Earlyface

WAEC 2020 MATHEMATICS THEORY ANSWERS
===========================================
(1a)
Given A={2,4,6,8,...}
B={3,6,9,12,...}
C={1,2,3,6}
U= {1,2,3,4,5,6,7,8,9,10}


A' = {1,3,5,7,9}
B' = {1,2,4,5,7,8,10}
C' = {4,5,7,8,9,10}
A'nB'nC' = {5, 7}


(1b)
Cost of each premiere ticket = $18.50
At bulk purchase, cost of each = $80.00/50 = $16.00


Amount saved = $18.50 - $16.00
=$2.50


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




(2ai)
P = (rk/Q - ms)⅔
P^3/2 = rk/Q - ms
rk/Q = P^3/2 + ms
Q= rk/P^3/2 + ms


(2aii)
When P =3, m=15, s=0.2, k=4 and r=10
Q = rk/p^3/2 + ms = 10(4)/(3)^3/2 + (15)(0.2)
= 40/8.196 = 4.88(1dp)


(2b)
x + 2y/5 = x - 2y
Divide both sides by y
X/y + 2/5 = x/y - 2
Cross multiply
5(x/y) - 10 = x/y + 2
5(x/y) - x/y = 2 + 10
4x/y = 12
X/y = 3
X : y = 3 : 1


=====================
(3a)
Diagram
CBD = CDB (base angles an scales D)
BCD+CBD+CDB=180° (Sum of < in a D)
2CDB+BCD=180°
2CDB+108°=180°
2CDB=180°-108°=72°
CDB=72/2=36°
BDE=90°(Angle in semi circle)
CDE=CDB+BDE
=36°+90
=126


(3b)
(Cosx)² - Sinx given
(Sinx)² + Cosx
Using Pythagoras theory thrid side of triangle
y²= 1²+√3
y²= 1+ 3=4
y=√4=2
(Cosx)² - sinx/(sinx)² + cosx


(1/2)² - √3/2/
(√3/2)² + 1/2 = 1/4 - √3/2 = 1-2√3/4
3/4+1/2 = 3+2/4
=1-2√3/4 * 4/5
=1-2√3/5


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


(4a)
Given: r : l = 2 : 5 (ie l = 5/2r)
Total surface area of cone =πr² + url
224π = π(r² + r(5/2r))
224 = r² + 5/2r²
224 = 7/2r²
7r² = 448
r² = 448/7 = 64
r = root 64 = 8.0cm


(4b)
L = 5/2r = 5/2 × 8 = 20cm
Using Pythagoras theorem
L² = r² + h²
h² = l² - r²
h² = 20² - 8²
h² = (20 + (20 -
h² = 28 × 12
h = root28×12
h = 18.33cm


Volume of cone = 1/3πr²h
= 1/3 × 22 × 7 × 8² × 18.33
=1229cm³


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


(5a)
Total income = 32+m+25+40+28+45
=170+m
PR(²)=m/170+m = 0.15/1
M=0.15(170+m)
M=25.5+0.15m
0.85m/0.85=25.5/0.85
M=30


(5b)
Total outcome = 170 + 30 = 200


(5c)
PR(even numbers) = 30+40+50/200
=115/200 = 23/40


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


=== SECTION B ====
================================


(7a) Click here to view image


Using Pythagoras theorem, l²=48² + 14²
l²=2304 + 196
l²=2500
l=√2500
l=50m
Area of Cone(Curved) =πrl
Area of hemisphere=2πr²
Total area of structure =πrl + 2πr²
=πr(l + 2r)
=22/7 * 14 [50 + 2(14)]
=22/7 * 14 * 78
=3432cm²
~3430cm² (3 S.F)


(b)
let the percentage of Musa be x
Let the percentage of sesay be y
x + y=100 -------------------1
(x - 5)=2(y - 5)
x - 5=2y - 10
x - 2y=-5 -------------------2




Equ (1) minus equ (2)
y - (-2y)=100 - (-5)
3y=105
y=105/3
y=35
Sesay's present age is 35years


====================================
(8a)
Let Ms Maureen's Income = Nx
1/4x = shopping mall
1/3x = at an open market


Hence shopping mall and open market = 1/4x + 1/3x
= 3x + 4x/12 = 7/12x


Hence the remaining amount
= X-7/12x = 12x-7x/12 =5x/12


Then 2/5(5x/12) = mechanic workshop
= 2x/12 = x/6
Amount left = N225,000
Total expenses
= 7/12x + X/6 + 225000
= Nx


7x+2x+2,700,000/12 =Nx
9x + 2,700,000 = 12x
2,700,000 = 12x - 9x
2,700,000/3 = 3x/3
X = N900,000


(ii) Amount spent on open market = 1/3X
= 1/3 × 900,000
= N300,000


(8b)
T3 = a + 2d = 4m - 2n
T9 = a + 8d = 2m - 8n
-6d = 4m - 2m - 2n + 8n
-6d = 2m + 6n
-6d/-6 = 2m+6n/-6
d = -m/3 - n
d = -1/3m - n




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


(9a)
Draw the triangle


(9b)
(i)Using cosine formulae
q² = x² + y² - 2xycosQ
q² = 9² + 5² - 2×9×5cos90°
q² = 81 + 25 - 90 × 0
q² = 106
q = square root 106
q = 10.30 = 10km/h
Distance = 10 × 2 = 20km


(ii)
Using sine formula
y/sin Y = q/sin Q
5/sin Y = 10.30/sin 90°
Sin Y = 5 × sin90°/10.30
Sin Y = 5 × 1/10.30
Sin Y = 0.4854
Y = sin‐¹(0.4854), Y = 29.04


Bearing of cyclist X from y
= 90° + 19.96°
= 109.96° = 110°


(9c)
Speed = 20/4, average speed = 5km/h
=================
MATHS-OBJ
1CBCDACDCCD
11CADBDACBBC
21BDDABDADAD
31CDACCCCCDA
41BBBCDCACDB