# ðŸ’¯% CORRECT 2019 WAEC GENERAL MATHEMATICS ANSWERS HERE!

WAEC 2019- MATHEMATICS

Thursday 16th May, 2019
Mathematics 2 (Essay) â€“ 09:30 a.m. â€“ 12:00pm
Mathematics 1 (Objective) â€“ 3:00 p.m â€“ 4.30 p.m.

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MATHS OBJ
11-20: BCBCBBAACD
21-30: BCCBCCABBA
31-40: AABDDCDDCC
41-50: BBCDCCACCD

(2a)
The equation of the line through the points
A(-2,7) and B(2,-3)
Using the equation Y=mx+b
Where m=slope of the gradient, b=the intercept at the vertical axis
Hence slope=Change in Y/Change in X
=>Y2-Y1/X2-X1=Y-y1/X-x1
=(-3-7)/(2–2)=Y-7/X+2
=-10/4=(Y-7)/(X+2)
=4(y-2)=-10(x+2)
4y-28=-10x-20
4y=-10x+8
5x+2y=4

(2b)
(5b-a)/(8b+3a)=1/5
5(5b-a)=1(8b+3a)
25b-5a=8b+3a
25b-8b=3a+5a
17b=8a
Therefore a/b=17/8

(4)
Since <PQR = <PRS = 90Â°
Using Pythagoras theorem
|PR|Â² = |PQ|Â² + |QR|Â²
|PR|Â² = 3Â² + 4Â²
|PR|Â² = 9 + 16
|PR|Â² = 25 PR = âˆš25
|PR| = 5cm
Considering PRS
|PS|Â² = |PR|Â²+|SR|Â²
13Â² = 5Â² + |SR|Â²
169 = 25 + |SR|Â²
|SR|Â² = 169 – 25
|SR|Â² = 144
|SR| = âˆš144 = 12cm

Hence the area of the quadrilateral = Area of triangle PQR + area of PRS
= 1/2bh + 1/2bh
= 1/2Ã—4Ã—3 + 1/2Ã—12Ã—5
= 6+30 = 36cm

(5a)
No of red balls = 3
No of green balls = 5
No of blue balls = x
Prob.(red ball) = no of total outcome/no of possible outcome
Pr(red) = 3/3+5+x = 1/6
3/8+x = 1/6
6(3) = 1(8+x)
18 = 8 + x
X = 18 – 8 = 10
Therefore the no of blue ball = 10

(5b)
Probability of picking a green ball
P(g) = no of green balls/no of possible outcome
P(g) = 5/3+5+10 = 5/18
=5/18

(6ai)
F Î± M1M2/dÂ²
F = KM1M2/dÂ²
Given F = 20N, M1= 25kg, M2 = 10kg and d = 5m
20 = k(25)(10)/5Â²
250k = 500
k = 500/250 = 2
Expression is
F = 2M1M2/dÂ²

(6aii)
Making d subject
d = âˆš2M1M2/F
d = âˆš2 Ã—7.5Ã—4/30
d = âˆš60/30 = âˆš2
d = âˆš2m or 1.41m

(6b)
Draw the diagram
X+X+60+X+80+X+40+X+20 = 540(sum of angles in a Pentagon)
5x + 200 = 540
5x = 540 – 200
5x = 340
X = 340/5
X = 68

(8a)
1/3x – 1/4(x+2)>_ 3x -1â…“
1/3x – 1/4(x+2)>3x – 4/3 Multiply through by the L. C. M(12), we have 4x – 3(x + 2)>_36x – 16 4x – 3x – 6 > 36x – 16
-6+16 >36x + 3x – 4x 10 > 35x
35x _< 10
X = 10/35
X = 2/7

(8bi)
Draw the triangle
|AB|/66 = sin35
|AB| = 66sin35 = 66Ã—0.5736 = 37.8576

Draw the right angled triangle
|AD| = 37.8576 Ã— Tan52Â° = 37.8576 Ã— 1.2799 = 48.45m
Height of tower = 48.45m

(10)
130kg of tomatoes for #52,000
Half of the tomatoes
130/2 = 65kg sold at 30%
Profit = #52,000/2 = 26,000

# 26,000 = 100%

X = 130%
X = 26000 Ã— 130/100
= #33,800

Then 65kg was then sold at reduction of 12% per kg
Recall that the initial cost price = 52000/130
=400kg
65kg sold at = 33,000/65
=#520/kg
Then for 12% reduction
520 Ã— 88/100 = 457.6/kg
(a)
The new selling price per kg = #457.6/kg

(b) 65kg – 5kg = 60kg
(60kgÃ—457.6kg)+33,800
= #61,256.00

# profit = selling price /cost price Ã— 1000/1

=61256/52000Ã—100/1= 117.8
= 17.8%

(11ai)
arÂ² = 1/4 â€¦â€¦(1)
ar^5= 1/32 â€¦..(2)
Divide eqn (2) by eqn(1)
ar^5/arÂ² = 1/32Ã·1/4
rÂ³ = 1/32 Ã— 4/1
rÂ³= 1/8
rÂ³ = 2-Â³
r = 2-Â¹
r = 1/2
Common ratio = 1/2
Put this into eqn (1)
a(1/2)Â² = 1/4
a(1/4) = 1/4
a = (1/4)/(1/4) = 1
First term, a = 1

(11aii)
Seventh term, T7 = ar^6
=(1)(1/2)^6
=1/64

(1b)
Given : X = 2 and X = -3
(X – 2)(X + 3) = 0
XÂ² + 3x – 2x – 6 , 0
XÂ² + x – 6 = 0
Comparing with axÂ²+bx+c = 0
a = 1
b = 1
C = -6

(12a)
Given : siny = 8/17
Draw the right angle
From Pythagorean triple, third side is 15
Draw the right angle triangle
tan y = 8/15

tan y/1+2tany = 8/15/1+2(8/15) = 8/15/1+16/15

tany /1+2tan y = 8/31

(12b)
Amount shared = #300,000
Otobo’s share = #60,000
Ade’s share = 5/12 Ã— #(300,000-60,000)
= 5/12 Ã— #240,000
=#100,000

Adeobi’s share = #300,000 – (#60,000 + #100,000)
= 300,000 – 160,000
=#140,000

60,000 : 100,000 : 140,000
60 : 100 : 140
6 : 10 : 14
3 : 5 : 7

(13a)
T^0S=2TU^0 (angle at centre = 2 time angle at circumstance)
TOs=2*68Â°=136Â°

Now RT^0+RS^0+T^0S+SRT^0=360Â°(sum of angle in a quadrilateral)
90Â° + 90Â° + 136Â° + x = 360Â°
X+316Â°=360Â°
X=360Â°-316
X=44Â°

(13b)
Let tank B hold x litres
; Tank A hold (x+600)literally
3(x-100)=(x+600-100)
3x-300=x+500
3x-x=500+300
2x=800
X=800/2=400
Tank B holds 400 litres
Tank A holds (400+600)=1000litres