Tuesday, 12 September 2017

RADICALS 1


Radicals are among the challenging concepts in maths.

With this video below you can learn one of them and reach to the solution.





See more Math Videos and ease your mathematics learning.



Saturday, 9 September 2017

ARITHMETICS 1


Evaluate 13 x 369 + 331 x 13.

Solution

= 13 x 369 + 331 x 13.

= 13 x (369 + 331)     factoring out the common number

= 13 x 700   

= 9100      [after multiplying 16 and 7 and adding two zeros on the answer]

Hence 13 x 369 + 331 x 13= 9100

TRY THIS………….



Evaluate 127 x 516 + 484 x 127.

SUM OF A GP 1


Find the sum of the 1st ten terms of the geometrical progression 2+6+18+54+…….

solution

G1 = 2, r=3, n=10

Sn = G1(rn-1)/r-1
               
S10 = 2(310-1)/3-1            

S10 = 12(310-1)/21
               
S10 = (310-1)

S10 = 59049 - 1

S10 = 59048

Hence the sum of the 1st seven terms is 19682.

TRY THIS………………



Find the sum of the 1st eight terms of the geometrical progression 3+9+27+81+…..

ALGEBRA 2


If │4x – 7 │= 15; Find  x

Solution

±(4x – 11 )= 17

4x -11= 15   OR   –(4x-11) = 15

4x – 11 = 15    OR   -4x+11=15

4x = 15 + 11    OR   -4x= 15-11

4x = 26     OR   -4x  =   4
4      4               -4        -4

x = 13/2  OR  x = -1


Hence x = 13/2  OR  x = -1


TRY THIS………………………. 


If │2x – 7 │= 25; Find  x

FUNCTIONS 3


If F(x) = log2x, Find F(32)

Solution

F(x) = log2x

F(32) = log2(32)

F(32) = log232-1

F(32) = log2(25)-1

F(32) = log22(5 x -1)

F(32) = log22-5

F(32) = -5log22

F(32) = -5 x 1

F(32) = -5

Therefore F(32) = -5


TRY THIS…………………



If F(x) = log2x, Find F(512)

EXPAND 3


Expand 8vw(5w – 3)

Solution


= 8vw(5w – 3)

= (8vw x 5w) – (8vw x 3)

= 40vw2 – 24vw answer


TRY THIS………..



Expand 4ab(7a+ 20)

FACTORIZE 1


Factorize 625x- 9y2

Solution

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

625x2- 9y2  = 252x2 - 32y2

                   = (25x)2 - (3y)2

                   = (25x - 3y)( 25x + 3y)

Hence 625x2 - 9y2 = (25x - 3y)(25x + 3y)

TRY THIS………………………….


Factorize 225c2- 36d2


Thursday, 7 September 2017

FUNCTIONS 2


Find a linear function f(x) with gradient -10 which is such that f(7)=16.

        Solution.

m=-10, points = [7,16] and [x, f(x)]

m = y2-y1/x2-x1

-10 = f(x) – 16/x-7
  
f(x)-16=-10(x-7) [after cross multiply]

f(x)-16=-10x+70

f(x)=-10x+70+16

f(x)=-10x+86

A  linear function is f(x) = -10x+86.

TRY THIS……….


Give out a linear function f(x) with gradient 6 and f(8)=-4

LOGARITHMS 4



Evaluate Log218 + Log28 - Log29

Solution

= Log218 + Log28 - Log29

= Log2(18 x 8 ÷ 9)

= Log216

= Log224

= 4Log22

= 4 x 1     [since Log22=1]

= 4 answer

TRY THIS………………….


Evaluate Log228 + Log216 - Log27

A. P. 1


The 1st term of arithmetic progression is 37 and the common difference is 40. Find the nth term

solution

A1=37, d= 40, n=?

An =A1 + (n-1) d

An=37 + (n-1)40

An=37 + 40n -40

An=40n + 37-40

An=40n – 3

Hence the nth term is An=40n – 7  

TRY THIS………………….. 

The 1st term of arithmetic progression is 48 and the common difference is 98. Find the nth term.