2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
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MATHS OBJ:
1-10: CDAAEABAEC
11-20: ACDDCDCDAC
21-30: CEADEDCABC
31-40: CBEECCBDCC
41-50: DDCBCDDBBA
51-60: BCECCBBCEE
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(1a)
Log10(20x – 10) – log10(x+3) = log10^5
Log10(20x-10/x+3)= log10^5
20x – 10/x + 3 = 5
Cross multiplying
20x – 10 = 5(x + 3)
5(4x – 2) = 5(x + 3)
4x – 2 = X + 3
4x – x = 3+2
3x = 5
X = 5/3 OR 1 whole no 2/3
(1b)
Let actual amount be #X
15% of #x = #600
15x/100 = 600
X = (100/15)*600
X = 100*40
X = 4,000
Actual amount = #4,000
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(2a)
(X^2 Y^-3 Z)^3/4/X^-1 Y^4 Z^5
= (X^2)^3/4/X^-1 * (Y^-3)^3/4/Y^4 * Z^3/4/Z^5
= X^3/2/X^-1 * Y^-9/4/Y^4 * Z^3/4/Z^5
=X^3/2+1 * Y^-9/4-4 * Z^3/4-5
=X^5/2 * Y^-25/4 * Z^-17/4
=X^10/4 * Y^-25/4 * Z^-17/4
=(X^10/Y^25 Z^17)^1/4
(2b)
√2/k + √2 = 1/k – √2
Multiply both sides by (k+√2)(k-√2)
√2(k-√2) = k+√2
√2k-√2 = k+√2
√2k-k = 2+√2
K(√2 -1) = 2+√2
K = 2+√2/√2-1
K = -(2+√2)/1-√2
Rationalizing
K = -(2+√2) * 1+√2/1-√2
K = -(2+√2)(1+√2)/1 – 2
K = (2+√2)(1+√2)
K = 2+2√2 + √2+2
K = 4+3√2
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(3)
V = Mg√1 – r²
Square both sides
V² = m²g²(1-r²)
V²/m²g² = 1-r²
r² = 1 – v²/m²g²
r = √1-(v/mg)²
If v = 15, m = 20, and g = 10
r = √1 – (15/20*10)²
r = √1 – (0.075)²
r= √(1.075)(0.925)
r = √0.994375
r = 0.9972
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(4)
Draw the diagram
(i) Arc length = Tita/360*2πr
= 72/360*2*22/7*14
=1/5*44*2
=88/5
=17.6cm
(ii) Perimeter of Sector = arc length +2r
=17.6+2(14)
=17.6+28
=45.6cm
(iii) Area of sector = Tita/360*πr²
=72/360*22/7*14/1*14/1
=1/5*22*2*14
=616/5
=123.2cm2
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(5a)
Mode = mass with highest frequency = 35kg
Median is the 18th mass
= 40kg.
(5b)
In a tabular form
Under Masses(x kg)
30,35,40,45,50,55
Under frequency(f)
5,9,7,6,4,4
Ef = 35
Under X-A
-10, -5, 0, 5, 10, 15
Under F(X-A)
-50, -45, 0, 30, 40, 60
Ef(X – A) = 35
Mean = A +
(Ef(X – A)/Ef)
= 40 + 35/35
= 40 + 1
= 41kg
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(7ai)
T3=>a+2d=6(eqi)
T7=>a+6d=30(eqii)
Eqii minus eqi gives
6d-2d=30-6
4d=24
d=24/4
d=6
Common difference=6
(7aii)
Putting d=6 into eqi
a+2(6)=6
a+12=6
a=6-12
a=-6
(7aiii)
10th term T10=a+9d
=-6+9(6)
=-6+54
=48
(7bi)
T3=>ar²=9/2(eqi)
T6=>ar^5=243/16(eqii)
Dividing eqii by eqi
ar^5/ar²=243/16 divided by 9/2
r³=243/16*2/9
r³=27/8
r³=3³/2³
r=3/2
Putting this into eqi
a(3/2)²=9/2
a(9/4)=9/2
a=9/2*4/9
a=4/2=2
(7bii)
Common ratio r=3/2 as above
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(8a)
x=a+by(eqi)
when y=5 and x=19
19=a+5b(eqii)
when y=10 and x=34
34=a+10b(eqiii)
solving eqii and eqiii
a+10b=34
a+5b=19
=>5b=15
b=15/5=3
putting b=3 in eqii
19=a+5(3)
19=a+15
a=19-15
a=4
(8ai)
Putting a=4 and b=3 in eqi
x=4+3y
This is the relationship between xand y
(8aii)
When y=7
x=4+3(7)
x=4+21
x=25
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==================================
(11a)
x+y/2 =11
x+y= 11*2
x+y= 22 —(1)
x-y= 4 —-(11)
x+y = 22—-(1)
–
x-y= 4—-(11)
____
2y = 18
y= 18/2
y=9
Substitute y=9 in equ 1
x+9=22
x=22-9
x=13
x=13, y=9
x+y= 13+9= 22
Sum of the two number
(11b)
(6x + 3) dx
(6x + 3)dx
(6x +3)^6 – (6x + 3)^1
(6 x + 3)^5
(7776x^5 + 243)
38,880x/6 + 243
6480 x^6 + 243x
9(720x^6 + 27x)
(11c)
y = x² + 5x – 3 (x = 2)
y = 2² + 5(2) – 3
y = 4 + 10 – 3
y = 14 – 3
y = 11
Gradient of the curve = 11
==========================
(12a)
Pr of Abu to pass = 3/7
Pr of Abu to fail = 1 – 3/7 = 7-3/7 = 4/7
Pr of kuranku to pass = 5/9
Pr of kuranku to fail = 1 – 5/9 = 9 – 5/9 = 4/9
Pr of musa to pass = 12/13
Pr of musa to fail = 1 – 12/13 = 13 – 12/13 = 1/13
Pr of only one of them passing is
=(3/7*4/9*1/13)+(5/9*4/7*1/13)+(12/13*4/7*4/9)
=12/819+ 20/819 + 192/819
=12+20+192/819 = 224/819
= 32/117
(12b)
10Red + 8green + 7blue = 25
(i)
pr of different colour is
Prof(RG)+(RB)+(GB)+(BG)+(BR) +(GR)
=(10/25*8/24)+(10/25*7/24)+(8/25*7/24)+(7/25*8/24)+(7/25*10/24)+(8/25*10/24)
=80/100 + 70/600 + 56/600 + 56/600 + 70/600 + 80/600
= 80+70+56+56+70+80/600
= 412/800 = 103/200
(ii)
pr of atleast one must be
=Pr[RB+BR+GB+BG+BB]
= (10/25*7/24)+(7/25*10/24)+(8/25*7/24)+ (7/25*8/24) + (7/25*7/24)
=70/600+70/600+56/600+56/600+49/600
=70+70+56+56+49
/600
=301/600
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2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
2018/2019 NECO RUNZ MATHEMATICS OBJ & ESSAY QUESTIONS AND ANSWERS
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