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Mathematics B
6 a y
b 10 m c 29 < x < 170
7 a k 5 3
b
p
5
0
–5
t 0 1 2 3 4
p 0 7 8 3 28
1 2 3 4
c (i) £8333 at t 5 1.7 months (ii) t . 3.3 months
8 a y
b y
c
y 0.2x 0.001x 2
0 200
r
O
y
r
O
x
x
Exercise 85
1 a 5 230°, b 5 25° 2 a 5 280°, b 5 50°
3 a 5 100°, b 5 260° 4 a 5 40°, b 5 320°
5 a 5 110°, b 5 35° 6 a 5 60°, b 5 60°
7 a 5 108°, b 5 72°, c 5 54° 8 a 5 62°, b 5 62°, c 5 28°
9 a 5 55° 10 a 5 45°
11 a 5 90°, b 5 32°, c 5 58° 12 a 5 50°
Exercise 85*
1 a 37° b 53°
2 a x b 2x
3 a 22.5° b 45°
4 OUT 5 x; TOU 5 180° 2 2x; TUV 5 90° 2 x
5 OBA 5 90° 2 x; AOB 5 2x; COB 5 180° 2 2x
​ ​ 6 a √ ________
(r 2 2 x 2 ) ​ b √ ________
(r 2 2 x 2 ) ​
7 a 12 cm b 54 cm 2
c 7.2 cm
8 a 9 cm b 108 cm 2
Exercise 86
1 a 5 124° 2 a 5 56°
3 a 5 102° 4 a 5 78°
5 a 5 56° 6 a 5 36°, b 5 36°
7 a 5 50°, b 5 130° 8 a 5 67°, b 5 113°
9 a 5 100°, b 5 160° 10 a 5 40°, b 5 140°
11 a 5 67°, b 5 85° 12 a 5 105°
x
Exercise 86*
1 Correct proof 2 Angle HOI 5 100° ⇒ x 5 50°
3 126°
4 Angle GOI 5 2 3 100 5 200 ⇒ x 5 160°
t
d
O
r
y
r
O
x
x
5 x 5 116°, y 5 64° 6 x 5 27°
7 Correct proof 8 Correct proof
Exercise 87
1 T 1 , T 2 2 x 5 6
3 x 5 5 y 5 8 4 a 3 cm b 14 cm
5 a 7.5 cm b 10.5 cm
6 1.5 m
Exercise 87*
1 E(4, 2), F(4, 4)
2 b 16 cm c 15 cm
3 a proof b DE 5 11.25 cm c BD 5 3.75
4 PQS, RPS, RPQ
a PS 5 ​ ___ 20 16
​, RS 5 ​
3 ___
3 ​ b ​ ___ 50
3 ​
5 18 m 6 15 m
7 239 litres 8 135°
Exercise 88
1 10.3 cm 2 8.94 cm 3 11.8 cm
4 29.2 km 5 3.16 m
6 a ​√ ________
(y 2 2 r 2 ) ​ b ​√ ________
(y 2 2 r 2 ) ​
Exercise 88*
1 12.4 cm 2 8.77 m 3 17 : 28
4 11.6 cm 5 27.5 m
6 a 48 m b 24 m
Exercise 89
1 Yes SAS 2 No 3 No
4 Yes ASA 5 Yes RHS
6 No
Exercise 89*
1 Correct proof 2 Correct proof
3 Correct proof 4 Correct proof
5 Correct proof 6 Correct proof
Exercise 90 (Revision)
1 a 5 50°, b 5 280° 2 a 5 90°, b 5 30°
3 a 5 70°, b 5 20° 4 a 5 55°, b 5 70°
5 a 5 60° 6 a 5 140°
7 a 5 50° 8 a 5 140°
9 a 5 40°, b 5 20° 10 a 5 120°, b 5 30°
11 a 5 65°, b 5 115° 12 a 5 50°, b 5 130°
13 a 5 18, b 5 14 14 a 5 10.5
15 a 5 12, b 5 12 16 a 5 16, b 5 3
17 a 5 6.40 18 b 5 4.47
19 c 5 15.0 20 AC 5 36.6 cm
21 a No b Yes SSS 22 SAS
Exercise 90* (Revision)
1 a 5 60°, b 5 300° 2 a 5 90°, b 5 45°
3 2a 5 36°, 3a 5 54° 4 a 5 55°, b 5 35°
5 a 5 100° 6 a 5 80°
7 a 5 290° 8 a 5 102°
9 a 5 40°, b 5 60° 10 a 5 35°, b 5 25°
11 a 5 110°, b 5 70° 12 a 5 60°, b 5 60°
13 a 5 4.5 14 a 5 6, b 5 4.5
15 a 5 4.5, b 5 2.5
16 a The angles of both triangles are the same: 55°, 60°, 65°
b a 5 3.61, b 5 2.87
17 a 5 5.39 18 a 5 5.20
19 a r 5 11.7 b a 5 18.7 20 a XC 5 2 b AC 5 4.47
21 Correct proof 22 Correct proof
20
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