052-076 UNIT 3/1 · 54 ·∫∫Ωñ° §≥ ‘µ»“ µ√ åæ Èπ∞“π ¡.3 ¿“§‡√...

52 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

°‘®°√√¡∑’Ë 1

1. „Àâπ—°‡√’¬πÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ ¡—∏¬∞“π ·≈–∞“ππ‘¬¡¢Õß¢âÕ¡Ÿ≈„π·µà≈–¢âÕµàÕ‰ªπ’È

(1) 5, 15, 7, 8, 10

§à“‡©≈’Ë¬‡≈¢§≥‘µ ( X) ∑ XN

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‡√’¬ß¢âÕ¡Ÿ≈®“°πâÕ¬‰ª¡“° ......................................................................

¡—∏¬∞“π (Med) §◊Õ ......................................................................

∞“ππ‘¬¡ (Mo) §◊Õ ......................................................................

(2) 10, 8, 13, 20, 11, 9, 1, 8

§à“‡©≈’Ë¬‡≈¢§≥‘µ ( X) ∑ XN

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1. °“√À“§à“°≈“ß¢Õß¢âÕ¡Ÿ≈∑’Ë¬—ß‰¡à‰¥â·®°·®ß§«“¡∂’Ë

∂‘µ‘3

53·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

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‡√’¬ß¢âÕ¡Ÿ≈®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È ......................................................................

¡—∏¬∞“π (Med) §◊Õ ......................................................................

∞“ππ‘¬¡ (Mo) §◊Õ ......................................................................

(3) 20, 30, 40, 50, 60, 70

§à“‡©≈’Ë¬‡≈¢§≥‘µ ( X) ......................................................................

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‡√’¬ß¢âÕ¡Ÿ≈®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È ......................................................................

¡—∏¬∞“π (Med) §◊Õ ......................................................................

∞“ππ‘¬¡ (Mo) §◊Õ ......................................................................

(4) 12, 20, 16, 15, 12

§à“‡©≈’Ë¬‡≈¢§≥‘µ ( X) ......................................................................

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‡√’¬ß¢âÕ¡Ÿ≈®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È ......................................................................

¡—∏¬∞“π (Med) §◊Õ ......................................................................

∞“ππ‘¬¡ (Mo) §◊Õ ......................................................................

(5) 18, 20, 30, 15, 20, 35, 50, 14

§à“‡©≈’Ë¬‡≈¢§≥‘µ ( X) ......................................................................

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54 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

‡√’¬ß¢âÕ¡Ÿ≈®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È ......................................................................

¡—∏¬∞“π (Med) §◊Õ ......................................................................

∞“ππ‘¬¡ (Mo) §◊Õ ......................................................................

2. ∂â“§à“‡©≈’Ë¬¢Õß¢âÕ¡Ÿ≈ 10, 20, k, 12, 24, k, 28, 29, 32, k, 30 ¡’§à“‡∑à“°—∫ 2 ®ßÀ“§à“ k

«‘∏’∑” §à“‡©≈’Ë¬‡≈¢§≥‘µ ( X) ...............................................................................

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3. „π°“√À“§à“‡©≈’Ë¬‡≈¢§≥‘µ¢Õß§–·ππ«‘™“«‘∑¬“»“ µ√å¢Õßπ—°‡√’¬π 5 §π ‰¥âº≈≈—æ∏å

‡∑à“°—∫ 35.2 ·µàæ∫µÕπÀ≈—ß«à“ Õà“π§–·ππ¢Õßπ—°‡√’¬πº‘¥‰ª °≈à“«§◊Õ Õà“π‡ªìπ 41

®“°§–·ππ®√‘ß 47 ®ßÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ∑’Ë∂Ÿ°µâÕß¢Õß§–·ππ¢Õßπ—°‡√’¬π°≈ÿà¡π’È

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4. §–·ππ Õ∫«‘™“¿“…“‰∑¬¢Õßπ—°‡√’¬π 5 §π ‡ªìπ¥—ßπ’È 15, 8, 17, 11, 9

(1) ®ßÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ¢Õß§–·ππ Õ∫

( X) ...............................................................................

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55·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(2) ∂â“‡æ‘Ë¡§–·ππ„Àâπ—°‡√’¬π§π≈– 2 §–·ππ §à“‡©≈’Ë¬‡≈¢§≥‘µ‡ªìπ‡∑à“‰√

( X)„À¡à ...............................................................................

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5. ‡¥Á°™“¬‡°àß‰¥â§–·ππ Õ∫¬àÕ¬ 5 §√—Èß ‡ªìπ 17, 14, 11, 13, 10 ®“°§–·ππ‡µÁ¡ 20

§–·ππ „π°“√ Õ∫«‘™“‡¥’¬«°—ππ—Èπ ‡¥Á°À≠‘ß¥“«‰¥â§–·ππ 9, 11, 18, 15, 18 ®ßÀ“«à“

„§√‰¥â§–·ππ‡©≈’Ë¬®“°°“√ Õ∫¬àÕ¬ Ÿß°«à“ ·≈– Ÿß°«à“‡∑à“‰√

«‘∏’∑” §–·ππ‡©≈’Ë¬¢Õß‡¥Á°™“¬‡°àß ......................................................................

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§–·ππ‡©≈’Ë¬¢Õß‡¥Á°À≠‘ß¥“« ......................................................................

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6. ÿ¥“ Õ∫§≥‘µ»“ µ√å§√—Èß∑’Ë 1, 2, 3, 4, 5, 6 ‰¥â§–·ππ¥—ßπ’È 51, 48, 48, 50, 52, 45

(1) „π°“√ Õ∫§√—Èßπ’È‡¢“‰¥â§–·ππ‡©≈’Ë¬‡∑à“‰√

«‘∏’∑” §–·ππ‡©≈’Ë¬ ...............................................................................

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(2) ∂â“ ÿ¥“µâÕß°“√„Àâ‰¥â§–·ππ‡©≈’Ë¬„π°“√ Õ∫ 7 §√—Èß ‡ªìπ 50 §–·ππ ‡∏Õ®–µâÕß

∑”§–·ππ Õ∫§√—Èß∑’Ë 7 „Àâ‰¥â°’Ë§–·ππ

«‘∏’∑” Õ∫§√—Èß∑’Ë 7 ‰¥â§–·ππ x §–·ππ

§–·ππ‡©≈’Ë¬ 7 §√—Èß §–·ππ√«¡ 6 §√—Èß x

7

56 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

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7. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß¡’ 7 µ—« §◊Õ k, k 2, 30, 28, 25, 30, 28 À“§à“‡©≈’Ë¬‡≈¢§≥‘µ‰¥â 29 ®ßÀ“ k

¡—∏¬∞“π ·≈–∞“ππ‘¬¡

«‘∏’∑” §à“‡©≈’Ë¬‡≈¢§≥‘µ ...............................................................................

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§à“¢Õß¢âÕ¡Ÿ≈‡√’¬ß®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È ..............................................................

¡—∏¬∞“π§◊Õ ................................................................................................................

∞“ππ‘¬¡§◊Õ ................................................................................................................

8. ¡™“¬√—∫®â“ß∑”ß“π™‘ÈπÀπ÷Ëß„Àâ∫√‘…—∑‡ªìπ‡«≈“ 20 «—π ‚¥¬ 7 «—π·√° ‰¥â§à“®â“ß«—π≈–

180 ∫“∑ Õ’° 7 «—πµàÕ¡“ ‰¥â§à“®â“ß«—π≈– 200 ∫“∑ à«π«—π∑’Ë‡À≈◊Õ‰¥â§à“®â“ß«—π≈–

220 ∫“∑ ®ßÀ“«à“ ¡™“¬‰¥â§à“®â“ß‡©≈’Ë¬«—π≈–‡∑à“‰√

«‘∏’∑” §à“®â“ß‡©≈’Ë¬ ...............................................................................

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9. ∫√√≥“√—°…åºŸâÀπ÷Ëß‰¥â ”√«®ª√‘¡“≥π—°‡√’¬π∑’Ë„™âÀâÕß ¡ÿ¥„π√Õ∫ 5 «—π ‡ªìπ¥—ßπ’È

«—π∑’Ë 1 578 §π «—π∑’Ë 2 648 §π «—π∑’Ë 3 615 §π

«—π∑’Ë 4 552 §π «—π∑’Ë 5 627 §π

57·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

®ßÀ“ (1) §à“‡©≈’Ë¬‡≈¢§≥‘µ∑’Ëπ—°‡√’¬π‡¢â“¡“„™âÀâÕß ¡ÿ¥«—π≈–‡∑à“‰√

(2) §à“¡—∏¬∞“π

(3) §à“∞“ππ‘¬¡

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10. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß¡’ 4 ®”π«π À“§à“‡©≈’Ë¬‡≈¢§≥‘µ‰¥â 37 ¡—∏¬∞“π‡∑à“°—∫ 39 ·≈–∞“ππ‘¬¡§◊Õ

42 §à“‡©≈’Ë¬‡≈¢§≥‘µ¢Õß§à“ Ÿß ÿ¥·≈–§à“µË” ÿ¥‡ªìπ‡∑à“‰√

«‘∏’∑” „Àâ¢âÕ¡Ÿ≈ 4 ®”π«π ‡√’¬ß®“°πâÕ¬‰ª¡“°‡ªìπ¥—ßπ’È x1, x2, x3, x4

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58 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

11. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß‡√’¬ß®“°πâÕ¬‰ª¡“°¥—ßπ’È 11, 11, 11, m, 15, 15, 17, 19, 20, 26, n ∂â“

∞“ππ‘¬¡¡’‡æ’¬ß§à“‡¥’¬«·≈–‰¡à‡∑à“°—∫ 15 ·≈–¡’§à“‡©≈’Ë¬‡≈¢§≥‘µ‡∑à“°—∫ 17 ·≈â« n

¡’§à“ Ÿß ÿ¥‡∑à“‰√

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12. π—°‡√’¬π™—Èπ ¡.3 “¡ÀâÕß ·µà≈–ÀâÕß¡’π—°‡√’¬π 30, 36 ·≈– 34 §π µ“¡≈”¥—∫ ·µà≈–

ÀâÕß¡’§–·ππ Õ∫‡©≈’Ë¬‡ªìπ 8, 7 ·≈– 9 §–·ππ µ“¡≈”¥—∫ §à“‡©≈’Ë¬‡≈¢§≥‘µ¢Õß

§–·ππ Õ∫¢Õßπ—°‡√’¬π∑—Èß “¡ÀâÕßµ√ß°—∫¢âÕ„¥

X√«¡ N X N X N X

N N N1 2 3

1 2 3

1 2 3+ ++ +

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59·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

13. ®ß‡¢’¬π Àπâ“¢âÕ§«“¡∑’Ë∂Ÿ° ·≈–‡¢’¬π Àπâ“¢âÕ§«“¡∑’Ëº‘¥

............. (1) „π¢âÕ¡Ÿ≈™ÿ¥‡¥’¬«°—π §à“‡©≈’Ë¬‡≈¢§≥‘µ ∞“ππ‘¬¡ ·≈–¡—∏¬∞“π ¬àÕ¡‡ªìπ

§à“‡¥’¬«°—π

............. (2) ∞“ππ‘¬¡‡ªìπ§à“°≈“ß¢Õß¢âÕ¡Ÿ≈ ‡À¡“–°—∫¢âÕ¡Ÿ≈∑’Ë‰¡à‡ªìπµ—«‡≈¢À√◊Õ

¢âÕ¡Ÿ≈‡™‘ß§ÿ≥¿“æ

............. (3) ∞“ππ‘¬¡¢Õß¢âÕ¡Ÿ≈™ÿ¥Àπ÷ËßÕ“®¡’¡“°°«à“ 1 §à“°Á‰¥â

............. (4) ¢âÕ¡Ÿ≈ 2, 15, 17, 16, 19, 18, 65 §«√À“§à“°≈“ß‚¥¬«‘∏’§à“‡©≈’Ë¬‡≈¢§≥‘µ

............. (5) ∂â“¡’¢âÕ¡Ÿ≈ 101 µ—« ¡—∏¬∞“π®–¡’µ”·Àπàß‡ªìπ 51 ‡¡◊ËÕ‡√’¬ß¢âÕ¡Ÿ≈®“°

¡“°‰ªπâÕ¬

............. (6) ∂â“¡’¢âÕ¡Ÿ≈ 6 µ—« ¡—∏¬∞“π§◊Õ¢âÕ¡Ÿ≈µ—«∑’Ë 3 ·≈– 4

............. (7) §à“‡©≈’Ë¬‡≈¢§≥‘µ¢Õß¢âÕ¡Ÿ≈ 5 µ—« À“‰¥â®“°

¢âÕ¡Ÿ≈µ—«∑’Ë ¢âÕ¡Ÿ≈µ—«∑’Ë 1 + 5

5

............. (8) ¢âÕ¡Ÿ≈ 15, 10, 8, 12, 9 ¡—∏¬∞“π§◊Õ 8

............. (9) ¢âÕ¡Ÿ≈ 13, 14, 15, 16, 17 ‡ªìπ¢âÕ¡Ÿ≈∑’Ë‰¡à¡’∞“ππ‘¬¡

............. (10) ∂â“¡’¢âÕ¡Ÿ≈‡æ’¬ß 3 µ—« ®–‰¡à “¡“√∂À“∞“ππ‘¬¡‰¥â

2. °“√π”‡ πÕ¢âÕ¡Ÿ≈

°‘®°√√¡∑’Ë 2.1

2.1 °“√π”‡ πÕ¢âÕ¡Ÿ≈„π√Ÿªµ“√“ß

1. π—°‡√’¬π 16 §π ¡’πÈ”Àπ—°‡ªìπ°‘‚≈°√—¡ ¥—ßπ’È

60 44 47 50 54 60 70 60

54 50 60 47 50 44 60 70

60 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

‡¢’¬π¢âÕ¡Ÿ≈„π√Ÿªµ“√“ß‰¥â¥—ßπ’È

πÈ”Àπ—° (°‘‚≈°√—¡) ®”π«ππ—°‡√’¬π (§π)

44 2

47

50

54

60

70

√«¡

®“°µ“√“ßπ”‡ πÕ¢âÕ¡Ÿ≈ ®ßµÕ∫§”∂“¡µàÕ‰ªπ’È

(1) π—°‡√’¬π∑’Ë¡’πÈ”Àπ—°¡“°∑’Ë ÿ¥¡’°’Ë§π ·≈–Àπ—°‡∑à“‰√

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(2) π—°‡√’¬π∑’Ë¡’πÈ”Àπ—°πâÕ¬∑’Ë ÿ¥¡’°’Ë§π ·≈–Àπ—°‡∑à“‰√

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(3) π—°‡√’¬π∑’Ë¡’πÈ”Àπ—° 47 °‘‚≈°√—¡ §‘¥‡ªìπ°’Ë‡ªÕ√å‡´Áπµå¢Õßπ—°‡√’¬π∑—ÈßÀ¡¥

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(4) π—°‡√’¬π∑’Ë¡’πÈ”Àπ—°µ—Èß·µà 50 °‘‚≈°√—¡¢÷Èπ‰ª §‘¥‡ªìπ°’Ë‡ªÕ√å‡´Áπµå¢Õßπ—°‡√’¬π

∑—ÈßÀ¡¥

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61·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

2. ®“°µ“√“ßµàÕ‰ªπ’È · ¥ß∂÷ß§–·ππ Õ∫«‘™“§≥‘µ»“ µ√å¢Õßπ—°‡√’¬π 100 §π ‚¥¬

·∫àß§–·ππÕÕ°‡ªìπ™à«ßÊ ‰¥â¥—ßπ’È

§–·ππ ®”π«ππ—°‡√’¬π

30-39 11

40-49 12

50-59 16

60-69 23

70-79 17

80-89 15

90-99 6

√«¡ 100

„Àâπ—°‡√’¬πµÕ∫§”∂“¡µàÕ‰ªπ’È

(1) π—°‡√’¬π∑’Ë‰¥â§–·ππ 40-49 §–·ππ ¡’ ................................................................... §π

(2) π—°‡√’¬π∑’Ë‰¥â§–·ππµ—Èß·µà 50-79 §–·ππ ¡’ ......................................................... §π

(3) ∂â“π—°‡√’¬π Õ∫‰¥â§–·πππâÕ¬°«à“ 50 §–·ππ ∂◊Õ«à“ Õ∫µ° ¥—ßπ—Èπ ¡’π—°‡√’¬π

Õ∫µ° ....................................................................................................................... §π

(4) π—°‡√’¬π∑’Ë Õ∫‰¥â 80 §–·ππ¢÷Èπ‰ª ¡’ ...................................................................... §π

§‘¥‡ªìπ .................................................................. ‡ªÕ√å‡´Áπµå¢Õßπ—°‡√’¬π∑—ÈßÀ¡¥

°‘®°√√¡∑’Ë 2.2

1. ®“°°“√ ”√«®π—°‡√’¬π‚√ß‡√’¬πÀπ÷Ëß∑’Ë™Õ∫°’Ã“øÿµ∫Õ≈ ®”·π°‰¥â¥—ßπ’È

¡. 1 450 §π ¡. 3 625 §π ¡. 5 400 §π¡. 2 500 §π ¡. 4 700 §π ¡. 6 550 §π

2.2 °“√π”‡ πÕ¢âÕ¡Ÿ≈¥â«¬·ºπ¿Ÿ¡‘√Ÿª¿“æ

62 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

„™â√Ÿª¿“æ 1 √Ÿª ·∑ππ—°‡√’¬π 100 §π ®–‡¢’¬π·ºπ¿Ÿ¡‘√Ÿª¿“æ‰¥â¥—ßπ’È

¡. 1

¡. 2

¡. 3

¡. 4

¡. 5

¡. 6

®“°·ºπ¿Ÿ¡‘√Ÿª¿“æ¢â“ßµâπ „Àâπ—°‡√’¬πµÕ∫§”∂“¡µàÕ‰ªπ’È

(1) π—°‡√’¬π√–¥—∫™—Èπ„¥∑’Ë™Õ∫°’Ã“øÿµ∫Õ≈¡“°∑’Ë ÿ¥

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(2) ®”π«ππ—°‡√’¬π∑’Ëπ”¡“‡ πÕ¢âÕ¡Ÿ≈¡’‡∑à“‰√

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(3) π—°‡√’¬π™—Èπ ¡.2 §‘¥‡ªìπ√âÕ¬≈–‡∑à“‰√¢Õßπ—°‡√’¬π∑—ÈßÀ¡¥

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(4) π—°‡√’¬π 100 §π ·∑π¥â«¬√Ÿª¿“æ 1 √Ÿª π—°‡√’¬π ¡.5 ®–·∑π¥â«¬√Ÿª¿“æ

ª√–¡“≥°’Ë√Ÿª

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2. °”Àπ¥·ºπ¿Ÿ¡‘√Ÿª¿“æ „Àâπ—°‡√’¬π»÷°…“·≈â«µÕ∫§”∂“¡

®”π«π‡ß‘π∑’Ë¢“¬Õ“À“√‰¥â·µà≈–«—π∑’Ë‡ªî¥∑”°“√

«—π®—π∑√å

«—πÕ—ß§“√

«—πæÿ∏

«—πæƒÀ— ∫¥’

«—π»ÿ°√å

√Ÿª¿“æ 1 √Ÿª ·∑π®”π«π®“π 200 „∫

63·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(1) «—π„¥¢“¬Õ“À“√‰¥âπâÕ¬∑’Ë ÿ¥ °’Ë®“π

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(2) «—πæƒÀ— ∫¥’¢“¬Õ“À“√‰¥â¡“°°«à“«—πæÿ∏‡∑à“„¥ ∂â“Õ“À“√®“π≈– 20 ∫“∑

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(3) «—πÕ—ß§“√¢“¬Õ“À“√‰¥â°’Ë®“π

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(4) «—π»ÿ°√å¢“¬Õ“À“√‰¥â°’Ë®“π

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(5) √“¬‰¥â‚¥¬‡©≈’Ë¬·µà≈–«—π‡ªìπ‡∑à“„¥

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°‘®°√√¡∑’Ë 2.3

1. ·ºπ¿Ÿ¡‘·∑àß· ¥ß®”π«π√∂¬πµå®”·π°µ“¡ ’√∂„π°√ÿß‡∑æ¡À“π§√√Õ∫ªï∑’Ëºà“π¡“

®ßµÕ∫§”∂“¡µàÕ‰ªπ’È

7

6

5

4

3

2

1

øÑ“ ‡∑“ ∫√Õπ å∑Õß ∫√Õπ å‡ß‘π ·¥ß ¥”

®”π«π√∂ (À¡◊Ëπ§—π)

’

2.3 °“√π”‡ πÕ¢âÕ¡Ÿ≈¥â«¬·ºπ¿Ÿ¡‘·∑àß

64 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(1) √∂ ’Õ–‰√‡ªìπ∑’Ëπ‘¬¡¡“°∑’Ë ÿ¥ ·≈–¡’°’Ë§—π

...........................................................................................................................................

(2) √∂ ’Õ–‰√‡ªìπ∑’Ëπ‘¬¡√Õß≈ß¡“Õ—π¥—∫Àπ÷Ëß ·≈–¡’°’Ë§—π

...........................................................................................................................................

(3) ¡’√∂ ’·¥ß¡“°°«à“√∂ ’øÑ“°’Ë§—π

...........................................................................................................................................

(4) √∂ ’‡∑“·≈–√∂ ’¥”√«¡°—π§‘¥‡ªìπ√âÕ¬≈–‡∑à“‰√¢Õß√∂∑—ÈßÀ¡¥

...........................................................................................................................................

2. ·ºπ¿Ÿ¡‘·∑àß· ¥ß¬Õ¥¢“¬ ∫Ÿà·≈–·ªÑß¢Õß∫√‘…—∑Àπ÷Ëßµ—Èß·µà‡¥◊Õπ¡°√“§¡-‡¡…“¬π

¥—ßπ’È

12

10

8

6

4

2

10

8

5

3

8

7.5

11.512

¡°√“§¡ °ÿ¡¿“æ—π∏å ¡’π“§¡ ‡¡…“¬π

·∑π ∫Ÿà ·∑π·ªÑß

¬Õ¥¢“¬ (≈â“π∫“∑)

‡¥◊Õπ

®ßµÕ∫§”∂“¡µàÕ‰ªπ’È

(1) ‡¥◊Õπ„¥∑’Ë¡’√“¬‰¥â·µ°µà“ß°—π¡“°∑’Ë ÿ¥

...........................................................................................................................................

65·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(2) ‡¥◊Õπ„¥√“¬‰¥â®“°°“√¢“¬ ∫Ÿà·≈–·ªÑß„°≈â‡§’¬ß°—π¡“°∑’Ë ÿ¥

...........................................................................................................................................

(3) ‡¥◊Õπ¡°√“§¡¢“¬º≈‘µ¿—≥±å∑—Èß 2 ™π‘¥ √«¡‡ªìπ‡ß‘π‡∑à“„¥

...........................................................................................................................................

(4) ‡¥◊Õπ„¥∫â“ß∑’Ë¢“¬ ∫Ÿà¥’°«à“·ªÑß

...........................................................................................................................................

(5) „π√Õ∫ 4 ‡¥◊Õπ √“¬‰¥â√«¡∑—ÈßÀ¡¥‡ªìπ‡∑à“‰√

...........................................................................................................................................

(6) „π‡¥◊Õπ°ÿ¡¿“æ—π∏å√“¬‰¥â§‘¥‡ªìπ√âÕ¬≈–‡∑à“‰√¢Õß√“¬‰¥â∑—ÈßÀ¡¥

...........................................................................................................................................

°‘®°√√¡∑’Ë 2.4

2.4 °“√π”‡ πÕ¢âÕ¡Ÿ≈¥â«¬·ºπ¿Ÿ¡‘√Ÿª«ß°≈¡

1. ™“¬§πÀπ÷Ëß‰¥â√—∫‡ß‘π‡¥◊Õπ ‡¥◊Õπ≈– 10,000 ∫“∑ ¡’√“¬®à“¬„π√Õ∫‡¥◊Õπ∑’Ëºà“π¡“

¥—ßµ“√“ß¥—ßπ’È

√“¬®à“¬ ®”π«π‡ß‘π (∫“∑)

§à“Õ“À“√ 4,000

§à“‡ ◊ÈÕºâ“ 1,500

§à“ºàÕπ∫â“π 2,000

Ω“°∏π“§“√ 500

‡∫Á¥‡µ≈Á¥ 2,000

√«¡ 10,000

66 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

§à“Õ“À“√§‘¥‡ªìπ 400010000

100% ....................................................................................

¢π“¥¢Õß¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß 40 3.6 ............................................................. Õß»“

§à“‡ ◊ÈÕºâ“§‘¥‡ªìπ ......................................................................................................................

¢π“¥¢Õß¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß .............................................................................................

§à“ºàÕπ∫â“π§‘¥‡ªìπ .................................................................................................................

¢π“¥¢Õß¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß .............................................................................................

Ω“°∏π“§“√§‘¥‡ªìπ ................................................................................................................

¢π“¥¢Õß¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß ............................................................................................

‡∫Á¥‡µ≈Á¥§‘¥‡ªìπ ......................................................................................................................

¢π“¥¢Õß¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß .............................................................................................

„Àâπ—°‡√’¬π‡µ‘¡«ß°≈¡„Àâ ¡∫Ÿ√≥å

67·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

2. ®“°°“√ ”√«®·¡à∫â“π°≈ÿà¡Àπ÷Ëß‡°’Ë¬«°—∫°“√‡≈◊Õ°√ ™“µ‘¢ÕßÕ“À“√ ª√“°Ø¥—ß

·ºπ¿Ÿ¡‘√Ÿª«ß°≈¡ ¥—ßπ’È

À«“π 10%

®◊¥ 12%

‡ª√’È¬« 40% ‡ºÁ¥ 18%

‡§Á¡ 20%


(1) ∂â“¡’·¡à∫â“π 300 §π ®–¡’·¡à∫â“π∑’Ë™Õ∫√ ‡ºÁ¥°’Ë§π

...........................................................................................................................................

(2) ∂â“¡’·¡à∫â“π™Õ∫Õ“À“√√ ®◊¥ 18 §π ®–¡’·¡à∫â“π™Õ∫√ À«“π°’Ë§π

...........................................................................................................................................

(3) ¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß¢Õß·¡à∫â“π∑’Ë™Õ∫√ ‡ª√’È¬«¡’¢π“¥°’ËÕß»“

...........................................................................................................................................

(4) ∂â“¡’·¡à∫â“π™Õ∫√ ‡§Á¡ 40 §π ®–¡’·¡à∫â“π™Õ∫√ ‡ª√’È¬«°’Ë§π

...........................................................................................................................................

(5) ¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß¢Õß·¡à∫â“π∑’Ë™Õ∫√ ®◊¥πâÕ¬°«à“¡ÿ¡∑’Ë®ÿ¥»Ÿπ¬å°≈“ß¢Õß·¡à∫â“π

™Õ∫√ ‡§Á¡‡∑à“‰√

...........................................................................................................................................

(6) ∂â“¡’·¡à∫â“π∑—ÈßÀ¡¥ 500 §π ®–¡’·¡à∫â“π™Õ∫Õ“À“√√ ‡ª√’È¬«¡“°°«à“√ ‡ºÁ¥°’Ë§π

...........................................................................................................................................

68 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

1. „Àâπ—°‡√’¬πæ‘®“√≥“°√“ø‡ âπµàÕ‰ªπ’È

°√“ø‡ âπ· ¥ßº≈°“√ Õ∫¬àÕ¬«‘™“¿“…“‰∑¬¢Õßπ—°‡√’¬π

°‘®°√√¡∑’Ë 2.5

2.5 °“√π”‡ πÕ¢âÕ¡Ÿ≈¥â«¬°√“ø‡ âπ

20

18

16

14

12

10

8

6

4

2

§–·ππ

§√—Èß∑’Ë

ÿ¥“¡“≈’ ¡»√’

1 2 3 4 5 6

®“°°√“ø ®ßµÕ∫§”∂“¡µàÕ‰ªπ’È

(1) „π°“√ Õ∫¬àÕ¬§√—Èß ÿ¥∑â“¬ „§√ Õ∫‰¥â§–·ππ¡“°∑’Ë ÿ¥ „§√ Õ∫‰¥â§–·πππâÕ¬

∑’Ë ÿ¥

...........................................................................................................................................

(2) „§√ Õ∫‰¥â§–·ππ√«¡¡“°∑’Ë ÿ¥ ·≈– Õ∫‰¥â°’Ë§–·ππ

...........................................................................................................................................

(3) π—°‡√’¬π·µà≈–§π‰¥â§–·ππ√«¡§π≈–°’Ë§–·ππ æ√âÕ¡∑—Èß®—¥≈”¥—∫º≈°“√ Õ∫

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

69·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

2. ®ß„™â°√“øµàÕ‰ªπ’ÈµÕ∫§”∂“¡

∂‘µ‘¢Õß®”π«πª≈“∑Ÿ∑’Ë®—∫‰¥âµ—Èß·µàªï æ.». 2543-2547

30

25

20

15

10

5

0

®”π«πª≈“ (≈â“πµ—«)

ªï æ.». 2543 2544 2545 2546 2547

20

18

25

20

17

(1) „π™à«ßªï„¥∑’Ë®—∫ª≈“∑Ÿ‰¥â‡æ‘Ë¡¢÷Èπ¡“°∑’Ë ÿ¥

...........................................................................................................................................

(2) „πªï„¥∑’Ë®—∫ª≈“∑Ÿ≈¥≈ß®“°ªï°àÕπ¡“°∑’Ë ÿ¥

...........................................................................................................................................

(3) ªï„¥®—∫ª≈“∑Ÿ‰¥âπâÕ¬∑’Ë ÿ¥

...........................................................................................................................................

(4) ®”π«πª≈“∑Ÿ∑’Ë®—∫‰¥â„πªï æ.». 2545 ‡æ‘Ë¡¢÷Èπ®“°ªï æ.». 2544 ‡∑à“„¥ ·≈–§‘¥

‡ªìπ√âÕ¬≈–‡∑à“„¥

...........................................................................................................................................

(5) µ≈Õ¥√–¬–‡«≈“ 5 ªï ®—∫ª≈“∑Ÿ‰¥â∑—ÈßÀ¡¥‡∑à“‰√

...........................................................................................................................................

(6) ‚¥¬‡©≈’Ë¬·≈â«®—∫ª≈“∑Ÿ‰¥âªï≈–‡∑à“„¥

...........................................................................................................................................

70 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

1. „π°“√™—ËßπÈ”Àπ—°‡ªìπ°‘‚≈°√—¡¢Õßπ—°‡√’¬π 50 §π ‰¥âº≈¥—ßπ’È

38 64 50 32 44 25 54 66 46 70

40 26 38 70 63 54 27 57 58 58

68 43 36 48 35 39 49 65 41 45

46 45 42 47 52 53 40 28 29 54

61 47 35 42 50 56 58 39 48 43

®“°µ“√“ß·®°·®ß§«“¡∂’Ë „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß„Àâ ¡∫Ÿ√≥å

Õ—πµ√¿“§™—Èπ √Õ¬¢’¥§–·ππ §«“¡∂’Ë

25-32 ......................................... .......................

33-40 ......................................... .......................

41-48 ......................................... .......................

49-56 ......................................... .......................

57-64 ......................................... .......................

65-72 ......................................... .......................

√«¡ .......................

3. ¢âÕ¡Ÿ≈∑’Ë·®°·®ß§«“¡∂’Ë

°‘®°√√¡∑’Ë 3.1

3.1 µ“√“ß·®°·®ß§«“¡∂’Ë

71·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2


(1) §«“¡°«â“ß¢Õß·µà≈–Õ—πµ√¿“§™—Èπ‡ªìπ‡∑à“‰√

...........................................................................................................................................

(2) Õ—πµ√¿“§™—Èπ„¥¡’§«“¡∂’Ë¡“°∑’Ë ÿ¥

...........................................................................................................................................

(3) ¡’π—°‡√’¬π°’Ë§π∑’Ë¡’πÈ”Àπ—°Õ¬Ÿà„π™à«ß 41-64

...........................................................................................................................................

(4) Õ—πµ√¿“§™—Èπ∑’Ë¡’§ππâÕ¬∑’Ë ÿ¥¡’°’Ë§π

...........................................................................................................................................

(5) ¡’π—°‡√’¬π∑’Ë¡’πÈ”Àπ—°„π™à«ß 65-72 °‘‚≈°√—¡ §‘¥‡ªìπ°’Ë‡ªÕ√å‡´Áπµå¢Õßπ—°‡√’¬π

∑—ÈßÀ¡¥

...........................................................................................................................................

2. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë· ¥ßº≈°“√ Õ∫«‘™“§≥‘µ»“ µ√å¢Õßπ—°‡√’¬π 80 §π

´÷Ëß¡’§–·ππ‡µÁ¡ 120 §–·ππ

§–·ππ ®”π«ππ—°‡√’¬π (§π)

31-45 8

46-60 17

61-75 10

76-90 25

91-105 15

106-120 5

√«¡ 80


(1) Õ—πµ√¿“§™—Èπ∑’Ë¡’§«“¡∂’Ë¡“°∑’Ë ÿ¥

...........................................................................................................................................

72 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(2) §«“¡°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ 61-75 ‡ªìπ‡∑à“‰√

...........................................................................................................................................

(3) ®ÿ¥°÷Ëß°≈“ß™—Èπ¢ÕßÕ—πµ√¿“§™—Èπ 46-60

...........................................................................................................................................

(4) ®”π«ππ—°‡√’¬π∑’Ë Õ∫‰¥â§–·ππµË”°«à“ 61 §–·ππ §‘¥‡ªìπ√âÕ¬≈–‡∑à“‰√¢Õß

π—°‡√’¬π∑—ÈßÀ¡¥

...........................................................................................................................................

(5) ®”π«ππ—°‡√’¬π∑’Ë Õ∫‰¥â 91-105 §–·ππ §‘¥‡ªìπ√âÕ¬≈–‡∑à“‰√¢Õßπ—°‡√’¬π

∑’Ë Õ∫‰¥â 76-90 §–·ππ

...........................................................................................................................................

(6) Õ—πµ√¿“§™—Èπ„¥¡’π—°‡√’¬π Õ∫‰¥â®”π«ππâÕ¬∑’Ë ÿ¥

...........................................................................................................................................

3. Õ“¬ÿ (ªï) ¢ÕßºŸâ¡“„™â∫√‘°“√ÀâÕß ¡ÿ¥ª√–™“™π·ÀàßÀπ÷Ëß‡ªìπ¥—ßπ’È

12 15 18 35 32 40 27 16 10 17

16 20 8 14 12 9 25 25 37 24

15 17 13 16 10 12 40 50 45 29

22 19 15 15 17 13 27 32 55 30


(1) Õ“¬ÿπâÕ¬∑’Ë ÿ¥¢ÕßºŸâ¡“„™â∫√‘°“√ÀâÕß ¡ÿ¥

...........................................................................................................................................

(2) Õ“¬ÿ Ÿß ÿ¥¢ÕßºŸâ¡“„™â∫√‘°“√ÀâÕß ¡ÿ¥

...........................................................................................................................................

(3) æ‘ —¬ ..............................................................................................................................

(4) ∂â“°”Àπ¥„Àâ§«“¡°«â“ß∑ÿ°™—Èπ‡∑à“°—π ·≈–µâÕß°“√ √â“ßµ“√“ß·®°·®ß§«“¡∂’Ë 1 ™—Èπ

®ßÀ“§«“¡°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ

...........................................................................................................................................

73·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(5) „Àâπ—°‡√’¬π √â“ßµ“√“ß·®°·®ß§«“¡∂’Ë ‚¥¬‡√‘Ë¡®“°Õ“¬ÿπâÕ¬∑’Ë ÿ¥

Õ“¬ÿ (ªï) √Õ¬¢’¥§–·ππ §«“¡∂’Ë

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

√«¡ .......................

(6) ™à«ßÕ“¬ÿ‡∑à“‰√∑’Ë¡“„™â∫√‘°“√ÀâÕß ¡ÿ¥¡“°∑’Ë ÿ¥

...........................................................................................................................................

(7) ™à«ßÕ“¬ÿ 32-39 ªï ¡’ºŸâ„™âÀâÕß ¡ÿ¥§‘¥‡ªìπ°’Ë‡ªÕ√å‡´Áπµå¢ÕßºŸâ„™â∫√‘°“√∑—ÈßÀ¡¥

...........................................................................................................................................

4. „π°“√ Õ∫«‘™“¿“…“‰∑¬¢Õßπ—°‡√’¬π 30 §π ∑”§–·ππ‰¥â¥—ßπ’È

46 50 70 60 76 87 97 83 93 65

73 75 76 71 71 59 79 48 70 78

78 94 65 76 71 60 67 70 83 98


(1) π—°‡√’¬π∑’Ë‰¥â§–·ππ Ÿß ÿ¥·≈–µË” ÿ¥‡ªìπ‡∑à“‰√

...........................................................................................................................................

(2) æ‘ —¬ ..............................................................................................................................

(3) ∂â“µâÕß°“√ √â“ßµ“√“ß·®°·®ß§«“¡∂’Ë„Àâ¡’§«“¡°«â“ß 9 ∑ÿ°™—Èπ ®–µâÕß √â“ß

µ“√“ß°’Ë™—Èπ

...........................................................................................................................................

74 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

(4) „Àâπ—°‡√’¬π √â“ßµ“√“ß·®°·®ß§«“¡∂’Ë‚¥¬‡√‘Ë¡µâπ¥â«¬ 46

§–·ππ √Õ¬¢’¥§–·ππ §«“¡∂’Ë

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

................................. ......................................... .......................

√«¡ .......................

5. „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß„Àâ ¡∫Ÿ√≥å

§«“¡ Ÿß (´¡.) ¢Õ∫≈à“ß-¢Õ∫∫π ®ÿ¥°÷Ëß°≈“ß™—Èπ

145-149 144.5-149.5145 149

2 +

147

150-154 .................................... ...............................

155-159 .................................... ...............................

160-164 .................................... ...............................

165-169 .................................... ...............................

6. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë¢Õß§«“¡ Ÿß¢Õßπ—°‡√’¬πÀâÕßÀπ÷Ëß „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß

„Àâ ¡∫Ÿ√≥å

§«“¡ Ÿß (´¡.) ¢Õ∫≈à“ß-¢Õ∫∫π ®ÿ¥°÷Ëß°≈“ß™—Èπ §«“¡°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ

µË”°«à“ 150 ¢Õ∫∫π§◊Õ 149.5 - -

150-159 .............................. ........................ ...............................................

160-169 .............................. ........................ ...............................................

170-179 .............................. ........................ ...............................................

µ—Èß·µà 180 ¢÷Èπ‰ª .............................. ........................ ...............................................

75·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

7. „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß„Àâ ¡∫Ÿ√≥å

™à«ß§–·ππ ¢Õ∫≈à“ß-¢Õ∫∫π ®ÿ¥°÷Ëß°≈“ß™—Èπ §«“¡°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ

50-54 49.5-54.550 54

2+

52 5

55-59 .............................. ........................ ...............................................

60-64 .............................. ........................ ...............................................

65-69 .............................. ........................ ...............................................

70-74 .............................. ........................ ...............................................

75-79 .............................. ........................ ...............................................

8. „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß„Àâ ¡∫Ÿ√≥å

πÈ”Àπ—° (°°.) §«“¡∂’Ë §«“¡∂’Ë – ¡ ¢Õ∫≈à“ß-¢Õ∫∫π

40-49 3 3 ......................................

50-59 12 15 ......................................

60-69 10 25 ......................................

70-79 7 ............................... ......................................

80-89 3 ................................ ......................................

√«¡ ........................

9. „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß„Àâ ¡∫Ÿ√≥å

πÈ”Àπ—° (°°.) §«“¡∂’Ë §«“¡∂’Ë – ¡ ¢Õ∫≈à“ß-¢Õ∫∫π ®ÿ¥°÷Ëß°≈“ß™—Èπ

40-49.9 20 .................... ................................ ............................

50-59.9 17 .................... ................................ ............................

60-69.9 8 .................... ................................ ............................

70-79.9 2 .................... ................................ ............................

80-89.9 2 .................... ................................ ............................

90-99.9 1 .................... ................................ ............................

√«¡ ...................

76 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

10. „Àâπ—°‡√’¬π‡µ‘¡µ“√“ß„Àâ ¡∫Ÿ√≥å

à«π Ÿß (´¡.) §«“¡∂’Ë §«“¡∂’Ë – ¡ ¢Õ∫≈à“ß-¢Õ∫∫π ®ÿ¥°÷Ëß°≈“ß™—Èπ

180-184 5 .................... ................................ ............................

175-179 3 .................... ................................ ............................

170-174 8 .................... ................................ ............................

165-169 10 .................... ................................ ............................

160-164 12 .................... ................................ ............................

155-159 7 .................... ................................ ............................

150-154 5 .................... ................................ ............................

√«¡ 50

11. „π°“√«—¥§«“¡ Ÿß¢Õßπ—°‡√’¬π°≈ÿà¡Àπ÷Ëß ‰¥â§«“¡ Ÿß∑—ÈßÀ¡¥‡ªìπ¥—ßπ’È

170 165 173 148 161 157 152 154 163 150

147 145 153 173 145 153 166 165 172 155

169 161 149 154 172 164 171 171 160 147

159 168 169 159 147 149 172 154 171 174

®ß √â“ßµ“√“ß·®°·®ß§«“¡∂’Ë„Àâ§«“¡°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ∑ÿ°™—Èπ‡ªìπ 5 ‚¥¬‡√‘Ë¡µâπ

§à“µË” ÿ¥ æ√âÕ¡∑—Èß∫Õ°¢Õ∫≈à“ß ¢Õ∫∫π ·≈–®ÿ¥°÷Ëß°≈“ß™—Èπ

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

77·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

1. ®ß‡¢’¬πŒ‘ ‚∑·°√¡·≈–√ŸªÀ≈“¬‡À≈’Ë¬¡¢Õß§«“¡∂’Ë®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È

πÈ”Àπ—° (°°.) ®”π«π§π

45-49 5

50-54 7

55-59 10

60-64 13

65-69 11

70-74 4

√«¡ 50

§«“¡ Ÿß (´¡.) √Õ¬¢’¥§–·ππ §«“¡∂’Ë ¢Õ∫≈à“ß-¢Õ∫∫π ®ÿ¥°÷Ëß°≈“ß™—Èπ

°‘®°√√¡∑’Ë 3.2

3.2 Œ‘ ‚∑·°√¡·≈–√ŸªÀ≈“¬‡À≈’Ë¬¡¢Õß§«“¡∂’Ë

78 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2


§«“¡ Ÿß (´¡.) ®”π«ππ—°‡√’¬π

145-149 5

150-154 12

155-159 7

160-164 11

165-169 4

79·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

3. ®ß‡¢’¬π√ŸªÀ≈“¬‡À≈’Ë¬¡¢Õß§«“¡∂’Ë®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È (®“°¢âÕ 1)

πÈ”Àπ—° (°°.) ®”π«π§π ®ÿ¥°÷Ëß°≈“ß™—Èπ

45-49 5 47

50-54 7 52

55-59 10 57

60-64 13 62

65-69 11 67

70-74 4 72

√«¡ 50

80 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2


§«“¡ Ÿß (´¡.) ®”π«ππ—°‡√’¬π (§π) ¢Õ∫≈à“ß-¢Õ∫∫π

110-119 6 ...................................

120-129 7 ...................................

130-139 12 ...................................

140-149 10 ...................................

150-159 8 ...................................

160-169 3 ...................................

√«¡ 46

81·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

1. ®ßÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ®“°µ“√“ß·®°·®ß§«“¡∂’Ë¢ÕßÕ“¬ÿ°“√„™âß“π¢ÕßÀ≈Õ¥‰ø„π

°“√ ”√«®‡ªìπ¥—ßπ’È

Õ“¬ÿ°“√„™âß“π (™¡.) §«“¡∂’Ë (f) ®ÿ¥°÷Ëß°≈“ß™—Èπ (X) fX

100-104 10 ................................ ....................................

105-109 22 ................................ ....................................

110-114 85 ................................ ....................................

115-119 92 ................................ ....................................

120-124 38 ................................ ....................................

125-129 40 ................................ ....................................

130-134 13 ................................ ....................................

√«¡ (N) 300 ....................................

X fX

N∑

....................................................................................

....................................................................................

4. °“√À“§à“°≈“ß¢Õß¢âÕ¡Ÿ≈∑’Ë·®°·®ß§«“¡∂’Ë

°‘®°√√¡∑’Ë 4.1

4.1 §à“‡©≈’Ë¬‡≈¢§≥‘µ

82 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

«‘∏’≈—¥

Õ“¬ÿ°“√„™âß“π (™¡.) §«“¡∂’Ë (f) d fd

100-104 10 ................................ ....................................

105-109 22 ................................ ....................................

110-114 85 ................................ ....................................

115-119 92 0 ....................................

120-124 38 ................................ ....................................

125-129 40 ................................ ....................................

130-134 13 ................................ ....................................

√«¡ N 300 ....................................

a .................................... (®ÿ¥°÷Ëß°≈“ß™—Èπ∑’Ë d 0)

i ....................................................................................

X ....................................................................................

....................................................................................

....................................................................................

....................................................................................

83·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

2. „π°“√ ”√«®√“¬‰¥âµàÕ —ª¥“Àå¢Õß 100 §√Õ∫§√—« · ¥ß¢âÕ¡Ÿ≈‚¥¬µ“√“ß·®°·®ß

§«“¡∂’ËµàÕ‰ªπ’È

√“¬‰¥âµàÕ —ª¥“Àå®”π«π§√Õ∫§√—« (f) d fd

(∫“∑)

1,001-2,000 18 .................... ................................

2,001-3,000 17 .................... ................................

3,001-4,000 25 .................... ................................

4,001-5,000 10 .................... ................................

5,001-6,000 20 .................... ................................

6,001-7,000 10 .................... ................................

√«¡ 100 ................................

a .................................... X ...................................................

i .................................... .........................................................

.........................................................

.........................................................

3. ®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È ®ßÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ

§–·ππ §«“¡∂’Ë (f) ®ÿ¥°÷Ëß°≈“ß™—Èπ (X) fX

20-29 4

20 292

24.5 4 24.5 98

30-39 6 ................................ ....................................

40-49 12 ................................ ....................................

50-59 8 ................................ ....................................

60-69 5 ................................ ....................................

........................ ....................................

84 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

X ....................................................................................

....................................................................................

....................................................................................

4. ®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È ®ßÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ

§–·ππ §«“¡∂’Ë (f) ®ÿ¥°÷Ëß°≈“ß™—Èπ (X) fX

30-34 4 ................................ ....................................

35-39 8 ................................ ....................................

40-44 12 ................................ ....................................

45-49 7 ................................ ....................................

50-54 5 ................................ ....................................

........................ ....................................

X ....................................................................................

....................................................................................

....................................................................................

5. ®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È ®ßÀ“§à“‡©≈’Ë¬‡≈¢§≥‘µ‚¥¬«‘∏’≈—¥

§–·ππ §«“¡∂’Ë (f) d fd

111-120 4 ................................ ....................................

121-130 5 ................................ ....................................

131-140 7 ................................ ....................................

141-150 13 ................................ ....................................

151-160 20 ................................ ....................................

161-170 8 ................................ ....................................

171-180 3 ................................ ....................................

N ......... ....................................

85·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

a .................................... X ...................................................

i .................................... ...................................................

...................................................

= .............................................

°‘®°√√¡∑’Ë 4.2

4.2 ¡—∏¬∞“π

1. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë§«“¡ Ÿß¢Õßπ—°‡√’¬π™—Èπª√–∂¡»÷°…“ªï∑’Ë 4 ¢Õß‚√ß‡√’¬π

·ÀàßÀπ÷Ëß ®ßÀ“¡—∏¬∞“π

§«“¡ Ÿß (´¡.) ®”π«ππ—°‡√’¬π (f) §«“¡∂’Ë – ¡ (F)

131-135 8 ...................................

136-140 12 ...................................

141-145 15 ...................................

146-150 6 ...................................

151-155 5 ...................................

N 46

µ”·Àπàß N2

................................ Med L I

N F

F F2 1

2 1

L ................................ ..............................................

I ................................ ..............................................

F1 ................................ ..............................................

F2 ................................ ..............................................

86 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

2. ®“°µ“√“ß·®°·®ß§«“¡∂’ËπÈ”Àπ—°¢Õßπ—°‡√’¬π ®ßÀ“¡—∏¬∞“π

πÈ”Àπ—° (°°.) ®”π«π§π (f) ...................................

40-49 5 ...................................

50-59 15 ...................................

60-69 20 ...................................

70-79 12 ...................................

80-89 5 ...................................

90-99 3 ...................................

N .................

µ”·Àπàß N2

................................ Med L I

N F

F F2 1

2 1

L ................................ ..............................................

I ................................ ..............................................

F1 ................................ ..............................................

F2 ................................ ..............................................

3. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë ®ßÀ“¡—∏¬∞“π

™à«ß§–·ππ §«“¡∂’Ë (f) §«“¡∂’Ë – ¡ (F)

60-65 3 ...................................

66-71 7 ...................................

72-77 6 ...................................

78-83 14 ...................................

84-89 10 ...................................

90-95 4 ...................................

N .................

87·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

µ”·Àπàß N2

................................ Med L I

N F

F F2 1

2 1

L ................................ ..............................................

I ................................ ..............................................

F1 ................................ ..............................................

F2 ................................ ..............................................

4. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë ®ßÀ“¡—∏¬∞“π

™à«ß§–·ππ §«“¡∂’Ë (f) §«“¡∂’Ë – ¡ (F)

100-104 10 ...................................

105-109 12 ...................................

110-114 13 ...................................

115-119 8 ...................................

120-124 7 ...................................

N ....................

µ”·Àπàß N2

................................ Med L I

N F

F F2 1

2 1

L ................................ ..............................................

I ................................ ..............................................

F1 ................................ ..............................................

F2 ................................ ..............................................

88 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

1. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë ®ßÀ“∞“ππ‘¬¡

§«“¡ Ÿß (´¡.) ®”π«ππ—°‡√’¬π

110-119 1 ∞“ππ‘¬¡®–µ°Õ¬Ÿà„πÕ—πµ√¿“§™—Èπ∑’Ë ..........

120-129 6 L .....................................................

130-139 15 I .....................................................

140-149 3 d1 .....................................................

150-159 1 d2 .....................................................

√«¡ 26

Mo L I

d

d d1

1 2

...........................................................................

...........................................................................

...........................................................................

...........................................................................

∂â“„™â«‘∏’‚¥¬ª√–¡“≥ ®–‰¥â∞“ππ‘¬¡ ®ÿ¥°÷Ëß°≈“ß™—Èπ∑’Ë∞“ππ‘¬¡Õ¬Ÿà

...........................................................................

...........................................................................

°‘®°√√¡∑’Ë 4.3

4.3 ∞“ππ‘¬¡

89·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

2. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë ®ßÀ“∞“ππ‘¬¡

§–·ππ §«“¡∂’Ë

34-54 6 ∞“ππ‘¬¡®–µ°Õ¬Ÿà„πÕ—πµ√¿“§™—Èπ∑’Ë ..........

55-75 8 L .....................................................

76-96 17 I .....................................................

97-117 26 d1 .....................................................

118-138 8 d2 .....................................................

139-159 5

√«¡ 70

Mo L I

d

d d1

1 2

...........................................................................

...........................................................................

...........................................................................

...........................................................................


...........................................................................

...........................................................................

¢âÕ —ß‡°µ ®–‡ÀÁπ«à“ ¢âÕ 2 ∞“ππ‘¬¡ 2 «‘∏’π’È §”µÕ∫®–µà“ß°—π¡“° ‡π◊ËÕß®“°§«“¡

°«â“ß¢Õß¢âÕπ’È¡’™à«ß°«â“ß¡“°

90 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

3. ®“°µ“√“ß·®°·®ß§«“¡∂’Ë ®ßÀ“∞“ππ‘¬¡

§–·ππ §«“¡∂’Ë

60-65 3 ∞“ππ‘¬¡®–µ°Õ¬Ÿà„πÕ—πµ√¿“§™—Èπ∑’Ë ..........

66-71 7 L .....................................................

72-77 6 I .....................................................

78-83 19 d1 .....................................................

84-89 10 d2 .....................................................

90-95 5

√«¡ 50

Mo L I

d

d d1

1 2

...........................................................................

...........................................................................

...........................................................................

...........................................................................


...........................................................................

...........................................................................

91·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

1. ®ÿ¥¡ÿàßÀ¡“¬‡¥‘¡¢Õß ∂‘µ‘§◊Õ¢âÕ„¥

1. °“√‡°Á∫‡Õ° “√À≈—°∞“π¢Õß

√“™°“√

2. °“√√«∫√«¡¢âÕ¡Ÿ≈

3. °“√ ”√«® ”¡–‚πª√–™“°√

4. °“√∫—π∑÷°·≈–√«∫√«¡¢âÕ¡Ÿ≈∑’Ë

‡ªìπµ—«‡≈¢

2. ¢âÕ„¥‡ªìπ§«“¡À¡“¬¢Õß ç ∂‘µ‘é

1. ¡’π—°‡√’¬π ¡.3 ∑—Ë«ª√–‡∑» 3

≈â“π§π

2. ª√–™“°√√âÕ¬≈– 80 ¡’Õ“™’æ

‡ªìπ‡°…µ√°√

3. ¡’π—°‡√’¬π ¡.3 ∑’Ë‡ªìππ—°‡√’¬π™“¬

1 ≈â“π§π

4. ¡’§π‰∑¬À—π¡“¡’Õ“™’æ§â“¢“¬

ª√–¡“≥ 10 ≈â“π§π

3. ª√–™“°√„π∑“ß ∂‘µ‘À¡“¬∂÷ß¢âÕ„¥

1. ¢âÕ¡Ÿ≈∑’Ë∫—π∑÷°‰«â

2. µ—«Õ¬à“ß¢Õß¢âÕ¡Ÿ≈

3. ®”π«π∑—ÈßÀ¡¥¢Õß¢âÕ¡Ÿ≈

4. ®”π«πª√–™“°√∑’Ë‰¥â®“°°“√

”√«®

„Àâπ—°‡√’¬π‡≈◊Õ°§”µÕ∫∑’Ë∂Ÿ°µâÕß

4. √–‡∫’¬∫«‘∏’°“√∑“ß ∂‘µ‘À¡“¬∂÷ß

¢âÕ„¥

1. °“√√«∫√«¡ °“√π”‡ πÕ ·≈–

°“√«‘‡§√“–Àå¢âÕ¡Ÿ≈

2. °“√√«∫√«¡ °“√π”‡ πÕ ·≈–

°“√µ’§«“¡À¡“¬¢âÕ¡Ÿ≈

3. °“√√«∫√«¡ °“√π”‡ πÕ °“√

«‘‡§√“–ÀåÀ√◊Õµ’§«“¡À¡“¬¢âÕ¡Ÿ≈

4. °“√√«∫√«¡ °“√π”‡ πÕ °“√

«‘‡§√“–Àå·≈–°“√µ’§«“¡À¡“¬

¢âÕ¡Ÿ≈

5. °“√π”‡ πÕ¢âÕ¡Ÿ≈¡’«—µ∂ÿª√– ß§å∑’Ë

”§—≠∑’Ë ÿ¥§◊ÕÕ–‰√

1. ‡æ◊ËÕ„Àâ∂Ÿ°µâÕßµ“¡°Æ‡°≥±å

2. ‡æ◊ËÕ –¥«°„π°“√§”π«≥

3. ‡æ◊ËÕ®—¥¢âÕ¡Ÿ≈„Àâ¡’√–‡∫’¬∫

4. ‡æ◊ËÕ„ÀâºŸâ π„®∑√“∫‰¥âßà“¬

6. π—°‡√’¬π 10 §π ¡’‡ß‘π¥—ßπ’È 6, 7, 2, 12,

9, 6, 14, 6, 11, 12 §à“‡©≈’Ë¬‡≈¢§≥‘µ

‡∑à“°—∫‡∑à“‰√

1. 12

2. 10

3. 9.5

4. 8.5

·∫∫∑¥ Õ∫º≈ —¡ƒ∑∏‘Ï∑“ß°“√‡√’¬πª√–®”Àπà«¬

92 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

7. ®“°¢âÕ 6 ¡—∏¬∞“πµ√ß°—∫¢âÕ„¥

1. 6 2. 8

3. 9 4. 9.5

8. ®“°¢âÕ 6 ∞“ππ‘¬¡¡’§à“‡∑à“‰√

1. 6 2. 8

3. 9 4. 10

„™â¢âÕ¡Ÿ≈π’ÈµÕ∫§”∂“¡¢âÕ 9-11

®“°°“√ ”√«®§à“„™â®à“¬„π·µà≈–«—π¢Õß

π—°‡√’¬π 9 §π ¥—ßπ’È 50, 55, 60, 65, 50,

60, 70, 80, 60

9. §à“‡©≈’Ë¬‡≈¢§≥‘µ§◊Õ¢âÕ„¥

1. 59.1 2. 60.1

3. 61.1 4. 62.1

10. ¡—∏¬∞“π¡’§à“‡∑à“„¥

1. 50 2. 60

3. 65 4. 70

11. ∞“ππ‘¬¡¡’§à“‡∑à“‰√

1. 50 2. 60

3. 65 4. 70

12. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß¡’¥—ßπ’È

2, 2, 3, 4, 4, 4, 5, 5, 6, 9, 12, 18

¢âÕ„¥ √ÿª∂Ÿ°µâÕß

1. Med X 2. X Med

3. Med Mo 4. X Mo

13. °”Àπ¥§–·ππ«‘™“§≥‘µ»“ µ√å¢Õß

‡¥Á°°≈ÿà¡Àπ÷Ëß 70, 50, 58, 40, 60, 52,

59, 46, 56, 49 ¢âÕ„¥‡ªìπ®√‘ß

1. X Med 2. X Med

3. X Med 4. Med Mo

14. π‘¥·≈–ÀπàÕ¬‡ªìπΩ“·Ω¥Õ“¬ÿ 20 ªï

‡¢“¡’‡æ◊ËÕπÕ’° 4 §π Õ“¬ÿ 20, 19, 16,

19 ªï ¥—ßπ—ÈπÕ“¬ÿ‡©≈’Ë¬¢Õß‡¥Á°°≈ÿà¡π’È

‡ªìπ‡∑à“„¥

1. 20

2. 19

3. 18

4. 17

15. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß‡ªìπ¥—ßπ’È 7, 8, 5, 10, 5,

7, 8, 10, 6, 4 ¢âÕ„¥‡ªìπ®√‘ß

1. §à“‡©≈’Ë¬‡≈¢§≥‘µ §◊Õ 7

2. ¡—∏¬∞“π §◊Õ 6

3. ∞“ππ‘¬¡¡’¡“°°«à“ 1 §à“

4. ∂Ÿ°¡“°°«à“ 1 ¢âÕ

16. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß‡ªìπ¥—ßπ’È

7, 12, 4, 6, 9, 10, 5, 11, 15, 16, 11, 5, 6

∂â“‡æ‘Ë¡¢âÕ¡Ÿ≈·µà≈–µ—«¥â«¬ 3 ·≈â«

¢âÕ„¥‡ªìπ®√‘ß

1. X Med 9

2. X Med 13

3. X Med 12

4. X 12, Mo 11

17. §πß“π°àÕ √â“ß 6 §π ¡’√“¬‰¥â¥—ßπ’È

115, 120, 200, 135, 180, 172

¢âÕ„¥∂Ÿ°µâÕß

1. X 153.6

2. Med 135.5

3. Med 135

4. X Mo

93·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

18. ¢âÕ¡Ÿ≈µàÕ‰ªπ’È· ¥ß√“¬√—∫ (∫“∑)

¢Õß√â“πÕ“À“√·ÀàßÀπ÷Ëß„π√–¬–‡«≈“

7 «—π

5,300, 5,800, 6,200, 6,500, 4,700,

5,800, 5,000

¢âÕ„¥∂Ÿ°µâÕß

1. §à“‡©≈’Ë¬‡≈¢§≥‘µ 5,600

2. ¡—∏¬∞“π 6,500

3. ∞“ππ‘¬¡ ¡—∏¬∞“π

4. ∞“ππ‘¬¡ 6,200

19. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß¡’ 8 µ—« ¥—ßπ’È 25, 30, 32,

27, 38, 40, A, A §à“‡©≈’Ë¬‡≈¢§≥‘µ

¢Õß¢âÕ¡Ÿ≈™ÿ¥π’È 32 ¥—ßπ—Èπ A ¡’§à“

‡∑à“‰√

1. 32

2. 30

3. 29

4. 28

20. ®“°¢âÕ 19 ¡—∏¬∞“π¡’§à“‡∑à“‰√

1. 32

2. 30

3. 29

4. 28

21. ®“°¢âÕ 19 ∞“ππ‘¬¡¡’§à“‡∑à“‰√

1. 32

2. 30

3. 29

4. 28

22. ¢âÕ§«“¡„¥„™â§à“°≈“ß∞“ππ‘¬¡‰¥â

‡À¡“– ¡

1. ‚¥¬‡©≈’Ë¬·≈â«§π‰∑¬¡’√“¬‰¥â

ªï≈– 6,000 ∫“∑

2. ‚¥¬‡©≈’Ë¬·≈â«§π‰∑¬„™â√Õß‡∑â“

‡∫Õ√å 10

3. ‚¥¬‡©≈’Ë¬·≈â«§π‰∑¬√ŸâÀπ—ß ◊Õ

‡°‘π 60%

4. ‚¥¬‡©≈’Ë¬·≈â«§π‰∑¬¢—∫√∂¥â«¬

§«“¡‡√Á« 80 °‘‚≈‡¡µ√µàÕ™—Ë«‚¡ß

23. ç‚¥¬‡©≈’Ë¬§π°√ÿß‡∑æœ ‡≈◊Õ°ºŸâ·∑π

®“°æ√√§∫Ÿ™“‰∑¬é ∑à“π§‘¥«à“

¢âÕ§«“¡¢â“ßµâπ°≈à“«∂÷ßµ—«°≈“ß„¥

1. ¡—∏¬∞“π

2. §à“‡©≈’Ë¬‡≈¢§≥‘µ

3. ∞“ππ‘¬¡

4. §à“‡©≈’Ë¬‡≈¢§≥‘µ·≈–∞“ππ‘¬¡

24. ¡’ºŸâ°≈à“««à“ ç‚¥¬‡©‹≈’Ë¬·≈â«§π‰∑¬

„™â√∂¢π“¥ 1,500 ´’´’ ´÷Ëß„™âπÈ”¡—π

‚¥¬‡©≈’Ë¬ 15 °‘‚≈‡¡µ√µàÕ≈‘µ√

§à“‡©≈’Ë¬¥—ß°≈à“«µ√ß°—∫§à“°≈“ß„¥

1. ∞“ππ‘¬¡ ∞“ππ‘¬¡ µ“¡≈”¥—∫

2. §à“‡©≈’Ë¬‡≈¢§≥‘µ §à“‡©≈’Ë¬

‡≈¢§≥‘µ µ“¡≈”¥—∫

3. ∞“ππ‘¬¡ §à“‡©≈’Ë¬‡≈¢§≥‘µ

µ“¡≈”¥—∫

4. §à“‡©≈’Ë¬‡≈¢§≥‘µ ∞“ππ‘¬¡

µ“¡≈”¥—∫

94 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

25. ¢âÕ„¥∂Ÿ°µâÕß

1. ¡—∏¬∞“π§◊Õ¢âÕ¡Ÿ≈∑’ËÕ¬Ÿà°÷Ëß°≈“ß

¢Õß¢âÕ¡Ÿ≈∑—ÈßÀ¡¥

2. °√≥’¢âÕ¡Ÿ≈‡ªìπ®”π«π§Ÿà ¡—∏¬∞“π

§◊Õ§à“‡©≈’Ë¬§Ÿà°≈“ß∑’Ë‡√’¬ß¢âÕ¡Ÿ≈

®“°πâÕ¬‰ª¡“°

3. °√≥’¢âÕ¡Ÿ≈‡ªìπ®”π«π§’Ë ¡—∏¬∞“π

§◊Õ¢âÕ¡Ÿ≈∑’ËÕ¬Ÿà°÷Ëß°≈“ß

4. ∂Ÿ°∑ÿ°¢âÕ

26. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß¡’ 6 ®”π«π ·µàÀ“¬

‰ª®”π«πÀπ÷Ëß §ß‡À≈◊Õ 28, 29, 28,

28, 32 ∂â“§à“‡©≈’Ë¬‡≈¢§≥‘µ¢Õß

¢âÕ¡Ÿ≈™ÿ¥π’È‡ªìπ 30 ·≈â« ¢âÕ¡Ÿ≈∑’Ë

À“¬‰ª§◊Õ¢âÕ„¥

1. 35 2. 36

3. 38 4. 40

27. ∂â“ a, b, c ¡’§à“‡©≈’Ë¬‡≈¢§≥‘µ‡ªìπ 11

·≈– a, b, c, d, e, f ¡’§à“‡©≈’Ë¬

‡≈¢§≥‘µ‡ªìπ 16 ¥—ßπ—Èπ §à“‡©≈’Ë¬¢Õß

d, e, f §◊Õ¢âÕ„¥

1. 20 2. 21

3. 22 4. 24

28. ®“°¢âÕ¡Ÿ≈¥‘∫§◊Õ 8, 7, x, 5, 6, 1

x 1, x 1, 13, 5 ¡’§à“‡©≈’Ë¬

‡≈¢§≥‘µ‡ªìπ 6 ®ßæ‘®“√≥“«à“¢âÕ„¥

∂Ÿ°µâÕß

1. §à“‡©≈’Ë¬‡≈¢§≥‘µ‡∑à“°—∫¡—∏¬∞“π

2. ¡—∏¬∞“π‡∑à“°—∫∞“ππ‘¬¡

3. §à“‡©≈’Ë¬‡≈¢§≥‘µ¡“°°«à“¡—∏¬∞“π

4. ∞“ππ‘¬¡¡“°°«à“¡—∏¬∞“π

29. ¡“≈’¡’Õ“¬ÿ·°à°«à“¡“≈—¬ 2 ªï ¡“≈—¬

¡’Õ“¬ÿπâÕ¬°«à“¡–≈‘ 1 ªï À“°¡–≈‘Õ“¬ÿ

6 ªï ·≈–æàÕÕ“¬ÿ 38 ªï §à“‡©≈’Ë¬Õ“¬ÿ

¢Õß§π∑—Èß ’Ë‡ªìπ‡∑à“‰√

1. 12 2. 12.5

3. 13.5 4. 14

30. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß‡ªìπ¥—ßπ’È 4, 5, 8, 7, 3,

6, 4, 9, 2 §à“‡©≈’Ë¬‡≈¢§≥‘µ¡“°°«à“

¡—∏¬∞“π‡∑à“‰√

1. 0.5 2. 0.4

3. 0.3 4. 0.2

31. π—°‡√’¬πÀâÕßÀπ÷Ëß¡’ 46 §π „π°“√

Õ∫µ—Èß‡°≥±å‰«â«à“ ºŸâ Õ∫‰¥âµâÕß∑”

§–·ππ‰¡àµË”°«à“ 50% ∂â“§–·ππ

¡—∏¬∞“π¢Õßπ—°‡√’¬πÀâÕßπ’È‡ªìπ 50%

π—°‡√’¬πÀâÕßπ’È Õ∫‰¥â°’Ë§π

1. 22 §π 2. 24 §π

3. 25 §π 4. 30 §π

32. ¢âÕ¡Ÿ≈™ÿ¥Àπ÷Ëß¡’ 4 √“¬°“√ a, b, c, d

¡’§à“‡©≈’Ë¬‡≈¢§≥‘µ 32 §à“‡©≈’Ë¬

‡≈¢§≥‘µ¢Õß 2a, 2b 3, 2c 7,

2d 6 ‡∑à“°—∫‡∑à“‰√

1. 64 2. 65

3. 66 4. 67

33. πÈ”Àπ—°¢Õß§π 8 §π ‡ªìπ¥—ßπ’È 57, x,

y, 60, x, y, 62, y ∂â“πÈ”Àπ—°‡©≈’Ë¬¢Õß

§π∑—Èß 8 §ππ’È ‡∑à“°—∫ 53 °‘‚≈°√—¡

·≈– xy 10 ·≈â« xy ¡’§à“‡∑à“‰√

1. 80 2. 90

3. 95 4. 100

95·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

34. „π°“√ Õ∫«‘∑¬“»“ µ√å§√—ÈßÀπ÷Ëß

¢Õßπ—°‡√’¬π ¡.3 ÀâÕß A ¡’π—°‡√’¬π

40 §π ‰¥â§–·ππ‡©≈’Ë¬ 54 §–·ππ

π—°‡√’¬πÀâÕß B ‰¥â§–·ππ‡©≈’Ë¬ 75

§–·ππ ∂â“§‘¥§–·ππ‡©≈’Ë¬√«¡∑—Èß

ÕßÀâÕß‰¥â 63 §–·ππ Õ¬“°∑√“∫

«à“ÀâÕß B ¡’π—°‡√’¬π°’Ë§π

1. 30 §π

2. 40 §π

3. 45 §π

4. 50 §π

35. Õ—πµ√¿“§™—Èπ¡’‰«â‡æ◊ËÕ ‘Ëß„¥

1. ·®°·®ß¢âÕ¡Ÿ≈

2. À“æ‘ —¬

3. ®—¥°≈ÿà¡§–·ππ

4. «‘‡§√“–Àå§«“¡°«â“ß¢Õß¢âÕ¡Ÿ≈

36. §«“¡·µ°µà“ß¢Õß§–·ππ Ÿß ÿ¥·≈–

§–·ππµË” ÿ¥‡√’¬°«à“Õ–‰√

1. Õ—πµ√¿“§™—Èπ

2. §«“¡∂’Ë

3. ®ÿ¥°÷Ëß°≈“ß™—Èπ

4. æ‘ —¬

37. ®ÿ¥°÷Ëß°≈“ß™—Èπ‡∑à“°—∫¢âÕ„¥

1. ¢Õ∫∫π ¢Õ∫≈à“ß

2. ¢Õ∫∫π ¢Õ∫≈à“ß

3.

¢Õ∫∫π ¢Õ∫≈à“ß 2

4.

¢Õ∫∫π ¢Õ∫≈à“ß 2

®“°¢âÕ¡Ÿ≈∑’Ë°”Àπ¥„Àâ„™âµÕ∫§”∂“¡¢âÕ

38-41

„π°“√ Õ∫¿“…“‰∑¬¢Õßπ—°‡√’¬πÀâÕßÀπ÷Ëß

ª√“°Ø§–·ππ¥—ßπ’È

35 37 58 57 51 37

57 42 36 45 43 48

36 47 55 48 42 38

40 40 59 45 53 43

41 38 45 47 44 39

38. æ‘ —¬¡’§à“µ√ß°—∫¢âÕ„¥

1. 59 2. 58

3. 35 4. 24

39. ∂â“µâÕß°“√ √â“ßµ“√“ß·®°·®ß

§«“¡∂’Ë∑’Ë¡’™à«ß°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ

5 ‚¥¬‡√‘Ë¡µâπ¥â«¬ 35 ®–‰¥â°’Ë

Õ—πµ√¿“§™—Èπ

1. 4 2. 5

3. 6 4. 7

40. ¢Õ∫≈à“ß¢ÕßÕ—πµ√¿“§™—Èπ Ÿß ÿ¥§◊Õ

¢âÕ„¥

1. 44.5

2. 49.5

3. 54.5

4. 59.5

41. ¢Õ∫∫π¢ÕßÕ—πµ√¿“§™—Èπ Ÿß ÿ¥§◊Õ

¢âÕ„¥

1. 59 2. 59.5

3. 60 4. 60.5

96 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

48. Õ—πµ√¿“§™—Èπ„π¢âÕ„¥∑’Ë¡’§«“¡°«â“ß

¢ÕßÕ—πµ√¿“§™—Èπ¡“°∑’Ë ÿ¥

1. 111-118 2. 104-110

3. 85-93 4. 73-79

¢âÕ¡Ÿ≈®“°µ“√“ß·®ß·®ß§«“¡∂’ËµàÕ‰ªπ’È

„™âµÕ∫§”∂“¡¢âÕ 49-54

™à«ß§–·ππ ®”π«ππ—°‡√’¬π

35-45 3

46-56 4

57-67 13

68-78 17

79-89 9

90-99 4

√«¡ 50

49. §«“¡°«â“ß¢Õß·µà≈–Õ—πµ√¿“§™—Èπ

‡ªìπ‡∑à“‰√

1. 8 2. 9

3. 10 4. 11

50. π—°‡√’¬π à«π¡“° Õ∫‰¥â§–·ππÕ¬Ÿà

„π™à«ß§–·ππ„¥

1. 57-67

2. 68-78

3. 79-89

4. 90-99

51. „π°“√ Õ∫§√—Èßπ’È¡’π—°‡√’¬π‡¢â“ Õ∫

°’Ë§π

1. 47 §π 2. 48 §π

3. 50 §π 4. 55 §π

¢âÕ¡Ÿ≈µàÕ‰ªπ’È„™âµÕ∫§”∂“¡¢âÕ 42-46

º≈°“√ Õ∫«‘™“ —ß§¡»÷°…“¢Õßπ—°‡√’¬π™—Èπ

¡.3/1

™à«ß§–·ππ §«“¡∂’Ë

40-49 2

50-59 7

60-69 10

70-79 15

80-89 6

√«¡ 40

42. §«“¡°«â“ß¢Õß·µà≈–Õ—πµ√¿“§™—Èπ

‡ªìπ‡∑à“‰√

1. 9 2. 10

3. 11 4. 12

43. ¢Õ∫≈à“ß¢Õß™—Èπ∑’Ë 2 ‡ªìπ‡∑à“‰√

1. 49 2. 49.5

3. 50 4. 50.5

44. ¢Õ∫∫π¢Õß™—Èπ∑’Ë 3 ‡ªìπ‡∑à“‰√

1. 68.5 2. 69

3. 69.5 4. 70

45. π—°‡√’¬π™—Èπ ¡.3/1 ¡’°’Ë§π

1. 35 2. 40

3. 45 4. 50

46. ®ÿ¥°÷Ëß°≈“ß™—Èπ∑’Ë 4 ¡’§à“‡∑à“‰√

1. 74.5 2. 75.5

3. 74 4. 75

47. Õ—πµ√¿“§™—Èπ„π¢âÕ„¥∑’Ë§«“¡°«â“ß

¢ÕßÕ—πµ√¿“§™—Èπ‰¡à‡∑à“°—∫¢âÕÕ◊Ëπ1. 77-80 2. 69-72

3. 61-64 4. 53-55

97·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

52. π—°‡√’¬π∑’Ë Õ∫‰¥â§–·ππ 57-78

§–·ππ §‘¥‡ªìπ°’Ë‡ªÕ√å‡´Áπµå¢Õß

π—°‡√’¬π∑—ÈßÀ¡¥1. 30% 2. 40%

3. 50% 4. 60%

53. π—°‡√’¬π∑’Ë‰¥â§–·πππâÕ¬°«à“ 46

§–·ππ ¡’°’Ë§π

1. 3 §π 2. 4 §π

3. 10 §π 4. 11 §π

54. ®“°¢âÕ 53 §‘¥‡ªìπ°’Ë‡ªÕ√å‡´Áπµå¢Õßπ—°‡√’¬π∑—ÈßÀ¡¥

1. 3% 2. 5%

3. 6% 4. 11%

55. „π°“√ √â“ßŒ‘ ‚∑·°√¡ §«“¡ Ÿß

¢Õß·∑àß°√“ø √â“ß¢÷Èπ®“° ‘Ëß„¥

1. §«“¡∂’Ë2. §«“¡°«â“ß¢ÕßÕ—πµ√¿“§™—Èπ

3. ™à«ß§–·ππ

4. §«“¡∂’Ë – ¡

56. Œ‘ ‚∑·°√¡À¡“¬∂÷ß°√“ø™π‘¥„¥

1. °√“ø·∑àß

2. °√“ø‡ âπµ√ß

3. °√“ø«ß°≈¡

4. °√“ø‡ âπ‚§âß

57. ®ÿ¥‡√‘Ë¡µâπ¢Õß√ŸªÀ≈“¬‡À≈’Ë¬¡¢Õß

§«“¡∂’Ë®–Õ¬ŸàÀà“ß®“°·∑àß‡À≈’Ë¬¡√Ÿª

√‘¡ ÿ¥‡∑à“„¥

1. 0.05 Àπà«¬ 2. 0.5 Àπà«¬

3. 0.75 Àπà«¬ 4. 1 Àπà«¬

58. °“√π”‡ πÕ¢âÕ¡Ÿ≈¥â«¬√ŸªÀ≈“¬

‡À≈’Ë¬¡¢Õß§«“¡∂’Ë ‡ªìπ°“√π”‡ πÕ

¢âÕ¡Ÿ≈„π√Ÿª„¥

1. °√“ø«ß°≈¡

2. °√“ø·∑àß

3. °√“ø‡ âπ‚§âß

4. °√“ø‡ âπµ√ß

Œ‘ ‚∑·°√¡·≈–√ŸªÀ≈“¬‡À≈’Ë¬¡¢Õß§«“¡∂’ËµàÕ‰ªπ’È„™âµÕ∫§”∂“¡ 59-62

Œ‘ ‚∑·°√¡· ¥ß§«“¡ Ÿß¢Õßπ—°‡√’¬π°≈ÿà¡Àπ÷Ëß

60

50

40

30

20

10

®”π«ππ—°‡√’¬π (§π)

§«“¡ Ÿß (´¡.)

129.

5

139.

5

149.

5

159.

5

169.

5

179.

5

A

98 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

59. ®”π«ππ—°‡√’¬π°≈ÿà¡π’È¡’°’Ë§π

1. 180 §π 2. 170 §π

3. 120 §π 4. 60 §π

60. A ¡’§à“‡∑à“‰√

1. 124

2. 124.5

3. 126

4. 126.5

61. ™à«ß§«“¡ Ÿß„¥‡ªìπÕ—πµ√¿“§™—Èπ∑’Ë

Õ¬Ÿàµ√ß°≈“ß„πµ“√“ß·®°·®ß§«“¡∂’Ë

1. 149-159 2. 149.5-159.5

3. 150-159 4. 150.5-159.5

62. §«“¡°«â“ß¢Õß°√“ø·µà≈–·∑àß‡ªìπ

‡∑à“‰√

1. 9 2. 10

3. 11 4. 12

√ŸªÀ≈“¬‡À≈’Ë¬¡¢Õß§«“¡∂’ËµàÕ‰ªπ’È„™âµÕ∫§”∂“¡¢âÕ 63-64

60

40

20

§«“¡∂’Ë

§–·ππ 44 55 66 77 88 99

63. ¢Õ∫≈à“ß·≈–¢Õ∫∫π¢ÕßÕ—πµ√¿“§

™—ÈπµË” ÿ¥¢Õß¢âÕ¡Ÿ≈™ÿ¥π’È§◊Õ¢âÕ„¥

1. 43.5 ·≈– 55.5 2. 44 ·≈– 55

3. 49.5 ·≈– 60.5 4. 50 ·≈– 60

64. Õ—πµ√¿“§™—Èπ„¥∑’Ë¡’§«“¡∂’Ë¡“°∑’Ë ÿ¥

1. 61-71

2. 60-70

3. 60.5-71.5

4. 66-77

µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È„™âµÕ∫§”∂“¡¢âÕ 65-69

§–·ππ §«“¡∂’Ë ®ÿ¥°÷Ëß°≈“ß™—Èπ §«“¡∂’Ë – ¡

a-b 4 6

c-d 10 11 A

e-f 8 16

g-h 3 21 B

99·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

65. §«“¡°«â“ß·µà≈–Õ—πµ√¿“§™—Èπ‡ªìπ

‡∑à“‰√

1. 3 2. 4

3. 5 4. 6

66. Õ—πµ√¿“§™—Èπ e-f §◊Õ¢âÕ„¥

1. 10-14

2. 12-16

3. 14-18

4. 16-20

67. ¡—∏¬∞“πÕ¬Ÿàµ√ß°—∫Õ—πµ√¿“§™—Èπ„¥

1. 4-8 2. 9-13

3. 14-18 4. 19-23

68. ∞“ππ‘¬¡Õ¬Ÿàµ√ß°—∫Õ—πµ√¿“§™—Èπ„¥

1. 4-8 2. 9-13

3. 14-18 4. 19-23

69. A ·≈– B µ√ß°—∫¢âÕ„¥

1. 14 ·≈– 25

2. 11 ·≈– 21

3. 10 ·≈– 3

4. 17 ·≈– 21

®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È „™â

µÕ∫§”∂“¡¢âÕ 70-77

§–·ππ §«“¡∂’Ë

100-109 2

110-119 5

120-129 8

130-139 3

140-149 2

√«¡ 20

70. µ“√“ßπ’È·µà≈–Õ—πµ√¿“§™—Èπ¡’§«“¡

°«â“ß‡∑à“‰√

1. 9 2. 10

3. 11 4. 12

71. ®ÿ¥°÷Ëß°≈“ß™—Èπ∑’Ë 2 ¡’§à“‡∑à“‰√

1. 114 2. 114.5

3. 115 4. 115.5

72. §«“¡∂’Ë – ¡™—Èπ∑’Ë 4 ¡’§à“‡∑à“‰√

1. 3 2. 5

3. 18 4. 20

73. ¢Õ∫≈à“ß™—Èπ∑’Ë 3 ¡’§à“‡∑à“‰√

1. 119 2. 119.5

3. 120 4. 120.5

74. ¢Õ∫∫π™—Èπ∑’Ë 5 ¡’§à“‡∑à“‰√

1. 139.5 2. 149

3. 149.5 4. 150

75. §à“‡©≈’Ë¬‡≈¢§≥‘µ¡’§à“‡∑à“‰√

1. 120.5 2. 121.5

3. 122.5 4. 123.5

76. ®“°µ“√“ßπ’È ¡—∏¬∞“πÕ¬Ÿà„π

Õ—πµ√¿“§™—Èπ„¥1. 110-119

2. 120-129

3. 130-139

4. 121-130

77. ®“°µ“√“ßπ’È ∞“ππ‘¬¡Õ¬Ÿà„π

Õ—πµ√¿“§™—Èπ„¥

1. 119-130

2. 120-129

3. 121-130

4. 119.5-129.5

100 ·∫∫Ωñ° §≥‘µ»“ µ√åæ◊Èπ∞“π ¡.3 ¿“§‡√’¬π∑’Ë 2

78. ∂â“¢âÕ¡Ÿ≈®“°µ“√“ß·®°·®ß§«“¡∂’Ë

¡’ X = 37.125 ®ßÀ“§à“ n

§–·ππ §«“¡∂’Ë

26-30 8

31-35 9

36-40 10

41-45 n

46-50 5

1. 7 2. 7.5

3. 8 4. 9

®“°µ“√“ß·®°·®ß§«“¡∂’ËµàÕ‰ªπ’È „™â

µÕ∫§”∂“¡¢âÕ 79-85

§–·ππ §«“¡∂’Ë

40-49 5

50-59 10

60-69 22

70-79 45

80-89 30

90-99 8

√«¡ N

79. ®“°µ“√“ß N ¡’§à“‡∑à“‰√

1. 120 2. 119

3. 118 4. 115

80. §«“¡°«â“ß·µà≈–™—Èπ¡’§à“‡∑à“‰√

1. 9 2. 10

3. 11 4. 12

81. §«“¡∂’Ë – ¡™—Èπ∑’Ë 3 ¡’§à“‡∑à“‰√

1. 22 2. 32

3. 37 4. 67

82. ®ÿ¥°÷Ëß°≈“ß™—Èπ∑’Ë 4 ¡’§à“‡∑à“‰√

1. 74.5 2. 75

3. 70.5 4. 69.5

83. ¢Õ∫∫πÕ—πµ√¿“§™—Èπ∑’Ë 2 ¡’§à“‡∑à“‰√

1. 49 2. 49.5

3. 59 4. 59.5

84. §à“‡©≈’Ë¬‡≈¢§≥‘µ¡’§à“‡∑à“‰√

1. 71.50 2. 72.58

3. 73.58 4. 73.85

85. ∞“ππ‘¬¡Õ¬Ÿà„πÕ—πµ√¿“§™—Èπ„¥

1. Õ—πµ√¿“§™—Èπ∑’Ë 1

2. Õ—πµ√¿“§™—Èπ∑’Ë 2

3. Õ—πµ√¿“§™—Èπ∑’Ë 4

4. Õ—πµ√¿“§™—Èπ∑’Ë 5

052-076 UNIT 3/1 · 54 ·∫∫Ωñ° §≥ ‘µ»“ µ√ åæ Èπ∞“π ¡.3 ¿“§‡√...

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Transcript of 052-076 UNIT 3/1 · 54 ·∫∫Ωñ° §≥ ‘µ»“ µ√ åæ Èπ∞“π ¡.3 ¿“§‡√...