Free NECO Mathematics Objective & Essay Expo 2020 - ZAZZAFA TV

Free NECO Mathematics Objective &Essay Expo 2020 - ZAZZAFA TV

2020 NECO MATHEMATICS (ESSAY) ANSWERS:

(1a) Equation: y - y1/x - x1=y2 - y1/x2 - x1 y - 5/x - 6 = 7 - 5/-2 - 6 y - 5/x - 6 = 2/-8 = 1/-4 y - 5 = 1/4(x - 6) y - 5 = -1/4x + 6/4 y = -1/4x + 6/4 + 5 y = -1/4x + 3/2 + 5 y = -1/4x + 13/2 OR 4y = -x+26 X + 4y = 26 (1b) 2 S(2x + 9)dx -1 = 2X¹+¹/1+1 + 9x]2 -1 = x²+9x]2 -1 =[2²+9(2)] - [(-1)² + 9(-1)] =[4 + 18] - [1 - 9] = 22 + 8 = 30

(2a)
No that traveled by bus
= u+18+5+12 = 52
=u+35 = 52
u = 52 - 35
u = 17

No that traveled by train
= 6+5+12+v = 35
V + 23 = 35
V = 35 - 23
V = 12

Total no of tourist
=u+v+w+18+12+6+5 = 100
17+12+w+18+12+6+5 = 100
W + 70 = 100
W = 100 - 70
W = 30

(2b)
No who travelled by at least two means of transportation
= 18 + 6 + 12 + 5
= 41

(3ai) EF = 50 Median = 25th + 26th/2 = 6+6/2 = 6 (3aii) Range = 10 - 3 = 7 Median + Range = 6 + 7 = 13 (3b) Prob(Olu passes) = 2/5 Prob(Tony passes) = 3/4 Prob(Olu fails) = 3/5 Prob(Tony fails) = 1/4 Prob(both passes) = 2/5 × 3/4 = 3/10

(4a)

X² + 3x - 28 = 0

X² +7x - 4x - 28 = 0

X(x+7)-4(x+7) = 0

(X - 4)(X + 7) = 0

X - 4 = 0 OR x + 7 = 0

X = 4 OR x = -7

(4b)

8x/9 - 3x/2 = 5/6 - x

Multiply by 18

18(8x/9) -18(3x/2) = 18(5/6) -18x

16x - 27x = 15 - 18x

18x + 16x - 27x = 15

7x = 15

X = 15/7

X = 2 whole 1/7

(5a)
d/dx(4x³ - 2x + 4)⁵
= 5(4x³-2x+4)⁴ × (12x² - 2)
= 10(6x² - 1)(4x³ - 2x + 4)⁴

(5b)
5/3(2-x) - (1-x)/(2-x) = 2/3
Multiply through with 3(2-x)
3(2-x)[5/3(2-x)] -3(2-x)[1-x/2-x] = 3(2-x)(2/3)
5 - 3(1-x) = (2 - x)(2)
5 - 3 + 3x = 4 - 2x
3x + 2x = 4 + 3 - 5
5x = 2
X = 2/5

(6ai)

Volume of sphere = 9 ⅓ ×(its surface area)

4/3πr³ = 28/3×4πr²

r = 28 units

Surface area = 4πr²

= 4x22/7×28×28

= 9856 units squared.

(6aii)

Volume = 9 ⅓ × 9856

= 28/3 × 9856

= 91989.33

=91989 cubic units

(6b)

log10(3x - 5)² - log10(4x -3)² = log10 25

Log10(3x - 5/4x - 3)² = log10 25

(3x - 5/4x - 3)² = 25

Square root of both sides gives

3x-5/4x-3 = ±5

3x-5 = 5(4x-3) OR 3x-5 = 5(4x-3)

3x-5 = 20x-15 OR 3x-5 = 20x+15

3x-20x = 5-15 OR 3x+20x = 15+5

-17x = -10 OR 23x = 20

X = 10/17 OR x = 20/23

(7a)

Given: 3x + 5y = 10

5y = -3x + 10 OR y = -3/5x+ 2

Gradient of the straight line = -1 ÷ (-2/5)

= 5/3

Equation of line:y-2/x-3 = 5/3

3y-6 = 5x - 15

3y = 5x - 15 + 6

3y = 5x - 9

y = 5/3x - 3

Intercept of line = -3

(7b)

Amount = P(1+R/100)³

=8000(1+5/100)³

=8000(1.05)³ OR 8000(1.05/100)³

=8000×1.157625

=#9261

Compound interest = Amount - principal

= 9261 - 8000

= #1261

(10a)

Let the woman's age be W

Let the daughter's age be d

Given: w = 4d-----(1)

Given:(w+5)²=(d+5)²+120--(2)

Put eqn(1)into(2)

(4d+5)² = (d+5)² + 120

(4d+5)² - (d+5)² = 120

[4d+5+d+5][4d+5-d-5] = 120

[5d+10][3d] = 120

5(d+2)(3d) = 120

15(d+2)(d) = 120

d(d+2) = 8

d² + 2d - 8 = 0

d² + 4d - 2d - 8 = 0

d(d+4) -2(d+4) = 0

(d - 2)(d + 4) = 0

d - 2 = 0 (only)

d = 2

Daughter is 2 years old

(10b)

t = w + wy²/PZ

Multiply through by PZ

Pat = PWZ + wy²

Wy² = ptz - pwz

y² = Pz(t - w)/w

y = ±√PZ(t - w)/w

If P = 5, Z = 10, t = 9, w=3

y = ±√(5)(10) (9-3)/3

y = ±√(5)(10)(6)/3

y = ±√100

y = ±10

(10a)

Let the woman's age be W

Let the daughter's age be d

Given: w = 4d-----(1)

Given:(w+5)²=(d+5)²+120--(2)

Put eqn(1)into(2)

(4d+5)² = (d+5)² + 120

(4d+5)² - (d+5)² = 120

[4d+5+d+5][4d+5-d-5] = 120

[5d+10][3d] = 120

5(d+2)(3d) = 120

15(d+2)(d) = 120

d(d+2) = 8

d² + 2d - 8 = 0

d² + 4d - 2d - 8 = 0

d(d+4) -2(d+4) = 0

(d - 2)(d + 4) = 0

d - 2 = 0 (only)

d = 2

Daughter is 2 years old

(10b)

t = w + wy²/PZ

Multiply through by PZ

Pat = PWZ + wy²

Wy² = ptz - pwz

y² = Pz(t - w)/w

y = ±√PZ(t - w)/w

If P = 5, Z = 10, t = 9, w=3

y = ±√(5)(10) (9-3)/3

y = ±√(5)(10)(6)/3

y = ±√100

y = ±10

(11)

|Score|5-9|10-14|15-19|20-24|25-29|30-34|

|Frequency|3|10-T|3T|8|2T+2|T+2|

(a)Ʃ+=50

3+10-T+3T+8+2T+2+T+2=50

3+10+8+2+2-T+3T+2T+T=50

25+5T=50

5T=50-20

5T/5=25/5

T=5

(11b)

|Score|5-9|10-14|15-19|20-24|25-29|30-34|

|Frequency|3|5|15|8|12|7|

The frequency of the modal class is 15.

(11c)

Tabulate.

|Score|5-9|10-14|15-19|20-24|25-29|30-34|

|F|3|5|1|5|8|1|2|7|50

|X|7|12|17|22|27|32|

|FX|21|60|255|176|324|224|1060

|X-x̅|-14.2|-9.2|-4.2|0.8|5.8|10.8|

|(X-x̅)²|201.64|84.64|17.64|0.64|33.64|116.64|

F|(X-x̅)|604.92|423.2|264.6|5.12|403.68|816.48|2518

Mean (x̅) =Ʃfx/Ʃf=1060/50=21.2

Variance =Ʃf(x-x̅)²/Ʃf

=2518/50

=50.36

2020 NECO MATHEMATICS (OBJECTIVE) ANSWERS:

1-10: ACBAECABAE
11-20: CCABBCAAEC
21-30: BBEBBBACBD
31-40: CCADBAAABD
41-50: DEBBBCCBBD
51-60: DACEADAEEA

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