Monday 29 February 2016

PRIME FACTORS 1


Write 420 as a product of prime factors.

Solution


2
420
2
210
3
105
5
35
7
7

1


 Then, 420 = 2 x 2 x 3 x 5 x 7

Hence   420 = 22 x 5 x 7.

TRY THIS........


Write 540 as a product of prime factors.


GEOMETRY 2


If x-150 and 4x + 350 are complementary angles, find the value of x.

Solution

Complementary angles add up to 900.

so,  x-150 + 4x + 350 = 900.
so,  x + 4x + 350 - 150 = 900.
so,  5x + 150 = 900.
so,  5x = 900 -  150
so,  5x = 750

so,  5x = 7515
       5       5

Hence x = 150

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


If 3x - 180 and 2x + 430 are complementary angles, find the value of x.



Monday 22 February 2016

EXPONENTIAL EQUATIONS - 2




If 2(6m-7) x 3(n+9) = (344) x (293); Find m and n.

solution

equating equal bases;

2(6m-7) =  293

2(6m-7)293

6m - 7 = 93

6m  = 93 + 7

6m  = 100

16m  = 10050
16           63

m = 50/3

again for n we equate equal bases.

3(n+9) = 344

3(n+9) = 344

n + 9 = 44

n = 44 - 9

n = 35

Hence m = 20 and n = 35

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


If 8(2m-9) x 11(n+40) = (1160) x (823); Find m and n.





FACTORIZATION - 8


Factorize completely ca + cr - ar - a2.  

Solution

= ca + cr - ar - a2.

= (ca + cr) – (ar - a2).      [Grouping the factors]

= c(a + r) - a(r + a).

 = (a + r)(c - a).

  Hence ca + cr - ar - a2. =  (a + r)((c - a).   

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

NECTA 1995 QN. 20a

Factorize completely pq + pr - rq - q2.   

LOGARITHMS-11



If Logay = Loga22 +  Loga3 ; find y.

solution

Logay = Loga22 +  Loga3

Logay = Loga(22x 3)         [since Logam +  Logan = Loga(m x n)] 

Logay = Loga66

Hence y = 66                  [since Loga cancels out]

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

NECTA 1997 QN 13a


If Logax = Loga5 +  Loga3 ; find x.


UNITS 2


Convert 4073m into km.

Solution

1km  = 1000m
  ?     = 4073m

After cross-multiplying;

= 1 x 4073
      1000

 4073
     1000

= 4.073 km

Hence 4073m = 4.073km

TRY THIS........


Convert 8023m into km.

FACTORIZATION - 7


Factorize completely   (3x-5)2 - x2  

solution

= (3x-5)2 - x2  

= [(3x-5) - x][ (3x-5) + x ]  --- since a2 + b2 = (a+b)(a-b) Here a is (x-2) and b is x.

= [3x-5 - x][ 3x-5 + x ] 

= [3x-x-5][ 3x+ x - 5  ] 

= [2x-5][ 4x - 5  ] 

= [2x-5][ 4x - 5 ] 

Hence  (2x-5)2 - x2  = (2x-2)(4x - 5) 

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


Factorize completely   (6x-1)2 - x2  


Friday 19 February 2016

POLYGONS-2


A regular polygon has 88 sides. Find the total angles of that polygon.

Solution

n = 88

Total angles = (n - 2)1800

                   = (88 – 2)1800

                   = 86 x 1800

                   = 154800

Total angles = 154800



TRY THIS……………………….



A regular polygon has 68 sides. Find the total angles of that polygon.


LOGARITHMS-10


If log5(3x + 101)=3; find x

   Solution

log5(3x + 92)=3

 (3x + 92)=53   
                      
 3x + 92=125

3x = 125 – 92

3x =  33

3x =  33   
3        3

X = 11

Hence x = 11

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


If log2(2x - 22)=5; find x

APPROXIMATIONS-4


Estimate the value of 2.3  x  0.034

solution

= 2.3  x  0.034

= 2.0 x 0.03      [ 2.3 ≈ 2.0 to ones and 0.034 ≈ 0.03 to hundredths]

= 0.06


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



Estimate the value of 6.2  x  0.083


FUNCTIONS - 2


If F(x) = 12x + 6; Find F-1(x).

Solution

HINT: F-1(x) means inverse.

PROCEDURE:
Make x the subject and then interchange x and y variables.

Let y=F(x)

So,  y= 12x + 6

y – 6 = 12x

y – 6  = 12x
 12        12

y – 6   = x
   12

x  =   y – 6     after rearranging
            12

 y-1 = x – 6     after interchanging x and y variables.
            12

F-1(x) = x – 6     after interchanging x and y variables.
               12

Hence, F-1(x) = x – 6     
                           12


TRY THIS……………………………


If F(x) = 5x + 28; Find F-1(x).


LOGARITHMS-9


Evaluate Log2(512 ÷ 8).

Solution

= Log2(512 ÷ 8)

= Log2512 -  Log28          (applying the quotient rule)

= Log229 -  Log223             ( 512= 28 and 8=23 )

= 9Log22 -  3Log22       ( remember  Logaac = cLogaa )

= (9 x 1) - (3 x 1)          ( remember  Logaa = 1 )

= 9 - 3

= 6


hence Log2(512 ÷ 8) = 6

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


Evaluate Log2(1024 ÷ 32). 


Monday 15 February 2016

FRACTIONS - 2


Express as a single fraction m - 5 + m+1
                                               6          4
solution

= m - 5 + m+1
      6          4

= 2(m – 5) + 3(m+1)
            12         

= 2m - 10 + 3m+3
            12          

= 2m + 3m + 3- 10
            12         

= 5m +  -7
       12         

= 5m - 7
     12         

=  5m - 7                 answer
       12       

TRY THIS...................
Express as a single fraction 4c - 1 + 2d+1

                                              4           2

RELATIONS - 2


Let R={(5,3), (6,1), (-2,-6), (14,-20)}. Find the domain and range of R.

solution

For domain we check on the values of x in each point.
Domain={5, 6, -2, 14}

For range we check on the values of y in each point.
Range={3, 1, -6, -20}

Hence Domain={5, 5, -2, 14} and Range = {3, 1, -6, -20}

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


Let R={(7,1), (-13,5), (-1,-2), (14, -9)}. Find the domain and range of R.



DIFFERENCE OF 2 SQUARES - 2


Evaluate 27972 – 27872

Solution

27972 – 27872 = (2797 + 2787)( 2797 – 2787)

                     = (5584)( 10)

                     = 55840

Hence 27972 – 27872 = 55840


TRY THIS…………….



Evaluate 9362 – 8362

SETS - 4


If n(A)= 176 , n(B)= 160 and n(AnB)=150, find n(AuB).

Solution

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

             = 176 + 160 – 150

             = 336 – 150

             = 186

Hence n(AuB) = 186 answer



TRY THIS…………………………….




If n(A)= 146 , n(B)= 164 and n(AnB)=100, find n(AuB).

SIMPLE INTEREST-3


Rayan deposited the amount of 80,000/= in a bank for 2 years and got a profit of 2500/=. Find the interest rate?

Solution

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

I  = PRT
      100

2500  = 80,000 x R x 2
                      100

2500  = 80,000 x R x 2
                      100

2500  = 800 x R x 2
                      
2500  = 4000R
           
52500  = 14000R
84000      14000


Hence the interest rate was  1.6%


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?