 Maths 2016 GCE Subscribers Portal

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# Maths 2016 GCE Subscribers Portal

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Saturday, 10th September, 2016
General Mathematics (Essay&Obje
9.30am-3.30pm
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VERIFIED MATHEMATICS OBJECTIVE
11~20 DCCCCACDBA
21~30 BDBAABDACA
31~40 CCACBDCDBD
41~50 DACBDABBBC           Dear Candidate
Here Are The Symbol To Be Use For Physic And Mathematics Exam
PHYSICS AND MATHEMATICS SYMBOLS TO BE USED FOR EXAM

/ 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 Dnt want to write Rubbish in you MATHEMATICS Exam Or Calculation Exam

Use this
1a )
6whole 1 / 2 - 3 whole 2/ 5 / 2whole 1 / 2 - 1 whole 3/ 5
25 / 4- 17 / 5 , / 5/ 2- 8/ 5
125 - 68 / , 20 , / 25 - 16,
/ 10
==> 57 / 20 / 9/ 10
=57 / 20 /9 / 10
=57 / 20 x 10 / 9
=57 / 20 x 10 / 9

=57 / 18
= 3whole 1 / 6
=======

3a)
c= -1, y= -3, z= -4 and w= -7
x^2 - y^2 / 2w - z
(-1)^3 - (-3)^2 / 2(-7) -(-4)
= -1-9/+4+4 = -10/-10
= 1

3b)
< MQN + < NQO = 90 degree
< MNQ + 46 = 90 degree
< MNQ = 90 - 46 degree
< MNQ = 44 degree
Considering < MNQ
y + n + MQN = 180 degree
y + 44 + 44 = 180
y = 180 - 88
Y =92 degree

4a)
2/3(1-4x) -1/2(5-3x) less/equal to 1/4(7+9x)-1/3
multiply through by 12
8(1-4x) -6(5-3x) less/equal to 3(7+9x)-4
8-32x-30+18x less/equal to 21+27x-4
-32x+18x - 27x less/equal to 21-4+30-8
-41x less/equal to 39
x less/equal to -39/41

4b)
DRAW THE ANGLE
from DTMR/
Tan65degree = TR/3
TR = 3Tan65
= 3 x 22.1445
From DRMB
Tan20 = RB/3
RB = 3Tan20
= 3 x 0.3640
= 1.092m

H = TR+RB
= 6.4335 + 1.092
= 7.5255
= 7.53m

5)
Area of shed segment = Area of Sector - Area of Triangle
=Φ/360*πr^2 - (½abSinc)
=\$90/360*22/7*7^2) - ½*7*7*sin90`
=154/4 - 42/2
=(754-98)/4
=56/4
=14cm^2
Cost of painting it =14*750
=N10500
========

6a)
Taxable income = x
25/100 x x/1
= 14,000
25x=1400000
X=1400000/25
X= 560000
Total income =
56,000/4 x 5
=70,000

6b)
Education = 2/5
Clothes = 1/6
Food = 3/8
Expenditure = 2/5 + 1/6 + 3/8
48+20+45/120
= 113/120 * 36,000/1
Le 39,000
Savings annually = Le 21,000
To save Le 63,000.00
To save Le 63,000/2100 yrs
= 30 years

(7a )
diagram

(7b )
Angula difference in long (tita)=42 - 12
tita=30 degree

(7bi )
lenght of chord Xy=2 Rsin tita /2
XY= 2*6400*Sin 30 /2
=2 *6400*sin 15 degree
=12800 *0. 2588
=3 . 312 . 64 km
=3312. 64 km
=3310km (to the nearest 10 km )

(7bii )
let the angle that the chord xy substends at the centre of the earth be alpha degree
diagram
sin alpha/ 2= opp / hyp =/ NY/ / 6400
/NY/ = 1/ 2 /XY /= 1/ 2 * 3312. 64
=1656. 32 km
sin alpha/ 2= 1656. 32 / 6400
sin alpha/ 2= 0 . 25888
alpha/ 2= sin ^ - 1(0. 2588)
alpha/ 2=14 . 999
alpha=14 . 999 *2
alpha= 29 . 998
alpha= 30 . 0 degree (to 1 dp )

(7biii)
XY bar= tita/ 360 * 2 pie R cos lat
=30 degeree / 360 * 2*3 . 142 * 6400* cos 60
XY bar= 30 / 360 * 2* 3. 142 * 6400* 0. 5
XY bar= 1675. 73 km

8a)
Drawing
8bi)
Using Pythagoras theory
|xz|² =550²+320²
= 302500+102400=404900
xz=√404999
=636km(3 s.f)
Total distance = 320+550+636
= 1506km

8bii)
Using SOHCAHTOA
Tan z = 320/550
Z= Tan-¹ (320/550)
Z= Tan-¹(0.5818)
Z = 30°
From the diagram in 8a
Bearing of X from Z = 55+30
= 085° or N85°E

9b)
Distance= speed * time
Distance= 3km/h * 3mins
= 3000m/60min * 3min
=50*3 =150min.

9bi)
Circumference= 150m
2π(r+1) = 150
22/1 * 22/7 * (r+1)= 150
r+1= 150*7/44
=1050/44
r+1 = 23.9 ≈ 24 to the nearest whole number.
r+1= 24
r=24-1 = 23min

9bii)
Volume of cylinder=πr²h
Volume= 22/7 * (23)² * 8
22/7 * 529/1 * 8/1
= 93104/7 = 13,300.57
13301m³ to the nearest whole number

10 a )
GIVEN : y = 2X ^2 - 3X – 1
When x = -3
Y = 2(- 3)^2 - 3(- 3) – 1 = 18 + 9 – 1 = 26
When x= - 1
Y = 2(- 1)^ 2 – 3 (-1 )-1 = 2+ 3- 1 = 4
When x = 1
Y = 2(- 1)^ 2 – 3 (1)- 1 = 2 – 3 – 1 = -2
When x = 2
Y =2 (2)^2 -3 (2)- 1= 8 – 6 – 1 = 1
When x = 3
Y = 2(3)3 -3 (3)- 1 = 18 - 9- 1 = 8
When x = 4
Y = 2(4 )^3 – 3(4 )-1 = 32 -12 - 1 = 19

TYPING IN PROGRESS
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IN Progressssss
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VERIFIED MATHEMATICS OBJECTIVE
11~20 DCCCCACDBA
21~30 BDBAABDACA
31~40 CCACBDCDBD
41~50 DACBDABBBC

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