Sunday 27 April 2014

RATIOS D1



The areas of two circles are in the ratio of 25:4 . Calculate the radius of the smaller circle when the radius of larger circle is 50 cm. 

solution

let R = radius of larger circle
let r = radius of smaller circle
R= 50cm, r = ? Ratio = 25:4.


For larger circle
A1 = R2 …………(i)

For smaller circle
A2 = r2 …………(ii)

A1 = R2
A2    r2

A1 = R2
A2     r2


A1 = (R/r)2 
A2

(A1/A2) =  (R/r)

(25/4) =  (50/r)

5 = 50                 cross multiply
2     r

(2 x 50) = (5 x r)

100 = 5r

100 = 5r
5         5

r = 20

radius of smaller circle is 20cm.


TRY THIS………..

NECTA 1997 QN 5(c)
The areas of two circles are in the ratio of 16:9 . Calculate the radius of the smaller circle when the radius of larger circle is 24 cm.

EXPONENTS D1



If (2x-7)(7y+8) = (220)(728) find x+y.

solution

2x-7 = 220

x – 7 = 20

x = 20+7

x = 27

…………………………

7y+8 = 728

y + 8 = 28

y = 28 - 8

y = 20

……………………

x + y = 27 + 20 = 47.

TRY THIS………….

 NECTA 2008 QN. 3a

If (2x-7)(7y+8) = (220)(728) find (i)x+y.      (ii) y/x

LOGARITHMS D1



Simplify Log2128 – Log5625

Solution

= Log2128 – Log5625

= Log227 – Log55

= 7Log22 – 4Log55   because Logaan =  nLogaa

= (7 x 1) – (4 x 1)   

= 7 – 4

= 3

Hence Log2128 – Log5625 = 3 

TRY THIS…………..

NECTA 1995 QN 24b

Simplify Log232 – Log39.

ALJEBRA D3



Expand 10(y – 7)

solution

= 10(y – 7)

= (10 x y) – (10 x 7)

= 10y – 70 answer

TRY THIS………..

Expand 3(W– 9)

CONGRUENCE OF TRIANGLES D2



Prove that the following triangle is isosceles.



Solution

Given: triangle UTW with T produced to V.
Required to prove: UTW is isosceles
Proof: 

UV = VW (given)

<UVT = <WVT = 900 (given)

TV = VT (common line)

UVT WVT by SAS rule 

TU = TW (Equal corresponding sides)

Hence UTW is isosceles (proved)