)

Solution

x1=11, x2=7, y1=4, y2=10.

Mid point = (x1 + x2, y1 + y2)
                         2             2

Mid point = (11 + 7,  4 + 10)
                        2          2

Mid point = (18, 14)
                     2    2

Hence midpoint = (9, 7)

TRY THIS……………………..



Find the midpoint of a line from (14, 8) to (2, 16)

FACTORIZE-4


Factorize 2x2 + 6x - 8

Solution

= 2x2 + 6x - 8.  We split the middle term (+6x) to be (-2x + 8x).

= 2x2 - 2x + 8x – 8                (-3x) = -14x + 5x.

= (2x2 -2x) + (8x - 8)

= 2x(x - 1) + 8(x - 1)

= (2x + 8) (x -1)

Hence 2x2 + 6x – 8 = (2x + 8) (x - 1) answer.

TRY THIS…..


Factorize 6x2 + x – 2.

ARITHMETIC PROGRESSION - 4


The 1st term of an A.P. is 70 and the common difference is 34. Find the 10th term.

Solution

A1= 70, d = 34

An = A1 + (n-1)d

A10 = A1 + (10-1)d

A10 = A1 + 9d

A10 = 70 + (9x34) [ after substituting A1= 70, d = 34 as given above]

A10 = 70 + 306

A10 = 376

Hence the 10th term is 376.



TRY THIS……………


The 1st term of an A.P. is 44 and the common difference is 33. Find the 7th term.

LOGARITHMIC EQUATIONS - 6


Find x if Logx625 = 4

solution

Logx625 = 4

625 = x4 .

54 = x4 . [since 625 = 54 by prime factorization]

54 = x4 . [ powers cancel out]

x = 5

Hence x = 5

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

Find y if Logy216 = 3


FUNCTIONS 7


If F(x) = 4x2 + 12x - 420; find F(6) - F(2).

solution

PROCEDURE:
i) Find F(6)
ii) Find F(2)
iii) Do F(6) - F(2).

i) Find F(6)

F(x) = 4x2 + 12x - 420

F(6) = 4(6)2 + 12(6) - 420

F(6) = 4(6x 6) + (12 x 6) - 420

F(6) = 144 + 72 - 420

F(6) = 216 - 420

F(6) = -204.

ii) Find F(2)

F(x) = 4x2 + 12x - 420

F(2) = 4(2)2 + 12(2) - 420

F(2) = 4(2 x 2) + (12 x 2) - 420

F(2) = 32 + 24 - 420

F(2) = 56 - 420

F(2) = -364

iii) Do F(6) - F(2).

      F(6) - F(2) = -204 - (-364) = -204 + 364 = 160.

Hence F(6) - F(2) = 160.

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



If F(x) = 11x2 + 2x - 10; find F(7) - F(4).

LOGARITHMIC EQUATIONS-5


If log6(3x + 6)=2; find x

   Solution

log6(3x + 6)=2

 (3x + 6)=62   
                      
 3x + 6=36


3x = 36 – 6

3x =  30


3x =  30   
3        3

X = 10


Hence x = 10

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

If log2(2x - 20)=4; find x