NOTE THE FOLLOWING SYMBOLS:
^ means rasie to power
# is naira sign
* multiply
pie is a pie sign
=============================
THEORY
==============================
(1)
TABULATE
No|Log|
5932|3.7732|
*6141|3.7882|
Num|7.5612|7.5612
3679|3.5657|
*3113|3.4931|
Den|7.0588|7.0588
| |0.5024/3=0.1675
Antilog:-1.471*10^0
=1.471
==================================
(2)
a = 3, b = 20, C = -7
Sum is
(A/1 1/B B/1 1/ A) Note A means Alpha and B
means beta
A^2 B B^2 A B / AB
= -7/3 (-20/3) (-20/3) = 140/9 - 20/3 / -7/3
= 80/9 x -3/7 = -80/21
Product:
-7/3 2 1/-7/3 = -7/3 2/1 - 3/7
= -49 42-9/21
= -16/21
x^2 - (sum)x product= 0
x^2 - 80/21x (-16/21) = 0
Final Answer : 21x^2 - 80x - 16 = 0
================================
(3a)
P=100I/RT=100*30,000/4*3
P=N250,000
(3b)
#7000 to Francs
#1 = 8 francs
.:.#7000 = ? france
CROSS MULTIPLY
8/1 * 7000 = 56,000 franc
Spending 49,400 franc
56, 000- 49,400 = 6600
Converting 6 ,600 franc to # AT 10 franc TO 1#
10 franc —– 1#
6600 FRANCS —? #
= 6,600/10 X 1
=#660
===================================
(4i )
difference in latitude = 36 degree 36 degree =
72degree
distance travelled =@/ 360* 2pir
= 72 / 360* 2* 22 / 77* 64
= 20275200 / 2520
= 8045 . 71
= 8050 km ( 35. f )
(4ii)
given that speed = 800 km / hr
distance travelled = 804571 km
time = distance travelled / speed
= 8045 . 71/ 800
= 10 .057
= 10 hrs ( to the nearest hour )
===================================
(5)
Tabulate
Mark - 21- 25, 26- 30, 31- 35,36 -40 ,41 -45 ,46-
50
F - 6 ,8, 12,4 ,6, 4= 40
X - 23,28 ,33 ,38, 43, 48
FX - 138, 224, 396, 152, 258, 192= 1360
Class Boundaries- 20 .5 -20 .5, 25 .5 -30 .5, 35.
5- 40. 50,40 .5 -45 .5
========================
========
(5i)
MEAN
( X )= EFX / EF = 1360/ 40 = 34
MODE
L 1 [Fm - Fa / 2fm - fa -fb ] c
= 30 .5 [12 -8/ 2 ( 12 ) -8- 4] 5
= 30 .5 [4/ 12 ]5
= 30 .5 1.67
= 32 .17
6i)
7 8 x = 47
15 2x =47
2x = 47- 15
2x/2 = 32/2
divide both side by 2
x=16
6ii)
tran only;:
7 8 3 y=30
18 y =30
y=30 -18 =12
:. Tran only =12
iii) at least two: 7 16 3 8 =34
iv)16 7 12 16 8 3 Q=95
62 Q =95
Q= 95 -62
Q=33 :. Car only = 33
========================
========
7a)
a 2d=11 —-eq (1)
-(a 8d)=29 —-eq (2)
-6d/-6d = -18/-6
d=3
sub for d=3 in —-eq (1)
a 2(3)=11
a 6=11
a=11-6=5
7b)
L = ar^n-1
729/3 = 3/3 x 3^n-1
243 = 3^n-1
3^5 = 3^-1
5 = n-1
N = 5 1
= 6
Sn = a(r^-1)/r-1 = 3(3^6 – 1)/3-1
Sn = 3( 729 -1)/2
S6 = 3 x 728/2
S6 = 1092
7c)
3x^3/3 x | 2,1
(2^3 2) – (1^3 1)
(8 2) – (1 1)
= 8
========================
========
8ai)
y=(4x 9)^3
let u =4x 9, y=U^3
du/dx=4, dy/du=3U^2
dy/dx=dy/du * du/dx = 4*3u^2=12u^2
recall= U=4x 9
dy/dx=12(4x 9)^2
8aii)
y=(3x-2)^3 (x^2 4)^2
u=(3x-2)^3 V=(x^2 4)^2
du/dx=3.3(3x-2)^3-1 , dv/dx=2x.2(x^2 4)^2-1
=4x(x^2 4)
in other words
dy/dx=Vdu/dx udv/dx
=(x^2 4)^2 9 (3x-2)^2 (3x-2)^3 4x(3x-2)
=(x^2 4) (3x-2)^2 (9x^2 36 12x^2-8x)
=(x^2 4) (3x-2)^2 (21x^2-8x 36)
8b)
y-y1=m(x-x1)
y-6=2(x-2)
y-6=2x-4
y=2x-4 6=2x 2
==============================
(9a)
y proportional x proportional 1/x
y=kx/1 k/x
4=2k/1 k/2
4=(4k k)/2
8=5k
k=8/5
Relationship:
y=kx/1 k/x
y=8x/5 8/5x
(9b)
4(3^x 1)-3^2x=27
4(3^x *3^1)-362x=3^3
let 3^x=p
4(3p)-p^2=27
12p-p2=27
p^2-12p 27=0
p^2-9p-3p 27=0
p(p-9)-3(p-9)=0
(p-9)(p-3)=0
p=9 or p=3
Recall 3^x=p
when p=9
3^x=3^3
x=3
when p=3
3^x=3^1
x=1
therefore x=2 or 1
==============================
==================================
(11a)
Tabulate
X- |-1| |0| |1| |2| |3| |4|
6 |6| |6| |6| |6| |6| |6|
X |-1| |0| |1| |2| |3| |4|
-X^2 |-1| |0| |-1| |-4| |-9| |16|
Y- |4| |6| |6| |4| |0| |-6|
(11b)
Draw the graph
(11ci)
gradient at x/x
dy/dx =B-A/B-C
=7-4/2-1=3/1=3
(11cii)
roots of equation from the graph
x=-2.2 and x=3
(11ciii)
minimum value of y
=6.4
============
12a)
From Economics
3x + 2y - 12
3x+2y=90+12
3x+2y=102...(1)
sum of angle in a circle = 360 degree
5x+y-9+3x+2y-12+3y+4x+21=360
5x+3x+4x+y+2y+3y-9-12+21=360
12x+6y=360....(2)
Solving equation (1) and (2) simultaneously
3x+2y=102
12x+6y=360
Using elimination method
3x + 2y=102 *4
12x+ 6y=360 *1
--------------
2y/2 = 48/2
y = 24
Substitute y=24 into equation (1) for x
3x+2y=102
3x+2*24=102
3x+48=102
3x=102-48
3x=54
x=54/3
x=18
.:.x+y=18+24
x+y = 42
12b)
Candidates that are registered for literature
=4x+21/360 * 1200
=4(18)+21/360 * 1200
=72+21/360 * 1200
=93/360 * 1200
=111600/360
=310
Candidates that registered for government
= 3y/360 * 1200
=3(24)/360 * 1200
=72/360 * 1200
=86400/360
=240
310-240=70
.:.The candidates that registered for literature are 70 higher than candidates that registered for government.
*COMPLETED*
Post a Comment