# NECO 2017 Mathematics OBJ And Essay Answer – June/July Expo

NECO Mathematics OBJ, THEORY/ESSAY Questions and Answer – June/July 2017 Expo Runz

/ 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 ∝

VERIFIED

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

———————————————-

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

3a)

P=100I/RT=100*30,000/4*3

P=N250,000

3b)

#7000 T0 FRANCS

8FRANS= #1

?FRANCS =7000

CROSS MULTIPLY

=#56,000 FRANCS

SPENDING 49,400 FRANCS

56,000-49,400 = 6600

CONVERTING 6,600 FRANCS TO # AT 10 FRANCS TO 1#

10 FRANCS—– 1#

6600 FRANCS—?#

=6,600/10 X1

4i)

difference in latitude=36degree + 36 degree =72degree

distance [email protected]/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)

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

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

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

9)

TYPING IT OUT

10)

TYPING IT OUT

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)

1ci)

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=90

3x+2y=90+12

3x+2y=102 —–(1)

sum of angle in a circle=360degree

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 1and2

simulteanously

13x+2y=102

12x+6y=360

using elimination method

3x+2y=102*4

12x+8y=408

12x+6y=360

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/3=54/3

x=18

x+y=18+24

x+y=42

12b)

candidate that registerd for literature

=4x+21/360 * 1200

=4*18+21/360 * 1200

=72+21/360 * 1200

93/360*1200 =111600/360

=310

candidate that registered for government

=3y/360 * 1200

=3*24/360 * 1200

=72/360 * 1200 =86400/360

=240

310 – 240 = 70

the candidate that registered for litereature are 70, more than candidate that registered for government

COMPLETED

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