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# 👑 2018 NABTEB GCE MATHEMATICS ANSWERS👑

__100% VERIFIED MATHEMATICS OBJ ANSWERS__

1-10: DCDBABBAAD

11-20: CDBDCCCBDA

21-30: CDABDACACC

31-40: BABCABABBC

41-50: DCDCCCDBDA

__100% VERIFIED MATHEMATICS THEORY ANSWERS__

__SECTION A__

__(Answer ALL QUESTIONS From This Section)__

(1a)

6^n+1*9^n*4^2n/18^n*2^n*12^2n

=(2*3)^n+1*(3*3)^n*(2*2)^2n/(2*3*3)^n*2^n*(2*2*3)^2n

=2^n+1*2^n+1*3^n*3^n*2^2n*2^2n/2^n*3^n*3^n*2^n*2^n*2^n*3^2n

= 2^n*2^1*2^n*2^1*3^n*3^n*2^n*2^n*2^n*2^n/2^n*3^n*3^n*2^n*2^n*2^n*2^n*2^n*3^n*3^n

= 2^6n*3^2n*2*2/2^6n*3^4n

= (2^6n / 2^6n) *(3^2n / 3^4n)*2*2

=2^6n – 6n * 3^2n – 4n * 4

= 2^0 * 3^-2n * 4

= 4*3^-2n

= 4 * 1/3^2n

= 4/3^2n

(1b)

Log 243/log 27

= log 3^5/log 3^3

= 5log3/3log3 = 5/3 = 1 whole no 2/3

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

(2a)

3t – 2p = 8×2 …(I)

2t – 3p = 14×2…(II)

6t – 4p = 16 …(III)

6t – 9p = 42 …(IV)

9P – 4P = -42 + 16

5p = -26

P = -26/5 = -5 1/5

Put p = -26/5 into eqn (I)

3t – 2(-26/5) = 8

3t + 52/5 = 8

3t = 8 – 52/5

3t = 40 – 52/5 = -12/5

Divide both sides by 3

36/3 = -12/5 / 3

t = -12/5 × 1/3

= -12/15 = -4/5

(2b)

3/√3(2/√3 – √12/6)

2/√3 × 3/√3 – 3/√3 × √12/6

6/√9 – 3√12/6/√3

6/3 – 3√12/6√3

2 – √12/2√3

2 × 2√3 – √12/2√3

4√3 – (√4 × 3)/2√3

= 4√3 – 2√3/2√3

= 2√3/2√3 = 1

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

(3)

P(k) = 2/3

P(Y) = 5/8

P(I) = 3/4

P(k fail) = 1- 2/3 = 1/3

P(Y fail) 1 – 5/8 = 3/8

P(I fail) = 1 – 3/4 = 1/4

(a) 2/3*5/8*3/4 = 5/16

(b) 1/3*3/8*1/4 = 1/32

(c) 2/3*5/8*1*4 = 5/48

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(4)

Draw the triangle

Sum of angles in a Δ

= 180 – 158 = 22°

Sin 22/|GN| = Sin 68/8

|GN|= 8sin22/sin68

= 8×0.3746/0.9272

= 2.9969/0.9272

= 3.2322cm

|GT| = |TN| = 3.2322

= 1.616≈ 1.62cm

Let tita = <ftg

(i) tan tita = 8/1.6161 = 4.9502

tita = tan^-¹(4.9502)

tita = 78.6°

FTN = 180 – tita

= 180 – 78.6

(sum of angles on a straight line) = 101.4

(ii) >TFN

= 180 – (68+101.4)

Sum of angles in a Δ

180 – 169.4

=10.6°

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(5a)

4 1/2 – 3(y – 2) = 2y + 1/3

= 9/2 – 3y + 6 = 2y + 1/3

= -3y + 6 + 9/2 = 2y + 1/3

6 + 9/2 = 2y + 1/3 + 3y

12 + 9/2 = 2y + 1/3 + 3y

21/2 = 2y + 1 + 9y/3

21 × 3 = 2(2y + 1 + 9y)

63 = 4y + 2 + 18y

63 = 22y + 2

22y = 63 – 2

22y = 61

y = 61/22 = 2 17/22

(5b)

Let the number be y

7 – 2y >_ 16

-2y >_16 – 7

-2y >_ 9

y _< _9/2 = 4 1/2

The greatest possible values of y are; -4, -3, -2, -1, 0

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__SECTION B__

__(All Candidates should Answer FOUR while SECRETARIAL & BUSINESS CANDIDATES Should Answers Only TWO from this Section)__

(6a)

Let the water melon be x

Let the mango be y

12x + 24y = 432 …(i) × 24

24x + 12y = 360…(ii) × 12

288x + 576y = 10368 …(iii)

288x + 144y = 4320 … (iv)

-144y + 576y = -4320+10368

432y = 6048

y = 6018/432 = 14

Put y = 14 into eqn (i)

12x + 24(14) = 432

12x + 336 = 432

12x = 432 – 336

12x = 96

X = 96/12 = 8

(i) Water melon per kg = 8

(ii) Mango per kg = 14

(iii) (3 × 8) + (2 × 14)

= 24 + 28

= 52

(6b)

123x = 83ten

1*X² + 2*X¹ + 3*X^0

= 83

X² + 2x + 3 = 83

X² + 2x + 3 – 83 = 0

X² + 2x – 80 = 0

X² + 10x -8x – 80 = 0

X(x+10) – 8(x+10) = 0

Then either

X – 8 = 0 or X + 10 = 0

X = 8 or X = -10

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(8a)

Distance /xy/ = tita/360 × 2πr

tita = 45° – 15° = 30°

r = Rcosα

r = 6400 × cos40°

r = 6400 × 0.7600

r = 4902.4km

Distance /xy/ = 30/360 × 2 × 22/7 × 4902.4

= 30 × 2 × 22 × 4902.4/2520

=6471168/2520 = 2567.9238

= 2600km

(8bi)

Time taken to fly from X to y

Speed = Total distance/Total time taken

850 = 2600/t

t = 2600/850 = 3.0588hrs

t = 3hours

Time taken to fly to Y from X

Time = Distance/Speed

= 6700/850 = 7.8824hrs = 8hrs

Total time = 3hrs + 8hrs = 11hrs

(8bii)

Latitude of Z

Distance /yz/ = tita/360 × 2πr

6700 = Z-40/360×2×22/7×6400

6700×360×7 =(Z – 40)281600

16884000 = 281600Z – 11264000

281600Z = 16884000 + 11264000

281600Z = 28148000

Z = 28148000/281600

Z = 99.9574 = 100°

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(9a)

DRAW THE TRIANGLE DAIGRAM

|YX| = x + 620

From ∆ YFP

Tan56 = R/620

R = 620 x tan56

= 620 x 1.4826

h = 919.19m

To find x

Tan 20 = h/x

X = h/tan20 = 919.19/0.3639

X = | XF | = 2525.45m

|YX| = |XF| + |FY|

|YX| = 2525.45 + 620

= 3145.5.45m

Hence the value of |YX| correct to the four significant figure is 3145m

|XY| = 3145m

(9b)

DRAW THE DAIGRAM

|YX|² = |OY|² + |OX|² – 2|OY| |OX| cosØ

(6)² = (5)² + (5)² – 2 (5) (5) cosØ

36 = 25 +25 – 50cosØ

36 = 50 – 50cos Ø

50cosØ = 50 – 36

50cos = 14

cosØ = 14/50 = 0.28

Ø = cos-¹ (0.028) = 73.34º

Therefore

(9bii)

Let |XZ| = |YZ| = y

|XY|² = |YZ|² + |XZ|² – 2 |YZ| |XZ| Cos〆

(6)² = y² + y² – 2y² cos 36.87

36 = 0.4y²

y² = 36/0.4 = 60

y = √60 = 7.75m

hence, |XZ| = 7.8m (1dp)

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

(11a)

In a tabular form

Under scores(x)

2, 3, 4, 5, 6, 7

Under frequency(f)

2, 4, 5, 3, 4, 2 Ef, = 20

Under fx

4, 12, 20, 15, 24, 14 Efx = 89

(i) Modal score = 4

(ii) Median = n1+n2 = 4+4/2 = 8/2 = 4

(iii) Mean X = Efx/Ef = 89/20 = 4.45

(11b)

A = P(1+r/100)n

A = amount in compound interest.

P = principal, r = rates, n = no of years the compound interest is charged.

A = 53000(1+7/100)^5

= 53000(1+0.07)^5 = 53000(1.07)^5

In a tabular form

No | Log

53000| 4.7243 = 4.7243

| 0.0294×5 = 0.1469

4.8712

Antilog of 4.8712 = ₦74436.14

Compound interest = 74436.14 – 53000 = ₦21336.14

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

__SECTION C__

__(Only For SECRETARIAL & BUSINESS Candidates. They shoud answers only TWO from this section)__

(12a)

If passengers paid ₦8,400.00 per trip

Commission on each trip = 5/100 × 8400 = ₦420.00

For 52 trips, his commission would be 52 × ₦420 = ₦21,840.00

His take home for the month = ₦6000.00 + ₦21,840.00 = ₦27,840.00

(12bi)

Gross pay = ₦125018.35 per month.

5% income tax = 5/100 × 125018.35 = 6250.9175

2% Union dues = 2/100 × 125018.35 = 2500.3670

1% housing fund = 1/100 × 125018.35 = 1250.1835

7.5% pension scheme = 7.5/100 × 125018.35 = 9376.3763

2.5% health insurance scheme = 2.5/100 × 125018.35 = 3125.4588

10% cooperative contribution = 10/100 × 125018.35 = 12501.8350

Total deductions = 6250.9175+2500.3670+1250 1835+9376.3763+3125.4588+12501.8350 = 35005.14

(12bii)

His net pay = ₦125018.35 – 35005.14 = ₦90013.21

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

(13a)

4 – point moving average.

16, 18, 20, 27, 28, 31, 32

16+11+20+27/4 = 81/4 = 20.25

18+20+27+28/4 = 93/4 = 23.25

20+27+28+31/4 = 106/4 = 23.25

20+27+28+31/4 = 106/4 = 26.5

27+28+31+32/4 = 118/4 =

29.5

(13b)

First 20weeks, she earns ₦400×20 = ₦8000

The next 20weeks she earns ₦720×20 = ₦14400

Total earns for 40weeks = ₦8000 + ₦14400 = ₦22400

Total earns for the whole

year = ₦52×600 = ₦31200

Amount earns for the remaining 12months = ₦31200 – ₦22400 = ₦8800

Average weekly earns for the last 12 months = 8800/12 = ₦733.33

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

(15a)

Rent = 15/100 * ₦365,500 = ₦54,825

Personal allowance = 12/100 ×₦365,500 = ₦43,860

Annual tax free allowance

= ₦54825 + ₦43860 = ₦98685

(15b)

Taxable income = ₦(365500 – 98685) = ₦266,815

Tax calculation

The first ₦65,000 = 0% = ₦0

Next ₦100,000 = 10/100 × 100,000 = ₦10,000

Next 100,000 = 15/100 × 100,000 = ₦15,000

The remaining ₦1815 = 20/100 × 1815 = ₦363

Annual income tax = ₦(0 + 10,000 + 15,000 + 363)

=₦25,363

(15c)

Percentage of his salary paid as tax = 25,363/365,500 × 100 = 6.94%

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__IMAGE SOLUTIONS:__

(1a & 3)

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(1b & 4)

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(2)

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(5)

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(6)

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(7)

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(8)

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(9)

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(11)

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(12)

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(13)

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(14)

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(15)

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