第1章：有向數



Chapter 11 Inequalities and Linear Programming

|Warm-up Exercise |

1. Draw the graphs of the following equations.

(a) x ( 2 (b) y ( (3

[pic] [pic]

2. Draw the graphs of the following equations.

(a) y ( x (b) y ( (2x ( 1

[pic] [pic]

3. Draw the graphs of the following equations.

(a) 5x ( 2y ( 10 (b) 8x ( 5y ( 20 ( 0

[pic] [pic]

4. When x ( 3 and y ( (5, find the value of each of the following expressions.

(a) 2x ( 3y ( 1 (b) 9 ( 3x ( 5y

5. If f (x) ( 5x ( 3, find the values of the following.

(a) f (10) (b) f ((4)

6. If [pic], find the values of the following.

(a) f (2) (b) f ((3)

7. What is the common feature of each of the following groups of straight lines?

(a) x ( 3y ( 0, x ( 3y ( 2, x ( 3y ( 6 (b) x ( 2y ( 0, x ( 2y ( 1 ( 0, x ( 2y ( 4 ( 0

|Build-up Exercise |

[ This part provides three extra sets of questions for each exercise in the textbook, namely Elementary Set, Intermediate Set and Advanced Set. You may choose to complete any ONE set according to your need. ]

Exercise 11A

((((((((((((((( Elementary Set [pic] (((((((((((((((

Level 1

Solve the following inequalities and represent the solutions graphically. (1 – 12)

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. [pic] 12. [pic]

Level 2

13. Find the least values of two consecutive odd numbers such that the smaller number is greater than [pic] of the larger number.

14. Donald is 7 cm taller than Joyce and Joyce is 15 cm shorter than Kelvin. If the sum of their heights is not greater than 484 cm, find the maximum height of Joyce.

((((((((((((((( Intermediate Set [pic] (((((((((((((((

Level 1

Solve the following inequalities and represent the solutions graphically. (15 – 24)

15. [pic] 16. [pic]

17. [pic] 18. [pic]

19. [pic] 20. [pic]

21. [pic] 22. [pic]

23. [pic] 24. [pic]

Level 2

25. Find the largest values of two consecutive even numbers such that 2 times the sum of the larger number and 2 is not less than 3 times the smaller number.

26. (a) Write down three consecutive multiples of 6 if the smallest number is x.

(b) Hence find the greatest values of three consecutive multiples of 6 whose sum is less than 1 000.

27. (a) Write down three consecutive multiples of 11 if the largest number is x.

(b) Hence find the least values of three consecutive multiples of 11 whose sum is greater than 1 023.

28. A wire with a length of at most 98 cm is bent to form a rectangle. If the width of the rectangle is 5 cm longer than the length, find the maximum area of the rectangle.

(((((((((((((((( Advanced Set [pic] ((((((((((((((((

Level 1

Solve the following inequalities and represent the solutions graphically. (29 ( 36)

29. 5(3x ( 2) ( 15 30. [pic]

31. [pic] 32. [pic]

33. [pic] 34. [pic]

35. [pic] 36. [pic]

Level 2

37. (a) Write down four consecutive multiples of 6 if the largest number is x.

(b) Hence find the least values of four consecutive multiples of 6 whose sum is not less than 180.

38. Mary is 15 years older than John. Four years later, Mary’s age will not be greater than twice of John’s. Find the minimum possible age of Mary at present.

39. One side of a rectangle is 32 cm. If the perimeter of the rectangle is at most 100 cm, find the maximum area of the rectangle.

40. Mr. Ho and Mr. Lee drive from city A to city B. Mr. Lee leaves city A 30 minutes earlier than Mr. Ho does. If Mr. Lee and Mr. Ho drive at 65 km/h and 80 km/h respectively, how long does Mr. Ho take to drive at least 65 km ahead of Mr. Lee?

41. There are altogether 6 tests in a mathematics course. In order to obtain grade A at the end of the course, the average score of a student must not be less than 85. John got 79, 84, 90, 76 and 93 for the first 5 tests. What is the minimum score that John should get in the last test if he wants to obtain grade A at the end of the course?

42. A shop sells batteries in two packages A and B. Package A contains 8 batteries and package B contains 12 batteries. If Cathy needs at least 144 batteries and she will buy packages A and B in the ratio of 3 : 2, find the minimum number of packs of packages A and B that she will buy.

Exercise 11B

((((((((((((((( Elementary Set [pic] (((((((((((((((

Level 1

Solve the following simultaneous inequalities and represent the solutions graphically. (1 ( 14)

1. 1 ( x and x ( 3 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. [pic] 12. [pic]

13. [pic] 14. [pic]

Level 2

Solve the following simultaneous inequalities and represent the solutions graphically. (15 ( 20)

15. [pic] 16. [pic]

17. [pic] 18. [pic]

19. 1 ( 2x ( 3 ( 5 20. 3  ................
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