# 2020/2021 WAEC/NECO Answers: Nabteb Gce 2020. Maths answers

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## Refresh this page in every 5 minutes starting from 3 hours to the exam.IRS OBJECTIVE1-10: AAEDCEBBDA11-20: DACDACECAE21-30: ACEEDBBECB31-40: AACEEABCDC41-50: AAADEBECCC51-60: CEDDAEACCE This is actually the Nabteb Gce 2019. Maths answers Answers as questions sent to our subscribers on WHATSAPP, if you are looking for 2020 WAEC/NECO Answers midnight before the exam, try contacting us.

*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 = 8Ã—2 ...(I)

2t - 3p = 14Ã—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 Ã— 1/3

= -12/15 = -4/5

(2b)

3/âˆš3(2/âˆš3 - âˆš12/6)

2/âˆš3 Ã— 3/âˆš3 - 3/âˆš3 Ã— âˆš12/6

6/âˆš9 - 3âˆš12/6/âˆš3

6/3 - 3âˆš12/6âˆš3

2 - âˆš12/2âˆš3

2 Ã— 2âˆš3 - âˆš12/2âˆš3

4âˆš3 - (âˆš4 Ã— 3)/2âˆš3

= 4âˆš3 - 2âˆš3/2âˆš3

= 2âˆš3/2âˆš3 = 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

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

(4)

Draw the triangle

<GFN = 180 - ( 68+90)

Sum of angles in a Î”

= 180 - 158 = 22°

Sin 22/|GN| = Sin 68/8

|GN|= 8sin22/sin68

= 8Ã—0.3746/0.9272

= 2.9969/0.9272

= 3.2322cm

|GT| = |TN| = 3.2322

= 1.616â‰ˆ 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 Î”

180 - 169.4

=10.6°

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

(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 Ã— 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

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

*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) Ã— 24

24x + 12y = 360...(ii) Ã— 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 Ã— 8) + (2 Ã— 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

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

(8a)

Distance /xy/ = tita/360 Ã— 2Ï€r

tita = 45° - 15° = 30°

r = RcosÎ±

r = 6400 Ã— cos40°

r = 6400 Ã— 0.7600

r = 4902.4km

Distance /xy/ = 30/360 Ã— 2 Ã— 22/7 Ã— 4902.4

= 30 Ã— 2 Ã— 22 Ã— 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 Ã— 2Ï€r

6700 = Z-40/360Ã—2Ã—22/7Ã—6400

6700Ã—360Ã—7 =(Z - 40)281600

16884000 = 281600Z - 11264000

281600Z = 16884000 + 11264000

281600Z = 28148000

Z = 28148000/281600

Z = 99.9574 = 100°

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

(9a)

DRAW THE TRIANGLE DAIGRAM

|YX| = x + 620

From âˆ† 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| cosÃ˜

(6)² = (5)² + (5)² - 2 (5) (5) cosÃ˜

36 = 25 +25 â€“ 50cosÃ˜

36 = 50 â€“ 50cos Ã˜

50cosÃ˜ = 50 â€“ 36

50cos = 14

cosÃ˜ = 14/50 = 0.28

Ã˜ = cos-¹ (0.028) = 73.34º

Therefore <XZY = ½ (73.74) (Angle at the center twice the angle at the circumference)

<XZY = ½ (73.74) = 36.87º

<XZY = 37º (nearest degree)

(9bii)

Let |XZ| = |YZ| = y

|XY|² = |YZ|² + |XZ|² - 2 |YZ| |XZ| Cosã€†

(6)² = y² + y² - 2y² cos 36.87

36 = 0.4y²

y² = 36/0.4 = 60

y = âˆš60 = 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

| 0.0294Ã—5 = 0.1469

4.8712

Antilog of 4.8712 = â‚¦74436.14

Compound interest = 74436.14 - 53000 = â‚¦21336.14

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

*SECTION C*

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

(12a)

If passengers paid â‚¦8,400.00 per trip

Commission on each trip = 5/100 Ã— 8400 = â‚¦420.00

For 52 trips, his commission would be 52 Ã— â‚¦420 = â‚¦21,840.00

His take home for the month = â‚¦6000.00 + â‚¦21,840.00 = â‚¦27,840.00

(12bi)

Gross pay = â‚¦125018.35 per month.

5% income tax = 5/100 Ã— 125018.35 = 6250.9175

2% Union dues = 2/100 Ã— 125018.35 = 2500.3670

1% housing fund = 1/100 Ã— 125018.35 = 1250.1835

7.5% pension scheme = 7.5/100 Ã— 125018.35 = 9376.3763

2.5% health insurance scheme = 2.5/100 Ã— 125018.35 = 3125.4588

10% cooperative contribution = 10/100 Ã— 125018.35 = 12501.8350

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

(12bii)

His net pay = â‚¦125018.35 - 35005.14 = â‚¦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 â‚¦400Ã—20 = â‚¦8000

The next 20weeks she earns â‚¦720Ã—20 = â‚¦14400

Total earns for 40weeks = â‚¦8000 + â‚¦14400 = â‚¦22400

Total earns for the whole

year = â‚¦52Ã—600 = â‚¦31200

Amount earns for the remaining 12months = â‚¦31200 - â‚¦22400 = â‚¦8800

Average weekly earns for the last 12 months = 8800/12 = â‚¦733.33

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

(15a)

Rent = 15/100 * â‚¦365,500 = â‚¦54,825

Personal allowance = 12/100 Ã—â‚¦365,500 = â‚¦43,860

Annual tax free allowance

= â‚¦54825 + â‚¦43860 = â‚¦98685

(15b)

Taxable income = â‚¦(365500 - 98685) = â‚¦266,815

Tax calculation

The first â‚¦65,000 = 0% = â‚¦0

Next â‚¦100,000 = 10/100 Ã— 100,000 = â‚¦10,000

Next 100,000 = 15/100 Ã— 100,000 = â‚¦15,000

The remaining â‚¦1815 = 20/100 Ã— 1815 = â‚¦363

Annual income tax = â‚¦(0 + 10,000 + 15,000 + 363)

=â‚¦25,363

(15c)

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

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

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