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WAEC 2018/19 MAY/JUNE MATHEMATICS OBJECTIVE AND THEORY, QUESTIONS and ANSWERS

WAEC 2018/19 MAY/JUNE MATHEMATICS OBJECTIVE AND THEORY, QUESTIONS and ANSWERS

Wednesday, 18th April, 2018
Mathematics 2 (Essay) – 09:30 a.m. – 12:00pm
Mathematics 1 (Objective) – 3:00 p.m – 4.30 p.m.
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WE RE-SOLVED NUMBER 6. PLS CHECK.
WE WILL BE UPLOADING IMAGES SOON!!!

MATHS OBJ:
1-10: ACBCDDCBAA
11-20: CDCABCCCAC
21-30: DADBABCDAD
31-40: BADADBCACB
41-50: ADDDBDADCA

(1)
On February 28th 2012, value = (100-30/100) * #900,00.00
= 70/100 * #900,00
= #630,000.00

On february 28th 2013, value = (100-22/1000 * #630,00
= 78/100 8 #630,000
= #491,400
On february 28th 2014, value = 78/100 8 #491,400
=383,292
On february 28th 2015, value = 78/100 * #383,292
= #298,967.76
= #299,000

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(4ai)
Draw the diagram
ai X + 90 = 3x + 15
90 = 3x – X + 15
90 = 2x + 15
2x + 15 = 90
2x = 90 – 15
X = 75/2
X = 37.5•

(4aii)
(4b)
2N4seven = 15Nnine
Converting both to base 10
2×7+N×7¹+4×7 = 1×9²+5×9¹+N×9
98 + 7N + 4 = 81 + 45 + N
7N + 102 = 126 + N
7N – Ń = 126 – 102
6N = 24
Ń = 24/6
Ń = 4

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(3a)
Using pythagoras theorem
L^2=5.1^2 + 4.65^2
L^2=26.01 + 21.6225
L^2=47.6325
L=sqroot(47.6325)

L=6.9cm(1 d.p)
Perimeter of rhombus=4
=4*6.9
=27.6cm

(3b)
Sin x=3/5
DRAW THE TRIANGLE
Using pythagoras tripple the third side=4
therefore cosx=4/5
tanx=3/4
therefore 5cosx-4tanx
=5(4/5)-4(3/4)
=4-3
=1

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(4ai)
Draw the diagram
ai X + 90 = 3x + 15
90 = 3x – X + 15
90 = 2x + 15
2x + 15 = 90
2x = 90 – 15
X = 75/2
X = 37.5•

(4aii)
(4b)
2N4seven = 15Nnine
Converting both to base 10
2×7+N×7¹+4×7 = 1×9²+5×9¹+N×9
98 + 7N + 4 = 81 + 45 + N
7N + 102 = 126 + N
7N – Ń = 126 – 102
6N = 24
Ń = 24/6
Ń = 4

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6
Total number of cars on road worthiness = 240
60% passed ie 60/100×240/1 = 144cars.
Number that failed = 240-144 = 96cars

6a) draw the Venn diagram
C = clutch
B = brakes
S = steering

(b) From the diagram above
E = 28+12+8+6+x+6+2x
96=60+3x
96-60=3x
36/3 = 3x/3
Therefore X = 12

(i) The no of cars that had faulty brakes
=12+8+6+x (Since X = 12)
=12+8+6+12 = 38

(ii) Only one fault = (no of clutch only) + (no of brakes only) + (no of steering only)
=28+x+12x = 28+12+24
=64cars
==================

(7a)
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(y-5)/(x-2)=(-7-5)/(-4-2)
(y-5)/(x-2)=-12/-6
(y-5)/(x-2)=2
Cross multiply
y-5=2(x-2)
y-5=2x-4
2x-y-4+5=0
2x-y+1=0

(7bi)
DRAW THE DIAGRAM

(7bii)
(I)
p^2=q+r^2-2qrcosP
p^2=8^2+5^2-2*8*5*cos90
p^2=64+25-0
p^2=89
p=sqroot(89)
p=9.4339km
therefore |QR|=9.43km(3 sf)

(II)
q/sinQ=p/sinP
8/sinQ=9.4339/sin90
sinQ=(8*sin90/9.4339
sinq=(8*1)/9.4339 =0.8480
Q=sin^1(0.8480)=57.99 degrees
but Q=30+ A
A=Q-30
=57.99-30
A=27.99 degrees
The bearing of R from Q
=180-A
180-27.99
=155.01
=>152 degrees

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(8a)
Cost price for Lami= #300.00
Profit made by lami = x%
Ie selling price for lami=(100+x/100)×#300
=#3(100+x)
=#(300+3x)

Bola’s cost price = #3(100+x)
Profit made by bola =x%
Selling price for bola =(100+x/100)×#3(100+x)
=#3/100(100+x)²

James cost price =#3/100(100+x)²=300+(6x+3/4)
expanding;
3/100(10000+200+x²) = 300+3/4+6x
3(10000+200x+x²)=30000+75+600x
30000+600x+3x²=30000+75+600x
3x²=75
X² = 75/3
X² = 25
X = square root 25
X = 5

(8b)
3x-2<10+x<2+5x 3x-2<10+x & 10+x<2+5x 3x-x<10+2 & 10-2<5x-x 2x<12 8<4x X<12/2 4x>8
X<6 x>8/4
X>2

Also; 3x-2<2+5x -4<2x 2x > -4
X > -2
Therefore; Range is -2

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(9a)
Draw the diagram
Angles PTR and PSR are similar
|PT|/|PS| = |TQ|/|SR|
In angle PTR
|TQ|²=|PT|²+|PQ|²-2|PT||PQ|cos30degrees
=4²+6²-2×4×6×cos30
=16+36-48×0.8660
=52-41.568
=10.432
|TQ|=√10.432 =3.22cm
4/10 = 3.22/|SR|
4|SR| = 10×3.22
|SR| = 32.2/4
|SR| = 8.05cn
Approximately 8cm(to the nearest whole number)

(9b)
Atqrs = AΔPSR – AΔPTR
AΔPTR = 1/2×4×6×sin30
=2×6×0.5
=6cm²
AanglePTQ/AanglePSR = |PT|²/|PS|²
6/AanglePSR = 4²/10²
6/AanglePSR = 16/100
16×AanglePSR = 6×100
AanglePSR = 600/16 = 37.5cm2
ATQRS = 37.5 – 6
=31.5cm2
=32cm2

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(13a)
Frequency=16+x+y
16+x+y=30
x+y=30-16
x+y=14–(eqi)
(900+30x+50y)/30=52
900+30x+50y=52*30
30x+50y=1560-900
30x+50y=660
divide through by 10
3x+5y=66–(eqii)
From (i)
x+y=14
x=14-y–(eqiii)
sub for x in eqii
3(14-y) +5y=66
42-3y+5y=66
2y=66-42
y=24/2
y=12
feom eqiii
x=14-12
x=2

(13b)
TABULATE
Class interval:1-10,11-20,21-30,41,50,51-60,61-70,71-80,81-90
Freq:1,1,2,5,12,1,4,3,1
Class boundary:0.5-10.5,10.5-20.5,20.5-30.5,30.5-40.5,40.5-50.5,50.5-60.5,60.5-70.5,70.5-80.5,80.5-90.5

(13C)
DRAW THE GRAPH

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