Earlyface

MATHEMATICS ANSWER*

*Obj*
01-10BDBADCDBBB
11-20BACDCCCACD
21-30BACCDBABAC
31-40CCCADBCBCB
41-50ACCDADACBD

*​Theory​*
1a)
123.24base8 - ()base10
= 1*8^2 + 2*8^1 + 3*8^0 + 2*8^-1 + 4*8^-2
= 64 + 16 + 3 + 2/8 + 4/64
= 83 + 1/4 + 1/16
= 83 + 4+1/16
= 83 + 5/16
= 83^5/16base10

1b)
8^1/3 * 5^2/3 * 10^-2/3
2^3/3 * 5^2/3 * (2*5)^2/3
2^1 * 5^2/3 * 2^-2/3 * 5^-2/3
2^1 * 2^-2/3 * 5^2/3 * 5^-2/3
2^1-2/3 * 5^2/3-2/3
2^3-2/3 * 5^0
2^1/3 * 1
= 2^1/3

2a)
y=1+2x/x-2
:- 2x+y = ?
= 2x/1 = 1+2x/x-2
= 2x/1+1+2x/x-2
= 2x(x-2)+(1+2x)/x-2
= 2x^2-4x+1+2x/x-2
= 2x^2-2x+1/x-2

2b)
if x+1/2 = x-3+5/x
:- x+2/2 - 5/x = x-3
x(x+1)-5(2)/2x = x-3
x^2+x-10 = 2x(x-3)
x^2+x-10 = 2x^2-6x
x^2-2x^2+x+6x-10 = 0
-x^2+7x-10 = 0
x^2-7x+10 = 0
x(x-5)-2(x-5) = 0
(x-2)(x-5) = 0
x=2 or x=5

3a)
victor investment = N6m
nasiru investment = N3.6m
total investment = N9.6m
proft = turnover-investment
= Nxm-N9.6m
nasiru total take home
= 30%+3.6/9.6*70% = 56.25%
= 56.25/100*[Nxm-N9.6m]
3b)
Victor's collection rate
=N6m/N9.6m*70%
=43.75%

4a)
S = n/2{2a+(n-1)d}
2S = 2an+(n^2-n)d
2S - (n^2-n)d = 2an
a = 2S-(n^2-n)d/2n

4b)
a=?, S= -890, d= -5, n=20
but a=2S-(n^2-n)d/2n
a=2(-890)-(20^2-20)-5/2(20)
a=-1780-(400-20)-5/40
a=-1780+380(S)/40
a=-1780+1900/40
a=120/40 = 3
a=3

5a)
X={1,3,5,7,9,11}
Y={2,3,5,7,11,15}
Z={3,6,9,12,15}
U={1,2,3,...15}


5b)
A≡X
b≡Y
C≡X
(i)AnBnC={3}
A^1={4,6,8,10,12,13,14,15}
B^1={1,4,6,8,10,12,13,14}
:- n(A^1nB^1nC) = {6,12}

<font color="red">SECTION B</font>
8a)
2x-1/x^2+2x-15
i)for zero, numerator = 0
2x-1=0
2x=1
x=1/2

ii)for undefined fraction, denominator = 0
x^2+2x-15=0
x^2+5x-3x-15=0
x(x+5)-3(x+5)
(x-3)(x+5)=0
x=3 or -5

8bi)
internal diameter = 12cm
internal radius = 12/2 = 6cm
thickness = 2cm
extrenal diameter = 12+4=16cm
external radius = 8cm

i)volume = 2/3πr^3
= 2/3*22/7{R^3 - r^2}
= 44/21{8^3-6^3}
= 44/21{512-216}
= 44/21{296} = 13024/21
= 620.19cm^3

8bii)
Area of top = πr^2
= 22/7{8^2 - 6^2}
= 22/7{64 - 36}
= 22/7{28}
= 22*4
= 88cm

10)
x̅ = Ʃfx/Ʃf = 3035/50 = 60.7
a)mean deviation = Ʃf|d|/Ʃf
= 748.8/50
= 14.98
b)standard deviation = rootƩfd^2/Ʃf
= root16224/50
= root324.48
= 18.01

11ai)
education = 350
medicine = 150
engineering = 200
law = 100
arts = 100
total = 900
angular sector
i)
education = 350/900*360
= 140°
ii)
medicine = 150/900*360
= 60°
iii)
engineering = 200/900*360
= 80°
iv)
law = 100/900*360
= 40°
v)
arts = 100/900*360
= 40°
11aii)
% of students admitted into faculty of education = 350/900*100%
= 350/9
= 38.9%

11bi)
P(B)=3/12 = 1/4
P(W)=4/12 = 1/3
P(R)=5/12
P(one of each ball)=1/4*4/11*5/10* + 1/3*3/11*4/10* + 5/12*3/11*4/10
= 1/22+2/55+1/22
= 5+4+5/110
= 14/110 = 7/55

11bii)
P(at least two red)
= 5/12*P(RRR1)+P(RR1R)+P(RRR)
= 5/12*4/11*7/10 + 5/12*7/11*3/10 + = 5/12*4/11*3/10
= 7/66 + 7/88 + 1/11
= 28+21+24/264
= 73/264

13a)
gross income = 2,500,000
personal allowance = 150,000
children(3) = 60,000
insurance(2) 2% of gross = 50,000
contribution(2) 8% of gross = 200,000
total = 460,000
taxable income = 204000

a)
Monthly gross pay
= 2,500,000/12
= N208333.33

b)Tax pay
5% 0f 1st N30,000
= 5/100*30,000
= N15,000
10% of next N30,000
= 10/100*30000
= N3,000
15% of next N50,000
= 15/100*50,000
= 7,500
20% of next 50,000
20/100*50,000
N10,000
25% on remaining = 25/100*(2040000-160,000)
= 25/100*1880000
= N470,000
therefore:
tax pay = 1500+300+7500+470000+110,000
= 492,000
monyhly tax = 492,000/12
= N41,000

c)Next pay = 2,500,000 - 49,200
= N2008000
monthly next pay = 2008000/12
= N167333.33

15a)
R=4%
T=5years
A=142,000
I=?
P=?
But I=PRT/100 = P*4*5/100 = 20P/100
I=P/5
but A=P+I
:- 142,000 = P+P/5
142,000 = 5P+P/5
142,000*5 = 6P
P = 142,000*5/6
P = N118333.33

15b)
cash price = N82,000
deposit = N40,000
instalment = N2,500 for 24months
:- Total instalment = 2,500*24
=N60,000
Total amount paid on hire purchase = 40,000+60,000
= N100,000
difference between cash price and hire purchase
=100,000 - 82,000
N18,000

15c)
​for the first year​
Depreciates = 3.5/100*55,000 = N1925
actual cost in 1st quarter = N53075
in 2nd quarter
Depreciate 3.5/100*53075 = N1857.63
actual cost in 2nd quarter = N51217.37
3rd quater
Dep = 3.5/100*51217.37 = N1792.61
actual cost in 3rd quarter = N49424.76
4th quarter
Dep = 3.5/100*49424.76 = N1729.87
actual cost in 4th quarter = 47694.76.89
:- at the end of the first year, the bike cost N47694.89
​for the second year​
1st quarter
dep = 3.5/100*47694.89 = N 1669.32
actual cost = N46025.57
2nd quarter
dep = 3.5/100*46025.57 = N1610.89
actual cost = N44414.68
3rd quarter
dep = 3.5/100*44414.68 = N1554.51
actual value = N42860.06
4th quarter
dep = 3.5/100*42860.06 = 1500.10
actual cost = N41359.96
at the end of 2years cost = N41359.96