NECO 2013:- 100% REAL MATHEMATICS AVAILABLE HERE

MATHEMATICS SYMBOLS TO BE USED IN THE EXAM

/ means DIVISION * means multiplication tita u should know dat.

rais means raise to power ^ means raise to power sqr rut/ squar rut means
square root

----(1) means equation 1 yr means year f(x-xbar) 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
FX-Xbar: 10,8,6,4, DRAW A TABLE WITH X|FX|(FX-
Xbar)
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 FX-Xbar 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
fx-xbar : 10,8,6,4

x|fx |fx-x�¯�¯|
1| 4 | 10 |
2| 6 | 8 |
3| 8 | 6 |
4| 10| 4

ANOTHER EXAMPLE: Class interval:
60-64,65-69,70-74,75-79,80-84,85
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(x-x bar)2:
561.12,414.18,273.36,33.66,84.48,4

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 60-64 is unda Class interval,
then 65-69 is unda
60-64,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
fx-xbar : 7,8,9

x|fx |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 = �¸ eg Sin�¸.

10)Root or Rut or Sqrt or sqr
root = � ; eg Root2 means �2

11)/ means �·

12)----(1) means equation 1                                                                                VISIT WWW.NAIJABUX.TK FOR THE QUESTION & ANSWER      VISIT WWW.NAIJABUX.TK FOR THE QUESTION & ANSWER                               VISIT WWW.NAIJABUX.TK FOR THE QUESTION & ANSWER                       VISIT WWW.NAIJABUX.TK FOR THE QUESTION & ANSWER

why spamming? u really need hammer on ur big head

people sef. u promise finish come disappoint. thought u can deliver dat was y i neva cared to post. na wa oooooo. e don late sha bt na d solvin b this

MATHS ANSWERS.

MATHS OBJ:
1-10: BCABCADDAA
11-20: DDEACDBACA
21-30: ABAACECADB
31-40: ACAEBEBBCD
41-50: EDEDDEDDCA
51-60: CADCEDDEAB

(1) n(AUBUC)=n(A)+n(B)+n(C)-n(AnB)-n (BnC)+n(AnBnC) 55=21+24+23-6-8-5+2x+x 55=49+3x 3x=6 x=2 (1i) 21-6-5-x = 21-11-2 physics only=8 (1ii) 6+5+8= 19

(2a) Using almighty formular x= -b+sqrt(b^2- 4ac)/2a =5+sqrt(25-4(2)(3))/2(2) =(5+1)/4 or (5-1)/4 = 1 or (1)1/2
(2b) Volume of cylinder= pieR^2h 352=22/7*4*4*h h=7

(3a) RD^2=(37)^2- (12)^2 = 1369-144 RD^2=1225 RD=sqrt(1225) =35cm Area= 35*12=420cm^2
(3b) ((2p+q)/(p-3q))^1/2=h sqrt(h)=(2p+q)/(p-3q) Psqrt(h)- 3qsqrt(h)=2p+q Psqrt(h)-2P= q+3qsqrt(h) P(sqrt(h)-2)= q+3qsqrt(h) P=q+3qsrt(h)/sqrt(h)-2

(4a) (n-2)180= xn+x=180 x(n+1) 180n-360=xn+x 180n-360=x(n+1) x=180n-360/n+1
(4b) (x+5)/3-(2x-1)/5=5/6 30((x+5)/3) - 30((2x-1)/5)= 30(5/6) 10x + 50-12x+6=25 56-2x=25 -2x=-31 x=15.5

(5a) perimeter of sector= (tita/360)2pieR+2r =2(9)+120/360*2*22/7*9 =18+18.86 =36.9cm
(5b) 150/h=tan30 h=150/tan30 h=259.8 approx 260

(6a) Snth= n/2(2a+11d) -192=24a+132d -96=12a+66d -32=4a+22d -16=2a+11d ----equ(1) -252=18(2a+17d)/2 -504=18(2a+17d) -28=2a+17d-------equ(2) (-16=2a+11d) -(-28=2a+17d) 12=-6d d=-2
(6b) from equ(1) -16=29+11(-2) -16=29-22 2a=6 a=3
(6c) Tnth= a+(n-1)d =3+(15-1)(-2) T15th= -25 T4th=a+(4-1)d =3+3(-2) =-3 Product of 15th and 4th= -3*-25=75

(7ai) STB= 180-75-40 (sum of angles on a straight line) STB= 65 SRP= 180-65(opposite angles are complementary) =115degree
(7aii) SQP= 115(angles substended from the same circumference are equal)
(7aiii) SPQ=180-115-12 (sum of angle in a triangle) =53degree
(7b) C=R+KT 2800=R+K(6) 2800= R+6k ---------equ(1) - 3600= R+10K------equ(2) -800 = -4k k=200 From eqn(1) 2800=R+200(6) 2800-1200=R R=1600 at 4hours, C= 1600 + 200(4) = 800 +1600 =#2400

( Distance from Airport to the North= Time*Speed = 500*1(1/2)= 750km 2nd distance= xkm From cosine rule, a^2=b^2+c^2-2bc CosA x^2=750^2+400^2-2(750)(400)cos127 =562500+160000-(-361089.01) x^2=1083589.01 x=sqrt(1083589.01)= 1,040.96km Bearing from the airport from sine rule, a/sinA=b/sinB 1040.96/sin127=750/sinb sinb=0.5754 b=35.13 d= 150-127-35.13(sum of anglesin a triangle) d= 17.89 approx = 17.9 Bearing from the airport=180+17.9=197.9

(9a) a^2= b^2+c^2(pythagora's theorem) h^2=40^2+16^2 =1600+256 =1856 h=sqrt(1856)= 43.1cm
(9b) Total surface area Area of one of the four triangular faces=40*16=640cm^2 for four triangles= 4*640=2560cm^2 Area of square base=32*32=1024cm^2 Total surface area=1024+2560=3584cm^2

(12) TABULATE THE TABLE MARK%: 51-60, 61-60, 71-80, 81-90, 91-100 BOUNDARIES: 50.5-60.5, 60.5-70.5, 70.5-80.5,80.5-90.5, 90.5-100.5 CLASS MARK(X): 55.5,65.5,75.5,85.5,95.5 FREQUENCY: 11, 23,39,17,10 (FX): 610.5,1506.5,2944.5, 1453.5, 955 /X-XBAR/: 19.2, 9.2, 0.8, 10.8, 20.8 /X-XBAR/^2: 368.64, 84.64, 0.64, 116.64, 432.64 F/X-XBAR/: 211.2, 211.6, 31.2, 183.6,208
(i) Mean= Efx/fx = (610.5+1506.5+2944.5+1453.5+955)/100 =7470/100 =74.7 approx =7
(ii) Mean Deviation= sqrt(Ef/x-xbar/)/Efx sqrt(211.2+ 211.6+31.2+183.6+208)/100 845.6/100=8.456 approx = 8
(iii) Standard Deviation=sqrt(Ef/x-xbar/^2)/ Efx sqrt(12336/100)=sqrt(123.36) =11

too bad