# Question & answer for OBJ – General Mathematics – 10:00am – 11:45am Essay – General Mathematics – 12:00noon –2:30pm

OBJ – General Mathematics – 10:00am – 11:45am
Essay – General Mathematics – 12:00noon –2:30pm (9)
Log10(20x-10) – log10(x+3)= log10^5
Log10(20x-10)/x+3) =log10^5
20x-10/x+3 = 5
Cross multiply
20x-10 = 5(x+3)
5(4x-2) = 5(x+3)
4x-x = 3+2
3x= 5
X=3/5

(9b)
Let actual amount be #x
15% of #x = #600
15x/100 =600
x =(100/15) * 600
x = 100 * 40
x = 4,000
Actual amount = 4,000
===========================
(1a)
Log10(20x – 10) – log10(x+3) = log10^5
Log10(20x-10/x+3)= log10^5
20x – 10/x + 3 = 5
Cross multiplying
20x – 10 = 5(x + 3)
5(4x – 2) = 5(x + 3)
4x – 2 = X + 3
4x – x = 3+2
3x = 5
X = 5/3 OR 1 whole no 2/3

(1b)
Let actual amount be #X
15% of #x = #600
15x/100 = 600
X = (100/15)*600
X = 100*40
X = 4,000
Actual amount = #4,000
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(8)
x=a+by(eqi)
when y=5 and x=19
19=a+5b(eqii)
when y=10 and x=34
34=a+10b(eqiii)
solving eqii and eqiii
a+10b=34
a+5b=19
=>5b=15
b=15/5=3
putting b=3 in eqii
19=a+5(3)
19=a+15
a=19-15
a=4
(8i)
Putting a=4 and b=3 in eqi
x=4+3y
This is the relationship between xand y
(8ii)
When y=7
x=4+3(7)
x=4+21
x=25
11a)
x+y/2 =11
x+y= 11*2
x+y= 22 —(1)
x-y= 4 —-(11)
x+y = 22—-(1)

x-y= 4—-(11)
____________
2y = 18
y= 18/2
y=9
Substitute y=9 in equ 1
x+9=22
x=22-9
x=13
x=13, y=9
x+y= 13+9= 22
Sum of the two number

(11b)
(6x + 3) dx
(6x + 3)dx
(6x +3)^6 – (6x + 3)^1
(6 x + 3)^5
(7776x^5 + 243)
38,880x/6 + 243
6480 x^6 + 243x
9(720x^6 + 27x)

(11c)
y = x² + 5x – 3 (x = 2)
y = 2² + 5(2) – 3
y = 4 + 10 – 3
y = 14 – 3
y = 11
Gradient of the curve = 11

: 7a)
A) T3=6 & T7 =30
I)common difference using Tn=a+(n-1)d
In the 3rd term; n =3
=>T3=a+(3-1)d=6
=>a+2d=6 equation (1)
In the 7th term ;n =7
=> T7=a+(7-1)d=30
=>a + 8d=30 equation (1) & (2)
Simultaneous
A+2d =6 equation (1)
A+ 8d=30 equation (2)
0+(1-6d) =-24
=> -6d= -24
=>d = -24/-6 =4
II) first term put d=4 into equation

1a)
Log 10(20*-10)-log10(*+3)=log105
(20*-10/*+3)=log10 =5
20*-10/*+3=5
5(*+3)=20*-10
5*+15=20*-10
15+10=20*-5*
25=15*
*=25/15
*=5/3=1 2/3
1b
[6/4, 10:01 AM] Prosper: No 4(i)
length of Arc of the sector
Titter= 72?, r = 14cm
L= titter / 360 x 2 pie r
==> L= 72/360 x 2 x 22/7 x 14
=44352/2520 = 17.6cm

(ii) perimeter of the sector
Perimeter = titter/360 x 2 pie r + 2r = 17.6 +(2×14) =17.6+28= 45.6cm

(iii) Area of the sector
Area = Titter/360 x pie r? =
72/360 x 22/7 x (14)? = 72 x 22 x 196/2520
Area= 310464/2520 = 123.2cm?
[6/4, 10:01 AM] Prosper: 1a)
Log 10(20*-10)-log10(*+3)=log105
(20*-10/*+3)=log10 =5
20*-10/*+3=5
5(*+3)=20*-10
5*+15=20*-10
15+10=20*-5*
25=15*
*=25/15
*=5/3=1 2/3
1b)
Discount percent =15%
Discount amount =#600
Actual amount paid on the article =?
Original amount on the article =*
15%*=#600
15/100* =600
15*=600*100
15*=60000
*=60000/15
*=#4,000
Therefore actual amount paid on the article
=#4,000-#600
=#3,400
Actual amount paid on the article =#3,400
*NECO 2018 MATHS SYMBOLS TO BE USED FOR EXPO*

NOTE: IF YOU HAVE NOT SUBSCRIBED/PAID FOR ANSWER DON’T BOTHER STUDYING.

/ means DIVISION

* means Multiplication

tita You Should Know that.

rais means Raise to power

Or

^ means Raise to power

sqr rut/square 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 its Following ie. UNDER. It is usually used during STATISTICS when drawing a table.

EXAMPLE 1.

X:1,2,3,4,5,6
FX: 4,6,8,10,12
FX-Xbar: 10,8,6,4,2,1

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….

ANOTHER EXAMPLE:
Class interval: 60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99.
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: 561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06

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 60-64 is unda Class interval, then 65-69 is unda 60-64,etc .So comma means unda.

NOTE: When You See Something Like the above to Examples, You are requered to Draw a Table.

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WARNING: Please Study the above Symbols, If you Don’t want to write Rubbish in you MATHEMATICS Exam.

NOTE: WE WILL TRY TO MAKE OUR ANSWERS AVAILABLE IN PICTURE FORMAT, but still study the above symbols incase!!!!