CORRECT: 2017/2018 NABTEB GCE MATHEMATICS Questions And Answer Expo/Runs « on: December 04, 2017, 12:56:07 pm » 

 MATHEMATICS ANSWER*
 *Obj*
01-10BDBADCDBBB
11-20BACDCCCACD
21-30BACCDBABAC
31-40CCCAABCBCB
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}

  SECTION B

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
=16mth  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 15b5b) 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 7
= 40,000+60,000
= N100,000 difference between cash price and hire purchase
=100,000 - 82,000 N18,000 1ıc) ​for the first year​ Depreciates
= 3.5/100*55,000
= N1925 actual cost in 1st quarter
]=7 N53075 in 2nd quarter Depreciate 3.5/100*53075ű
= N1857.63 actual cost in 2nd quarter
= N51217.37 3rd quater Dep
= 3.5/100*51217.37
=7 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