Maths expo waec 2017

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Maths- Obj
1-10: CBBDCADBBC
11-20: CACBAAACAB
21-30: BBACBCCAAB
31-40: CBCACBDADB
41-50: DBDCCDBDAB
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NOTE
Where ever you see ^ means raise to power
/ division
* means multiplication x
sqr root means √
tita means θ
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SECTION A ANS ALL QUESTIONS
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11 a )
8 students finished
12 tanks in 2 /3 ( 60 ) mins
= 40 mins
4 student wil finish
X tanks in 1 / 3 (60 )min
= 20 mins
X = 4 x 20 x12 /8 x 40
= 3 tanks
11 b )
L (AB ) = 200 m |ON | = 12 cm
r 2 = (AN )2 + (ON ) 2
r 2 = (10 ) 2 +( 12 )2
r 2 = 100 + 144
r 2 = 244
r = Sqr 244
r = 15 .6 CM
11 bii )
L (AB ) = 2 r sin 0 / 2
20 = 2 (15 . 6 ) sin 0 /2
20 = 31 .2 sin 0 /2
sin 0 / 2 = 20 / 31 .2
sin 0 / 2 = 0 .6410
0 /2 = sin - 1 (0 .6410)
0 /2 = 39 .87
0 = 2 ( 39 .87 )
0 = 79 . 74
= 79 . 7 ' (1 d .p )
11 bii )
p 2 r + 0 / 360 x 2 TTr
= 2 ( 15 .6 ) + 79 .7 / 360 x 2 x 3 x 42 x 15 .6
= 31 .2 + 21 .7
= 52 . 9 cm
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12 a )
3 y ^ 2 - 5 y + 2 = 0
y ^2 - 5 /3 y + 2 / 3 = 0
y ^2 - 5 / 3 y = - 2 /3
y ^2 - 5 / 3 y + (^- 5 /6 )^ 2 = (- ^5 / 6 )^ 2 - 2 /3
( y - 5 / 6 )^ 2 = 25 / 36 - 2 /3
( y - 5 / 6 )^ 2 = 25 / - 24 / 36
( y - 5 / 6 )^ 2 = 1 / 36
( y - 5 / 6 )=+ sqr 1 /36
y = 5 / 6 + 1 /6
y = 5 + 1 /6 or 5 - 1 / 6
y = 6 / 6 or 2 /3
y = 1 or 2 /3
12 b )
given
M N = [2 , 3 1 , 4 ]
hence
[1 , 4 2 , 3 ] * [m, n x , y ] = [2 , 3 1 , 4 ] [m+ 2 n , x *2 y ]
[4 m+ 3 n , 4 x+ 5 y ] = [2 , 3 , 1 , 4 ]
therefore
m+ 2 n = 2 - - - - - - (i )
4 m+ 3 n = 3 - - - - - - (ii )
from - - - - - - ( i)
m= 2 - 2 n
4 (2 - 2 n )+ 3 n = 3
8 - 8 n +3 n = 3
8 - 5 n = 3
8 - 3 = 5 n
5 = 5 n
n = 1
hence
m= 2 - 2 (1 )
M= 0
also
x +2 y = 1 - - - - - - (i)
4 x+ 3 y = 4 - - - - - - ( ii)
from - - - - - - ( iii )
x = 1 - 2 y
4 (1 - 2 y )+ 3 y = 4
4 - 8 y +3 y = 4
y = 0
therefore x = 1 - 2 ( 0 )
x = 1
this N = [i i]
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