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Thursday 11th June Paper III: Objective –
General
Mathematics – 10:00am – 11:45am
Paper II: Essay – General
Mathematics – 12:00noon – 2:30pm
=========================================
Maths OBJ Type A
1- 10: DEDEDADBDA
11- 20: BBDADCDACC
21- 30: BBCCAEBABA
31- 40: AADEDDBABC
41- 50: CCADEDECCA
51- 60: DBEBDABAAD


Maths TYPE B

1-10: CABBAEBACC

11-20: AEBCDAEDDB

21-30: DEBDBEDEDC

31-40: BBBABBABED

41-50: ECDEBBDBBC

51-60: ADADCECAED


Maths TYPE C

1-10: BEBDAEDEDA

11-20: EDAEBBDBAB

21-30: ADADDCABEA

31-40: AABBCAEDDB

41-50: DBDBABBBCC

51-60: BBBAEBABEE


Maths Type D

1-10: ABADCEBAED

11-20: BBBAEBABEE

21-30: AEBCDAEDDB

31-40: DCDEBCBCDB

41-50: BEBDBEDEDA

51-60: CABBEEBABC


1. D - 3 3/ 10
2. A - 1 year
3. D - 1 + (2 )^
4. A - - 12288
5. D - #27500
6. C - ( anc )uB '
7. D - 5
8. A - x > equal 21
9. D - m=10 , n = 12
10.A - 41. 4deg
11.B - (4 - 3 1 ) ( -1 7 4 ) (7 - 4 -2 )
12.B - 46-
13.D - 15km
14.A - 66. 4dgr
15.D - 1 /3
16.C - 9
17.D - 33 1/ 3
18.A - # 20000
19.C - 2sqrt 2m
21 sqrt 3m
20.C - 4 .2
21.B - 3
22.B - 6
23.C - 3
24. D - 4 sqrt 3
25. A- 41 deg
26. E- v = fu/u -f
27.B - 47.1 cm
28. A- 1 + sqrt 10/ 3
29. B- II and III only
30. A- (0 , 2 1/ 4 )
31. E- 3 x +4 y > equal 9
32. A (n -3 ) (n +27 )
33. D - 2
34. C- 6
35. C- y less or equal to -3 or y less or equal to 4
36. A- - 5 X ≤ 1 4/ 9
=========================================
5a )
3/ X + 2 - 6 /3 X - 1
3( 3 X - 1) - 6 (X + 2 )/ ( X + 2) ( 3 X - 1)
9X - 3 - 6 X - 12/ (X + 2 )( 3 X - 1)
3X - 15 /( X+ 2 )( 3X - 1 )

5b )
C .I= P [1 + r/ 100 ]^
=25000 [1 +12 /100 ]^ 3
=25000 [1 +0 .12 ]^ 3
=25000 * 1 .4049
=35122 .50
=N 35 ,122 .50
=========================================
6a )
X +- 3 /2
X =2 /3 or X =2
(X + 3 /2 )^ 2 or ( X - 2)
(X + 3 /2 ) (X - 2 )
X (X - 2 ) + 3/ 2 (X - 2 )
X ^2 - 2 X + 3 X /2 - 3
2X ^ 2 - 4X + 3 X - 6
2X ^ 2 - X - 6

6b )
h/ h +8 = 6 / 10
10h = 6 h + 48
h = 12
H = h + 8
H = 12 + 8
H = 20
Volume = 1 /3 A .h
= 1/ 3 (10 *10 ) * 20 - 432 /3
= 200 /3 - 432 / 3
=1568 / 3
=522 . 67cm 3
=========================================
7a )
titan/ 360 ×2 pie r cos t
d= 55/ 360 × 2× 22/ 7 ×640 cos 4
d= 55× 44× 6400 cos 4 / 2520
d= 55× 44× 6400 ×0496 / 2520
d= 15, 449 .28/ 2520
d= 6130 .67
d~ 6130 km .
ii) distance along gent circle
D =tita / 360 ×2 pie r
D =55 /360 × 2 /7 ×22 /7 × 6400/ 1
D =55 ×44 ×6400 /2520
D =15 ,488 × 6400/ 2520
D =6144 .03
D =~6146 km.

7b )
Length of sector tita/ 360 × 2pie r
L= 120 / 360 ×2 / 1× 22/ 7× 42/ 1
L= 120 × 44× 42/ 2520
L= 221760 / 2520
L= 88cm
L= 2 pie r
Where r is the radius of circumference
88= 2× 22/ 7 ×r
88× 7= 44r
R =88 ×7 /44
R =616 / 44
R =14 cm.
Curved surface area
= pie rc
A =22 /7 ×14 ×42 /1
A =22 ×14 ×4 ^2 / 7
A =12936/ 7
A =1848 cm ^2 .
=========================================
8a )
X =60 /t -- - -- -- - -- >( i)
Y =180 / t - - -- -- - -- -> ( ii)
T 1= 60/ X
T 2= 100 /Y
T 1+ T 2= 5
60/ X+ 180 / Y = 300 - -- -- - -- -- > (i)
180 /X + 60 /Y = 260 -- -- - -- -- - >( ii)
Let P = 1/ X
2 = 1/ Y
60p + 180 Q = 300
180 p + 6Q = 200
P + 3 Q =5
9P + 3Q = 13
Substract ( i)from (ii )
8p = 8
P = 8 /8 ÷ P = 1
Subtract P into (i )
P + 3 Q =5
1 + 3Q =5
3Q =5 - 1
3Q =4
Q = 4 /3
P = 1 ÷ 1 = 1 /X ÷ X = 1
4/ 3 = 1 /Y ÷ Y = 3 / 4

8b )
2001 -- -- - -- -- 25 ,700
2002 -- -- - -- -- 15 /100 X 25,700 + 25 ,700 =
29,555
Amount of tax in 2002
= 29,555 * 12.5 /100
= N 3694. 375
=N 3690

8c )
Log 25
Log 16 25 /100
Log 16 2 / 4
Log 4 6- 1
-1 / 2 Log 4^ 4
-1 / 2
=========================================
9ai )
W=K + C /2
24 = k + C /16
384 = 16K + C -- -- - -- (i)
18 = K + C / 4
72 + 4 K + C - -- - -- -- - (ii )
16K + C = 384
4K + C = 72
Substact (ii ) from ( i)
12k /12 = 312 /12
K = 26
Substract K into (i)
16k + C = 384
C = 384 - 416
C = -32
W=k + C /t 2
W=26 -32 /t 2
(ii )
When W= - 46,t =?
-46 = 26 -32/ t2
t2 = - 32/ -72
t = Sqrt 16/ 36 = 4 / 6
=2 / 3

9b )
V = Pie r2 . d = 14, r = 7 cm
1232 = 22/7 * 7 ^ 2 * h
h = 7* 1232 /22* 49
h = 8624/ 1074
h = 8cm
=========================================
11a )
y^ 1 =x ^ 2( 3x + 1)^ 2
v= ( 2x + 1)^ 2
v= m^ 2
dm/ dx= 2
dv/ dm= 2 m
dy/ dx= dv/dm × dm/ dx
=2 m× 2
=4 m
dy/ dx= 4( 2x + 1)
dy/ dx= udv /dx+ v whole no . dy /dx
=x ^ 2 4( xx+ 1)^ 2 ,× 3 x
=4 x ^2 (2 x + 1) +2 x (2 x +1 )^ 2 .

11b )
[3 3 -1 ]
[1 0 2 ]
[3 - 2 3 ]
+2 [ 0- (- 4 )- 3[ 63]
+- 1 (- 2)
8+ 9 + 2
=19 .

11c )
m=y 2 -y 1 /x 2 -x 1
y- y 1= m( x -x 2 )
m=4 - 3/ - 1- 2
m=- 1 /3
y1 - y2 = -1 / 3( x- x 2)
y- 3 =1 / 3( x- 2 )
y- 3 =- 4 /3 + 2/ 3
3y = -x + 11
y= - 1/ 3 x+ 11/ 3 .

=========================================

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