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NECO 2017 - MATHS ANSWERS

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NECO - MATHS ANSWERS

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Exam Time: Wednesday 14th June 2017
Paper III: OBJ – General Mathematics – 10am – 11:45am
Essay – General Mathematics – 12pm – 2:30pm
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MATHS OBJ:
1-10: CCAADDEECE
11-20: EEBACAADCC
21-30: BBCEAAEECD
31-40: BCCCDCAADA
41-50: BACBDCDECD
51-60: BCDCAEDCDB

NOTE THE FOLLOWING SYMBOLS:
^ means rasie to power
# is naira sign
* multiply
pie is a pie sign

(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

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(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

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(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

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(4i )
difference in latitude = 36 degree + 36 degree = 72degree
distance travelled =@/ 360* 2pier
= 72 / 360* 2* 22 / 77* 64
= 20275200 / 2520
= 8045 . 71
= 8050 km ( 3 s.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 )

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(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


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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

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(7a)
a+2d=11---eq1
-(a+8d)=29
-6d/-6=-18/-6
d=3
Sub for d=3 in eq1
a+2(3)=11
a+6=11
a=11-6
a=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

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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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(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

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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.


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(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
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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.




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COMPLETED.
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