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MATHS OBJ:
1-10: DCCCCCBAAB
11-20: BBCAAABBCD
21-30: DCDCBCBBBD
31-40: AADCDBCCAB
41-50: CDABBCDDAD
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(1a)
(3x-12)/(4x^2-8)*(2x^2-4)/(9x-36)
=3(x-4)/4(x^2-2)*2(x^2-2)/9(x-4)
=3*2/4*9
=1/6
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(1b)
(3x-y)/(2x+y)-(x+2y)/(3x+4y)
=(3x-y)(3x+4y)-(2x+3y)(x+2y)/(2x+3y)(3x+4y)
=(9x^2-12xy-3xy-4y^2-2x^2-3xy-4xy-6y^2)/(6x^2+17xy+12y^2)
=(7x^2-22xy-10y^2)/(6x^2+17xy+12y^2)

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(2a)
V=KR/T
VT=KR
K=VT/R
V=60, R=25, T=20
K=VT/R=60*20/25
=12*4
=48
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(2b)
Given: 2(1/2)/(1(1/4)/3(1/3)
(5/2)/(5/4/10/3)
=(5/2)/(5/4*3/10)
=5/2*8/3
=20/3
=6(2/3)

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(3a)
Sum of roots =2/3+3
=(2+15)/5
=17/5
Product of roots=2/5*3=6/5
x^2-(sum of root)x+product of the root=0
x^2-17/5x+6/5=0
5x^2-17x+6=0
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(3b)
3y^2=27y
3y^2-27y=0
3y(y-9)=0
3y=0 or y-9=0
y=0 or y=9

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(4a)
Using pythagoras theorem
(y+6)^2=(y+4)2+y^2
y^2+12y+36=y^2+8y+16+y^2
12y+36=y^2+8y=16
y^2-4y-20=0
y=-b+_sqroot(b^2-4ac)/2a
=-(-4)+_sqroot(-4^2-4*1*-20/2*1
=4+_sqroot(16+80)/2
y=4+_sqroot96/2
y=4+_9.8/2
=4+9.8/2 or 4-9.8/2
y=13.8/2 or -5.8/2
y=6.9 or y=-2.9
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(4b)
Area(A)=Length * Breadth
=y*y+4
=6.9*(6.9+4)
=6.9*10.9
=75m^2
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(5ai)
Sum of interior angles=(n-2)180
(n-2)*180=1260
n-2=1260/180
n=7+2
n=9
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(5aii)
Size of exterior angle=360/n
=360/9
=40 degrees
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(5b)
log54=log(3*3*3*2)
=log3+log3+log3+log2
=0.4771+0.4771+0.4771+0.3010
=1.7323

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(6a)
TABULATE
No log
0.847 1^-.9279
3.536 0.5485
=0.4764
0.00249 3^-.3962
0.847*3.536 0.4764
/0.00249 =3^-.0802
sqroot(0.847* 3^-.0802/2
3.536/0.00249)=1^-.4599
Antilog =288.3
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(6b)
PQ=300^2+400^2-2(300(400)cos90
PQ^2=250000
PQ=sqroot250000
PQ=500km
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(7a)
log(3x-1)-log^2=3
log(3x-1/2)=3
=3x-1/2=10^3
3x-1/2=1000
3x-1=2000
3x=2000+1
x=2001=3
x=667
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(7b)
E proportional R proportional 1/d^2
E=KR/d^2
=16=K*8/5^2
K*8=16*5
K=400/8
K=50
Equation connecting E,R and d is E=50R/d^2
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(i)E=16, d=3, R=?
16=50*r/3^2
=16*9=50*R
R=16*9/50
=R=144/50
R=72/25
R=2(22/25)
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(iii)
E=50R/d^2
3%E=50R2/3%d^2
9%Ed^2=50R2
Hence R increases by 9%

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(8a)
Sinx=5/13
13^2=5^2+A^2
A^2=169-25
A=sqroot144
A=12
(cosx-2sinx)/2tanx
=(12/13)-2(5/13)/2(5/12)
=(12/13)-(10/13)/10/12
=(2/13)/(10/12)
=2/13*12/10
=12/65
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(8b)
Distance KL =20km
Using sine rule
LM/sin25=KL/sin45
LM=20*sin25/sin45
LM=(20*0.4226)/0.7071
LM=11.95km
LM=12.0km(3s.f)
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(9a)
F5=19, F14=55
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(i)F5=a+4d
19=a+4d(eq1)
F14=a+13d
55=a+13deq2)
19=a+4d
55=a+13d
subtract eq2 from eq1
55-19=a-a+13d-4d
=36=9d
d=36/9
d=4
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(i)Using eq1
55=a+13d
55=a+13(4)
a=55-52
a=3

(ii)common difference d=4
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(iii)Sum of first eighty term(S80)
S80=n/2[2a+(n-1)d] =80/2[2*3+(80-1)4] =40[6+79*4] =40[6+316] S80=12880
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(9b)
142base p=47base10
(1*p^2)=(4*p^1)+(2*p^0)=47
p^2+4p+2=47
p^2+4p-45=0
p^2-5p+9p-45=0
p(p-5)+9(p-5)=0
(p+9)(p-5)=0
p+9=0 or p-5=0
p=-9 or p=5

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(11a)
sqroot32+8/sqroot2
=sqroot(2*2*2*2*2)+(8/sqroot2*(sqroot2/sqroot2)
4sqroot2+8sqroot2/2
=4sqroot2+4sqroot2
=8sqroot2
7/sqroot2(sqroot32+6/sqroot2)
=7/sqroot2*8sqroot2
=7*8=56
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(11b)
E=(1,2,3,4,5,6,7,8,9,10,11,12,13,14)
A=(2,3,7,11,13)
B=(3,5,7,9)
C=(1,2,3,4,6,12)
AnBnC=(3)
AuB=(2,3,5,7,9,11,13)
AuBuC=(2,3)

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(13)
Ex=7+8+6+9+10+12+17+13
Ex=82
Average=82/8=10.25
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(13b)
principal(p)=N12000
Time(n)=4yrs, R=12(1/2)%
R=0.125
Amount(A)=P(1+R)^n
A=12000(1+0.125)^4
A=12000*(1.125)^4
A=12000*1.6018
Amount(A)=N19222

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(15)
TABULATE
x,f,fx,fx^2,x^2
2,4,8,4,4
3,4,12,9,9
4,10,40,16,16
5,11,55,25,25
6,5,30,36,36
7,7,49,49,49
8,6,48,64,64
9,2,18,81,81
10,1,10,100,100
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(i)Range(R)=10-2
=8
(ii)Mean(x)=Efx/Ef
mean=270/50
=5.4
(iii)Variance=Efx^2/Ef-(Efx/Ef)^2
Efx^2=165.6
=1656/50-(5.4)^2
=33.12-29.16
=3.96
(iv)Standard deviation(S.D0
=sqroot Variance
=sqroot3.96
=1.99

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