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**MATHS OBJ**

**+++++++++++++++++++++++++**

MATHS OBJ:

1-10: ADADDDCEBE

11-20: CCDCAACECA

21-30: DCDAECAEED

31-40: EAADBEEADC

41-50: BBDCCBCECD

51-60: CADBAECDECMATHS OBJ:

1-10: ADADDDCEBE

11-20: CCDCAACECA

21-30: DCDAECAEED

31-40: EAADBEEADC

41-50: BBDCCBCECD

51-60: CADBAECDEC

(1a)

Tabulate: Draw both vertical and horizontal lines across the digits. I drew only verticals cos it's txt messaging.

x|1|2|3|4

1|1|2|3|4

2|2|4|0|2

3|3|0|3|0

4|4|2|0|4

(1b)

S.I=PRT

P=N15,000, R=10%, T=3yrs

S.I=#15,000, R=10%, T=3yrss

S.I=15,000* 10/100 *3

S.I=N4,500

A=P+S.I

A=N15,000+N4,500

A=#19,500

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

3)

Let x represent Donald's age

and let y represent his son's age

x=5y---(1)

(x-4(y-4)=448---(11)

substitute for x in (11)

5y^2-20y-4y+16=448

5y^2-24y+16-448=0

5y^2-24y-432=0

y=-b+_sqroot(b^2-4ac)/2a

a=5, b=-24 c=-432

y=24+_sqroot[(-24^2)-4*5*-432]/2*5

y=24+_sqroot(576+8640)/10

y=24+_sqroot(9216)/10

y=24+_96/10

y=24+96/10 or 24-96/10

y=120/10 or -72/10

y=12 or -7.2

since age cannot be negative

y=12years

but x=5y

x=5*12

x=60years

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

(4a)

Convert 30000 litres to metres

= 30000/1000 metres

= 30metres

Depth of fuel = h * 7.5*4.2 = 30m^3

= 31.5hm^3 = 30m^3

= h = 30m^3/31.5m

= h = 0.9m

(4b)

Depth of the tank = l*b*h

where l= 7.5, b = 4.2, h = 1.2

=(7.5 * 4.2 * 1.2)m^3

=37.8m^3

Convert metres to litres = 37.8*

1000litres

= 37800litres

Litres of fuel needed to fill the tank=37800litres/30800litres

=7800litres

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

(5a)

sector for building project =48000/144000*360=120degree

sector for education = 32,000/144000*360=80degree

sector for saving = 19200/144000*360=48degree

sector for maintenance = 12000/144000*360=30degree

sector for miscellaneous = 7200/144000*360=18degree

sector for food items = 360-(120+80+48+30+18)

=360-296

=64degree

THEN DRAW A PIE CHART WITH THE ANSWERS YOU GOT ABOVE.

(5b)

Food = 48000 + 32000 + 19200 +

1200 +7200 + x = 144000

Food => 118400 + x = 144000

Food => x = 144000 — 118400

Food = x = #25,600

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

(6)

3sqroot[(41.02*sqroot0.7124)/(42.87*0.207*0.0404)]

Tabulate

No|log

41.02|16130

*sqroot0.7124|(1^-.8527)/2

|(2^-+1.8527)/2

|1^-9264

41.02*sqroot0.7124|1.6130

|+1^-.9264

|=1.5394

42.87|1.6322

*0.207|+1^-.3160

|0.9482

*0.0404|+2^-.6064

|=1^-.5546

|1.5394

|1^-.5546

|=(1.9848)/3

antilog4.588|0.6616

Answer=4.588

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

(7a)

3^2n+1 - 4(3^n+1)+9=0

3^2-3 - 4(3^n -3)+9=0

(3^n)^2-3 - 4(3^n -3)+9=0

let 3^n = p

p^2 -3 - 4(p-3)+9=0

3p^2/3 - 12p/3 + 9/3 = 0

p^2 - 4p + 3 = 0

p^2 - 3p - p + 3 = 0

p^2p(p-3) - 1(p-3) = 0

(p-1)(p-3) = 0

p-1 = 0 or p-3 = 0

p = 1 or 3

Recall 3^n = p

when p=1

3^n = 3^0

n = 0

when p = 3

3^n = 3^1

n = 1

(7b)

log(x^2+4) = 2+logx - log^20

log(x^2+4) = log^100 = log^x - log^20

(x^2+4) = log(xx)

x^2+4 = 5x

x^2-5x+4 = 0

x^2-4x - x +4 = 0

x(x-4) - 1(x-4) = 0

(x-1)(x-4) = 0

x-1 = 0 or x-4 = 0

x = 1 or 4

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

(8ai)

In <> ABC

Cos B=(a^2+c^2-b^2)/2ac

Cos B=(13^3+13^2-10^2)/(2*13*13)

Cos B=(338-100)/338

Cos B=238/338

Cos B=0.7041

B=cos^-0.7041

B=45.2degrees

therefore =90.4degrees

In <>AOC

By sine rule

r/sine44.8=10/sine90.4

r=10sin44.8/sin90.4

r=7.05cm

(8aii)

Circumference =2*pie*R

=2*22/7*7.05

=44.31

=44.3cm(1d.p)

(8b)

p(-1,2) , (2,6)

(y-y1)/(y2-y1)=(x-x1)/(x2-x1)

(y-2)/(6-2)=(x+1)/(2+1)

(y-2)/4=(x+1)/3

3(y-2)=4(x+1)

3y-6=4x+4

3y-4x=10

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

(9a)

Let the lens digit x and unit digit be y,

therefore x-y=5 ---(1)

3xy-(10x+y)=14 ----(2)

3xy-10x-y=14 -----(3)

frm eq(1); x=5+y --- (4)

therefore, 5(5+y)(y)-10(5+y)-y=14

(15+3y)y-50-10y-y=14

3y^2+4y-50-14=0

3y^2+4y-64=0

3y^2 -12y + 16y-64=0

3y(y-4)+16(y-4)=0

(3y+16)(y-4)=0

y=-16/3 or 4

therefore from eqn(1);

x+4=5

x=5+4=9

the number is 94

(9b)

(3-2x)/ 4 + (2x-3)/3

(3(3-2x)+4(2x-3))/12

(9-6x+8x-12)/12

=(2x-3)/12

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

(10a)

y=(2x^2 + 3)^5

let U=2x^2 + 3

Y=u^5

du/dx = 4x

dy/du = 5u^4

dy/du = (2x^2 + 3)^4

dy/dx = du/dx dy/du

dy/dx = 4x.5(2x^2 + 3)^4

dy/dx = 20x(2x^2 + 3)^4

(10b)

y=3x^2 + 2x +5

dy/dx =6x + 2

dy/dx =6(3) +2

dy/dx =18+2

dy/dx =20

(10c)

R-W=Wv^2/gx

Wv^2=gx(R-W)

Wv^2=gRx-Wgx

Wv^2+Wgx=gRx

W(v^2 + gx) =gRx

W=gRx/V^2 + gx

R=2, g=10, x=3/2, V=3

W= 10*2*3/2/3^2 + 10*3/5

W=30/9+15

W=30/24

W=5/4

(12a)

TABULATE

class interval:50-54,55-59,60-64,65-69,70-74

F:5,5,15,12,3=40

x:52,57,62,67,72

x:260,285,930,804,216=2495

x-x^-:-10.4,-5.4,-0.4,4.6,9.6

(x-x^-)^2:108.16,29.16,0.16,23.16,92.16

F(x-x^-)^2:540.8,145.8,2.4,253.92,276.48=1219.4

(12bi)

Mean(x^-)=Efx/Ef=2495/40

=62.4

(12bii)

Variance=Ef(x-x^-)^2/Ef=1219.4/40

=30.485

(12biii)

Standard deviation=sqroot[Ef(x-x^-)^2/Ef

=Sqroot1219.4/40

=sqroot30.485

=5.52

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**THIS IS HOW ANSWERS WILL COME TO YOUR PHONE, THE INTERPRETATION IS HOW U ARE GONNA WRITE IT ON YOUR PAPER!!!**

/ means DIVISION

* means multiplication

degree means °

tita u should know dat ( Θ ).

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: 60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99.

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 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 = θ eg Sinθ.

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

11)/ means ÷

12)----(1) means equation 1

/ means DIVISION

* means multiplication

degree means °

tita u should know dat ( Θ ).

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: 60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99.

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 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 = θ eg Sinθ.

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

11)/ means ÷

12)----(1) means equation 1

*FOR THOSE WHO CANT UNDERSTAND THE SYMBOLS AS WRITTEN ABOVE CAN VIEW IT IN IMAGE FORMAT BELOW!!!*__NOTE:__Symbols |

**GOODLUCK!!!**

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