Neco Gce 2016 Mathematics Obj And Theory Answers – Nov/Dec

MATHS OBJ


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SECTION A(ANSWER ALL QUESTIONS 1-5)

1a)
(6y²)³ / 2+y^6
= 6³y^6 / 24y^6
=6³*y^6/24*y^6
= 216/24
=9

1b)
Log10(2m²+5m-2)=1
2m²+5m-2=10
2m²+5m-2-10=0
2m²+5m-12=0

Using m=-b+-√b²-4ac/2a
a=2
b=5
c=-12

m=-5+-√5²-4*2*(-12)/2*2
m=-5+-√2+96/4
m=-5+-√98/4
m=-5+-9.9/4
m=-5+9.9/4 or m=-5-9.9/4

M=1.225 or -3.725
==========

2a)
w*3√D
W=k 3√D
10=k*3√27
10/3 =k*3/3 k=10/3
W=10/3*3√64 = 10/3*4*40/3=13 1/3

2b)
X/2 + y/6 = 2/3
L.C.M = 6
Rx + y = 4 -----(1)
X/3 - y/2 = 5/3
L.C.M = 6
2x - 3y = 10 -----(2)

From eq (1)
3x + y = 4
Y= 4 - 3x ------(3)
Sub for y in eq (2)
2x - 3(4-3x) = 10
2x - 12 + 9x = 10
11x = 22
X=2

Sub for x in eq (3)
Y = 4-3(1)
Y = 4-3-
Y = 1
===========

3a)
Sn = a(r^n - 1)
a = 5
r = 3
n= 8
5(3^8 - 1)/ (3-1) = 5(6561-1)/2
= 32800/2 = 164000

3b
Cos30°=12/P
PCos30°=12
Divide through by cos 30°
PCos30°/Cos30°=12/Cos30°

P=12/cos30°
P=12/0.8660
P=13.8568
==========

4a)V=2/3Πr
1527.4=2/3*22/7*r
1527.4=44r/21
32075.4=44rb
r=32075.4/44
r=728.98
=729cm

4b)
3^3y+1 = 81^-y
3^3y= 3^-4y
3y+1=-4y
1=-4y-3y
1=-7y
Y= - 1/7
===========

5a)
Red=4
Green = 6
Black= 10
Total=20

1)p(Red) = 4/20 = 1/5
2)p(green)= 6/20 = 3/10
3) p (black)= 10/20= 1/2

5b)
( X-1)(X-8)+12=0
X²-8x-X+8+12=0
X²-9x+20=0
X= -b +√b²-4ai
X= 9+/-√-9²-4×1×20÷ 2×1
X=9+/-√81-80÷2
X=9+/-√1÷2
X= 9+1/2 or 9-1/2
X= 10/2 or 8/2
X= 5 or 4
============

+++++++++++++
SECTION B(ANSWER 5 QUESTIONS 7-11)
+++++++++++++

7a)
lets k and p be our constant
R=k+P3√5
S = speed
k + P3√64 = 182...(i)
k + P3√343 = 200...(ii)

subtitute eqn (i) from (ii)
k+4p=182
k+7p=200
3p/3 = 18/3
p=6

subtitute 6 in eqn(i)
k+4p=182
k+4(6)=182
k=182-24
k=158

recall R=k+p3√5
R=158+63√5

(a)find S when R is 188
188=158+6x3√s
188-158 = 6 3√s
30/s = 6 3√s/s
√s=30
(s) = 30^3
s = 30^3
s= 27,000k/h

7b)
find R when S = 27
R=158+6 3√27
R=158+6x3
R=158+18
R=176 newtons
============

(8a)
4a^2 b*3ab^-2/4a^3*(3ab)

=12 a^4 b^1/12a^4 b
=6^-1/b^1
=b^-1-1 =b^2
6^-2 or 1/b^2

8b)
Let the pocket money be x
2x/5 =stations
X/4=school levies
X/6= food
X-(24x/5+x/4+x/6)=55
X-(24x+15x+10x)/60 =55
X-49x/60 =55
60*x-60-49x/60 = 55*60
60x-49x=#3,300
11x/11=3300/11
X=#300
The pocket money =#300

8c)
16^x-4 = 64^x+4/8^x
24^x-16 = 2^6x+24/2^3x
2^4x-16 = 2^6x+24-3x
2^4x-16 = 2^3x+24
4x-16 = 3x + 24
4x - 3x = 16+24
x = 40
============

9a)
solve using cosine rule
m^2 = 70^2+40^2 - (2 x 70 x 40 x cos135)
m^2 = 4900 + 1600 - (5600 x cos135)
m^2 = 6500 - (5600 x cos135)
m√6500-(5600 x cos135)
m = √6500+5578.2
m = √12078.16
m = 109.9006
m == 109.9

9b)
lets find tita (θ)
using sine rule
70/sinθ = 109.9/sin135
70sin135/109.9 = 109.9sinθ/109.9
sinθ = 70 x sin135/109.9
sinθ = 0.45038
θ = sin^-1(0.45038)
θ = 26.76935
θ == 27

:- Bearing of k from R
180° + 85° + 27°
= 292°
==============

10a)
1/27^(x-2)=9^(2-x)
3^3(x-2)-1=3^2(2-x)
3-1(x-2)=4-2x
2x-4=4-2x
2x+2x=4+4
4x=8
X=8/4
X=2

10b
5x+y/x+5y= 3/1
5x+y= 3(x+5y)
5x+y=3x+15y
5x-3x=15y-y
2x=14y
X/y= 14/2 =7, y/x= 1/7
X2-y2/4xy
Divide all through by my
(X²- y²/) ÷(4xy/xy)
Xy- xy

(X/y- y/x) ÷4
(7- 1/7)÷4 ~~~49-1/7×1/4
48/7× 1/4= 24/7
= 4
============

11a)
A=(1 7,3 2) and B=(2 5,4 6)

i)A^-1=1/det(2 -7,-3 1)
Det= 2 -21=-19
A^-1=1/-19(2 -7,-3 1)
-1/19(2 -7,-3 1)
ii)B^T =(2 -4,5 6)
iii)AB =(1 7,3 2) (2 5,4 6)
(2 -28,6-8, 5+46,15+12)
(-26,-2, 51,27,)

11b)
7x^2 + 12x + 5 = 0
7x^2/7 + 12x/7 = -5/7
X^2 + 12x/7 = -5/7
X^2 12x/7 + (6/7)^2 - -5/7 + (6/7)2
(X+6/7)^2= -5/7 + 36/49
(X+6/7)^2 = -35+36/49
(X +6/7)^2 = 1/49
(X +6/7) = + and - √1/19
X+ 6/7 = + and - 1/7
X = -6/7 + and - 1/7
X = -6+1/7 or -6-1/7
X= -5/7 or -7/7
X = -5/7 or -1






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