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*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


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



(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 =


(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°


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




(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


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



*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


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




(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°


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



(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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You can use WAEC GCE, NECO GCE, NABTEB GCE to gain admission into UNILAG. And any possible combination is acceptable by the university.
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Buy WAEC Scratch Cards Online ? Buy WAEC Result Checker ...

Which bank sells WAEC scratch card?

WAEC Scratch cards can also be purchased at the National Office of WAEC and at any of its zonal and branch offices across Nigeria. It may also be bought from any of the branch offices of Fountain Trust Bank Plc across Nigeria.
WAEC Scratch cards can also be purchased at the National Office of WAEC and at any of its zonal and branch offices across Nigeria. It may also be bought from any of the branch offices of Fountain Trust Bank Plc across Nigeria.

WAEC grading system 2020-2021 ? Legit.ng

Is c6 a good grade?

C6 (50-54%), C5 (55-59%) and C4 (60-64%) are credit grades. B3 (65-69%) is a Good grade. B2 (70-74%) is a Very Good grade. A1 (75-100%) is an Excellent grade.
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Top 20 Best Secondary Schools In Nigeria - PropertyPro Insider

Which school is the best in Nigeria?

waec expo runs is real. WAEC Answers, NECO ANSWERS and GCE answers comes a night before exam or Hours before exam

How To Pass WAEC Examination: 2020/2021 WAEC Secret

How can I prepare for Waec?

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Minimum age of admissions - University of Kent

What is the age limit for university?

Minimum age of admissions. The minimum age to study a degree programme at the university is normally at least 17 years old by the 20 September in the year the course begins. There is no upper age limit. The University will continue to review the minimum age requirement in light of recent changes to national legislation ...
Minimum age of admissions. The minimum age to study a degree programme at the university is normally at least 17 years old by the 20 September in the year the course begins. There is no upper age limit. The University will continue to review the minimum age requirement in light of recent changes to national legislation ...

11 Ways To Study SMART & Study EFFECTIVELY - Do More in ...

How can I study smart?

Universities & Courses that Accepts D7 in English Language

Can I gain admission with d7 in English?

List of Universities that accepts O'level Pass (D7) in English and courses you can use D7 in English Language to study. Most universities requires at least a O'level credit pass (C6) in English language to gain admission in their school both some accepts O'level D7 (Pass) in English.
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HOW TO PASS ANY TEST WITHOUT STUDYING - YouTube

How can I get full marks in exam without studying?

Studying 101: Study Smarter Not Harder ? Learning Center

What is the best study method?

The most effective practice is to work a short time on each class every day. The total amount of time spent studying will be the same (or less) than one or two marathon library sessions, but you will learn the information more deeply and retain much more for the long term?which will help get you an A on the final.

How Much Is WAEC 2020 Form? See Price Of WAEC Registration ...

How much is Waec fees in Nigeria?

Candidates are expected to pay a registration fee of Thirteen Thousand, Nine Hundred and Fifty Naira (N13,950) only. There's an extra bank charge of N500.
Candidates are expected to pay a registration fee of Thirteen Thousand, Nine Hundred and Fifty Naira (N13,950) only. There's an extra bank charge of N500.Jan 6, 2020

2020 WAEC GCE Registration Form | Instructions & Guidelines

How much is Waec this year?

How to Apply for the 2020 WAEC GCE. Candidates arc expected to pay a registration fee of Thirteen Thousand, Nine Hundred and Fifty Naira (N13,950) only, at branches of any of the following banks or any accredited agent and obtain the Registration PIN and Information VCD: Access Bank Plc.
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WAEC ONLINE CERTIFICATE REQUEST - ONLINE REQUEST FORM

Can I get my Waec certificate online?

Private Candidates are now required to apply for their certificates online. The certificates will be dispatched to the WAEC Office of their choice for collection. Candidates are also informed that the certificates for private candidates will be printed only on request and should be collected within 48 hours.
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