 EXAM RUNS HELPDESK

Exam Time: Monday, 17th August, 2020

General mathematics(core) 2(Essay) � 9:30am � 12:00noon (2hrs 30mins)
General mathematics(core) 2(objective) � 3:00pm � 4:30pm
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MATHS OBJ
31-40:
41-50:

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(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)
Draw the diagram

CBD = CDB(Base angles of an issoceles triangle)
BCD + CBD + CDB = 180�(sum of angles in a triangle)
2CDB + BCD = 180�
2CDB + 108� = 180�
2CDB = 180� – 108� =72�
CDB = 72/2 = 36�
BDE = 90�(angle in a semi-circle)
CDE = CDB + BDE
= 36� + 90�
= 126�

(3b)
(CosX)� – SinX/(SinX)�+ CosX
Using Pythagoras theorem, third side of triangle
y� = 1� + |3�
y� = 1 + 3 = 4
y = square root e = 2
Sin X = root 3/2(opp/hyp)
(CosX)� – SinX/(SinX)� + CosX
= (1/2)� – root3/2 / (root3/2)� + 1/2
= 1/4 – root3/2 / 3/4 + 1/2
= 1 – 2root3/4 / 3+2/4
= 1-2root3/5 =================================================

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

(4b)
L = 5/2r = 5/2 � 8 = 20cm
Using Pythagoras theorem
L� = r� + h�
h� = l� – r�
h� = 20� – 8�
h� = (20 + 8)(20 – 8)
h� = 28 � 12
h = root28�12
h = 18.33cm

Volume of cone = 1/3πr�h
= 1/3 � 22 � 7 � 8� � 18.33
=1229cm� ================================================

(5a)
Prob(2) = no of 2s/Total outcomes
0.15 = m/32+m+25+40+28+45
0.15 = m/m + 170
m = 0.15m + 25.5
m – 0.15m = 25.5
0.85m = 25.5
m = 25.5/0.85 = 30

(5b)
Number of times dice was rolled = m + 170
= 30 + 70
= 200

(5c)
Prob(even number) = no of even numbers/Total outcome
= m+40+45/200
=30+40+45/200
=115/200
= 23/40 = 0.575 ================================================

(7a)
Total surface area = url + 2πr�
=πr(l + 2r)

Draw the diagram
From pythagoras theorem
L� = 14� + 48�
L� = 196 + 2304
L� = 2500
L = /2500 = 50m

=πr(L + 2r)
= 22/7 �14(50 + 2(14))
= 44(50 + 28)
= 3432m�
Total surface area = 3432m�
~3430m�(to 3s.f)

(7b)
Five years ago,
Let Musa’s age = x
Let Sesay’s age = y
X – 5 = 2(Y – 5)
X – 5 = 2y – 10
X – 2y = 5 – 10
X – 2y = -5 ….. (1)
-X + y = 100 ….. (2)
-3y = -105
Subtracting eqn 2 from 1
-3y/3 = -105/-3
y = 35
Sesay’s present age = 35 years ================================================

(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
q� = x� + y� – 2xycosQ
q� = 9� + 5� – 2�9�5cos90�
q� = 81 + 25 – 90 � 0
q� = 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‐�(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 ======================================================

(11a) (11b)
Given 8y+4x=24
8y=-4x + 24
y=4/8x + 24/8
y=-1/2x +3
Using m = y-y/x-x� and given (x�=-8) (y�=12)
-1/2=y-12/x+8
2(y-12)=-x-8
2y-24=-x-8
2y+x=24-8
2y+x=16 ======================================================

(12a)
BCD=ABC=40�(alternate D)

DDE=2*BCD([at centre = twice [ at circle)

DDE = 2*40 = 80�
OD3=OED(base [ of I sealed D ODE)
ODE + OED + DOE= 180�(sum of [ is in D)
2ODE+DOE=180�
2ODE+80�=180
2ODE+180=180
2ODE+100�
ODE+100/2=50�

(12bi)
Digram

(12bii)
Area of parallelogram = absin
=5*7*sin125�
=35*sin55�
=35*0.8192
=28.67
=28.7cm�(1dp)

(12c)
Given x=1/2(1-√2)
2x�-2x=2[1/2(1-√2]�-2(1/2(1-√2)}
=2[1-2√2+2/4]-(1-√2)
=(3-2√2/2)-(1-√2)
=3-2√2-2+2√2/2=1/2 