Thursday 30 March 2017

MATRIX 6


LOGARITHMS 7


Evaluate Log100 -  log 0.001 - log 0.0001+ log 0.00001

Solution

= Log100 -  log 0.001 -  log 0.0001+ log 0.00001

= Log102 -  log 10-3 – log 10-4 + log 10-5

= 2Log10 - (-3 log 10) – (-4log 10) + (-5log 10)

= (2x1) - (-3x1) - (-8x1) + (-5 x 1)

= 2 - (-3) – (-4) -5

= 2 + 3 + 4 - 5

= 9 - 5
  
Hence Log100 -  log 0.001-  log 0.0001+ log 0.00001 = 4


TRY THIS……………………… 



Evaluate Log10,000 -  log 0.001 - log 0.00001+ log 0.00001

MATRIX 5


FACTORIZING 1


Factorize 81-m2

Solution

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

81-m2 = 92-m2       

        = (9 - m)(9 + m)

Hence 81 - m2 = (9 - m)(9 + m)


TRY THIS…………….


Factorize 169 - c2



MATRIX 4



SIMPLE INTEREST 1

Asad deposited the amount of 200,000/= in a bank for 3 years and got a profit of 72000/=. Find the interest rate?

Solution

I = 72000/=, P = 200,000/=, T = 3 years, R = ?

I  = PRT
      100

72,000  = 200,000 x R x 3
                      100

72,000  = 200,000 x R x 3
                      100

72,000  = 2000 x R x 3
                     
72,000  = 6000R
          
1272,000  = 6000R
   6000       6000

Hence the interest rate was 12%

TRY THIS…………………..


Sonali deposited the amount of 300,000/= in a bank for 6 years and got a profit of 27,000/=. Find the interest rate?

Tuesday 28 March 2017

MATRIX 3




LOGARITHMS 6


If Logax = 0.9, find Loga(x2)

Solution

= Loga(x2)

= Logax2

= 2 x Logax

= 2 x 0.9

= 1.8


TRY THIS………..


If Logaw= 3.2, find Loga(w2)

MATRIX 2




LOGARITHMS 5


Evaluate Log100 -  log 0.001 -  log 0.0001

Solution

= Log100 -  log 0.001 -  log 0.0001

= Log102 -  log 10-3 – log 10-4

= 2Log10 - (-3 log 10) – (-4log 10)

= (2x1) - (-3x1) - (-8x1)

=2 - (-3) – (-4)

= 2 + 3 + 4

=9
  
Hence Log100 -  log 0.001-  log 0.0001 = 9


TRY THIS……………………… 


Evaluate Log10000 -  log 0.000001 -  log 0.00000001


ALGEBRA 1



VARIATIONS 1


x is inversely proportional to y. x=18 while y=5. Find y when x is 15.

Solution

x k
      y

x = k
      y

18 = k
        5

k = 18 x 5

k = 90

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 90, y= ?, x = 15.

x = k
      y

15 = 90
         y

y x 15 = 90  x  y   (multiply by y on both sides)
                y


15y = 90
15      15

Hence y = 6  .


TRY THIS…………….



x is inversely proportional to y. x=80 while y=4. Find y when x is 10. 

MATRIX 1



LOGARITHMS 4


If log9(2x + 33)=2; find x.

   Solution

Log9(2x + 33)=2

(2x + 33)=92           
                                            
2x + 33=81

2x =81 – 33

2x = 48

2x =   48   
2        2

x = 24

Hence x = 24


TRY THIS………………



If log7(2t - 39)=2; find t

ARITHMETIC PROGRESSION 1


The first term of an AP is 41 and the last term is 97.If the arithmetic progression consists of 20 terms, calculate the sum of all the terms. 

Solution

A1 = 41, n=20, An = 97

Sn = n(A1 + An)
       2

S20 = 20(41 + 97)
         2

S20 = 10 x 138

S20 = 1380


Hence the sum of all 20 terms is 1380.


TRYTHIS………………….



The first term of an AP is 11 and the last term is 53.If the arithmetic progression consists of 40 terms, calculate the sum of all the terms. 

EXPONENTIALS 1


Simplify the following by writing in power form:
w90
w40

Solution

= w90 - 40 

=w50

TRY THIS……………….

Simplify the following by writing in power form:
h59


h21 

LOGARITHMS 3


If Logax = 0.2, find Loga(1/x2)

Solution

= Loga(1/x2)

= Logax-2

= -2 x Logax

= -2 x 0.2

= -0.4


TRY THIS………..

If Logaw= 1.6, find Loga(1/w2)


Saturday 25 March 2017

ARITHMETIC 1


Evaluate 3962 – 3862

Solution

We apply difference of two squares: a2 - b2 = (a+b)(a-b)

3962 – 3862  = (396 + 386)( 396 – 386)

                   = (782)( 10)

                   = 7820   [only add a zero at 782]

3962 – 3862 = 13820

TRY THIS…………….
  

Evaluate 5082 – 4082

LOGARITHMS 2


If Logax = 0.9, find Loga(1/x)

Solution

= Loga(1/x)

= Logax-1

= -1 x Logax

= -1 x 0.9

= -0.9


TRY THIS………..


If Logaw= 3.6, find Loga(1/w)

SLOPE OR GRADIENT 1


Find the slope of a line which passes through (-1, -8) and (6,-9)

Solution

x1 = -1,  y1 =-8,  x2 = 6,  y2 = -9

m = y2 –y1
       x2 – x1

m =   -9 –(-8)
         6 –(-1)

m =   -9 + 8
         6 + 1

m =    - 1
            7

Hence the slope is -1/7


TRY THIS……………………… 


Find the slope of a line which passes through (-11, -2) and (9,-12).


BINARIES-1


If p*k = 4pk + p – 2k; find 3*2.

Solution

p*k = (4 x p x k) + p – (2xk)   [rewriting the given expression more clearly]


3*2 = (4 x 3 x 2) + 7 – (2x2)   [substituting 7 for p and 2 for k]


3*2 = 24 + 7 – 4


3*2 = 31 – 4   [we add first before subtracting]


3*2 = 27.


Hence   (3*2) = 27.



 TRY THIS........



 If p*k = 2p - k – 5pk; find (-3*4).

QUADRATICS-1



Find the maximum value of the quadratic equation:5-6t-8t2.

Solution

a=-8, b=-6, c=5

Maximum = 4ac-b2
                        4a

Maximum = (4 x -8 x 5) - (-6)2
                          4(-8)

Maximum = (-160)- 36
                         32

Maximum= -196                         since (-160)- 36=-196
                       32

Maximum = -98 -49
                      16         8

Hence maximum value is -49/8

TRY THIS………………………………..

NECTA  2003 QN. 10c


Find the maximum value of the quadratic equation:3+30t-5t2.

POLYGONS 2

A regular polygon has 62 sides. Find the total degrees of that polygon.

Solution

n = 62

Total degrees = (n - 2)1800

                       = (62 – 2)1800

                       = 60 x 1800

                       = 108000

Total degrees = 108000


TRY THIS……………………….


A regular polygon has 53 sides. Find the total angles of that polygon.

LOGARITHMS 1


Evaluate Log10000 +  log 0.001 -  log 0.00000001

Solution

= Log10000 +  log 0.001 -  log 0.00000001

= Log104 +  log 10-3 – log 10-8

= 4Log10 + (-3 log 10) – (-8log 10)

= (4x1) + (-3x1) - (-8x1)

=4 + (-3) – (-8)

= 4 – 3 + 8

=9


Hence Log10000 +  log 0.001-  log 0.00000001 = 9


TRY THIS……………………… 



Evaluate Log100 +  log 0.0000001 -  log 0.00000001

MID-POINT 1


Find the midpoint of a line from (23, 12) to (5, 20)

Solution

x1=23, x2=5, y1=12,y2=20.

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

Mid point = (23 + 512 + 20)
                         2          2

Mid point = (28, 32)
                    2     2

Hence midpoint = (14, 16)

TRY THIS……………………..



Find the midpoint of a line from (-6, 14) to (6, -4)

Friday 24 March 2017

PIE CHARTS 1


In a survey of 60 people, 28 people said their favourite sport was football. What angle in a pie chart would this represent?

Solution

We make a fraction of 28 ot of 60, then multiply by 3600.
= 28 x 3600.
   60

= 28 x 36006
   601

= 28 x 6

= 1680.

Hence the angle is 168

TRY THIS………………………   

In a survey of 30 people, 23 people said their favourite sport was football. What angle in a pie chart would this represent?


POLYGONS 1


An interior angle of a regular polygon is 740 greater than an exterior angle. Find the interior angle.

Solution

Let i = interior angle, e = exterior angle.

Now i  + e=1800…………………(1)

But i = e+740 …………………(2)

Substitute (2) in (1) above.

e+740   + e=1800

e+ e+740   =1800

2e+ 740   =1800

2e=1800 - 740   

2e=1060

2e=1060          dividing by 2 both sides.
2      2

e = 530

But i  + e=1800…………………(1)

i  + 530=1800.

i  =1800 - 530

i = 1270

Hence i = 127


TRY THIS………………………   


An interior angle of a regular polygon is 780 greater than an exterior angle. Find the interior angle.