1. Chapter 3 Equations and Graphs Additional Example 3.1Additional Example 3.1 Additional Example 3.2Additional Example 3.2 Additional Example 3.3Additional Example 3.3 Additional Example 3.4Additional Example 3.4 Additional Example 3.5Additional Example 3.5 Additional Example 3.6Additional Example 3.6 Additional Example 3.7Additional Example 3.7 Additional Example 3.8Additional Example 3.8 Additional Example 3.9Additional Example 3.9 Additional Example 3.10Additional Example 3.10 Example 1Example 1 Example 2Example 2 Example 3Example 3 Example 4Example 4 Example 5Example 5 Example 6Example 6 Example 7Example 7 Example 8Example 8 Example 9Example 9 Example 10Example 10 New Trend Mathematics - S4A Quit

2. Chapter 3 Equations and Graphs Additional Example 3.11Additional Example 3.11 Additional Example 3.12Additional Example 3.12 Additional Example 3.13Additional Example 3.13 Additional Example 3.14Additional Example 3.14 Additional Example 3.15Additional Example 3.15 Additional Example 3.16Additional Example 3.16 Example 11Example 11 Example 12Example 12 Example 13Example 13 Example 14Example 14 Example 15Example 15 Example 16Example 16 New Trend Mathematics - S4A Quit

3. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

4. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

5. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.1 Solution: (a)Plot the graph of the equation from x =  3 to x = 0.5. (b)Write down the x-intercepts and y-intercept of the graph.

6. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

7. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

8. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.2 The figure shows the graph of. Solve the quadratic equation graphically. (Correct your answer(s) to 1 decimal place.) Solution: From the graph, the two x-intercepts are  1.1 and 2.6 (corr. to 1 d.p.).

9. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

10. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

11. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.3 The figure shows the graph of. Solve the quadratic equation graphically. (Correct your answer(s) to 1 decimal place.) From the graph, the only x-intercept is 1.5. Solution:

12. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

13. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

14. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.4 The figure shows the graph of. Solve the quadratic equation graphically. From the graph, there is no x-intercept. Solution:

15. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

16. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.5 If the graph of the equation cuts the x-axis at two distinct points, find the range of values of k. Solution: [Since the graph cuts the x-axis at 2 distinct points,  > 0.]

17. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

18. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

19. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

20. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.6 Solution: (a)[ From the graph, when x =  2, y = 2.5; when x = 0, y = 0.5; when x = 4, y =  3.5. When y =  1, x = 1.5; when y =  2, x = 2.5.] The figure shows the graph of the equation y  ax  b from x   2 to x  4. (a)By reading the graph, complete the following table. (b)Find the range of values of x of the given graph such that y  1.

21. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

22. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

23. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

24. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

25. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.7 The following is the graph of the equation from x   4 to x  2. (a)By reading the graph, complete the following table. (b)Find the value of k. (c)Find the values of x when y  3. (d)Find the range of values of x of the given graph such that (i)y  2. (ii)y <  1. (Correct your answers to the nearest 0.2 if necessary.)

26. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit (b)When x =  1, y = 4. Solution: (a)From the graph, Additional Example 3.7

27. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

28. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

29. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

30. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.8 The following is the graph of the equation from x   1.5 to x  3. (a)Find the x-intercepts of the graph. (b)Find the values of x when y   1. (c)Find the range of values of x when y > 1.2. (Correct your answers to 1 decimal place if necessary.)

31. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.8 Solution:

32. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

33. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

34. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

35. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.9 (a)The y-intercept is  48. When x = 0, y =  48. When x = 3, y =  12. Solution: The figure shows the graph of the linear equation y  ax  b which passes through the point (3,  12). The y-intercept of the graph is  48. (a)Find the values of a and b. (b)Hence find the x-intercept of the graph of y  ax  b.

36. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.9 (b)From (a), the equation of the graph is y = 12x  48. When y = 0, Solution:

37. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

38. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.10 Solve the following simultaneous equations. Solution: Substitute (2) into (1), Substitute x =  1 into (2),

39. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.10 Substitute (2) into (1), Substitute x = 3 into (2), Solution:

40. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

41. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

42. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.11 Solve the following simultaneous equations. (Correct your answers to 1 decimal place if necessary.)

43. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Solution: Substitute x =  2 into (2), Substitute x = 1 into (2), Additional Example 3.11

44. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.11 Solution:

45. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

46. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.12 Solve the following simultaneous equations.

47. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Solution: Additional Example 3.12

48. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.12 Solution:

49. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

50. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

51. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.13 By using the graph in Example 13, solve the following simultaneous equations graphically. (Correct your answers to 1 decimal place if necessary.)

52. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Solution: Additional Example 3.13

53. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

54. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

55. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.14 By using the graph in Example 14, solve the following simultaneous equations graphically. (Correct your answers to 1 decimal place if necessary.)

56. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Solution: Additional Example 3.14

57. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

58. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

59. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.15 By using the graph in Example 15, solve the following simultaneous equations graphically. (Correct your answer(s) to 1 decimal place if necessary.)

60. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Solution: Additional Example 3.15

61. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

62. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

63. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

64. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example

65. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.16 The figure shows the graphs of and. A is one of the points of intersection of two graphs. (a)Referring to the figure, find a solution of (b)Find the values of a and b. (c)Based on the answer to (b), find another solution of

66. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Additional Example 3.16 Solution:

67. Chapter 3 Equations and Graphs 2004 Chung Tai Educational Press © Quit Substitute x =  4 into (1), Substitute (1) into (2), we have Additional Example 3.16 Solution: