Answers 233
ANSWERS
Chapter 7Warm-up Exercise
1. (a) (b)
2. (a) (b)
3. (a) No (b) Yes
4. (a) (b) 20
5. (a) 2 (b)
6. (a) sin cos (b) 2
Build-up Exercise
Exercise 7A
1. (a) 32.0 (b) 55.2
(c) 19.5
2.
3.
4.
5.
6. 1
7.
8.
9.
10.
11. 45
12. 60.5
13. (a) 33.7 (b) 51.3
(c) 10.8 cm
14. 61.9
15.
16.
17.
18.
19. 51.1, x 9.3
20.
21.
22.
23. 0
24. 60
25. 45.2
26. (a) 58.0 (b) 15.1 cm
27. (a) 366.6 cm (b) 107.3
28.
29.
30.
31.
32. x 8.3, y 24.4
33.
34.
35.
36. 30
37. 30
38. 456
39. (a) 21.4 cm (b) 24.6
(c) 8.9 cm
40. (a) 153.2 m (b) 128.6 m
(c) 98.5
41. (a) 90 cm (b) 28.2
Exercise 7B
1. (a) 215 (b) 130
(c) 330
2. (a) 57 (b) 37
(c) 63
3. Quadrant III
4.
5. sin 20
6. cos 10
7. 1
8.
9.
10.
11.
12.
13. (a) 68 (b) 0
(c) 31
14. Quadrants II, IV
15.
16. tan 10 17. sin 40
18. 19.
20. 1 21.
22. 11 23.
24. 25. 0
26. Quadrants I, III
27.
28. cos 60 29. tan 20
30. 31. 1
32. 33.
34. 35.
36. 37.
Exercise 7C
1. 0 180 or 360
2. 90 270
3. 0 or 90 180 or 270 360
4.
5.
6.
7.
8.
9.
10. 3
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23. 3
24. (a)
(b)
(c)
25. (a) (b)
(c)
26.
27.
28.
29.
30.
31.
32.
33.
34.
35. (a) (b)
(c)
36. (a)
(b)
37.
38. (a) (b) 164.7
39. (a) (b)
40. (a) Quadrant IV (b)
(c) 300 (d)
Exercise 7D
1. (a) sin (b) 1 sin2
2. (a) sin cos (b) cos2
3. (a) 3 tan (b)
4. sin 5. cos
6. tan 7. sin 2
8. cos 2 9.
10. 1 11. 1
12. 15. sin
16. a cos a sin 17. 1
18. 19.
20. 21.
22. 23. 1
24. 1 27. 4 sin2
28. 6 29.
30. 1
34. (a) (b)
(c)
35.
36. cos 2
37. sin2
40.
41. 3 tan
42. 2a
43. 1
44.
49. (a)
(b) 1 3 sin2 2 sin4
50. (a) (b)
51. (a) (i) (ii)
(b)
52. (a) 3 (b) No
Exercise 7E
1. (a) 0.9 (b) 235, 305
(c) 45 x 135
2. (a) 0.3 (b) 50, 305
(c) 120 x 240
3. Max. 2, min. 2
4. Max. 5, min. 5
5. Max. 6, min. 2
6. Max. 6, min. 2
7. Max. 5, min. 1
8. Max. 3, min. 3
12. (a) Period 360, amplitude 4
(b) A 4, B 2
(c) 2 y 2
13. Max. 0, min. 4
14. Max. 16, min. 0
15. (a) (i) 0.4 (ii) 0.95
(b) 45, 225
(c) 0 x 45 or 225 x 360
16. (a) 0.9
(b) 102.5, 167.5
(c) 27.5 x 62.5
17. (a) 0.6
(b) 90, 630
(c) 180 x 240 or 480 x 540
18. Max. 1, min. 9
19. Max. , min.
20. Max. 3, min. 1
24. (a) Period 360, amplitude 2
(b) A 2, B 1
(c) 1 y 1
25. (a) Max. 4, min. 1
(b) Max. 6, min. 10
26. (a) Max. 9, min. 1
(b) Max. , min.
27. (a) Max. 6, min. 2
(b) Max. 11, min. 2
28. (a) Max. 1, min.
(b) Max. , min.
29. (a) (i) 0.9 (ii) 0.8
(b) 30, 90, 150, 270
(c) 0 x 30 or 90 x 150 or 270 x 360
30. (a) 0.3
(b) 72.5, 107.5
(c) 0 x 30 or 150 x 180
31. (a) 0.6
(b) 410, 670
(c) 0 x 470 or 610 x 720
35. (a) Period 360, amplitude 4
(b) A 4, B 4
(c) 4 y 8
36. (a) Max. 3, min. 1
(b) Max. 7, min. 1
37. (a) Max. 36, min. 0
(b) Max. 9, min. 0
38. (a) Max. , min.
(b) Max. , min.
39. (a) Max. , min.
(b) Max. , min.
40. (a) Max. 7, min. 1
(b) Max. 25, min. 1
41. (a) (i) 0.65 (ii) 0.45
(b) 60, 180, 300
(c) 0 x 60 or 180 x 300
42. (a) A 1, B
(b) Yes
Exercise 7F
1. 15, 195 2. 24, 156
3. 79, 281 4. 57, 123
5. 100, 260 6. 111, 291
7. 45, 135 8. 60, 300
9. 60, 240
10. 0, 90, 180, 270, 360
11. 216.9, 323.1
12. 47.9, 132.1, 227.9, 312.1
13. 40, 160
14. 30, 150
15. 45, 225
16. 0, 70.5, 180, 289.5, 360
17. 0, 90, 270, 360
18. 90
19. 35.3, 144.7, 215.3, 324.7
20. 45, 135, 225, 315
21. 135, 315
22. 30, 150, 210, 330
23. (a) (b) 32.5, 212.5
24. 50, 310 25. 15, 165
26. 15, 195 27. 135, 225
28. 104.0, 284.0 29. 240, 300
30. 120 31. 38.5, 241.5
32. 115, 295 33. 138.7, 318.7
34. 118.1, 241.9 35. 170.5, 350.5
36. 0, 180, 360 37. 0, 180, 360
38. 30, 150, 210, 330
39. 26.6, 45, 206.6, 225
40. 30, 150
41. 30, 150
42. 63.4, 153.4, 243.4, 333.4
43. (a) (b) 23.2, 203.2
44. (a) 2 sin2 5 sin 2 0
(b) 200.5, 339.5
45. (a) cos2 3 cos 1 0
(b) 72.4, 287.6
46. 30, 210
47. 92, 268
48. 61.5
49. 190.3
50. 107.6, 162.4, 287.6, 342.4
51. 200, 260
52. 0, 45, 180, 225 360
53. 32.8, 147.2, 212.8, 327.2
54. 75, 165, 255, 345
55. 0, 45, 180, 225, 360
56. 0, 180, 360
57. 90, 210, 330
58. 30, 90, 150
59. 56.3, 153.4, 236.3, 333.4
60. (a) 3 sin2 4 sin 3 0
(b) 32.4, 147.6
61. (a) 6 cos2 cos 1 0
(b) 70.5, 120, 240, 289.5
62. (a) 3 sin2 8 sin 3 0
(b) 19.5, 160.5
63. 26.6, 116.6, 206.6, 296.6
64. 47.5, 132.5, 244.7, 295.3
65. (a) x
4 4x
3 6x
2 4x 1
(b) 0, 360
Exercise 7G
1. 0, 180, 360
2. 90, 270
3. 150, 330
4. 45, 135
5. 0, 120, 360
6. (a) 85, 265 (b) 100, 275
(c) 85, 265
7. (a) 1 (b) 35
8. (a) a 2, b 1.5 (b) 60
9. 0, 180, 360
10. 60, 120, 240, 300
11. 150, 330
12. (a) 70, 330 (b) 130, 270
(c) 90, 310
13. (a) 85, 265 (b) 105, 290
(c) 60, 245
14. (a) a 4, b 3 (b) 70, 110
(c) 10, 50, 130, 170
15. (a) a 2, b 1 (b) 90, 145
(c) 245, 350
16. (a) A 3, B 1
(b) (i) 162 (ii) 63
17. 0, 180, 360
18. (a) 20, 70, 200, 250 (b) 100, 170, 280, 350
(c) 110, 160, 290, 340
19. (a) 45, 225 (b) 100, 170
(c) 280, 350
20. (a) 120, 300 (b) 150, 270
(c) No solution
21. (a) 255, 320 (b) 95, 275
(c) 85, 265
22. (a) a 3, b (b) 265
(c) 165
23. (a) a 4, b 1 (b) 15, 135
(c) 210, 300
24. (a) 4 (b) 90, 345
(c) 0 x 360
25. (a) a 3.5, b 36 (b) 129
Chapter Test
1.
2.
3. 64.8, 244.8
4.
5.
6.
7. (a) Max. 2, min. 0 (b) Max. 1, min.
8. (a) 2 sin2 3 sin 2 0
(b) 210, 330
(c) (i) (ii) Max. ,
min. 3
9. (a) Max. 1.8, min. 1.5
(b) (i) 90 (ii) 5
(iii) 0
(c) k 1.5 or k 1.8
10. C 11. B
12. D 13. C
14. A 15. B
16. C 17. A
18. D 19. C
Chapter 8Warm-up Exercise
1. (a) 33 (b) 102
2. (a) 4% (b) 20%
3. (a) (b) 10%
4. (a) $2 716 (b) km/min
5. (a) 3 (b)
6. (a) 100 (b)
7. (a) (b) 3n 1
8. (a) 6 : 3 : 2 (b) 12 : 4 : 9
9. (a) 8 : 6 : 15 (b) 2 : 1 : 12
10. (a) (b) 7
Build-up Exercise
Exercise 8A
1. p 18 15n
2. P 50 3t
3. A 450n 300m
4. (a) A h
(b) 1 2 3 4 5 6
h 36 18 12 9 7.2 6
5. (a)
(b) b 3 4.47 7 8.06 9.6
c 9 6 8.06 9 10.4
6. (a) V x
2h
(b) x 2 2.4 3 4 4.8
h 14.4 10 6.4 3.6 2.5
7. (a) y 4x (b)
8. A 50 11p
9. M 4.5p 5q
10. (a)
(b) b 1 2 3 4 5 6
A 5.5 11 16.5 22 27.5 33
11. (a) V r2h
(b) r 2 3 4 5 6
h 18 8 4.5 2.88 2
12. (a) C 2r (b) A r2
(c)
13. (a) (b) y x
2
(c) y x
2 3 (d) y 4x 1
14. Y 15n 23m
15. (a) A r
2 2rh
(b) r 2 4 5 6 8
h 24
16. (a) P 2(x y) (b) A xy
(c) (d)
17. (a) y x
3 (b)
(c) y x
2 2 (d) y 12 x
18. P 280 2n
19. (a) S 2x 3y
(b) (i) x 4p 5q (ii) S 8p 10q 3y
Exercise 8B
1. x 8 20 28 36 40
y 2 5 7 9 10
2. x 2 3 4 5
y 12 27 48 75
3. (a) 3 (c) 1.5
4. (a) (b) 25
5. (a) p 15, q 12 (b)
6. (a) 5 (b) 20
7. (a) (b)
8. (a) (b) 108
9. (a) (b) 2
10. (a) y 6x
2 (b) 36
11. (a) (b)
12. (a) (b) 32
13. (a) (b)
14. 15%
15. 30%
16. 32.25%
17. 20%
18. 19%
19. (a) 4 (b) y3 4x
(c)
20. (a) (b)
(c) 8%
21. (a) (b) 4 100 625
22. x 2 3 6 8 24
y 1 3 4 12
23. x 2 4 6 8 10
y 6 24 54 96 150
24. (a) (c) 2.5
25. (a) y 8x (b) 56
26. (a) m 15, n 40 (b)
27. (a) (b) 32
28. (a) (b)
29. (a) (b)
30. (a) (b) 1 512
31. (a) (b)
32. (a) (b) 4
33. 43.75%
34. 119.7%
35. 25%
36. (a) (b) 256
37. (a) y 4x
2 (b) 100
(c) 10%
38. (a) y 13x
3 (b) 832
(c) 20%
39. (b) y 2u (c)
40. (a) (i) (ii) y 2x
(iii)
(b) 40
41. (a) a 3(b 2) (b) 9
(c) 8
42. x 1
y 1
43. (a) (b) 6
44. (a) p 22, q 22, r
(b)
45. (a) s 3h2 (b) 147
46. (a) (b)
47. (a) (b) 30
48. (a) h 8c3 (b) 1 000
49. (a) (b)
50. 174.4%
51. 51%
52. 5%
53. (a) (b) 2
(c) 64%
54. (a) (b)
(c) 25%
55. (a) (b) 2
(c) 100%
56. (a) (b) 12
(c) y 12
57. (b) y 5u (c) y 5x
2
58. (a) (i) x 10z2 (ii)
(iii)
(b)
59. (a) 3 (b) y 2(3x 2)
(c)
60. (a) (b) 8
(c) 4
61. (a) (b)
(c)
Exercise 8C
1. x 2 4 7 8 28
y 28 14 8 7 2
2. (a) p , q 5 (b)
3. (a) (b) 4
4. (a) (b)
5.
6. (a) (b) 4
7. (a) (b)
8. (a) (b)
9. (a) (b)
10. (a) (b)
11. (a) (b)
12. (a) (b)
13.
14. (a) (b) 11
15. x 2 5 10 20 40
y 5 2 1
16. (a) p , q 25 (b)
17. (a) 100 (b)
(c) 1
18. (a) (b)
19. (a) (b)
20. (a) (b)
21. (a) (b) 0 m 3
22. (a) (b)
23. (a) x 1 2 3 6 12
y 12 6 4 2 1
3 12
xy 12 12 12 12 12
(b) (ii)
24. (a) (b)
(c) 3
25. (a)
(b) s 2, t 15; s 15, t 2
26. (a)
(b) x 1, y 36; x 6, y 1
27. (a) (b)
(c)
28. 10.8%
29. x 5 10 20 25 40
y 5 2.5 1.25 1 0.625
30. (a) (b) 2 187
31. (a) (b) 36
32. (a) (b)
33. (a) 42 (b)
(c) (d)
34. (a) (b)
35. (a) x 1 2 4 5 8
y 240 60 15 9.6 3.75
xy 240 120 60 48 30
240 30
x2y 240 240 240 240 240
(b) (iii)
36. (a) (b) 6
(c) 33
37. (a) m , n 4
38. (a) (b)
(c) 20%
39. 23.1%
40. (a) 7 (b)
(c) 2
41. (a) 9 (b)
(c)
42. (a) 3 : 2 (b) a 9, b 6
Exercise 8D
1. (a) (b)
(c)
2. (a) 2 (b)
3.
4.
5.
6. p , q , r 10
7. (a) (b) 120
8. (a) (b)
9. (a) (b)
10. (a) A kxy (b) 10.25%
11. 56.8%
12. (a) (b) 81
13. (a) (b) G k(h 1)2
(c)
14.
15.
16. u 3, v 3, w 8
17. (a) (b)
18. (a) (b)
19. (a) (b)
20. 44%
21. 12%
22. (a) (b) 9, 5
23. (a) 4 (b)
(c)
24. (a) z 2x2y (b) 100%, 300%
25.
26. (a) (b)
27. (a) p 24, q 5 or 7, r = 9
28. (a) (b)
29. (a) (b) 900
30. 50%
31. (a) 2 (b) y 4(x 2)(x 1)
32. (a) (b) 9
33. (a) (b)
34. (a) (b)
35. (a) (b)
(c) 25%
36. (a) (b) 32.3%, 232%
Exercise 8E
1. (a) y k1 k2x
2 (b)
(c)
2. (a) k1 4, k2 3 (b) 34
3. (a) k1 5, k2 8 (b)
4. (a) k1 13, k2 2 (b) 5
5. (a) k1 3, k2 12 (b) 27
6. (a) (b)
7. (a) (b)
8. (a) u = 2v v2 (b) 80
9. (a) (b) 5
10. (a) (b) 700
11. (a) (b) 261
12. (a) (b) 8
13. (a) (b) 48
14. (a) (b) 9
15. (a) (b) 8
16. (a)
(b) (i) (ii)
17. (a) y 2x
2 3x 4 (b)
18. (a) (b)
(c)
19. (a) k1 1, k2 4 (b) 5
20. (a) k1 45, k2 2 (b)
21. (a) k1 56, k2 120 (b) 38
22. (a) k1 2, k2 150 (b)
23. (a) y 1 2x
2 (b) 19
24. (a) (b)
25. (a) (b) 640
26. (a) (b) 23
27. (a) (b)
28. (a) (b)
29. (a) (b)
30. (a) (b)
(c)
31. (a) (b)
32. (a) y 2x
2 10x (b) 1, 4
(c)
33. (a) k1 2, k2 3 (b) 500
34. (a) k1 15, k2 21 (b) 6
35. (a) (b)
36. (a) (b) 222
37. (a) (b)
38. (a) (b)
39. (a) (b) 12
40. (a) (b) 45
41. (a) z 2x
2 16xy (b) 270
42. (a) (b)
43. (a) z 9 4(x 3)(y 2) (b)
44. (a) (b) 120
(c) 11
45. (a) (b)
46. (a) y 3x
2 2x 3 (b) No real solution
(c)
47. (a) y 8x
2 8x 6 (b)
(c)
Exercise 8F
1. I 2x
2.
3.
4. 115.2 m
5. (a) (b) 75
6. 3.125 cm
7. (a) (b) 32 s
8. (a) V 35 000 W
2 (b) $560 000
(c) $280 000
9. (a) (b) $2 025 000
10. (a) (b) 10 800
11. 8.70%
12. (a) S 2rh (b) 1%
13. (a) C 24r
3 (b) 5 cm
14. (a) (b) 12.8
(c) 7.3 hours
15. (a) E 78N 103T (b) $3 667
(c) 20
16. (a) I 12n 15m (b) $11 394
(c) $17 724
17. N 800HM
18. E 15m 12n
19. (a) (b) $10 000
20. (a) (b) 56.375 kg
21. (a) (b) 20 days
22. (a) (b) 50%
23. (a) (b) 884
(c) 20%
24. (a) (b)
(c) 15 cm (d) 33.1%
25. (a) V 4td
2 (b) $864
(c) 36%
26. (a) (b) 70.7 km/h
(c) 13.0%
27. (a) S 75P 885Y (b) $8 655
28. (a) h 25t 5t
2 (b) 26.25 m
29. (a) A 3 000(1 r%)2 (b) $3 630
(c) 6%
30. (a) (b) $15 850
(c) $550 000
31. (a) (i) $8 000 (ii) $120
(b) 250
32. P 200n 500
33. (a) 700% (b) 26.0%
34. days
35. (a) (b) $2 343.75
36. (a) (b) $169 706
(c) 2012
37. (a) (b) 6 cm
(c) cm
38. (a) (b) 60%
39. (a) (b) 61.5
40. (a) P 100 80h (b) $164
(c) $48
41. (a) (b) 250
(c) 25%
42. (a) (b) $28 320
(c) 5 400
43. $2 160
44. (a) (b) $495
(c) $153
45. (a) V 52 000x 150xy (b) $4 046 400
(c) 23
46. (a) (b) $400
(c) 8 cm
47. (a) $780 (b) C 15r
2 40r
(c) $590.625
Chapter Test
1. 72.8%
2. (a) (b) 50 625
3. (a) m , n 8 (b)
4. (a) (b) 0.8
5. (a) (b) 85.5%
6. (a) (b) 2.75
7. (a) S 40 1.2t
(b) (i) C 1.4t (ii) Network B
8. (a) (i) B 24(n 1) (ii) C 24n 4
(b) $236 (c) 1 hour
9. B 10. C
11. B 12. A
13. D 14. D
15. C 16. A
17. C 18. A
Chapter 9Warm-up Exercise
1. (a) adj. s on st. line (b) adj. s supp.
2. (a) vert. opp. s
alt. s, AB // CD
corr. s, AB // CD
int. s, AB // CD
(b) vert. opp. s
int. s supp.
3. (a) sides opp. eq. s
sum of
(b) ext. of
4. (a) mid-point theorem (b) intercept theorem
5. (a) alt. s, AC // BD
A.A.S.
(b) S.S.S.
corr. s, s
6. (a) vert. opp. s
ratio of 2 sides, inc.
corr. sides, ~ s
(b) 3 sides proportional
corr. s, ~ s
Build-up Exercise
Exercise 9A
5. (a) a c or x b
14. (a) AEP 36, EPA 72
Exercise 9B
9. (a)
12. (a) MN , ON
34. (a) (b)
Exercise 9C
3. (a) 60
19. (a) 45
Exercise 9D
9. (a) 90 (b) ADB 90 b
37. (a) 36
Exercise 9E
31. (a) b 90 a
Chapter Test
9. D 10. D
11. B 12. A
13. C 14. A
15. B 16. C
17. C 18. B
Chapter 10Warm-up Exercise
1. (a) (b)
2. (a) 1 (b) 1
3. (a) 2 (b) 4
4. (a) (3, 5) (b) (3, 2)
5. (a) (b)
6. (a) 4 (b)
Build-up Exercise
Exercise 10B
1. (a) 3x y 1 0 (b) 4x y 18 0
2. (a) 3x y 15 0 (b) 4x y 16 0
3. (a) 2x 3y 12 0 (b) 3x 2y 20 0
4. (a) 2x y 6 0 (b) 4x y 8 0
5. (a) 2x 5y 5 0 (b) 13x 3y 55 0
6. (a) 4x y 2 0 (b) 3x y 6 0
7. (a) 2x y 6 0 (b) 3x y 2 0
8. (a) (b) 2
9. (a) Undefined (b) 0
10. (a) x-intercept 0; y-intercept 0
(b) x-intercept 4; y-intercept 12
11. (a) x-intercept 3; No y-intercept
(b) No x-intercept; y-intercept 3
12. (a) Yes (b) No
13. (a) Yes (b) Yes
14. 3
15. 8
16. 4
17. 2
18. (a) (b)
(c) x-intercept 3; y-intercept
19. (a) 2x 3y 5 0
(c) x-intercept ; y-intercept
20. (a) (b) 10x 26y 21 0
(c)
21. (a) 2x y 4 0 (b) x y 8 0
22. (a) 7x y 26 0 (b) 4x y 4 0
23. (a) x y 4 0 (b) x y 2 0
24. (a) x y 2 0 (b) 2x y 6 0
25. (a) x y 5 0 (b) 2x 3y 6 0
26. (a) (b) 2
27. (a) x-intercept 0; y-intercept 0
(b) No x-intercept; y-intercept 3
28. (a) No (b) Yes
29. (a) Yes (b) No
30. 7
31. 7
32. (a) 13 (b) 10x 3y 19 0
33. (a) x 2y 5 0
(b) x-intercept 5; y-intercept
(c) Yes
34. (a) 2x y 2 0 (b) 2
(c) 2x 5y 6 0
35. (a) (b)
36. (a) (b) 14x 5y 3 0
37. (a) y 2 0 (b) 4x 2y 1 0
38. (a) 12x 7y 1 0 (b) 2x 2y 3 0
39. (a) x 2y 2 0 (b) 9x 2y 3 0
40. (a) (b) Undefined
41. (a) x-intercept 2; y-intercept
(b) x-intercept ; y-intercept
42. 4
43. (a) (b)
(c) 3x 2y 7 0
44. (a) 5x 14y 17 0 (b)
(c) (d) 140x 420y 17 0
45. (a) (b) 2x y 1 0
46. (a) (b) 3x 9y 64 0
47. (a) (b) 5x 3y 3 0
(c) No
48. (a) 3x 4y 9 0 (b)
(c)
49. x 2y 9 0
50. (a) (b) 44x 6y 137
0
(c) 13 : 20
51. 2x y 10 0, 2x 5y 10 0
Exercise 10C
1. (2, 2) 2. (4, 2)
3. (13, 2) 4. (3, 6)
5. (3, 2) 6. (4, 11)
7. (1, 2) 8. (4, 12)
9. (1, 1) 10. (3, 1)
11. (8, 8) 12. (2, 3)
13. (a) (1, 5) (b) 5x y 0
14. (a) 5x 3y 15 0 (b) (6, 5)
15. (2, 3) 16. (1, 6)
17. (2, 3) 18. (3, 1)
19. (1, 5) 20.
21. (0, 2) 22. (4, 5)
23. (a) 11x 7y 1 0 (b) (47, 74)
24. (a) 4x 2y 11 0 (b)
(c) x y 3 0
25. (a) (2, 1)
(b) (i) (ii) 3x 2y 4 0
(c) L1: x y 3 0, y-intercept 3
(d) 5
26. (a) (1, 2) (b) 3x 2y 1 0
(c)
(d) 2 : 1
27. 28. (1, 1)
29. (1, 2) 30.
31. 32.
33. (a) (b) 14x 3y 9 0
34. (a) A(5, 4), C(7, 2) (b) x 2y 3 0
(c) x 2y 1 0 (d) (1, 1)
35. (a) A(3, 4), P(15, 0), Q(5, 0)
(b)
(c)
36. (a) A(3, 2), B(2, 7), C(3, 1)
(b) (c) 4x 19y 26 0
37. (a) (2, 3) (b) x 1 0, y 3 0
(c) AB : 3x y 9 0, AD : 3x y 15 0
38. (a) P(2, 3), A(1, 0), B(3, 0)
(b) 3x 2y 12 0 (c) (4, 0)
(d) 5 : 2
Exercise 10D
1. (a) 18 (b) 153
2. (a) 0.577 (b) 0.625
3. 3x 2y 0 4. x y 2 0
5. x y 0 6. x y 4 0
7. 3x y 11 0 8. 7x 4y 17 0
9. 4x 14y 21 0 10. 5x 5y 3 0
11. (a) m1 , m2 (b) 6
(c)
12. (a) m1 , m2 (b) 8, 4
(c) No
13. (a) 35 (b) 166
14. (a) 1.54 (b) 19.1
15. x y 5 0
16. 4x 3y 14 0
17. 2x 3y 13 0
18. 3x 5y 4 0
19. x y 23 0
20. 2x 4y 9 0
21. 6x 18y 5 0
22. L1: 4x 5y 13 0, L2: 5x 4y 35 0
23. (a) 8x 11y 91 0
(b) Slope of AD , slope of CD ,
slope of BC
(c) AD: 11x 8y 102 0, BC: 11x 8y 83 0
25. (a) (b) 2
(c) 8x 4y 11 0
26. 2x 3y 3 0
27. 6x 15y 4 0
28. 54x 84y 55 0
29. 2x 6y 17 0
30. 25x 15y 24 0
31. 18x 4y 9 0
32. (a) Slope of L1 , slope of L2
(b) (c) Yes
33. (a) (b) 3x y 0
(c)
34. (a) (b)
(c) 15x 5y 86 0
35. (a) 8x 2y 23 0 (b)
36. (a) mx y 0
(b)
(c) 7x y 0
Exercise 10E
1. (a) Centre (2, 1), radius 2
(b) Centre (3, 9), radius 3
2. (a) Centre (1, 5), radius 5
(b) Centre (4, 8), radius 3
3. (a) Centre (1, 0), radius 2
(b) Centre (2, 1), radius
4. (a) Centre , radius
(b) Centre (1, 3), radius
5. (a) x
2 y 2 2y 8 0
(b) x
2 y 2 4x 6y 12 0
6. (a) x
2 y 2 13 0
(b) x
2 y 2 4x 10y 21 0
7. (a) x
2 y 2 2x 0
(b) x
2 y 2 4x 6y 3 0
8. (a) x
2 y 2 6x 6y 9 0
(b) x
2 y 2 10x 10y 25 0
9. (a) x
2 y 2 4x 5y 0
(b) x
2 y 2 2x 6y 0
10. (a) x
2 y 2 6x 7 0
(b) x
2 y 2 10x 4y 4 0
11. x
2 y 2 8x 16y 64 0
12. (a) x
2 y 2 8x 6y 0 (b) Centre (4, 3), radius
5
13. (a) P(1, 2), radius 6 (c) x 4y 7 0
14. x
2 y 2 20 0
15. (a) Centre (3, 7), radius 2
(b) Centre (2, 3), radius 3
16. (a) Centre (2, 5), radius
(b) Centre , radius
17. (a) 4x
2 4y 2 24x 4y 63 0
(b) x
2 y 2 8x 6y 2 0
18. (a) x
2 y 2 2x 4y 5 0
(b) x
2 y 2 4x 6y 0
19. (a) x
2 y 2 10x 2y 6 0
(b) x
2 y 2 3x 4y 1 0
20. (a) x
2 y 2 8x 8y 16 0
(b) 7x
2 7y 2 7x 37y 84 0
21. (a) x
2 y 2 6x 2y 6 0
(b) x
2 y 2 8x 4y 4 0
22. x
2 y 2 8x 4y 18 0, x
2 y 2 4x 4y 6 0
23. x
2 y 2 20x 30 0
24. (a) 2x
2 2y 2 61x 23y 0
(b) Centre , radius
(c) No
25. (a) 3x 2y 5 0 (b) (7, 0)
(c)
26. (a) 7
(b) Centre (7, 3), radius 5
27. (a) x
2 y 2 2x 10y 1 0
(b) Yes, centre (1, 5), radius 5
28. (a) 3x
2 3y 2 14x 12y 39 0
(b) No
29. (a) Centre (3, 4), radius
(b) Centre , radius
30. (a) 4x
2 4y 2 16x 4y 47 0
(b) 36x
2 36y 2 24x 60y 43 0
31. (a) x
2 y 2 2x 6y 103 0
(b) 4x
2 4y 2 24x 32y 1 0
32. (a) x
2 y 2 2x y 41 0
(b) 6x
2 6y 2 39x 62y 157 0
33. (a) x
2 y 2 6x 4y 0
(b) x
2 y 2 8x 8y 16 0
34. (a) x
2 y 2 8x 6y 0 (b) (0, 0), (8, 0)
35. 2
36. (a) (b)
37. x
2 y 2 2x 2y 24 0
38. (a) C1: centre , radius ;
C2: centre , radius
(b) 5x 2y 5 0 (c) No
39. (a) x
2 y 2 14x 6y 4 0
(b) Yes, centre (7, 3), radius
40. (a) C1: centre (2, 1), radius 3;
C2: centre (2, 7), radius 5
(b) (i) Centre (2, 4), radius 8
(ii) x
2 y 2 4x 8y 44 0
41. (a) (p, q)
(b) (i) r
2 p
2 q
2 (ii) r
2 a
2 b
2
Chapter Test
1. (b) Circumcentre
2. (2, 3)
3. Slope , y-intercept 2
4. x 2y 8 0
5. 8x 3y 1 0
6. (a) 3, 2 (b) x
2 y 2 6x 2y 6 0
7. (a) (b) 4x 5y 19 0
(c) x-intercept , y-intercept
8. (a) A(2, 1), radius
(c) x
2 y 2 3x 5y 6 0
9. A 10. C
11. B 12. B
13. C 14. B
15. C 16. C
17. D 18. D
Chapter 11Warm-up Exercise
4. (a) 8 (b) 43
5. (a) 53 (b) 17
6. (a) 0 (b)
7. (a) Parallel lines (b) Parallel lines
Build-up Exercise
Exercise 11A
1. x 13 2. x 5
3. x 15 4. x 17
5. x 16 6. x 1
7. 8.
9. 10. x 1
11. x 1 12. x 16
13. 5, 7 14. 154 cm
15. 16.
17. 18.
19. x 8 20. x 12
21. x 7 22. All real numbers
23. 24. x 29
25. 8, 10
26. (a) x, x 6, x 12 (b) 324, 330, 336
27. (a) x 22, x 11, x (b) 341, 352, 363
28. 594 cm2 29.
30. 31. x 20
32. x 39 33. x 1
34. 35.
36.
37. (a) x 18, x 12, x 6, x
(b) 36, 42, 48, 54
38. 26
39. 576 cm2
40. 6.5 hours or above
41. 88
42. Package A: 9 packs, package B: 6 packs
Exercise 11B
1. x 3 2. 2 x 4
3. No solution 4. x 4
5. x 1 6. 4 x 6
7. 8.
9. 1 x 2 10. No solution
11. 12.
13. x 3 14. 1 x 4
15. No solution 16. 3 x 3
17. x 3 18. x 1
19. 1 x 1 20. 1 x 0
21. 22.
23. 24.
25. 5 x 0 26. x 2
27. 6 x 27 28.
29. No solution 30.
31. x 1 32. No solution
33. 34. x 2
35. 17 x 4 36. x 28
37. x 2 38. 1 x 38
39. 2 x 2 40.
41. x 4 42. x 4
43. 44. No solution
45. No solution 46.
47. 48.
49. x 9 50. x 24
51. No solution 52.
53. No solution 54.
55. 56.
57. 2 x 5 58. 28 x 2
59. (a) (b) 1, 2, 3, 4
60. (a) (3x 4) (x 4) 30 2x,
(30 2x) (x 4) 3x 4,
(3x 4) (30 2x) x 4
(b)
Exercise 11C
13.
26. (a)
(b)
38. (a)
(b)
(c)
39. (a) x 3y 0, x y 0, x y 4, x 6, y 4
(b)
Exercise 11D
1. (a) x y 40 (b) 2x 5y 150
2. (a) 3x 5y 200 (b) x y 50
3.
4.
5.
6.
7. (a)
8. (a)
9. (a) x y 100 (b) 4x 7y 500
10.
11.
12.
13. (a)
14. (a)
15. (a)
16. (a)
17.
18.
19. (a)
20. (a)
21. (a)
22. (a)
23. (a)
24. (a)
Exercise 11E
1. Max. 10, min. 6
2. Max. 25, min. 8
3. Max. 1, min. 11
4. Max. 8, min. 0
5. Max. 19, min. 2
6. Max. 18, min. 6
7. Max. 21, min. 5
8. Max. 22, min. 12
9. Max. , min. 11
10. Max. 7, min. 0
11. Max. 15, min. 29
12. Max. 9, min.
13. 15 private cars and 5 motor cycles
14. (b) (i)
(ii) $720
15. (a) (i) x y 60 (ii) x 3y
(iii) 40x 80y 6 000
(c) x 90, y 30
16. (a)
(c) 175 units on production line A,
10 units on production line B
17. (a)
(c) W $(700x 2 000y)
(d) $16 300; 9 part-time staff and 5 full-time staff
18. Max. 6, min. 18
19. Max. 17, min. 17
20. Max. 35, min. 5
21. Max. 10, min. 2
22. Max. 3, min. 2
23. Max. 15, min. 0
24. Max. , min. 2
25. Max. 26, min. 34
26. Max. 2, min. 8
27. Max. 4, min. 10
28. (a) (i) (ii) x y 24
(iii) (iv)
(b) $4 680
29. (a) (i) (ii)
(c) P $(18x 11y)
(d) 15 boxes of set lunch A, 20 boxes of set lunch B
30. $435
31. Machine A: 9 hours, machine B: 6 hours; $228
32. (a)
(c) P $(275x 50y)
(d) 70 sheep
33. (a)
(c) 5 container A and 8 container B; $19 500
34. (b) Max. 10.4, min. 4
(c) Max. 9.2, min. 2.5
35. Max. 11, min. 15
36. Max. 33, min. 63
37. Max. 27, min. 6
38. Max. 23, min. 6
39. Max. 13, min.
40. Max. , min.
41. Max. 52, min. 12
42. Max. 10, min. 14
43. (a)
(c) 4 robots Adams and 18 robots Eva; $530
44. (a)
(c) 4 physics past papers and 1 chemistry past paper.
45. (a)
(c) 40 kg of mixture A and 250 kg of mixture B
46. (a)
(b)
(c) (i) Max. : D, min. : A
(ii) Max. , min.
(d) Max. 5, min. 7
47. (b) Max. , min. 15
(c) Max. , min. 15
(d) Max. , min.
48. (a)
(c) (i) 10 packs of set A and 5 packs of set B; fish-
ball
(ii) $280
(d) 8 packs of set A and 8 packs of set B; $20
49. (a)
(c) 5 hours on gardening and 5 hours on house
cleaning
(d) 4 hours on gardening and 4 hours on house
cleaning
50. (a)
(c) 7 service hours and 9 service hours; $3 000 000
(d) 12 service hours and 4 service hours; $3 600 000
51. (a) (i) 30 x y
(ii) Walter : 20 x, Lily : 45 y, Fiona : x y 5
(iii)
(c) From factory A: Walter: 0, Lily: 5, Fiona: 25;
From factory B: Walter: 20, Lily: 40, Fiona: 0
Chapter Test
1. 4, 3, 2
2.
3.
4.
6. Max. 17, min. 6
7. (a) 10x y 36 0, x 4y 12 0, 8x 7y 18 0
(b) Max. 22, min. 28
(c) Max. 22, min.
8. (a)
(c) Economy class: 72, business class: 36
9. D 10. D
11. B 12. B
13. B 14. C
15. A 16. D
17. A 18. C
Chapter 12Warm-up Exercise
1. (a) 5 (b)
2. (a) 5.8 (b) x 11.3, y 12.8
3. (a) 2 (b) x
4. (a) 17.5, 162.5 (b) 137.7
5. (a) cos 80 (b) sin 58
6. (a) (b)
Build-up Exercise
Exercise 12A
1. b 9.9, A 45, C 45
2. b 2.9, c 4.1, C 55
3. (a) 6.5 cm
(b) AD 18.9 cm, CD 9.5 cm
4. (a) 16.0 cm (b) 43.3
5. (a) 66.4 (b) 6.5 cm
6. 6 cm2
7. 14.3 cm2
8. 5.9 cm2
9. 67.7 cm2
10. 41.8
11. 16
12. 245.1 cm2
13. 16.4 cm2
14. 9.8 cm2
15. (a) ADB 30, ADC 60
(b)
(c) 26.0
16. (a) 46.0 cm2 (b) 6.1 cm
(c) x 11.6 cm, B 31.9
17. c 15.0, A 33.7, C 56.3
18. b 13.1, c 8.4, C 40
19. (a) DAB 45, BDC 60
(b) 7.1 cm (c) 19.3 cm
20. (a) 3.9 cm (b) 31.1
21. 20.8 cm2
22. 17.8 cm2
23. 107.2 cm2
24. 65.4
25. 7.6
26. 2.6 cm2
27. 34.6 cm2
28. 102.8 cm2
29. 122.7 cm2
30. (a) 20.6 cm
(b) CBD 60.9, ABD 41.1
(c) 184.7 cm2
31. (a) 63.2 cm2 (b) 7.4 cm
(c) b 12.7 cm, A 96.2, C 35.8
32. (a) 104.2 cm2 (b) 39.0 cm2
33. c 11.6, A 15.3, C 74.7
34. a 3.2, c 5.1, B 50
35. (a) 68.8 cm (b) 35.0
36. 40.2 cm2
37. 56.9 cm2
38. 20.3, 69.7
39. 14.6
40. 22.5 cm2
41. 74.5 cm2
42. (a) (b)
(c) 21.6 cm
43. (a) 16.6 cm (b) 28.0 cm2
45. (a) 25.5 cm2 (b) 6.9 cm
(c) 51.4 cm2
46. (a) 60 (b) 27.7 cm2
(c) 166.3 cm2
47. (a) COD 4 180 (b) 72
(c) 17.0 cm2
Exercise 12B
1. 4.9
2. 3.5
3. 40.1
4. 41.0
5. 69.4, 110.6
6. B 66.4, C 83.6, c 11.9 cm
7. C 10, b 6.0 cm, c 1.4 cm
8. A 60, a 11.3 cm, c 12.3 cm
9. A 55.5, C 54.5, a 13.2 cm
10. No solution
11. No solution
12. A 59.0, C 81.0, c 9.2 cm;
A 121.0, C 19.0, c 3.0 cm
13. (a) 8.6 cm (b) 4.4 cm
14. (a) A 90, B 45, C 45
(b)
15. 8.8
16. 24.2
17. A 59.4, B 85.6, b 7.0 cm
18. C 58, a 7.2 cm, c 6.2 cm
19. A 10.7, B 49.3, a 3.4 cm
20. A 33.0, B 102.0, b 18.0 cm
21. B 84.8, C 45.2, c 9.3 cm;
B 95.2, C 34.8, c 7.4 cm
22. No solution
23. A 16.4, C 18.6, a 4.4 cm
24. b 45, c 45
25. (a) 4.5 cm (b) 4.6 cm
26. (a) BAC 40, ABC 40, ACB 100
(b) 7.7 cm (c) 50.6 cm2
27. (a) 48 (b) 82.2
(c) 82.4 cm2
28. (a) ACD 20.9, ADC 119.1
(b) 19.7 cm2 (c) 7.2 cm
29. 9.3
30. 25.7
31. B 75, a 12.4 cm, c 10.1 cm
32. A 45.7, B 34.3, a 12.6 cm
33. A 93.6, C 56.4, a 24.0 cm;
A 26.4, C 123.6, a 10.7 cm
34. B 56.7, C 76.3, c 9.3 cm;
B 123.3, C 9.7, c 1.6 cm
35. B 30.0, C 10.0, c 2.4 cm
36. No solution
37. (a) 46 (b) 9.6 cm
(c) 53.1 cm2
38. (a) 18.3 cm (b) 181.5 cm2
39. (a) 64.9 (b) 10.6 cm
40. 12 cm
41. (a) 8.2 cm (b) 58.8 cm2
42. (a) AB 12.4 cm, BD 12.4 cm
(b) 112.0 cm2
Exercise 12C
1. 9.2 2. 11.2
3. 23.6 4. 44.4
5. 108.2 6. 35.7
7. a 7, B 38.2, C 81.8
8. A 27.3, C 102.7, b 13.3
9. A 10.9, B 22.1, c 8.7
10. A 94.1, B 46.5, C 39.4
11. No solution
12. A 125.6, B 18.4, C 36.0
13. AC 13.9 cm, AD 8.1 cm
14. (a) BDC 23.6, BCD 124.4
(b) BD 8.2 cm, AB 6.9 cm
(c) 33.1 cm2
15. (a) 5.4 cm
(b) AD 4.0 cm, DAB 94.3
(c) 10.9 cm2
16. 4.4
17. 20.4
18. 125.5
19. 37.4
20. (a) 128.7 (b) 10.9 cm2
21. B 9.4, C 157.6, a 8.3
22. A 35.2, C 59.8, b 24.2
23. A 34.1, B 105.9, c 8.0
24. A 44.4, B 34.0, C 101.5
25. No solution
26.
27. AC 11.3 cm, AD 6.5 cm
28. (a) 16.9 cm (b) 10.9 cm
29. (a) 27.8 (b) 21.3
30. (a) A 78.5, B 57.1, C 44.4
(b) a 49 cm, b 42 cm, c 35 cm
(c) 720.1 cm2
31. 7.9
32. 51.6
33. 86.3
34. 29.6
35. A 45.4, B 94.6, c 10.1
36. A 42.3, B 39.3, C 98.5
37. A 122.8, B 22.4, C 34.8
38. (a) 77.4 (b) 15.6 cm2
39. (a) AED 108, CAD 36
(b) 25.9 cm (c) 440.4 cm2
40. 18.2
41. (a) 9.0 cm (b) 58.8
42. (a) 7 : 4 : 5 (b)
43. (a) 112.0 (b) 68.0
(c) 28.6
44. (a) 162.2 (b) 17.8
(c) AC 4.3 cm, BD 27.7 cm
45. (a) AOB 120, BOC 160, COA 80
(b) 5.8 cm (c) 36.5 cm2
Exercise 12D
1. 21.3 cm2
2. 9.9 cm2
3. 31.2
4. 9.8
5. 49.2
6. 72.3
7. 1.5
8. (a) a 16 cm, b 24 cm, c 16 cm
(b) 127.0 cm2 (c) 190.5 cm2
9. 106.7 cm2
10. 48.0 cm2
11. 19.9
12. 18.6
13. 8.9
14. (a) a 12 cm, b 21 cm, c 27 cm
(b) 120.7 cm2
15. (a) 7.2 cm (b) 9.4 cm
(c) 28.7 cm2
16. 10
17. 62.5
18. 64.4
19. 52.4
20. 2.8
21. (a) 15.5 cm (b) 30 cm2
(c) 106.5 cm2
22. (a) a 20 cm, b 16 cm, c 16 cm
(b) 124.9 cm2 (c) 83.3 cm2
23. (a) 8.8 (b) 36.7 cm2
(c) 60.6 cm2
24. (a) 2x cm (b) 2
(c) 48 cm
25. 5
Exercise 12E
1. (a) 015 (b) 143
2. (a) N20E (b) S75W
3. 310 4. S73E
5. S45E 6. 130, x 16.3
7. 19.5 8. 25, y 8.5
9. (a) 63 (b) 46.7
(c) 86.6 m
10. (a) (b)
(c) 112.8
11. 128
12. S23E
13. 065
14. S80E
15. N35W
16. 119.7
17. 27, y 10.0
18. (a) 25 (b) 2.0 km
(c) 1.4 km
19. (a) (b) 600.1 m
(c) 385.7
20. (a) 124 (b) 38.1 m
(c) 16.8 m
21. S36E
22. 306
23. 7.1
24. 7.7
25. 256.8
26. 85, y 48.8
27. (a) 58 (b) 89.2 m
(c) 57.3 m
28. (a) 154.5 m
(b) DAB 65, ABD 40
(c) 109.6
29. 5.1 m
30. (a) 054.7 (b) 0.2 ms1
Exercise 12F
1. (a) BF (b) AE
(c) GE
2. (a) (i) HBG (ii) AEB
(iii)ABH
(b) ABH
3. (a) (i) HBG, EAF (ii) HBC, EAD
(iii)FBA, ECD (iv) FBG, ECH
(b) ABCD, ABGF, CDEH, EFGH, ABHE
4. 90
5. 31.1
6. 43.2
7. 40.9
8. 38.3
9. 43.2
10. (a) 4.95 cm (b) 63.7
11. (a) 201 m (b) 313 m
(c) 9.58
12. (a) 34.9 (b) 53.1
(c) 57.0
13. (a) 8.60 (b) 17.4 cm
(c) 106 cm2
14. 50.2
15. 26.6
16. 61.6
17. 63.4
18. 22.6
19. (a) MN 8.85 cm, MH 12.3 cm, NH 9.85 cm
(b) 81.8
20. (a) 90 (b) 51.1
(c) 60.3
21. (a) 33.0 (b) 81.9
22. (a) 30.0 m (b) 26.5 m
(c) 30.0 m
23. (a) 21.8 (b) 15.8
(c) 10.1
24. (a)
(b) 480 m
(c) HC 316 m, HD 471 m, ED 346 m
(d) 985 m
25. (a) 4.28 m (b) 33.1 m2
26. (a) 1.03 km (b) 1.78 km
(c) 1.32 km2
27. 30.6
28. 75.3
29. (a) MN 13.5 cm, NC 10 cm, MC 16.8 cm
(b) 53.4
30. (a) 15.8 cm (b) 71.6
(c) 18.4 (d) 78.7
(e) 22.6
31. (a) 20.3 cm (b) 58.0
(c) 58.0
32. 70.5
33. (a) 3.03 m (b) 58.7
(c) 14.0
34. (a) 2.92 m (b) 1.03 m
(c) 20.3
35. (a) DBA 35, BDA 93
(b) 27.6 m (c) 59.1 m
36. (a) 16.5 cm (b) 26.2 cm
(c) 39.1 (d) 9.18 cm
(e) 50.7
37. (a)
(b) 222 (c) N83.6E
38. (a) 22.3 (b) 13.2 cm
(c) 57.9
39. (a) 322 m (b) 388 m
(c) 083.1
40. (a) AC 3.06 m, BC 2.57 m
(b) 3.14 m (c) 45
Chapter Test
1. 48.0
2. 4.3 cm
3. 12.9
4. 30.1, y 10.2 cm
5. B 46.3, C 83.7, a 8.5 cm
6. (a) 32.0 cm (b) 274.1 cm2
7. (a) 24.8 km (b) 43.0
(c) 223.0 (d) 101.5 km2
8. (a) DH 10 cm, DB 6.7 cm, BH 8.5 cm
(b) 28.3 cm2 (c) 71.5
9. B 10. B
11. B 12. C
13. B 14. A
15. D 16. C
17. D 18. D
Open-Ended Question Zone
Exercise 7
1. 420, 300
2. a 2, b 1; a 4, b 2
3. ABC 40, BAC 50, ACB 90;
DEF 140, EDF 10, DFE 30
4. 45, 225, 405, 585
5. 90, 270
6.
7. a 2, b 0; a 2, b 4
8. y 3 sin (x 30)
9.
10. w 30, x 210, y 150, z 330
Exercise 8
3. Yes
4.
5. No
6. x 2, y 1.125; x 1, y 0
7. No
8. 2 pieces of chocolate, 80 sit-ups
Exercise 9
1. AB DC
3. a 3, b 3; a 4.5, b 4.5
4. OE CD
5. x 90, y 35, z 55
7. BAE CDE (A.S.A),
EBC ~ EAD (equiangular)
Exercise 10
1. (0, 3), (2, )
3. x 3y 0, x 3y 4 0
4. 2x y 0, 2x y 7 0
5. a 8, b 0, c 5, d 3
6. x y 1 0, x y 2 0, x y 2 0
7.
8. y 2x, y 2, y 3x 1
11. (2, 2), (2, 1); 3x 4y 2 0
Exercise 11
2. a 3, b 1; a 2, b 3
3. 2x 1 4; 2x 11 6
4.
5. a 1, b 1, c 5; a 0, b 1, c 6
6.
8. (b) 6 balls
9. a 1, b 1
10.
11. 13 cm, 15 cm; 5 cm BC 25 cm
Exercise 12
3. a 10, b 8.2, c 11.2; a 16, b 13.1, c 17.8