# NABTEB GCE 2017 Mathematics Obj and Essay Answer — Nov/Dec Expo

## NABTEB GCE Mathematics Obj And Essay/Theory Solution Questions and Answer – NOV/DEC 2017 Expo Runz.

**Maths OBJ:**

1-10=BDBADCDBBB

11-20=BACDCCCACD

21-30=BACCDBABAC

31-40=CCCADBCBCB

41-50=ACCDADACBD

1-10=BDBADCDBBB

11-20=BACDCCCACD

21-30=BACCDBABAC

31-40=CCCADBCBCB

41-50=ACCDADACBD

NOTE:

* means MULTIPLICATION/TIMES

/ means DIVISION

^ means RAISE TO POWER

NOTE:

* means MULTIPLICATION/TIMES

/ means DIVISION

^ means RAISE TO POWER

SECTION A: Answer All Questions(1 to 5)

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

SECTION A: Answer All Questions(1 to 5)

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

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%

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

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}

•CLICK HERE FOR THE DIAGRAM

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}

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}

•CLICK HERE FOR THE DIAGRAM

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}

SECTION B: Answer according to instruction

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

SECTION B: Answer according to instruction

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)

•CLICK HERE FOR THE TABLE

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

10)

•CLICK HERE FOR THE TABLE

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

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

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

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

GOOD LUCK

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

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