Tuesday, 7 November 2017

EXPAND 1


Expand 8w2(5w – 7)

solution

= 8w2(5w – 7)

= (8w2 x 5w) – (8w2 x 7)

= 40w3 – 56w2 answer

TRY THIS………..


Expand 4a2(7a+ 30)

VECTORS 1


Write (9,6) in terms of i and j.

Solution

= (9,6)

= (9,0) +  (0,6)

= 9(1,0) +  6(0,1)

= 9i + 6j   [since (1,0)=i and (0,1=j)

Hence (9,6) = 9i +  6j  

TRY THIS……………………..


Write (11,16) in terms of i and j.

Sunday, 5 November 2017

FUNCTIONS 1


If F(x) = 8x + 20; 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= 8x + 20

y – 20 = 8x

y – 20  = 8x
   8          8

y – 20   = x
   8

x  =   y – 20     after rearranging
           8

 y-1 = x – 20     after interchanging x and y variables.
             8

F-1(x) = x – 20     after interchanging x and y variables.
                8

Hence, F-1(x) = x – 20     
                              8

TRY THIS……………………………


If F(x) = 2x - 26; Find F-1(x).


PERFECT SQUARES 1


Evaluate 6602 – 3402

Solution

6602 – 3402 = (660 + 340)( 660 - 340)

                   = (1000)( 320)

                   = 320000

Hence 6602 – 3402 = 320000


TRY THIS……………………


NECTA 2003 QN. 9a


Evaluate 3652 – 1352



Saturday, 4 November 2017

LOGARITHMS-1


Simplify Log2256 - Log3729

Solution

= Log2256 - Log3729

= Log228 - Log335    [Since 256=28 and 729=36].

= 8Log22 - 6Log33    [since Logaa = 1]

= (8 x 1) - (6 x 1)

= 8 - 6

= 2

Hence Log2256 - Log3729 = 2

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


Simplify Log22048 – Log5625 

ALGEBRA 1


If 27x + 5y -9 = 0; find x-intercept.

Solution

x-intercept is when y=0.

27x + 5y -9 = 0

27x + 5(0) - 9 = 0

27x - 9 = 0

27x = 0+ 9

27x = 9
27      27

x= 9/27

Hence x= 9/27

TRY THIS………..


If 11x - 5y - 55 = 0; find x-intercept.

Wednesday, 18 October 2017

FUNCTIONS 3


If f(x) = x4 - kx2 - 6x + 7 has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x4 - kx2 - 6x + 7

x + 2 = 0

x = -2

f(x) = (-2)4 - k(-2)2 - 6(-2) + 7 = 22

16 - 4k + 12 + 7 = 22

16 - 4k + 19 = 22

16 + 19 = 22 + 4k

16 + 19 - 22=4k

35 - 22=4k

13 = 4k


k = 13/4    after dividing by 4 both sides.

hence k=13/4

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


If f(x) = x4 - kx2 - 5x - 31 has a remainder of 18 when divided by x-2; find k.

PERCENTAGE PROFIT1


A man got a profit of 7400/= after selling an item. Find the buying price if the percentage profit was 5%.

Solution

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

5% = 7400   X  100   
           B.P.

B.P. x 5% = 740,000   x B.P.  [multiplying by B.P. both sides]
                       B.P.

B.P. x 5 = 740,000   

B.P. x 51 =   740,000  148000 
  15                   51

B.P. = 148000
                      
Hence Buying Price was 148000/=
  
TRY THIS………………


A man got a profit of 27,500/= after selling an item. Find the buying price if the percentage profit was 20%.

VARIATION 2


x is directly proportional to y. x=24 while y=4. Find y when x is 60.

Solution

x y

x = ky

24 = k x 4

24 = 4k
4      4

k = 6
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 6, y= ? x = 60.


x = ky

60 = 6 x y

60 = 6y
6      6


y = 10.


TRY THIS…………….



x is directly proportional to y. x=48 while y=12. Find y when x is 70.

LOGARITHMS 3


If log 2= 0.3010; find the value of log 400,000 without using tables.

solution

= log 400,000

=log(100,000 x 4)


=log100,000 + log4


=log105 + log22


=5log10 + 2log2


=(5x1) + 2(0.3010)


=5– 2(0.3010)


=5 – 0.6020


=4.398


Hence log2500=3.398



TRY THIS……………



If log 2= 0.3010; find the value of log 80,000 without using tables.