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(8aii)
Sn = n/2 [2a + (n – 1)d]
= 12/2 [ 2 x (1) + 11 x 3]
= 6 [ -2 + 33)
= 6 (31)
= 186
(9i) DRAW THE DIAGRAM
n (U) = 110
n (P) = 25
n (B) = 45
n (M) = 48
n (Pnm) = 10
n (Bnm) = 8
n (pnBnm) = 5
(9ii) for biology = 45 = 36
(9iii)
x + 14 + 1 + 5 + 5 + 36 + 3 + 35 = 110
x + 25 + 36 + 38 = 110
x = 110 – 99
x = 11
(9b)
15 = 22 + 18 + 2 x 1 + 10 +20/5
15 x 5 = 40 + 2x + 31
45 = 71 + 2x
45 – 71 + 2x
2x/2 = -26/2
X = 13
22, 18, 2x + 1, 10 , 20
For 2x (-B) +1 = -26 +1 = -25
22, 18, -25, 10, 20
-25, 10, 18, 20, 22
The media is 18
(10a)
Loan borrowed = 80/100 × 350,000
=280,000
Amount paid to the bank after 8 years = P + I
= P + PRT/100
=280000 + 280000×7×8/100
=280,000 + 156,800
Amount = #436,800
Total cost of house to the man = #350,000 + Interest
= #350,000 + 156,800
= #506,800
(10b)
Percentage increase in cost of house = 506,800 – 350,000 × 100%
= 156,800/350,000 × 100%
= 44.8%
(12)
Draw the diagram
x² = 20² + 8² – 2x 20 x 8 x Cos 50º
x² = 400 + 64 – 320 x 0.6427
x² = 464 – 205.7
√x² = √258.3
x = 16.1
x = 16km
(12ai)
TJ = 16km
(12aii)
sinØ/20 = sin50/16
sinØ = 20 x sin 50/16
sinØ 0.9576
Ø = sinˉ¹ 0.9576 = 73.3º
The bearing 90 -73.3 = 16.7º
(12b)
Draw the diagram
y = √12² + 5²
y = √144 + 25
y = √169 = 13
tan Ø = 5/12 = (0.04167)
Ø = tanˉ¹ (0.4167) = 22.6º
Sin Ø = 5/6 + x
Sin 22.6º = 5/6 + x
(0.3843) (6 + x) = 5
2.3058 + 0.3843x = 5
0.3843x = 5-2.3058
0.3843x/0.3843 = 2.6942/0.3943
X = 7.01
X ≈ 7
(13a)
Draw the diagram
(i) Extend DO to touch AB at M
AOD + AOM = 180°(<s on a straight line)
130 + AOM = 180°
AOM = 180 – 130 = 50°
Also;
BMO = BAO + AOM(Ext < = sum of two opposite interior <s of a triangle)
BMO = 26 + 50 = 76°
Also; ABD = 1/2AOD(angle at centre = twice angle at circum)
ABD = 1/2 × 130
=65°
Hence ODB + ABD + BMO = 180°(sum of <s in a triangle)
ODB + 65° + 76° = 180°
ODB = 180 – 141
= 39°
(ii) BOD + ODB + DBO = 180°(sum of <s in a triangle)
But ODB = DBO(base angles of an isosceles triangle)
BOD + 39° + 39° = 180°
BOD + 78° = 180°
BOD = 180 – 78 = 102°