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2553 Êèǹ·Õ‹ 1 36 (¢éÍ 1–36) 1. ¢éÍ ãËé ẺÃкÒµÑÇàÅ×Í¡ ¢éÍÅÐ 1 A = {1, 2, 3, . . .} 1. A−B àÇÅÒ 11.30 - 13.30 ¹. áµèÅТéÍÁդӵͺ·Õ‹¶Ù¡µéͧ·Õ‹ÊØ´à¾Õ§¤ÓµÍºà´ÕÂÇ ¤Ðá¹¹ áÅÐ ÁÕÊÁÒªÔ¡ 5 B = {{1, 2}, {3, 4, 5}, 6, 7, 8, . . .} µÑÇ 2. ¨Ó¹Ç¹ÊÁÒªÔ¡¢Í§à¾ÒàÇÍÃì૵¢Í§ 3. ¨Ó¹Ç¹ÊÁÒªÔ¡¢Í§ 4. 2. A∩B B−A (A − B) ∪ (B − A) ¤×Í૵¢Í§¨Ó¹Ç¹¹Ñº·Õ‹ÁÕ¤èÒÁÒ¡¡ÇèÒ 1) A 2) ¼Å àËç´à»š¹¾×ªÁÕ´Í¡ àËç´à»š¹¾×ªªÑŒ¹ÊÙ§ ¢éÍÊÃØ»¢éÒ§µé¹ÊÁà˵ØÊÁ¼Å ¶éÒ A á·¹¢éͤÇÒÁã´ 1. ¾×ªªÑŒ¹ÊÙ§·Ø¡ª¹Ô´ÁÕ´Í¡ 2. ¾×ªªÑŒ¹ÊÙ§ºÒ§ª¹Ô´ÁÕ´Í¡ 3. ¾×ªÁÕ´Í¡·Ø¡ª¹Ô´à»š¹¾×ªªÑŒ¹ÊÙ§ 4. ¾×ªÁÕ´Í¡ºÒ§ª¹Ô´à»š¹¾×ªªÑŒ¹ÊÙ§ à·èҡѺ 4 ໚¹¨Ó¹Ç¹¤Ùè ¾Ô¨ÒóҡÒÃãËéà˵ؼŵèÍ仹Ռ à赯 2 5 ¢éÍã´à»š¹à·ç¨ ¨Ó¹Ç¹
2.
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2553 3. àÇÅÒ 11.30 - 13.30 ¹. ¾Ô¨ÒóҢéͤÇÒÁµèÍ仹Ռ ¡. ¨Ó¹Ç¹·Õ‹à»š¹·È¹ÔÂÁäÁèÃÙ騺ºÒ§¨Ó¹Ç¹à»š¹¨Ó¹Ç¹ÍµÃáÂÐ ¢. ¨Ó¹Ç¹·Õ‹à»š¹·È¹ÔÂÁäÁèÃÙ騺ºÒ§¨Ó¹Ç¹à»š¹¨Ó¹Ç¹µÃáÂÐ ¢éÍã´¶Ù¡µéͧ 1. ¢éÍ ¡. áÅТéÍ ¢. 2. ¢éÍ ¡. à·èҹь¹ 3. ¢éÍ ¢. à·èҹь¹ 4. 4. ¢éÍ ¡. áÅТéÍ ¢. ¼Ô´ ¡Ó˹´ãËé s, t, u áÅÐ v ໚¹¨Ó¹Ç¹¨ÃÔ§ «Ö‹§ s<t áÅÐ u<v ¾Ô¨ÒóҢéͤÇÒÁµèÍ仹Ռ ¡. s−u<t−v ¢. 3 s−v <t−u ¢éÍã´¶Ù¡µéͧ 1. ¢éÍ ¡. áÅТéÍ ¢. 2. ¢éÍ ¡. à·èҹь¹ 3. ¢éÍ ¢. à·èҹь¹ 4. ¢éÍ ¡. áÅТéÍ ¢. ¼Ô´
3.
04 ÃËÑÊÇÔªÒ ¤³ÔµÈÒʵÃì ˹éÒ ÇѹàÊÒÃì·Õ‹ 20 ¡ØÁÀҾѹ¸ì
2553 5. ¼Åà©Å¢ͧÊÁ¡Òà 2|5 − x| = 1 àÇÅÒ 11.30 - 13.30 ¹. ÍÂÙè㹪èǧ㴠1. ¶éÒ (−10, −5) 2. (−6, −4) 3. 6. (−4, 5) 4. (−3, 6) 3 4 ໚¹¼Åà©ÅÂ˹֋§¢Í§ÊÁ¡Òà 4x2 + bx − 6 = 0 àÁ×‹Í b ໚¹¨Ó¹Ç¹¨ÃÔ§áÅéÇ ÍÕ¡¼Å à©ÅÂ˹֋§¢Í§ÊÁ¡ÒùՌÁÕ¤èҵç¡Ñº¢éÍã´ 1. −2 2. 3. 7. 1 2 − 4. 1 2 2 ¢éÍã´ÁÕ¤èÒµèÒ§¨Ò¡¢éÍÍ׋¹ 1. (−1)0 2. (−1)0.2 3. 8. 4 (−1)0.4 4. (−1)0.8 √ √ √ √ √ √ |4 3 − 5 2| − |3 5 − 5 2| + |4 3 − 3 5| 2 à·èҡѺ¢éÍã´ 1. 0 2. 180 3. 192 4. 200
4.
ÃËÑÊÇÔªÒ 04 ¤³ÔµÈÒʵÃì ˹éÒ ÇѹàÊÒÃì·Õ‹ 20 ¡ØÁÀҾѹ¸ì
2553 9. ¡Ó˹´ãËé a àÇÅÒ 11.30 - 13.30 ¹. ໚¹¨Ó¹Ç¹¨ÃÔ§ºÇ¡ áÅÐ n ໚¹¨Ó¹Ç¹¤ÙèºÇ¡ ¾Ô¨ÒóҢéͤÇÒÁµèÍ仹Ռ ¡. ¢. √ n √ n a n = |a| an = |a| ¢éÍã´¶Ù¡µéͧ 1. ¢éÍ ¡. áÅТéÍ ¢. 2. ¢éÍ ¡. à·èҹь¹ 3. ¢éÍ ¢. à·èҹь¹ 10. ¶éÒ 4. ¢éÍ ¡. áÅТéÍ ¢. ¼Ô´ f (x) = −x2 + x + 2 1. f (x) ≥ 0 àÁ×‹Í 5 áÅéÇ ¢éÍÊÃػ㴶١µéͧ −1 ≤ x ≤ 2 2. ¨Ø´Ç¡¡ÅѺ¢Í§¡ÃÒ¿¢Í§¿˜§¡ìªÑ¹ 3. ¿˜§¡ìªÑ¹ f ÁÕ¤èÒÊÙ§ÊØ´à·èҡѺ 2 4. ¿˜§¡ìªÑ¹ f ÁÕ¤èÒµ‹ÓÊØ´à·èҡѺ 2 f ÍÂÙè㹨µØÀÒ¤·Õ‹Êͧ
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ÃËÑÊÇÔªÒ 04 ¤³ÔµÈÒʵÃì ˹éÒ ÇѹàÊÒÃì·Õ‹ 20 ¡ØÁÀҾѹ¸ì
2553 àÇÅÒ 11.30 - 13.30 ¹. 11. ¤ÇÒÁÊÑÁ¾Ñ¹¸ìã¹¢éÍã´à»š¹¿˜§¡ìªÑ¹ 1. {(1, 2), (2, 3), (3, 1), (3, 3)} 3. {(1, 3), (1, 2), (1, 1), (1, 4)} 4. 12. ¶éÒ {(1, 2), (2, 3), (3, 2), (2, 4)} 2. {(1, 3), (2, 1), (3, 3), (4, 1)} f (x) = √ 3−x áÅÐ g(x) = −2 + |x − 4| 6 áÅéÇ Df ∪ Rg 1. (−∞, 3] 2. [−2, ∞) 3. [−2, 3] 4. (−∞, ∞) ¤×Í¢éÍã´
6.
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2553 13. ¡Ó˹´ãËé¡ÃÒ¿¢Í§¿˜§¡ìªÑ¹ àÇÅÒ 11.30 - 13.30 ¹. f ໚¹´Ñ§¹ÕŒ ß½¼ ß ¼ ß ¤èҢͧ 7 11f (−11) − 3f (−3)f (3) ¤×Í¢éÍã´ 1. 57 2. 68 3. 75 4. 86
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