2018 NABTEB GCE Mathematics Questions And Answers

2,106 total views, 6 views today

NABTEB GCE Mathematics Questions and Answers, NABTEB GCE 2018 Mathematics Questions and Answers, NABTEB GCE 2018 Mathematics Expo, NABTEB GCE 2018 Mathematics Runs, NABTEB GCE 2018 Mathematics Choke, NABTEB GCE 2018 Mathematics Dubs, NABTEB GCE 2018 Mathematics Link, NABTEB GCE Mathematics Questions and Answers, NABTEB GCE Mathematics Expo, NABTEB GCE Mathematics Runs, NABTEB GCE Mathematics Choke, NABTEB GCE Mathematics Dubs, NABTEB GCE Mathematics Link

ATTENTION:- PLEASE NOTE THAT OUR SUBSCRIBERS ALWAYS GET ANSWERS A DAY BEFORE EACH PAPER, ALWAYS SUBSCRIBE FOR EARLY ANSWERS.

👑 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

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

(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°

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

(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%

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

IMAGE SOLUTIONS:

(1a & 3)
name

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

(1b & 4)
name

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

(2)
name

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

(5)
name

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

(6)
name

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

(7)
name
name
================================

(8)
name

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

(9)
name

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

(11)
name

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

(12)
name

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

(13)
name

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

(14)
name

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

(15)
name

======COMPLETED======

 

Don’t Just Copy Alone, Drop your Comments, Share with your friends on Facebook, Twitter And Google Using the below share buttons and like our Facebook fan pages Here and Here
BEST OF LUCK

We Update Our Social Media Platform With Latest Updates, Don’t Miss Out Join US On Facebook and For Latest Updates.

Be the first to comment

Leave a Reply

Your Phone Number will not be published.




This site uses Akismet to reduce spam. Learn how your comment data is processed.