MATHS-OBJ!!
1ABBDBCBCAC
11ABDDACCCDD
21ADCDBBCBCC
31CCBCABBCCD
41CDCBCDDCBC

Completed
MATHEMATICS-THEORY-ANSWERS!
(1a)
T1 = 7 – 2x
T2 = 9
T3 = 5x + 17
r = T1/T2 = T3/12
9/(7- 2x) = (5x + 17)/9
(5x + 17)(7 – 2x) = 81
35x – 10x² + 119 – 34x = 81
x – 10x² + 119 = 81
10x² – x + 81 – 119 =0
10x² – x – 38 = 0
10x² – 20x + 19x – 38 =0
10x(x – 2) + 19 (x – 2) =0
(10x + 19) (x – 2) = 0
x = – 19/10 or x =2
.: x = 2

(1b)
p/q = 3/4
. : 4p = 3q
.: p = 3q/4
3p + 2q = 68
3(3q/4) + 2q = 68
9q/4 + 2q = 68
9q + 8q = 272
17q = 272
q = 16
.: p = 3×16/4
p = 12
.: The smaller number = 12
=============================

(2a)
y= (Pr/m – P²r) -³/²
Multiply both index by -⅔
y-⅔= (Pr/m – P²r)-³/²*-⅔
y-⅔/1 = Pr/m – P²r/1
my-⅔ = Pr – mP²r
my-⅔/P-mP² = r (P-mP²)/P-mP²
m/(P-mP²)y⅔ = r

(2b)
y= -8, m=1, P=3

r = m/(P-mP²)y⅔
r = 1/(3-1*3²)* -8⅔
r = 1/(3-9)*(³√-8)²
r = 1/-6*(-2)² = 1/-6*4 = 1/-24
:. r = -1/24
=============================

(3)
Perimeter of minor segment= AB + AB
AB = 2AM = 2rSin36°
= 2*24.5*Sin36°
= 28.8m

AB = 72°/360° * 2*22/7* 24.5
= 72/360* 154 = 30.8m
:. Perimeter= 30.8+28.8
= 57.6m
=============================

(4a)
2(2y+10) = 5x-35 (angle at centre = twice at circle)
4y+20= 5x-35
5x = 4y+55
x = 4/5y +11……….(1)

(2y+10)+(2x+40) = 180 (supplementary angle)
2x+2y+50 = 180
x+y = 65……..(2)

Put (1) into (2)
4/5y +11+y =65
9/5y = 54
y = 5/9*54 = 30
From (2) x=65-y = 65-30= 35

(4b)
= 360 – (175-35+40+70+40)
= 360-290
= 70°
=============================

(5a)
Given m= tan30° = 1/√3
n = tan45° = 1
m -n/mn= 1/√3 -1/(1/√3)(1)
= √3(1/√3 -1)
= 1 – √3

(5b)
15-x+x+10-x =20
25-x = 20
x= 25-20 = 5
PnB(both) = 5/20 = 1/4
=============================

(6a)
On x-axis: 2cm to 2units
On y-axis: 2cm to 10units

(6b)
(x+2)(x-4) = 0
x²-4x+2x-8 = 0
x²-2x-8= 0
mx² + nx + r = y
:. m=1, n= -2, r = -8

(6c)
Gradient= y2 -y1/x2 -x1
= -27 -5/-5 -3
= -32/-8 = 4

(6d)
(x+2)(x-4) > 0
x+2<0 or x-4<0
x< -2 or x<4
And x-4>0
x+2>0 or x-4>0
x> -2 or x>4
:. x> -2
=============================

(7a)
Given; cost price = ₦250.00 per book
Total cost price = 250*180 books
= ₦45,000

Selling Price = (₦300*y books) + 95% of ₦250*(180-y)
= ₦300 + ₦237.5(180-y)
= ₦(62.5y + 42750)

Now, Profit = S.P – C.P
ie 62.5y + 42750 – 45000 = 7125
62.5y = 7125 +2250
62.5y = 9375
y = 9375/62.5
y = 150

(7b)
(i) Profit = S – C
= 33x – x²/20 – 24x -103
P = -x²/20 + 9x -103

(ii) When x = 20
P= -20²/20 + 9(20) – 103
= -20+180-103= 57

Cost price, C = 24x +103
= 24(20)+103
= 583
%Profit= P/C *100%
= 57/583 * 100%
= 9.777%
=============================

(10a)
[TABULATE]

Age X; 3|| 4|| 5|| 6|| 7|| 8|| 9|| 10||

Number of children F; 2 || 6 ||5 || x=4 || 6 || 9 || 8 || 5||

Fx; 6 || 24 || 25 || 6x=24 || 42 || 72 || 72 || 50||

x – x̄; -4 || – 3 || – 2 || – 1 || 0 || 1 || 2 || 3||

(x – x̄)²; 16|| 9 || 4 || 1 || 0 || 1 || 4 || 9 ||

f(x – x̄)²; 32 || 54 || 20 || 4 || 0 || 9 || 32 || 45||

Σf = x + 41
Σfx = 6x + 291
Σf(x – x̄)² = 196

Mean x̄ = Σf/Σf
x̄ = 7 = (6x + 291)/(x +41)
7x + 287 = 6x + 291
7x – 6x = 291 – 287
x = 4

(10b)
S.D = √[(Σf(x – x̄)²]/Σf
S.D = √(196/x+41)
S.D = √(196/45)
S.D = 2.1
=============================

(11a)
Given: y = x +7 – – – – – – (1)
42 + 38 + 57 + x + (x+y) + (2x – 15) + (3x – y) = 360° (external angle of a polygon)
122 + 7x = 360°
7x = 360 – 122 = 238
x = 238/7
x = 34
y = x +7
y = 34 + 7
y = 41

(11b)
= 180° – 34 – 34
= 112°

= 360° – 112 – 146
= 102°

But 102 + 2 2 =============================

(12a)
Pr (loose) = 1/4
Pr (Win) = 1- 1/4 = 3/4
(i) Pr (LWL) = 1/4*3/4*1/4 = 3/64
(ii) Pr (WWW) = 3/4*3/4*3/4 = 27/64
(iii) Pr (Only two) = Pr (WWL) or Pr(LWW) or Pr(WLW)
= (3/3*3/4*1/4) + (1/4*3/4*3/4) + (3/4*1/4*3/4)
= 9/64 + 9/64 + 9/64 = 27/64

(12b)
Volume= 1/3πr²h
1200 = 1/3*22/7*r²*24
25200/528 = 528r²/528
r² = 525/11
Volume= 1/3πr²h
Volume= 1/3*22/7*525/11*84
Volume = 4200cm³
=============================

(13a)
Total surface area, S = 2πrh + 2πr²
= 2πr(h + r)
209 = 2 x (22/7) x (7/2)(h+7/2)
209 = 22(h + 22/7)
209/22 = h + 7/2
19/2 = h + 7/2
h = 19/2 – 7/2
h = 12/3
h = 6cm

(13bi)
Draw the diagram

(13bii)
h/(Fx̄ + 19) = Tan38°
h/Fx̄ = Tan43°
(Fx̄ + 19) = Fx̄ Tan43°
(Fx̄ + 19) = Fx̄ (Tan43°/Tan38°)
Fx̄ + 19 = 1.19356Fx̄
1.19356Fx̄ – Fx̄ = 19
0.19356 Fx̄ = 19
Fx̄ = 19/0.19356

But h = Fx̄ Tan43
h = (19/0.19356) x 0.9325
Height, h = 91.5meters
=============================

(1)

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

(2)

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

(3)

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

(4)

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

(5)

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

(6)

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

(7)

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

(10)

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

(11)

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

(12)

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

(13)

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

Completed!.