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Maths 2015 Expo Runz




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+Thursday, 23rd April, 2015:
Mathematics 2(Essay) --- 9.30am - 12.00am
Mathematics 1(Obj) --- 2.00pm - 3.30pm
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NOTE:
PLS DON'T WRITE THE FOLLOWING ON UR PAPER. CHANGE THEM TO WHAT THEY ARE SUPPOSED TO BE IN MATHEMATICS:
^ Means Raise to power
< equal to Means minus will be under < ie _<
whole no means Fraction eg 3 5/2, here 3 will be a whole number, then 5/2
square root or root means square root sign i.e _/ eg 4 root 3 means 4_/3
++++++++++++++++++++++++++++=




(1a)
= 3 whole no 4/9 ÷ (5 whole no 1/3 - 2 whole no 3/4) + 5 9/10
= 31/9 ÷ Lcm (3 whole no 4-9/12 ) + 5 9/10
= 31/9 ÷ 3 whole no -5/12 + 5 whole no 9/10
= 31/9 ÷ 2 whole no 7/12 + 5 whole no 9/10
= 31/9 ÷ 31/12 + 5 whole no 9/10 = 31/9 x 12/31 + 5 whole no 9/10
= 4/3 + 59/10
Find the Lcm
= 40+177/30
= 217/30
= 7 whole no 7/30


(1b)
A { 2,3,4 }
B { 1,3,5 }
= Possibility are { 1,2 }, {2,3}, {3,1},{3,3},
{3,5},{4,1},{4,3},and {4,5}
= Prob! Of sum greater than 3 = 8/9 = Prob of sum less than 7 = 5/9
= Prob of sum greater than 3 and less
than 7 = 8/9 x 5/9
= 40/81
=======================



(2a)
4 + 3/4 (x+2) < equal to 3/8x + 1
Multiply through by 8
= 8(4) + 3(2)(x+2) < equal to 3x + 8(1)
= 32 + 6(x+2) < equal to 3x + 8
= 32 + 6x + 12 < equal to 3x + 8 = 6x - 3x < equal to 8 - 44
= 3x < equal to -36
= x < equal to -36/3
= x < equal to -12

(2b) Area of the shaded portion = total
area - area of the removed square
484 = 20(20+x) - x^2
484 = 400 + 20x - x^2
X^2 - 20x + 84 = 0
X^2 - 6x - 14x + 84 = 0 X(x-6) - 14
( x-6 ) = 0
(X-14) , (x-6) = 0
X=14 or 6
Ie x= 6cm or 14cm.
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(3a)
5/2 = Interior Each Ext. Each interior (n-2)180/n *n/360=5/2
(n-2)/2=5/2
n-2=5
n=7

(3b)
74+SPR+40=180(sum of 114degrees + SPR =180
SPR=180-114
SPR=66 degrees

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


4a)
Sum of 3(2/3) and 2(1/5)
=3(2/3) + 2(1/5)
=11/3 + 11/5
=(55+33)/15
=88/15
=5.87
Amount=7-5.87
=1.13
=7-5(13/15)
=7-(88/15)
=17/15
4b)
i)h=6+4cos(15p)degrees
h=6+4cos(15*4)
h=6+4cos60degrees
h=6+(4*0.5)
h=6+2
=8m
ii)9=6+4cos(15p)degrees
4cos(15p)degrees=3
Cos15p=3/4
=0.75
15p=Cos^-1(0.75)
15p=41.4
P=41.4/15
=2.76
=============================


(6ai)
I:yes
II:NO
III:NO

(6b)
Cost(c)=h+y
c=h+y
h=fixed amount
y=variable
y is directly proportional to n=>Y=kn
C1=GHc 950.00
n1=600 bricks
c2=GHc 1030
n2=1000 bricks
c=h+kn
950=h+600k=> eq(1)
1030=h+1000k=> eq(2)
from eq(2) and eq(1)
substract eq(1) from eq(2)
1030-950=h-h+1000k-600k
80=400k
k=80/400
k=8/40=1/5
=0.2
substitute k=0.2 into eq(1)
950= h+ 600k
950=h +6000(0.2)
950=h+120
h=950-120,
h=830
h=830, k=0.2
c=h+kn
c=830+0.2n

(6bii)
c=830+0.2n
n=500
c=830+(0.2*5000
c=830+100, c=930
c=GHc930
=============================



(9a)
a= -8
a + 6d : a + 8d
5:8
a+6d/a+8d = 5/8
8a + 48d = 5a + 40d 8a - 5a = 40d - 48d
3a = -8d
3 (-8) = -8d
-24 = -8d
d= 24/8
d = 3
===========================

(10a)
Given; (2tan60 + Cos 30)/Sin60
Tan60=root3
cos30=roo3/2
sin60=root3/2
=(2*roo3+roo3/2)/root3/2
=(2root3 + root3/2)/root3/2
=(4root3 + root3)/2 * 2/root3
=root3(4+1)/root3=5

(10b)
(i)tan 30=h/1050
h=tan36 * 1050
h=0.7265 * 1050
h=762.9m

(ii)tan41= h/(1050-x)
h=(1050-x) * tan41
h=(1050-x) * 08693
762.9 = (1050-x)0.8693
1050-x=762.9/0.8693
1050-x=877.6
x=1050-877.6
x=172.4m








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