CURRENT EXAMINATION:
NECO May/June Civic Education Objectives & Theory Questions & Answers;
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MATHS OBJ
+++++++++++++++++++++++++
MATHS OBJ:
110: ADADDDCEBE
1120: CCDCAACECA
2130: DCDAECAEED
3140: EAADBEEADC
4150: BBDCCBCECD
5160: CADBAECDEC
(1a)
Tabulate: Draw both vertical and horizontal lines across the digits. I drew only verticals cos it's txt messaging.
x1234
11234
22402
33030
44204
(1b)
S.I=PRT
P=N15,000, R=10%, T=3yrs
S.I=#15,000, R=10%, T=3yrss
S.I=15,000* 10/100 *3
S.I=N4,500
A=P+S.I
A=N15,000+N4,500
A=#19,500
============================
3)
Let x represent Donald's age
and let y represent his son's age
x=5y(1)
(x4(y4)=448(11)
substitute for x in (11)
5y^220y4y+16=448
5y^224y+16448=0
5y^224y432=0
y=b+_sqroot(b^24ac)/2a
a=5, b=24 c=432
y=24+_sqroot[(24^2)4*5*432]/2*5
y=24+_sqroot(576+8640)/10
y=24+_sqroot(9216)/10
y=24+_96/10
y=24+96/10 or 2496/10
y=120/10 or 72/10
y=12 or 7.2
since age cannot be negative
y=12years
but x=5y
x=5*12
x=60years
================================
(4a)
Convert 30000 litres to metres
= 30000/1000 metres
= 30metres
Depth of fuel = h * 7.5*4.2 = 30m^3
= 31.5hm^3 = 30m^3
= h = 30m^3/31.5m
= h = 0.9m
(4b)
Depth of the tank = l*b*h
where l= 7.5, b = 4.2, h = 1.2
=(7.5 * 4.2 * 1.2)m^3
=37.8m^3
Convert metres to litres = 37.8*
1000litres
= 37800litres
Litres of fuel needed to fill the tank=37800litres/30800litres
=7800litres
================================
(5a)
sector for building project =48000/144000*360=120degree
sector for education = 32,000/144000*360=80degree
sector for saving = 19200/144000*360=48degree
sector for maintenance = 12000/144000*360=30degree
sector for miscellaneous = 7200/144000*360=18degree
sector for food items = 360(120+80+48+30+18)
=360296
=64degree
THEN DRAW A PIE CHART WITH THE ANSWERS YOU GOT ABOVE.
(5b)
Food = 48000 + 32000 + 19200 +
1200 +7200 + x = 144000
Food => 118400 + x = 144000
Food => x = 144000 — 118400
Food = x = #25,600
=================================
(6)
3sqroot[(41.02*sqroot0.7124)/(42.87*0.207*0.0404)]
Tabulate
Nolog
41.0216130
*sqroot0.7124(1^.8527)/2
(2^+1.8527)/2
1^9264
41.02*sqroot0.71241.6130
+1^.9264
=1.5394
42.871.6322
*0.207+1^.3160
0.9482
*0.0404+2^.6064
=1^.5546
1.5394
1^.5546
=(1.9848)/3
antilog4.5880.6616
Answer=4.588
==================================
(7a)
3^2n+1  4(3^n+1)+9=0
3^23  4(3^n 3)+9=0
(3^n)^23  4(3^n 3)+9=0
let 3^n = p
p^2 3  4(p3)+9=0
3p^2/3  12p/3 + 9/3 = 0
p^2  4p + 3 = 0
p^2  3p  p + 3 = 0
p^2p(p3)  1(p3) = 0
(p1)(p3) = 0
p1 = 0 or p3 = 0
p = 1 or 3
Recall 3^n = p
when p=1
3^n = 3^0
n = 0
when p = 3
3^n = 3^1
n = 1
(7b)
log(x^2+4) = 2+logx  log^20
log(x^2+4) = log^100 = log^x  log^20
(x^2+4) = log(xx)
x^2+4 = 5x
x^25x+4 = 0
x^24x  x +4 = 0
x(x4)  1(x4) = 0
(x1)(x4) = 0
x1 = 0 or x4 = 0
x = 1 or 4
==========================
(8ai)
In <> ABC
Cos B=(a^2+c^2b^2)/2ac
Cos B=(13^3+13^210^2)/(2*13*13)
Cos B=(338100)/338
Cos B=238/338
Cos B=0.7041
B=cos^0.7041
B=45.2degrees
therefore =90.4degrees
In <>AOC
By sine rule
r/sine44.8=10/sine90.4
r=10sin44.8/sin90.4
r=7.05cm
(8aii)
Circumference =2*pie*R
=2*22/7*7.05
=44.31
=44.3cm(1d.p)
(8b)
p(1,2) , (2,6)
(yy1)/(y2y1)=(xx1)/(x2x1)
(y2)/(62)=(x+1)/(2+1)
(y2)/4=(x+1)/3
3(y2)=4(x+1)
3y6=4x+4
3y4x=10
=============================
(9a)
Let the lens digit x and unit digit be y,
therefore xy=5 (1)
3xy(10x+y)=14 (2)
3xy10xy=14 (3)
frm eq(1); x=5+y  (4)
therefore, 5(5+y)(y)10(5+y)y=14
(15+3y)y5010yy=14
3y^2+4y5014=0
3y^2+4y64=0
3y^2 12y + 16y64=0
3y(y4)+16(y4)=0
(3y+16)(y4)=0
y=16/3 or 4
therefore from eqn(1);
x+4=5
x=5+4=9
the number is 94
(9b)
(32x)/ 4 + (2x3)/3
(3(32x)+4(2x3))/12
(96x+8x12)/12
=(2x3)/12
============================
(10a)
y=(2x^2 + 3)^5
let U=2x^2 + 3
Y=u^5
du/dx = 4x
dy/du = 5u^4
dy/du = (2x^2 + 3)^4
dy/dx = du/dx dy/du
dy/dx = 4x.5(2x^2 + 3)^4
dy/dx = 20x(2x^2 + 3)^4
(10b)
y=3x^2 + 2x +5
dy/dx =6x + 2
dy/dx =6(3) +2
dy/dx =18+2
dy/dx =20
(10c)
RW=Wv^2/gx
Wv^2=gx(RW)
Wv^2=gRxWgx
Wv^2+Wgx=gRx
W(v^2 + gx) =gRx
W=gRx/V^2 + gx
R=2, g=10, x=3/2, V=3
W= 10*2*3/2/3^2 + 10*3/5
W=30/9+15
W=30/24
W=5/4
(12a)
TABULATE
class interval:5054,5559,6064,6569,7074
F:5,5,15,12,3=40
x:52,57,62,67,72
x:260,285,930,804,216=2495
xx^:10.4,5.4,0.4,4.6,9.6
(xx^)^2:108.16,29.16,0.16,23.16,92.16
F(xx^)^2:540.8,145.8,2.4,253.92,276.48=1219.4
(12bi)
Mean(x^)=Efx/Ef=2495/40
=62.4
(12bii)
Variance=Ef(xx^)^2/Ef=1219.4/40
=30.485
(12biii)
Standard deviation=sqroot[Ef(xx^)^2/Ef
=Sqroot1219.4/40
=sqroot30.485
=5.52
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THIS IS HOW ANSWERS WILL COME TO YOUR PHONE, THE INTERPRETATION IS HOW U ARE GONNA WRITE IT ON YOUR PAPER!!!
/ means DIVISION
* means multiplication
degree means °
tita u should know dat ( Θ ).
rais means raise to power
^ means raise to power
sqr rut/ squar rut means square root
(1) means equation 1
yr means year
f(xxbar) means x MINUS x BAR as in statistics which means that MINUS WILL BE ON TOP OF x.
,
(Comma) means NEXT LINE, THIS MEANS THAT THE FOLLOWING NUMBER IS UNDER
THE NUMBER IT IS FOLLOWING i.e UNDER. It is usually used during
STATISTICS when drawing a table.
EXAMPLE 1.
X:1,2,3,4,
FX: 4,6,8,10
FXXbar: 10,8,6,4,
DRAW A TABLE WITH XFX(FXXbar)
The above statement means that:
~For X, it has 1 2 3 4 5 6 under it. which means 1 is under 2, 2 is under 1, 3 is under 2, 4 is under 3 and so on...
~Under FX you have 4, then 6 under 4, then 8 under 6, then 10 under 8, then 12 under 10.....
~Under FXXbar you have 10, then 8 under 10, then 6 under 8, then 4 under 6, then 2 under 4, then 1 under 2....
IN A CLEARER WAY:
→ comma means NEXT LINE(e.g)
x : 1,2,3
fx : 4,5,6
fxxbar : 10,8,6,4
xfx fxx¯¯
1 4  10 
2 6  8 
3 8  6 
4 10 4 
ANOTHER EXAMPLE:
Class interval: 6064,6569,7074,7579,8084,8589,9094,9599.
X: 62,67,72,77,82,87,92,97.
F: 2,3,6,11,8,7,2,1.
FX: 124,201,432,847,656,609,184,97.
F(xx bar)2: 561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06
MEANING OF THE ABOVE EXPRESSION:
Bar
means Minus on top of d number or Variable and comma means next line
which means each of them are unda. Eg 6064 is unda Class interval, then
6569 is unda 6064,etc .So comma means unda.
NOTE THAT WHEN U SEE SOMETHING LIKE THE ABOVE TWO EXAMPLES, U WILL NEED TO DRAW A TABLE..
YOU NEED TO KNOW THESE ALSO:
MATHS CODES:
1) ,(comma) means next line.
(e.g)
x : 1,2,3
fx : 4,5,6
fxxbar : 7,8,9
xfx x¯¯
1 4  7 
2 5  8 
3 6  9 
2)*=multiplication sign.
3)^ = Riase to pwer
4)P also means raised to power eg 10P6 means 10 raised to power six.
5)log3(base 4) ..Note:the base must be SUBSCRIPT .
6)x bar = mean symbol(x¯¯)
7)Pie = pie symbol eg Area of a circle is (Pie r2).
8)Tita = θ eg Sinθ.
10)Root or Rut or Sqrt or sqr root = √ ; eg Root2 means √2
11)/ means ÷
12)(1) means equation 1
NOTE: FOR THOSE WHO CANT UNDERSTAND THE SYMBOLS AS WRITTEN ABOVE CAN VIEW IT IN IMAGE FORMAT BELOW!!!

Symbols 
GOODLUCK!!!
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