Thursday, 10 August 2017

ALGEBRA 4


Expand 10w(5w – 3)

solution

= 10w(5w – 3)

= (10w x 5w) – (10w x 3)

= 50w2 – 30w answer

TRY THIS………..


Expand 4y(9y+ 10)  


VECTORS 2


If u = 20i + 2j and v = 3i + 10j find 5u + 3v

solution

= 5u + 3v

= 5(20i + 2j) + 3(3i + 10j)

= 100i + 10j + 9i + 30j

= (100i + 9i) + (10j + 30j)

= 109i + 40j

Hence 5u + 3v = 109i + 40j .

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

NECTA 2001 QN. 12a (i)


If u = 4i + 3j and v = 2i + 4j;  find 2u + 3v.

FUNCTIONS 2


If F(x) = log2x, Find F(1/ 8192)

Solution

F(x) = log2x

F(1/8192) = log2(1/ 8192)

F(1/8192) = log2 8192-1

F(1/8192) = log2(213)-1

F(1/8192) = log22(13 x -1)

F(1/8192) = log22-13

F(1/8192) = -13log22

F(1/8192) = -13 x 1

F(1/8192) = -13

Therefore F(1/ 8192) = -13


TRY THIS…………………


If F(x) = log5x, Find F(1/3125)

PROBABILITY 1


A number is chosen at random from 1 – 15 inclusive. Find the probability that it is a multiple of five or an even number greater than 8.

Solution

THIS IS A NON-MUTUALLY EXCLUSIVE EVENT.

Let n(S) represent sample space
P(E) = probability of even number greater than 8
P(M) = probability of a multiple of 5

n(S) = {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15} = 15
n(E) = {10, 12, 14} = 3
n(M) = {5, 10, 15} = 3
But 10 appears on both categories.
P(E) = 3/15
P(M) = 3/15
P(EnM) = 1/15
………………………….
P(EuM) = P(E) + P(M) - P(EnM)  

P(EuM) = 3/15 + 3/15 -1/15

              = 5/15

              = 1/3  after simplification

P(EuM) = 1/5

TRY THIS………………


A number is chosen at random from 17 – 30 inclusive. Find the probability that it is a multiple of 5 or an even number.

Wednesday, 9 August 2017

FACTORIZE 2


Factorize 289x- 169y2

Solution

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

289x2- 169y2  = 172x2 - 132y2

                   = (17x)2 - (13y)2

                   = (17x - 13y)( 17x + 13y)

Hence 289x2 - 169y2 = (17x - 13y)(17x + 13y)

TRY THIS………………………….



factorize 121c2- 49d2

ALGEBRA 3


Multiply 2x - 4y by -5a

solution

= -5a(2x - 4y)

= (-5a x 2x) - (-5a x 4y)

= (-10ax) - (-20ay) [since -5a x 4y = -20ay ]

= -10ax + 20ay    

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


Multiply 40p - 3q by  -4m


EXPONENTIALS 3


If 52w (40w) = 10w+40 ; Find w.

Solution

52w (40w) = 10w+40

(52)w (40w) = 10w+40

(25)w (40w) = 10w+40

(25 x 40)w = 10w+40

(1000)w = 10w+40

(103)w = 10w+40

103w = 10w+40  (Bases are alike, so they cancel out)

3w = w+40

3w - w = 40

2w = 40

2w = 4020
2       2

w = 20

TRY THIS…………………………….


If 32t (4t) = 6t+10 ; Find t.



VARIATIONS 2


x is directly proportional to y. x=12 while y=4. Find y when x is 69.

Solution

x y

x = ky

12 = k x 4

12 = 4k
4      4

k = 3
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 3, y= ? x = 69.

69 = 3 x y
69 = 3y
3      3

y = 23.

TRY THIS…………….

x is directly proportional to y. x=20 while y=5. Find y when x is 68.


Ans. y=17

LOGARITHMS 3


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

solution

=log200,000

=log(4 x 100,000)

=log4 + log100,000

=log22 + log105

=2log2 + 5log10

=2(0.3010) + (5 x 1)  [since log10=1 and Log3=0.3010]

=(0.6020) +  5

=5.6020

Hence log400,000=5.6020


TRY THIS……………


If log 2= 0.3010; find the value of log 4,000,000 without using tables.


Sunday, 6 August 2017

ALGEBRA 2


If 13w2 = 325; find w

Solution

13w2 = 325

13w2 = 325               [Dividing by 13 both sides]
13          13

w2 = 25

w = 5          Because the square root of 25 is 5.   

Hence w = 5 .          

TRY THIS……………………….


If 14y2 = 5600; find y.