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Mathematics Maths (OBJ/ESSAY) Waec GCE 2016 Free Expo Answers




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Saturday, 10th September, 2016
General Mathematics (Essay&Obje
9.30am-3.30pm
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VERIFIED MATHEMATICS OBJECTIVE
1~10 ABCDBCBADB
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.

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WARNING : Please Study the above Symbols, If you Dnt want to write Rubbish in you MATHEMATICS Exam Or Calculation Exam



NOTE THAT ANSWERS ARE ARRANGED ACCORDINGLY, SO ALWAYS SCROLL DOWN TO SEE NEW/MORE ADDED ANSWERS


MATHEMATICS ANSWERS INFINITYGURU]

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


VERIFIED MATHEMATICS OBJECTIVE
1~10 ABCDBCBADB
11~20 DCCCCACDBA
21~30 BDBAABDACA
31~40 CCACBDCDBD
41~50 DACBDABBBC









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