# 2019 WAEC GCE Mathematics Questions and Answers

West Africa Examination Council, WAEC GCE Mathematics Questions and Answers for 2019 June/July Examination are now available, always subscribe to get the already available questions and answers by Examrelief an hour before each paper.

# ðŸ‘‘ 2019 WAEC GCE MATHEMATICS ANSWERSðŸ‘‘

1-10: BBDCCBCBBA
11-20: BCBDCDBDDB
21-30: BCBDDBAACA
31-40: AABBDABCCB
41-50: BBBDBCBCDB

(1a)
Table for multiplication (x) in mod 8
Using (2, 3, 5, 7)

In a tabular form.
Under (x) 2, 3, 5, 7
Under 2 4, 6, 2, 6
Under 3 6, 1, 7, 5
Under 5 2, 7, 1, 3
Under 7 6, 5, 3, 1

(1bi)
3(x)n = 5
3 Ã— n = 5 + cont. Of mod 8 to be divisible by 3;
3n = 5 + 8 + 8
3n = 21
n = 21/3
n = 7

(1bii)
n(x)n = 1
n * n = 1 + 8
nÂ² = 9
n = âˆš9
n = 3
=============================

(2a)
Given; slant height l = 18.7cm
Diameter, d = 24cm
Ï€ = 22/7
But, Curved surface area of cone = Ï€rl
=Ï€(d/2)l
= 22/7 Ã— 24/2 Ã— 18.7
=9873.6/14 = 705cmÂ²

(2b)
128^x Ã— 2/16^(1-x) = 8â…”x
= 2^7x Ã— 2/2^4(1-x) = 2Â³(â…”x)
= 2^7x + 1/2^4(1-x) = 2^2x
Cross multiply
2^4(1 – x) + 2x = 2^7x + 1
4(1 – x) + 2x = 7x + 1
4 – 4x + 2x = 7x + 1
4 – 2x = 7x + 1
9x = 3
X = 3/9 = 1/3
======================

(3a)
3âˆš3/2 – 4âˆš2/3 – âˆš24
=3âˆš3/2 – 4âˆš2/âˆš3 -âˆš6*4
=(3âˆš3/âˆš2 Ã— âˆš2/âˆš2) – (4âˆš2/âˆš3 Ã— âˆš3/âˆš3) – 2âˆš6
=3âˆš6/2 – 4âˆš6/3 – 2âˆš6
=(3/2 – 4/3 – 2)âˆš6
=(9 – 8 – 12)âˆš6
= -11/6âˆš6

(3bi) prob(only one passes) = m passes and N fails or M fails and N passes
Prob (M passes) = 2/3; prob(M fails) = 1 – 2/3 = 1/3
Prob(N passes) = 4/5; prob(N fails) = 1 – 4/5 = 1/5
Prob(only one passes) = (2/3 Ã— 1/5) + (1/3 Ã— 4/5)
= 2/15 + 4/15
= 6/15
= 2/15

YOU MAY ALSO LIKE:  Waec Gce 2016 Commerce Questions & Answers Now Available Here

(3bii)
prob(at least one passes) = prob(only one passes) + prob(both parties)
= 2/5 + (2/3 Ã— 4/5)
= 2/5 + 8/15
= 6/15 + 8/15
= 14/15
===========================

(4a)
17Â²=XÂ²+15Â²
17Â²=XÂ²+225
289-225=XÂ²
64=XÂ²
C=âˆš64=8
TanÎ¸=18/15
TanÎ¸/1+2tanÎ¸=18/15/1+2(8/15)=8/15/1+16/15
=8/15Ã·31/15=8/15*15/31=8/31

(4b)
Log10 y/log10 64 = 1/2
Cross multiply
2log y = log10 64
Log10 yÂ² = log10 64
y = âˆš64
y = Â±8
===========================

(5a)
Obtuse Reflex
Obtuse Obtuse = 164Â°

OMP + OPM + Obtuse MOP = 180Â°(angles in a triangle)
But OMP = OPM = x(radius of the circle and hence base angles are the same)

2x + 164 = 180
2x = 180 – 164
2x = 16Â°
X = 16/2 = 8Â°

Also MNP = 1/2Ã—obtuseMOP
= 1/2 Ã— 164Â°
= 82Â°

Now; MNP + NMP + NPM = 180Â° (angles in a triangle)
82 + (52+8) + (m+8) = 180Â°
m + 150 = 180Â°
M = 180 – 150
M = 30Â°

(5b)
Portion of land for cassava = 2/5
Portion of land for plantain = 1/3 Ã— (1 – 2/5)
= 1/3 Ã— 3/5
= 1/5

Portion of land for yam = 1 -(2/5 + 1/5)
1 – (3/5)
=2/5
(5b)
============================

(6)
=================================

(8ai)
a + 4d = 11 …..i
a + 7d = 20 …. ii

a + 7d = 20
– a + 4d = 11
3d = 9

d = 9/3
d = 3
Using eqn i
a + 4(3) = 11
a + 12 = 11
a = 11 – 12
a = -1

T12 = a + 11d
= -1 + 11(3)
= -1 + 33
= 32

(8aii)
Sn = n/2[20 +(n – 1)d]

S12 = 12/2[2(-1)+(12-1)3]
=6[-2 + (11)3 ]
= 6[-2 + 33]
= 6[31]
= 1806

(8b)
Let the S.p = M
15% of m = 15m/150
= 3m/20 (Discount)

Therefore; collected = M -3m/20
So M/1 – 3M/20 =36000/1
20m – 3m = 720000
17m = 720000
m = 720000/17
M = 42352.94%

Discount = 42352.94 Ã— 3/20
Discount = #6,352.94
===================================

(9ai)
Draw the Venn diagram

(9aii)
No selected for biology but neither physics nor mathematics = 36

YOU MAY ALSO LIKE:  WAEC 2018 Government OBJ And Theory Questions and Answers

(9aiii)
No not selected for any of three subjects = 11

(9b)
Mean = 22+18+(2x+1)+10+20/5 = 15
2x + 71 = 75
2x = 75 – 71
2x = 4
X = 4/2 = 2

The numbers are: 22, 18, 5, 10 and 20
Arranging in ascending order, we have 5, 10, (18), 20, 22

The median is 18

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

(10a)
Loan borrowed = 80/100 Ã— 350,000
=280,000
Amount paid to the bank after 8 years = P + I
= P + PRT/100
=280000 + 280000Ã—7Ã—8/100
=280,000 + 156,800
Amount = #436,800

Total cost of house to the man = #350,000 + Interest
= #350,000 + 156,800
= #506,800

(10b)
Percentage increase in cost of house = 506,800 – 350,000 Ã— 100%
= 156,800/350,000 Ã— 100%
= 44.8%

(c) Percentage loss = loss/cost price Ã— 100%
=(506,800 + 10,000) – 460,000/(506,800 + 10,000) Ã— 100%
= 516,800 – 460,000/516,800 Ã— 100%
56,800/516,800 Ã— 100%
= 0.1099 Ã— 100%
= 10.99%
=====================================

(12)
====================================

(13a)
Draw the diagram

(i) Extend DO to touch AB at M
AOD + AOM = 180Â°( 130 + AOM = 180Â°
AOM = 180 – 130 = 50Â°

Also;
BMO = BAO + AOM(Ext < = sum of two opposite interior BMO = 26 + 50 = 76Â°
Also; ABD = 1/2AOD(angle at centre = twice angle at circum)
ABD = 1/2 Ã— 130
=65Â°
Hence ODB + ABD + BMO = 180Â°(sum of ODB + 65Â° + 76Â° = 180Â°
ODB = 180 – 141
= 39Â°

(ii) BOD + ODB + DBO = 180Â°(sum of But ODB = DBO(base angles of an isosceles triangle)
BOD + 39Â° + 39Â° = 180Â°
BOD + 78Â° = 180Â°
BOD = 180 – 78 = 102Â°

(13b)

|1 2 6

3|1,3 2,3 (6,3)
4|1,4 2,4 (6,4)
5|1,5 2,5 (6,5)

prob (greater than 7) = 3/9 = 1/3

=====COMPLETED=====

BEST OF LUCK