MATHEMATICS

/ means division or divide
Log means logarithm
* means multiplication
^ means Raise to power
Tita means θ
Pie means π
Base means subscript
Sqr root means √
bar means a dash on top a number of letter
—(1) means equation 1
Proportional means ∝

CLICK HERE TO STUDY THE SYMBOLS

Verified-Maths-Obj
1CDAAEDEECE
11EEBABAABCC
21BBCEDABECD
31BCCCDDCADE
41BDCBDCCECD
51BCDCBEDCDB

1)
tabulate
Number-
5932
*6141
num
3679
*3113
den
Log
3.7732
3.7882
7.5612
3.5657
3.4931
7.0588
anti log
7.5612
7.0588/0.5024/3=0.1675
anti log
=1471*10
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2)
a = 3, b = 20, C = -7
Sum is
(α/1 + 1/β + β/1 + 1/ α) Note α means Alpha
α^2 β + β^2 + α + β / α β
= -7/3 (-20/3) + (-20/3) = 140/9 – 20/3 / -7/3 (Note / means
Divided)
= 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
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4i)
difference in latitude=36degree + 36 degree =72degree
distance travelled=@/360*2pir
=72/360*2*22/77*64
=20275200/2520
=8045.71
=8050km(35.f)

4ii)
given that speed =800km/hr
distance travelled =804571km
time=distance travelled/speed
=8045.71/800
=10.057
=10hrs(to the nearest hour)
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3a)
P=100I/RT=100*30,000/4*3
P=N250,000

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
L1+[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
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SECTION B
ANSWER 5 QUESTIONS


6i)
7+8+x*x=47
15+2x=47
2x=47-15
2x/2 =32/2
x=16

6ii)
Tram only
7+8+3+y =30
18+y =30
y=30-18=12
Tram only =12

6iii)
at least two
7+16+3+8
=34//

6iv)
16+7+12+16+8+3+9=95
62+9=95
9=95-62
9=33// or 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

SEE ALSO:   Neco 2017 Fishery Practical Answers – May/June Expo

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
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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
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9)
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10)
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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)
CLICK HERE FOR 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.


12)
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