WAEC GCE 2016 MATHEMATICS OBJ IS AVAILABLE NOW CL!CK TH£ ADV£RT AB0V£ N0W TO GET TH£ ANSW£R ON YOUR PHONE

 

MATHS OBJ:
1-10: ABCDDCBCDB
11-20: DCCCCACDBA
21-30: BDBAABDACA
31-40: CCACBDCDBD
41-50: DBCBDABBBC

EXAM TIME: Saturday, 10th September, 2016
General Mathematics (Essay&Obje
9.30am-3.30pm
++++++++++++++++++++++++++

(1) / means division or divide
Examples:
2/2 means 2/2
2 whole no 3/4 means 2¾
M=wp+(1/3)yp^2 means m=wp + ¾y 2
(2) Log means logarithm
Example: (8) Log5 (base 8) means Log8 5
(3) * means multiplication
Example: 2*2 means 2×2
(4) ^ means Raise to power
Examples:
3^(-1) means 3 -1
5^(2) means 5 2
30cm^(-2) means 30cm -2
(5) Tita means θ
Example: Tan tita means tan θ
(6) Pie means π
Example: Pie R sqr h means πr 2 h
(7) Base means subscript
Example: 2 Base 3 means A 3
(8) Sqr root means √
Examples:
√3-√6+2√3 means Root 3-root6+2root 3
√(¾) means sqr root(3/4)
(9) bar means a dash on top a number of letter
Example: X bar means x̅
(10) —(1) means equation 1
(11) Proportional means ∝
Example: R is proportional to 3/4rut m means R
∝ ¾
(12) Alpha means α
(13) Beta means β
(14) Gamma means γ
(15) cube root means ∛
(16) Mu means μ
(17) Rho means ρ
(18) Delta means δ
(19) Sigma means σ
(20) Tau means τ
(21) Ohm means Ω
(22) Lamda means λ
(23) Omega means ω
(24) Intersection means ∩
Example: B intersection C means B∩C
(25) Union means U
Example: B union C means BUC
(26) Factorial means !
(27) complements in sets means ‘
(28) (aq),(g),(l),(s) is used in chemistry to show
the state
of matter in equations
(29) Equivalent to means ≡
(30) Not equal to means ≠

(31) Quotation means “ ”
(32) Less or equal to means ≤
(33) Greater or equal to ≥

Example: (3/4)>=(1/2) means ¾ ≥ ½
(34) Plus or minus (or +-) means ±
Example: (3/4)<=(1/2) means ¾ ≤ ½

(35) Element of means ∈
Example: 2 belongs to X or 2 is a member of X
means 2∈X
(36) Percent or percentage means %
(37) Degrees Fahrenheit means ℉
(38) Degrees Celsius means ℃
(39) Universal set means ξ or U
(40) Null or empty set means ∅ or {}
(41) (42) 2.S.F means 2 significant figures
(43) P=(2,3) means P={2,3} in sets
(44) Propotional to means ∝
(45) Therefore means ∴
(46) KNO(3)(s) means KNO3 (s)
(47) NaCl=> Na^(+) + Cl^(-) means NaCl → Na+
+ Cl-

(48) Summation means Ʃ
(49) Parallel lines means ǁ
(50) Perpendicular lines means ˩
(51) Reversible equation means ↔
(52) Infinity means ∞
(53) Approximately means ~
(57) Approximately equal to ≅
Other Symbols
(1) File means ɸ
(2) Δ means Change or Triangle
(3) slope or differentiation means dy/dx or ∂y/
∂x or δy/δx
or Δy/Δx
(4) Parenthesis means …
(5) Naira means ₦
(6) Integral means ∫

(7) Almost equal to means ≈
(8) For all means ∀
(9) There exist means ∃
(10) Epsilon means ε
(11) Vertical dots means ⁞
Tables, Radiativity Diagrams
Table1
A table of this would be computer as follows
X:1,2,3,4
FX:4,6,8,10
F(X-Xbar):10,8,6,4
Table2
A table like this would be computed as follows
Particulars: maintenance,salaries &wages,
Purchase of
Drugs, total
Amount: 2500,1000,2000,5500
Logarithm Table
Tabulate
No:92.63, Log:1.9667
No: 2.914, Log: 0.4645
2.4312
Antilog = 269.9
Therefore 92.63*2.914=2.4312

 

Radiativity Diagram
means
(238)U(92)=>(234)Th(90) + (4)He(2)
This is computed as follows
(1)(-b± sqr rut(b^2-4ac))/2a
(2)Sqr root ((2Qh)/100)
(3)Xbar=Efx/ef
(4)Summation (n=1 to infinity )P(n)
(5)S.D= Sqr Rut ((Ef|x-xbar|^2))/Ef
(6)R is proportional to1/ sqr root

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

KEEP REFRESH THIS PAGE EVERY 5MINS

MATHS OBJ:
1-10: ABCDDCBCDB
11-20: DCCCCACDBA
21-30: BDBAABDACA
31-40: CCACBDCDBD
41-50: DBCBDABBBC


DRAWING LINK

(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

(1b)
let the number of students be X therefore
total age of students be 15x
15x + 45/x + 1 = 18
15x + 45 = 18 (x + 1)
15x + 45 = 18x + 18
18x – 15x = 45 – 18
3x = 27
X = 27/3
X = 9 students

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

(2a)
m/m-y+2 = r/y+r-1
r(m-y+2)=m(y+r-1)
rm-ry+2r = my+mr-m
rm+2r-m+mr=my+ry
y(m+r)=rm+2r-m+mr
y=2mr+2r-m/m+r

(2b)
p[one of them owns a bicycle] [60/100+70/100] – [40/100 + 30/100] Because % of boys that don’t have bicycle =
40/100
% of girls without bicycle = 30/100
=130/100 – 70/100
=60/100
=0.6

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

(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)
< MNQ = 90 degree
< 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 -4 x) -1 /2 (5- 3x ) less /equal to 1/ 4(7 + 9x )- 1/ 3
multiply through by 12
8(1 -4 x) -6 (5- 3x ) less /equal to 3(7 + 9x )- 4
8- 32 x- 30 + 18 x less/ equal to 21 + 27 x -4
-32 x + 18 x – 27 x less /equal to 21 -4 + 30 -8
-41 x less /equal to 39
x less/ equal to -39 / 41

(4b)
DRAW THE ANGLE
from DTMR /
Tan 65 degree = TR/3
TR = 3Tan 65
= 3 x 22.1445
From DRMB
Tan 20 = RB / 3
RB = 3Tan 20
= 3 x 0.3640
= 1.092 m
H = TR + RB
= 6.4335 + 1 . 092
= 7.5255
= 7.53m

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

(5)
Area of shed segment = Area of Sector – Area of Triangle
=tita/360 *pie r^2 – (1/2 abSinc )
=90/ 360 * 22/7*7^2) – 1/2 * 7 *7*sin90degree
=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
25 x= 1400000
X =1400000 / 25
X = 560000
Total income =
56 ,000 / 4 x 5
=N70,000

[ 6b *Edited*]
(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
= 30 months
In years = 30/12
= 2 and half years

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

(7a)
Diagram LINK

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

(7bi)
lenght of chord Xy=2Rsin tita/2
XY=2*6400*Sin 30/2
=2*6400*sin15 degree
=12800*0.2588
=3.312.64km
=3312.64km
=3310km(to the nearest 10km)

(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
=1656.32km
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 * 2pie R cos lat
=30 degeree/360 * 2*3.142 * 6400* cos60
XY bar= 30/360 * 2* 3.142* 6400* 0.5
XY bar=1675.73 km

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

(8a)
Drawing
LINK

(8bi)
Using Pythagoras theory
| xz|^ =550^2 320^2
= 302500 102400 =404900
xz=√ 404999
=636 km( 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 degree
From the diagram in 8 a
Bearing of X from Z = 55 + 30
= 085 degree or N85 degree E

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

(9a)
3log10^2 – 2log10^3 = 1 + log(1/x)
log10^(2)^3 – log10^(3)^2 – log10^(1/x) = 1
Log10^( 8 /9 ) / (1 / x) = log10^10
8 / 9 * X / 1 = 10
8x = 9 *10
8x = 90
X = 90/8
=11.25

(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
13301m^3 to the nearest whole number

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

(10a)
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

(10b) DRAW THE GRAPH LINK

(10c)
(i) From the graph, the roots of 2x^2-3x-1 are
x=1.7 or x = -0.3

(ii) Coordinates are (0.8, -2.25)

(iii) PLS SHADE THE SURFACE AREA ON UR GRAPH BIKO. LINK

 

MATHS OBJ:
1-10: ABCDDCBCDB
11-20: DCCCCACDBA
21-30: BDBAABDACA
31-40: CCACBDCDBD
41-50: DBCBDABBBC