Opt Maths

12 a. (1, -3) (2, -5) (4, -1) (5 , -4) b. (0, 2) (2, 3) (3, -1) (4, -3) Exercise 7.3 4a. (5, 2) b. (-1, 7) 11 . (i) (5, -3) (1, -2) (6, 1) (ii) (4, -4) (7, -3) (6, -6) , (3, -6) b. (0, -5), (4, -4), (6, -6), (2, -7) Exercise 7.4 4. a.( -4, -6) b. (− 2 , 5) c. (-9, -5) 3 3 5. a. x = 3, y = 2 b. p = 3, q = 3 6. a. 1 b. k = 1 2 7. a (4, 2) (-4, 2) (-6, 2) b. (0, 0) (23, 23) ( 0, 32) 8. a (3, -2) (3, 0) (-3, 6) (-7, 2) b. (-7, -6) (-1, -12) (-1, -9) (2, -6) Exercise 8.1 2. (a) 26 (b) 75 3 (a) 20 (b) 20 4. (a) 42 (b) 59 5. (a) 6 (b) 20 6. (a) 40 (b) 45 7. (a) 16 (b) 40 8. (a) 23.75, 32, 52.25 (b) 23, 39, 48 9. (a) 69.75, 60, 60 (b) 24.17, 34, 50.45 10. (a) 5, 11 (b) 12, 25 11.(a) 45, 45, 45 (b) 55, 55, 55 Exercise 8.2 (A) 2. (a) 11.5, 0.333 (b) 19.35, 0.60 (c) 61 (d) 40 (e) 65.90 (f) 8.44 (b) 54.4, 105.6 3. (a) 46.5, 77.5 4. (a) 15.5, 0.216 (b) 2, 0.1404 (c) 3.625, 0.19 5. (a) 4, 0.2 (b) 10, 0.25 (c) 10, 0.222 Exercise 8.2 (B) 1. (a) 12.48, 0.17 (b) 1.5, 0.103 (c) 2.83, 0.145 2. (a) 12.42, 0.177 (b) 1.5, 0.1 (c) 2.76, 0.145 3. (a) 3.66, 0.189 (b) 12.29, 0.34 (c) 55.12, 1.17 297

4. (a) 24.39, 0.97 (b) 20.46, 6.821 (c) 11.82, 0.295 Exercise 8.2 (C) 3. (a) 11.33, 0.36 (b) 3.52, 0.15 (c) 8.92, 0.26 4. (a) 6.81, 0.172 (b) 3.9 , 0.05 (c) 4.78, 0.054 5. (a) 34.75, 0.25 (b) 33.78, 0.29 (c) 74.64, 23.9 6. (a) 63.01, 19.70 (b) 217.46, 24.7 7. (a) 39.88, 52.22 (b) 37.13, 61.89 8. (a) 5.76, 12.37 (b) 10.49, 6.9 298