# 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

(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

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