Wednesday 7 August 2013

CO-ORDINATE GEOMETRY-5


Find the slope of a line which passes through (-5, -2) and (6,-9)

Solution

x1 = -5,  y1 =-2,  x2 = 6,  y2 = -9

m = y2 –y1
       x2 – x1

m =   -9 –(-2)
           6 –(-5)

m =   -9 + 2
           6 + 5

m =    - 7
           11


Hence the slope is -7/11



Tuesday 6 August 2013

PYTHAGORAS - 3


Find the length AB



Solution

We will use the PYTHAGORAS theorem [ a2 + b2 = c2  ]

a2 + b2 = c2

AB2 + BC2 = AC2

AB2 + 102 = 262

AB2 + 100 = 676

AB2 = 676 - 100

AB2 = 576    [Find the square root of 576]


Hence AB= 24cm      




Saturday 3 August 2013

MATRIX-3






MATRIX-2




SETS-6



In Bibanja district the number of people who speak Kiswahili or Lingala is 400. 200 of them speak Kiswahili and 300 of them speak Lingala. How many speak both languages?

solution

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

Let Kiswahili=n(K), Lingala= n(L).

n(K)= 200 ,
n(L)= 300,
n(KuL) = 400,
n(KnL)=?



n(KuL) = n(K) + n(L) - n(KnL)


400  =  200 + 300 – n(KnL)


400  =  500 – n(KnL)


n(KnL) =  500 – 400


n(EnF) =  100



Hence n(EnF)=100 answer



LOGARITHMS-6


Evaluate Log100000 +  log 0.001 -  log 0.00000001


Solution


= Log100000 +  log 0.001 -  log 0.00000001

= Log105 +  log 10-3 – log 10-8


= 5Log10 + (-3 log 10) – (-8log 10)

= (5x1) + (-3x1) - (-8x1)

=5 + (-3) – (-8)

= 5 – 3 + 8

=10


Hence Log100000 +  log 0.001-  log 0.00000001 = 10


ALGEBRA-4


The sum of five consecutive numbers is 590. Find the 4th number.

Solution

Let the numbers be as shown in the table below


1st number
2nd number
3rd number
4th number
5th
number
TOTAL
n
n+1
n+2
n+3
n+4
590


Then, n + (n+1) + (n+2) + (n+3)+ (n+4) = 590


5n + 1+2+3 +4= 590


5n + 10= 590


5n = 590 -10


5n = 580


5n = 580
 5        5

n = 116


4th number = n +3
                       = 116 + 3
                       = 119



Hence the 4th number is 119




QUADRATIC-5


If zx2 + 12x + 4 = 0 is a perfect square, find the value of z .

Solution

In zx2 + 12x + 4 = 0;   a=z, b=12 and c=4.


For the perfect square, b2 = 4ac


(12)2 = 4 x z x 4


144 = 16z


144 =  16z
 16       16


9 = z



Hence the value of z is 9



CO-ORDINATE GEOMETRY-4


Find the slope of a line which passes through (8, 6) and (-11,-3)

Solution

x1 = 8,  y1 =6,  x2 =-11,  y2 = -3

m = y2 –y1
       x2 – x1

m =    -3 –6
         -11 –8

m =     - 9
          - 19

m =  9
       19


Hence the slope is 9/19

FUNCTIONS-5


Given that F(x) = 13x  +  65. Find F(8)

Solution

F(x) = 13x  +  65

F(8) = 13(8)  +  65

F(8) = 104  +  65

F(8) = 169


Hence  F(8) = 169




SEQUENCE&SERIES-4


The 1st term of an A.P. is 10 and the common difference is 58. Find the 12th term.

Solution

A1= 10, d = 58

An = A1 + (n-1)d   [ formula for n terms ]

A12 = A1 + (12-1)d

A12 = A1 + 11d    [ formula for 12 terms ]

A12 = 10 + (11 x 58)

A12 = 10 + 638

A12 = 648


Hence the 12th term is 648.



ABSOLUTE VALUE-3


If 4x + 7 = 47; Find  x


Solution


±(4x + 7 )= 47


4x +7= 47    OR   –(4x+7) = 47


4x+ 7 = 47    OR   -4x - 7=47


4x = 47- 7    OR   -4x= 47 + 7


4x = 40     OR     -4x  =  54
4       4                   4        4


x = 10  OR  x = 27/2 = 13.5



Hence,  x =10  OR  x = 13.5