OBJ – General Mathematics – 10:00am – 11:45am

Essay – General Mathematics – 12:00noon –2:30pm

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(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.

========================

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!!!!

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OMO BALO