第十六章 統計初步

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⛐㖍ⷠ䓇㳣ᷕ炻ㆹᾹ䴻ⷠ天㓞普㔠㒂ˣ䳗䧵屯㕁炻䃞⼴忂忶 㔜䎮ˣ妰䬿冯↮㜸炻⽆ᷕ㈦↢夷⼳炻忁⯙天䓐⇘䴙妰㕡㱽ˤ㛔䪈 ṳ䳡䴙妰䘬ᶨṃ⇅㬍䞍嬀ˤ

16.1

ᓁវᄃᇹώ

䚳ᶳ朊䘬ἳ⫸烉 1. 㚱斄悐攨天Ḯ妋㝸ᾳ⛘⋨ḅ⸜䳂⬠䓇䘬橼慵炻ẍ㌴㎉忁ṃ ⬠䓇䘬幓橼䘤做ね㱩ˤ㕤㗗炻忁ᾳ⛘⋨㇨㚱ḅ⸜䳂⬠䓇䘬橼慵炻 ⯙㗗㇨天侫⮇䘬⮵尉ˤỮ䓙㕤忁ᾳ⛘⋨䘬ḅ⸜䳂⬠䓇庫⣂炻徸ᶨ 侫⮇㭼庫⚘暋炻㕤㗗⎒傥㉥㞍℞ᷕᶨ悐ấ(㭼⤪婒炻2000 ⎵)⬠䓇 䘬橼慵炻䃞⼴㟡㒂忁ᶨ悐↮⬠䓇䘬橼慵⍣Ộ妰㇨㚱⬠䓇䘬橼慵ね 㱩ˤ 2. 天Ḯ妋ᶨ⟲䌱䰛⛘墉㇨㚱╖㟒䌱䰛䘬ね㱩(ἳ⤪炻Ḯ妋⬫ Ᾱ䘬⸛⛯䓊慷)ˤ忁㧋炻忁⟲⛘墉㇨㚱╖㟒䌱䰛䘬䓊慷⯙㗗㇨天侫 ⮇䘬⮵尉ˤỮ㗗炻䓙㕤忁⟲⛘墉䘬䌱䰛㟒㔠⼰⣂炻䃉㱽ᶨᶨ≈ẍ 侫⮇炻⎒傥⽆ᷕ㉥⍾ᶨ悐ấ(㭼⤪婒炻㉥⍾ 100 㟒)╖㟒䌱䰛炻䃞 ⼴䓐忁ᶨ悐↮╖㟒䌱䰛䘬䓊慷炻⍣Ộ妰忁⟲⛘墉㇨㚱╖㟒䌱䰛䘬 䓊慷ˤ 3. 天侫⮇㝸㈡䟚⻰䘬㭢 ⋲⼹(ἳ⤪炻侫⮇㭢 ⋲⼹䘬䭬 ⚵)ˤ忁䧖侫⮇㗗ⷞ㚱䟜⢆⿏䘬炻⚈䁢㷔慷ᶨᾳ⯙⼿䘤⮬ᶨᾳˤ忁 㧋炻⌛ἧ䟚⻰䘬ᾳ㔠ᶵ㗗⼰⣂炻ḇᶵ⎗傥ᶨᶨ忚埴娎槿炻侴㗗⽆ ᷕ㉥⍾ᶨ悐ấ(㭼⤪婒炻㉥⍾ 10 䘤)䟚⻰Ἦ忚埴娎槿炻䃞⼴䓐忁ᶨ 悐↮䟚⻰䘬㭢 ⋲⼹炻⍣Ộ妰忁㈡䟚⻰ᷕ㇨㚱䟚⻰䘬㭢 ⋲⼹ˤ ㆹᾹ㇨天侫⮇䘬⮵尉ᷳℐ橼⎓ ᕴᡏ炻℞ᷕ㭷ᶨᾳ侫⮇⮵尉 ⎓ ঁᡏ炻⽆䷥橼ᷕ㉥⍾䘬ᶨ悐ấᾳ橼⎓ ䷥橼䘬ᶨᾳኬҁ炻㧋 㛔ᷕᾳ橼䘬㔠䚖⎓ ኬҁޑ৒ໆˤ ⛐䫔ᶨᾳἳ⫸ᷕ炻㇨㊯⛘⋨ḅ⸜䳂⬠䓇橼慵䘬ℐ橼㗗䷥橼炻 㭷ᾳ⬠䓇橼慵㗗ᾳ橼炻⽆ᷕ㉥⍾䘬 200 ⎵⬠䓇ᷳ橼慵㗗䷥橼䘬ᶨ ᾳ㧋㛔炻㧋㛔䘬⭡慷㗗 200ˤ

⛐䫔Ḵᾳἳ⫸ᷕ炻䌱䰛⛘墉╖㟒䌱䰛䓊慷䘬ℐ橼㗗䷥橼炻㭷 ᾳ╖㟒䌱䰛䘬䓊慷㗗ᾳ橼炻⽆ᷕ㉥⍾䘬 100 ᾳ╖㟒䌱䰛ᷳ䓊慷㗗 ䷥橼䘬ᶨᾳ㧋㛔炻㧋㛔䘬⭡慷㗗 100ˤ ⛐䫔ᶱᾳἳ⫸ᷕ炻䟚⻰㭢 ⋲⼹䘬ℐ橼㗗䷥橼炻㭷䘤䟚⻰䘬 㭢 ⋲⼹㗗ᾳ橼炻⽆ᷕ㉥⍾䘬 10 䘤䟚⻰㗗䷥橼ᷳᶨᾳ㧋㛔炻㧋 㛔䘬⭡慷㗗 10ˤ ㆹᾹ䚳⇘炻⛐䴙妰墉㇨婯⇘䘬侫⮇⮵尉炻㗗ᶨ䧖㔠慷㊯䣢ˤ ⤪⛐䫔ᶨᾳἳ⫸ᷕ炻ㆹᾹ侫⮇䘬⮵尉㗗㇨㊯⛘⋨⎬ḅ⸜䳂⬠䓇䘬 橼慵炻侴ᶵ㗗䰈䴙㊯忁ṃ⬠䓇㛔幓ˤ ䷥橼ᷕ⊭⏓䘬ᾳ橼㔠⼨⼨⼰⣂(⤪䫔ᶨᾳἳ⫸冯䫔Ḵᾳἳ ⫸)炻㚱㗪䷥橼ᷕ⊭⏓䘬ᾳ㔠ᶵ㗗⼰⣂炻Ữ侫⮇㗪ⷞ㚱䟜⢆⿏(⤪ 䫔ᶱᾳἳ⫸)炻⚈㬌炻ㆹᾹ忂ⷠ㗗⽆䷥橼ᷕ㉥⍾ᶨᾳ㧋㛔炻䃞⼴㟡 㒂㧋㛔䘬䈡⿏⍣Ộ妰䷥橼䘬䚠ㅱ䈡⿏ˤ

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1. 婒㖶⛐ẍᶳ⓷柴ᷕ炻䷥橼ˣᾳ橼ˣ㧋㛔ˣ㧋㛔䘬⭡慷⎬㊯Ṩ 湤ˤ (1) 䁢Ḯ侫⮇㝸⛘⚳ᷕ䔊㤕䓇㔠⬠⋯⬠侫娎䘬ね㱩炻⽆ᷕ ㉥㞍Ḯ 200 ⎵侫䓇䘬ㆸ䷦烊 (2) 䁢ḮḮ妋ᶨ㈡䅰㲉䘬ἧ䓐⢥␥炻⽆ᷕ㉥⍾Ḯ 10 ᾳ忚埴 娎槿烊 (3) 䁢Ḯ侫⮇㝸℔⚺ᶨ⸜ᷕ㭷⣑忚⚺䘬Ṣ㔠炻⛐℞ᷕ䘬 30 ⣑墉⮵忚⚺䘬Ṣ㔠忚埴Ḯ䴙妰ˤ 2. 冱ᶨᾳ⛐⮎晃䓇㳣ᷕ忂忶㧋㛔䞼䨞䷥橼䘬ἳ⫸ˤ

16.2

πӮᇴ

㝸䎕䫔ᶨ⮷䳬⛐ᶨ㫉㔠⬠㷔槿ᷕ䘬ㆸ䷦⤪ᶳ烉 86ˣ91ˣ100ˣ72ˣ93ˣ89ˣ90ˣ85ˣ75ˣ95ˤ 忁ᾳ⮷䳬䘬⸛⛯ㆸ䷦㗗⣂⮹烎

⼰㖶栗炻忁ᾳ⸛⛯ㆸ䷦⯙㗗 86 91 100 72 93 89 90 85 75 95 87.6 10 + + + + + + + + + = _ˤ ᶨ凔⛘炻⤪㝄㚱 n ᾳ㔠 1 x ˣx ˣɃˣ₂ x 炻_n 恋湤 = + + + 1 2 1 ( _n) x x x x n (1) ⎓ 忁 n ᾳ㔠䘬ѳ֡ኧ炻 x 嬨ἄˬx-Bar˭ˤ 䁢Ḯ㚠⮓㕡ὧ炻㚱㗪⮯x₁ + x₂ + + x_n姀ἄ 1 n i i x = 炻℞ᷕˬ Σ ˭ 㗗㯪␴䫎嘇炻嬨ἄˬsigma˭ˤ 1 n i i x = 嬨ἄˬΣ − x i− _{炻i ⽆ 1 ⇘ n˭炻} 堐䣢⽆x ≈⇘₁ x 䘬␴ˤ㕤㗗℔⺷(1)⎗ẍ⮓ㆸ_n = = 1 1 n i i x x n (1)

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1. 妰䬿ᶳ↿⎬䳬㔠䘬⸛⛯㔠烉 (1) 1.4ˣ2.8ˣ5.3ˣ3.7ˣ2.3烊 (2) −0.3_{ǵ0.2ǵ0.3ǵ 0.4}− _{ǵ0.6ǵ0.3ǵ0.5ǵ 0.4}− _ˤ 2. 䓐㯪␴䫎嘇ˬ Σ ˭堐䣢ᶳ↿⎬⺷烉ˤ (1) P₁ +P₂ + +P_{10烊 (2)} 1 2 n y + y + + y _ˤ ⛐ᶨ㫉䔊㤕侫ᷕ炻侫䓇㚱ᶨ叔⣂⎵ˤㆹᾹ゛Ḯ妋忁ᶨ叔⣂⎵ 侫䓇䘬㔠⬠⸛⛯ㆸ䷦ˤỮ⤪㝄⮯ṾᾹ䘬ㆸ䷦ℐ悐≈⛐ᶨ崟ℵ昌ẍ 侫䓇䷥㔠炻⋩↮湣䄑ˤ忁㗪炻⎗ẍ㍉䓐㧋㛔Ộ妰䷥橼䘬㕡㱽炻⌛ ⽆ᷕ㉥㞍悐↮侫䓇䘬ㆸ䷦炻䓐ṾᾹ䘬⸛⛯ㆸ䷦⍣Ộ妰㇨㚱侫䓇䘬 ⸛⛯ㆸ䷦ˤ ䷥橼ᷕ㇨㚱ᾳ橼䘬⸛⛯㔠⎓ ᕴᡏѳ֡ኧ炻㧋㛔ᷕ㇨㚱ᾳ橼 䘬⸛⛯㔠⎓ ኬҁѳ֡ኧˤ⮵㕤䓙ᶨ叔⣂⎵侫䓇䘬ㆸ䷦䳬ㆸᷳ䷥

橼Ἦ婒炻㇨㚱侫䓇䘬⸛⛯ㆸ䷦⯙㗗䷥橼⸛⛯㔠炻㇨㉥㞍䘬悐↮侫 䓇ᷳ⸛⛯ㆸ䷦⯙㗗㧋㛔⸛⛯㔠ˤ忂ⷠㆹᾹ䓐㧋㛔⸛⛯㔠⍣Ộ妰䷥ 橼⸛⛯㔠ˤᶨ凔Ἦ婒炻㧋㛔⭡慷崲⣏炻忁䧖Ộ妰ḇ⯙崲䱦䡢ˤἳ ⤪炻㉥㞍䘬侫䓇崲⣂炻㇨㉥㞍䘬侫䓇ᷳ⸛⛯ㆸ䷦⯙崲㍍役䷥⸛⛯ ㆸ䷦ˤ Ȝּ 1ȝ ⽆⍫≈䔊㤕侫娎䘬⬠䓇ᷕ炻㉥㞍Ḯ 30 ⎵⬠䓇䘬㔠⬠ㆸ ䷦炻↮㔠⤪ᶳ烉 90 84 84 86 87 98 78 82 90 93 68 95 84 71 78 61 94 88 77 100 70 97 85 68 99 88 85 92 93 97 妰䬿㧋㛔⸛⛯㔠(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ

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ྋ !! 1 2562 (90 84 97) 85 30 30 x = + + + = ≈ _ˤ ⌛㧋㛔⸛⛯㔠䁢 85ˤ 㕤㗗⎗ẍỘ妰炻⍫≈䔊㤕侫娎䘬⬠䓇ᷳ㔠⬠⸛⛯ㆸ䷦䲬 䁢 85 ↮ˤ Ȝּ 2ȝ ⽆ᶨ㈡㨇☐暞ẞ㮃✗ᷕ⍾↢Ḯ 20 ẞ炻䧙⬫Ᾱ䘬慵慷⤪ ᶳ(╖ỵ烉kg)烉 210 208 200 205 202 218 206 214 215 207 195 207 218 192 202 216 185 227 187 215 妰䬿㧋㛔⸛⛯㔠(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ

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ྋ !! 1 4129 (210 208 215) 206 20 20 x = + + + = ≈ _kgˤ ⌛㧋㛔⸛⛯㔠䁢 206 kgˤ 㕤㗗⎗ẍỘ妰炻忁㈡㨇☐暞ẞ㮃✗⸛⛯㭷ẞ䲬慵 206 kgˤ 㛔柴ᷕ䘬㧋㛔㔠㒂⣏炻侴ᶼ悥⛐ 200 ⶎ⎛㲊≽ˤ忁㗪炻 ḇ⎗ẍ㍉䓐ᶳ朊䘬䬿㱽烉 ⮯ᶲ朊⎬㔠㒂⎴㗪㷃⍣ 200炻⼿⇘ᶨ䳬㕘㔠㒂烉 10 8 0 5 2 18 6 14 15 7 5 − _{7 18} −_{8 2 16} −_{15 27} −_{13 15}

妰䬿忁䳬㕘㔠㒂䘬⸛⛯㔠炻⼿ 1 129 (10 8 15) 6 20 20 x′ = + + + = ≈ _炻 㕤㗗炻㇨㯪䘬⸛⛯㔠ㅱ娚㗗 200 6 200 206 x = x′ + ≈ + = _kg炻 ㇨⼿䘬䳸㝄冯⇵朊ᷳ䳸㝄ᶨ㧋ˤㆹᾹ䚳⇘炻㍉䓐忁䧖䬿 㱽炻⎗ẍἧ⍫冯妰䬿䘬㔠㒂嬲⮷炻妰䬿崟Ἦ庫䯉ὧˤ ᶨ凔⛘炻⤪㝄⮯ᶨ䳬㔠㒂x ˣ₁ x ˣɃˣ₂ x ⎴㗪㷃⍣ᶨᾳ怑䔞_n 䘬ⷠ㔠 a 6炻⼿⇘ 1 1 x′ = x −a_ˣ 2 2 x′ = x −a_ˣɃˣ n n x′ = x −a_炻 恋湤 1 1 x = x′+a_ˣ 2 2 x = x′ +a_ˣɃˣ n n x = x′ +a_炻 ⚈㬌炻 1 2 1 2 1 2 2 1 ( ) 1 [( ) ( ) ( )] 1 [( ) ] 1 1 ( ) n n n n x x x x n x a x a x a n x x x na n x x x na n n x a = + + + ′ ′ ′ = + + + + + + ′ ′ ′ = + + + + ′ ′ ′ = + + + + ′ = + ⌛ _x = _x′ +_{a (2)} ⛐ἳ 2 䘬䫔Ḵ䧖䬿㱽ᷕ炻㬋㗗⇑䓐Ḯ℔⺷(2)ˤ 6 _{ⷠ㔠 a 忂ⷠ⍾㍍役㕤㧋㛔⸛⛯㔠(䲬䔍Ộ妰)䘬庫ˬ㔜˭䘬㔠ˤ}

Ȝּ 3ȝ 㝸ⶍṢ⛐ 30 ⣑ᷕ≈ⶍᶨ䧖暞ẞ䘬㖍䓊慷炻㚱 2 ⣑㗗 51 ẞˣ3 ⣑㗗 52 ẞˣ6 ⣑㗗 53 ẞˣ8 ⣑㗗 54 ẞˣ7 ⣑㗗 55 ẞˣ3 ⣑㗗 56 ẞˣ1 ⣑㗗 57 ẞˤ妰䬿忁ᾳⶍṢ 30 ⣑ ᷕ䘬⸛⛯㖍䓊慷(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ

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ྋ !! ⛐ᶲ朊 30 ᾳ㔠㒂ᷕ炻51 ↢䎦 2 㫉ˣ52 ↢䎦 3 㫉ˣ53 ↢ 䎦 6 㫉ˣ54 ↢䎦 8 㫉ˣ55 ↢䎦 7 㫉ˣ56 ↢䎦 3 㫉ˣ57 ↢䎦 1 㫉ˤ䓙㕤忁䳬㔠㒂悥㭼 50 䦵⣏ᶨ溆炻ㆹᾹ⇑䓐 ℔⺷(2)妰䬿⬫Ᾱ䘬⸛⛯㔠炻᷎⮯℔⺷ᷕ䘬ⷠ㔠 a ⍾ἄ 50ˤ ⮯㔠㒂 51ˣ52ˣ53ˣ54ˣ55ˣ56ˣ57 ⎴㗪㷃⍣ 50炻⼿ ⇘ 1 2 3 4 5 6 7 ⬫Ᾱ↢䎦䘬㫉㔠ὅ㫉㗗 2 3 6 8 7 3 1 恋湤炻忁䳬㕘㔠㒂䘬⸛⛯㔠㗗 1 2 2 3 3 6 4 8 5 7 6 3 7 1 118 4 30 30 x′ = × + × + × + × + × + × + × = ≈ 㟡㒂℔⺷(2)炻 4 50 54 x = x′ +a ≈ + = _ẞ炻 ⌛忁ᾳⶍṢ 30 ⣑ᷕ䘬⸛⛯㖍䓊慷䁢 54 ẞˤ 㕤㗗⎗ẍỘ妰炻忁ᾳⶍṢ⛐忁 30 ⣑⇵⼴䘬ᶨ㭝㗪攻ℏ炻 ⸛⛯㖍䓊慷䲬䁢 54 ẞˤ ᶨ凔Ἦ婒炻⤪㝄⛐ n ᾳ㔠ᷕ炻x ↢䎦₁ f 㫉ˣ₁ x ↢䎦₂ f 㫉ˣɃˣ₂ k x ↢䎦 f 㫉(忁墉_k f₁ + f₂ + + f_k = n_{)炻恋湤㟡㒂℔⺷(1)炻忁 n ᾳ㔠} 䘬⸛⛯㔠⎗ẍ堐䣢䁢 _x = x f1 1 + x f2 2 + + x fk k n 7 (1′ ) ㆾ䯉姀ἄ 7 _{忁ᾳ⸛⛯㔠⎓ у៾ѳ֡ኧ炻℞ᷕ} 1 f ˣ f ˣɃˣ₂ f ⎓ _k ៾ˤ

= = 1 1 k i i i x x f n (1′ ) 㬋⤪ἳ 3 恋㧋炻䔞㧋㛔ᷕ㚱ᶵ⮹㔠㒂⣂㫉慵墯↢䎦㗪炻⇑䓐℔ ⺷(1′ )妰䬿㧋㛔⸛⛯㔠㭼庫䯉ὧˤ

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1. ㉥㷔Ḯ 10 㟒勞㧡䘬檀炻䳸㝄⤪ᶳ(╖ỵ烉cm)烉 25 41 40 43 22 14 19 39 21 42 妰䬿㧋㛔⸛⛯㔠(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ 2. ⇑䓐℔⺷(2)妰䬿ᶳ朊⎬䳬㔠㒂䘬⸛⛯㔠(䳸㝄ᾅ䔁⇘ᾳỵ)烉 (1) 105ˣ103ˣ101ˣ100ˣ114ˣ108ˣ110ˣ106ˣ98ˣ102烊 (2) 4203ˣ4204ˣ4200ˣ4194ˣ4204ˣ4201ˣ4195ˣ4199烊 3. ⽆ᶨ㇨ᷕ⬠㝸⸜䳂䘬ℕᾳ䎕ᷕ㉥㷔Ḯ 24 ⎵䓟⎴⬠䘬幓檀炻 䳸㝄⤪ᶳ(╖ỵ烉cm)烉 155 157 159 162 162 163 164 164 165 165 165 166 166 167 167 167 168 169 169 170 171 171 172 174 忁ᾳ⸜䳂䓟⬠䓇䘬⸛⛯幓檀䲬㗗⣂⮹(䳸㝄ᾅ䔁⇘ᾳỵ)烎 4. ⛐ᶨᾳ䎕ᷕ䘬 40 ⎵⬠䓇ᷕ炻14 㬚䘬㚱 5 Ṣˣ15 㬚䘬㚱 30 Ṣˣ16 㬚䘬㚱 4 Ṣˣ17 㬚䘬㚱 1 Ṣˤ妰䬿忁ᾳ䎕⬠䓇䘬⸛ ⛯⸜漉(䳸㝄ᾅ䔁⇘⮷㔠溆⼴䫔ᶨỵ)ˤ

௫

!!

ᗟ

!!

Ȉ

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˟

! 1. ᶨᾳᷕ⬠嵛䎫昲䘬 20 ⎵昲⒉ᷳ幓檀⤪ᶳ(╖ỵ烉cm)烉 170 167 171 168 160 172 168 162 172 169 164 174 169 165 175 170 165 167 170 172 妰䬿⸛⛯幓檀(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ

2. 䁢Ḯ㩊㞍ᶨ㈡暞ẞ䘬岒慷炻⽆ᷕ㉥⍾ 10 ẞ炻慷⼿⬫Ᾱ䘬攟⹎ ⤪ᶳ(╖ỵ烉cm)烉 22.36 22.35 22.33 22.35 22.37 22.34 22.38 22.36 22.32 22.35 (1) ⛐忁ᾳ⓷柴ᷕ炻䷥橼ˣᾳ橼ˣ㧋㛔冯㧋㛔⭡慷⎬㊯Ṩ湤烎 (2) 妰䬿㧋㛔⸛⛯㔠(䳸㝄ᾅ䔁⇘⮷㔠溆⼴䫔Ḵỵ)ˤ (㍸䣢烉⇑䓐℔⺷(2)妰䬿㗪炻⎗⍾a = 22.30)ˤ 3. 䁢Ḯ侫⮇ᶨ⟲⮎槿㜿墉㧡剿䘬檀⹎炻⽆ᷕ㉥⍾Ḯ 20 㟒炻᷎慷 ⼿㟒檀⤪ᶳ(╖ỵ烉cm)烉 346 294 365 315 339 313 317 305 321 325 315 329 324 329 368 336 366 308 301 362 (1) ⛐忁ᾳ⓷柴ᷕ炻䷥橼冯㧋㛔⎬㊯Ṩ湤烎 (2) 妰䬿㧋㛔⸛⛯㔠(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ 4. 㝸彚㤕㓡列⟜䁢Ḯ怠㑯㯜䧣列䧖炻⛐ 10 ᾳ娎槿溆⮵䓚ˣḁℑ ᾳ⑩䧖ἄḮ⮵㭼娎槿炻䳸㝄⤪ᶳ烉 ⎬娎槿溆℔䔅䓊慷(╖ỵ烉kg) ⑩ 䧖 _{1 2 3 4 5 6 7 8 9 10} 䓚 779 817 853 793 740 963 794 777 875 864 ḁ 808 771 725 750 750 859 745 740 706 824 恋ᾳ⑩䧖䘬⸛⛯䓊慷庫檀烎 5. 㝸䎕ᶨ㫉婆㔯㷔槿䘬ㆸ䷦⤪ᶳ烉⼿ 100 ↮䘬 7 Ṣˣ90 ↮䘬 14 Ṣˣ80 ↮䘬 17 Ṣˣ70 ↮䘬 8 Ṣˣ60 ↮䘬 2 Ṣˣ50 ↮䘬 2 Ṣˤ 妰䬿忁㫉侫娎ℐ䎕䘬⸛⛯ㆸ䷦(䳸㝄ᾅ䔁⇘ᾳỵ)ˤ 6. ⤪㝄ℑ䳬㔠x ˣ₁ x ˣɃˣ₂ x 冯_n y ˣ₁ y ˣɃˣ₂ y 䘬⸛⛯㔠↮⇍_n 㗗 x 冯 y 炻恋湤ᶨ䳬㕘㔠 1 1 x + y _ˣ 2 2 x + y _ˣɃˣ n n x + y 䘬⸛⛯㔠㗗Ṩ湤烎䁢Ṩ湤烎

16.3

͞म

ℑ⎘㨇⸲⎴㗪䓇䓊䚜⼹㗗 40 mm 䘬暞ẞ炻⽆䓊⑩ᷕ⎬㉥↢ 10 ẞ忚埴㷔慷炻䳸㝄⤪ᶳ(╖ỵ烉mm)烉 㨇⸲䓚 40 39.8 40.1 40.2 39.9 40 40.2 39.8 40.2 39.8 㨇⸲ḁ 40 40 39.9 40 39.9 40.2 40 40.1 40 39.9 ⇑䓐℔⺷(2)↮⇍妰䬿忁ℑ䳬㔠㒂䘬⸛⛯㔠(⛐℔⺷(2)ᷕ⍾ 40 a = )炻⼿ 1 40 [0 ( 0.2) ( 0.2)] 40 10 1 40 [0 0 ( 0.1)] 40 10 x x = + + − + + − = = + + + + − = 䓚 ḁ ⌛忁ℑ䳬暞ẞ䚜⼹㔠㒂䘬⸛⛯㔠悥㗗 40 mm炻忁㗪傥ᶵ傥婒炻⛐ ἧ暞ẞ䘬䚜⼹䫎⎰夷⭂㕡朊炻ℑ⎘㨇⸲≈ⶍ䘬ね㱩ᶨ㧋␊烎 ᶲ朊堐ᷕ䘬㔠㒂⤪⚾ 16-1 ㇨䣢ˤ⽆⚾ᷕ䚳⇘炻㨇⸲䓚䓇䓊暞 ẞ䘬䚜⼹冯夷⭂⯢⮠ᷳῷⶖ庫⣏炻⎬溆ῷ暊 40 mm 䶂庫⣂烊㨇⸲ ḁ䓇䓊暞ẞ䘬䚜⼹冯夷⭂⯢⮠ᷳῷⶖ庫⮷炻⎬溆㭼庫普ᷕ⛐ 40 mm 䶂䘬旬役ˤ忁婒㖶炻⛐ἧ暞ẞ䘬䚜⼹䫎⎰夷⭂㕡朊炻㨇⸲ḁ 㭼㨇⸲䓚天⤥ˤ ⚾ 16-1 5 7 1 2 3 4 6 8 9 10 㨇⸲䓚 40.2 40.1 40 39.9 39.8 㔠㒂⸷嘇 暞ẞ 䚜⼹ (mm) 5 7 1 2 3 4 6 8 9 10 㨇⸲ḁ 40.2 40.1 40 39.9 39.8 㔠㒂⸷嘇 暞ẞ 䚜⼹ (mm)

⾶㧋䓐㔠慷Ἦ堐䣢㧋㛔䘬㔠㒂ῷ暊⸛⛯㔠ᷳ⣏⮷␊烎⛐㛔 ἳᷕ炻㨇⸲䓚䓇䓊䘬 10 ᾳ暞ẞ䚜⼹䘬 mm 㔠↮⇍冯㧋㛔⸛⛯㔠 40 䘬ῷⶖ㗗烉 0 −0.2 _{0.1 0.2} −_{0.1 0 0.2} −_{0.2 0.2} −_0.2 ㆹᾹ⭡㖻゛⇘炻㗗⏎⎗ẍ䓐ᶲ朊⎬ᾳῷⶖ䘬␴Ἦ堉慷暞ẞ䚜⼹䚠 ⮵㕤⸛⛯䚜⼹ᷳῷⶖ⣏⮷␊烎ᶵ⎗ẍ炻⚈䁢ᶵ暋槿嫱炻䓙㕤㬋ῷ ⶖ冯屈ῷⶖ䚠Ḻ㉝扟炻ᶲ朊⎬ῷⶖ䘬␴䫱㕤暞ˤ天妋㰢忁ᾳ䞃 䚦炻彎㱽ᶵ⎒ᶨ䧖炻忁墉㍉䓐⮯ᶲ朊⎬ῷⶖ⸛㕡⼴ℵ䚠≈䘬彎 㱽炻忁㧋炻℞ᷕ⎬枭⯙ᶵ⎗傥㗗屈㔠Ḯˤ怬㚱ᶨᾳ⓷柴炻⎬ῷⶖ 䘬⸛㕡␴冯㧋㛔⭡慷㚱斄炻㧋㛔⭡慷崲⣏炻⎬ῷⶖ䘬⸛㕡␴ḇ崲 ⣏ˤ䁢Ḯ㌺昌㧋㛔⭡慷䘬⼙枧炻ㆹᾹ⮯⎬ῷⶖ⸛㕡␴ℵ昌ẍ㧋㛔 ⭡慷 n炻⌛䓐⎬ῷⶖ⸛㕡䘬⸛⛯㔠(䓐 2 s 堐䣢)Ἦ堉慷㧋㛔䘬㔠㒂 ῷ暊㧋㛔⸛⛯㔠䘬⣏⮷ˤ㕤㗗炻⮵㕤㨇⸲䓚炻 2 2 2 2 2 2 2 2 1 [(40 40) (39.8 40) (39.8 40) ] 10 1 [0 ( 0.2) ( 0.2) ] 10 1 0.26 10 0.026 (mm ) s = − + − + + − = + − + + − = × = ⮵㕤㨇⸲ḁ炻 2 2 2 2 2 2 2 2 1 [(40 40) (40 40) (39.9 40) ] 10 1 [0 0 ( 0.1) ] 10 1 0.08 10 0.008 (mm ) s = − + − + + − = + + + − = × = 䓙㕤 0.026> 0.008炻婒㖶㨇⸲䓚䓇䓊䘬暞ẞ䚜⼹冯夷⭂⯢⮠ ῷⶖ庫⣏炻㨇⸲ḁ䓇䓊䘬暞ẞ䚜⼹冯夷⭂⯢⮠ῷⶖ庫⮷ˤ

ᶨ凔⛘炻㧋㛔ᷕ⎬㔠㒂冯㧋㛔⸛⛯㔠䘬ⶖᷳ⸛㕡䘬⸛⛯㔠 2 = − 2 + − 2 + + − 2 1 2 1 [( ) ( ) ( _n ) ] s x x x x x x n (3) ⎓ ኬҁБৡ炻䓐Ἦ堉慷ᶨᾳ㧋㛔䘬㲊≽⣏⮷(⌛㧋㛔ᷕ䘬㔠㒂ῷ 暊㧋㛔⸛⛯㔠䘬⣏⮷)ˤ㧋㛔㕡ⶖ崲⣏炻婒㖶㧋㛔䘬㲊≽崲⣏ˤ 䁢Ḯ㚠⮓㕡ὧ炻㧋㛔㕡ⶖⷠ⮓ἄ烉 = = − 2 2 1 1 ( ) n i i s x x n 䔞㧋㛔⭡慷⼰⣏㗪炻㧋㛔㕡ⶖ⼰㍍役⍵㗈䷥橼㲊≽⣏⮷䘬䈡 ⽝㔠ȹᕴᡏБৡˤ忂ⷠ㗗䓐㧋㛔㕡ⶖ⍣Ộ妰䷥橼㕡ⶖˤ忁㧋炻忂 忶㭼庫ℑᾳ㧋㛔㕡ⶖ炻⎗ẍ役Ụ⛘㭼庫䚠ㅱ䘬ℑᾳ䷥橼㕡ⶖᷳ⣏ ⮷ˤ Ȝּȝ ⶚䞍ℑᾳ㧋㛔烉 䓚烉 9.9 10.3 9.8 10.1 10.4 10 9.8 9.7 ḁ烉 10.2 10 9.5 10.3 10.5 9.6 9.8 10.1 ↮⇍妰䬿ℑᾳ㧋㛔㕡ⶖˤ

ś

ྋ !! 㟡㒂℔⺷(2)(⍾a =10)炻㚱 1 10 ( 0.1 0.3 0.2 0.1 0.4 0 0.2 0.3) 8 1 10 0 8 10 1 10 (0.2 0 0.5 0.3 0.5 0.4 0.2 0.1) 8 1 10 0 8 10 x x = + − + − + + + − − = + × = = + + − + + − − + = + × = 䓚 ḁ 㕤㗗炻

2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 [(9.9 10) (10.3 10) (9.7 10) ] 8 1 [( 0.1) 0.3 ( 0.3) ] 8 1 (0.01 0.09 0.09) 8 1 0.44 8 0.055 1 [(10.2 10) (10 10) (10.1 10) ] 8 1 [0.2 0 0.1 ] 8 1 (0.04 0 0.01) 8 1 0.84 8 0.105 s s = − + − + + − = − + + + − = + + + = × = = − + − + + − = + + + = + + + = × = 䓚 ḁ ⽆s_䓚2 < s_ḁ2 _{䞍忻炻㧋㛔ḁ㭼㧋㛔䓚䘬㲊≽⣏ˤ} ⛐㚱ṃね㱩ᶳ炻暨天䓐⇘㧋㛔㕡ⶖ䘬䬿埻⸛㕡㟡 = = − 2 1 1 ( ) n i i s x x n (4) ᷎㈲⬫⎓ ኬҁ኱ྗৡ炻⬫ḇ㗗ᶨᾳ䓐Ἦ堉慷㧋㛔㲊≽⣏⮷䘬慵天 ᷳ慷ˤ㧋㛔㔠㒂冯㧋㛔㕡ⶖ䘬⹎慷╖ỵ㗗ᶵᶨ农䘬ˤ⤪⛐㛔䭨㚱斄 暞ẞ䚜⼹䘬ἳ⫸ᷕ炻㧋㛔㔠㒂䘬╖ỵ㗗 mm炻侴㧋㛔㕡ⶖ䘬╖ỵ㗗 mm2ˤỮ㧋㛔㔠㒂冯㧋㛔㧁㸾ⶖ䘬⹎慷╖ỵ⌣㗗ᶨ农䘬ˤ ⛐㛔䭨㚱斄暞ẞ䚜⼹䘬ἳ⫸ᷕ炻ℑᾳ㧋㛔㧁㸾ⶖ↮⇍㗗烉 0.026 0.16 (mm) 0.008 0.089 (mm) s s = ≈ = ≈ 䓚 ḁ

ቚ

!

௫!

1. 妰䬿ᶳ↿⎬㧋㛔㕡ⶖ冯㧁㸾ⶖ(䳸㝄ᾅ䔁⇘⮷㔠溆⼴䫔ᶨỵ) (1) −2_{ˣ2ˣ0ˣ 3}− _{ˣ 2}− _ˣ3ˣ0ˣ1烊 (2) 28ˣ24ˣ25ˣ23ˣ27ˣ24ˣ22ˣ24ˣ25ˣ28ˤ 2. ⽆䓚ˣḁℑ⎵干ⶍ干↢䘬⎴ᶨ䧖暞ẞᷕ炻⎬㉥↢ 5 ᾳ炻慷⼿ ⬫Ᾱ䘬䚜⼹(╖ỵ烉mm)⤪ᶳ(⚾䳁ᶲ夷⭂䘬⯢⮠㗗 10 mm)烉 䓚䓇䓊䘬暞ẞ⯢⮠ 10.05 10.02 9.97 9.96 10.00 ḁ䓇䓊䘬暞ẞ⯢⮠ 10.00 10.01 10.02 9.97 10.00 ↮⇍妰䬿ᶲ朊ℑᾳ㧋㛔䘬⸛⛯㔠冯㕡ⶖ炻婒㖶⛐ἧ暞ẞ䘬䚜 ⼹䫎⎰夷⭂㕡朊炻婘 ⼿庫⤥ˤ

16.4

͞म۞ᖎ̼ࢍზ

8 ㊱䄏℔⺷(3)妰䬿㧋㛔㕡ⶖ炻妰䬿慷㭼庫⣏炻ᶳ朊ṳ䳡㕡ⶖ䘬 䯉⊾妰䬿㕡㱽ˤ 䁢Ḯ䯉⊾妶婾炻ㆹᾹ`⭂㧋㛔ᷕ⊭⏓ 3 ᾳ㔠㒂 x ˣ₁ x ˣ₂ x 炻₃ ⬫Ᾱ䘬⸛⛯㔠㗗 x 炻恋湤㧋㛔㕡ⶖ㗗 2 2 2 2 1 2 3 1 [( ) ( ) ( ) ] 3 s = x −x + x −x + x −x _ˤ ⮯㕡㊔嘇ℏ䘬⎬枭⯽攳⼴ℵ㔜䎮炻⼿⇘ 2 2 2 2 2 2 2 1 1 2 2 3 3 2 2 2 2 1 2 3 1 2 3 2 2 2 2 1 2 3 1 2 3 2 2 2 2 2 1 2 3 2 2 2 2 1 2 3 1 [( 2 ) ( 2 ) ( 2 )] 3 1 [( ) 2( ) 3 ] 3 1 [( ) 2 3 ( ) 3 ] 3 3 1 [( ) 2 3 3 ] 3 1 [( ) 3 ] 3 s x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x = − + + − + + − + = + + − + + + + + = + + − × × + = + + − × + = + + − 8 _{㕡ⶖ䘬䯉⊾妰䬿℔⺷ᶵἄ䁢天㯪ˤ}

ᶨ凔⛘炻⤪㝄㧋㛔䘬⭡慷㗗 n炻恋湤㧋㛔㕡ⶖ⎗ẍ䓐ᶳ朊䘬 ℔⺷妰䬿烉 2 = 2 + 2 + + 2 − 2 1 2 1 [( _n) ] s x x x n x n (5) ㆾ侭䯉姀ἄ = = − 2 2 2 1 1 n i i s x n x n (5) 䓐℔⺷(5)妰䬿㧋㛔㕡ⶖ炻㗗䚜㍍妰䬿⎬ᾳ㔠㒂䘬⸛㕡炻侴ᶵ ⽭妰䬿⎬ᾳ㔠㒂冯㧋㛔⸛⛯㔠䘬ⶖᷳ⸛㕡炻⚈㬌⬫㭼䓐℔⺷(3) 妰䬿⮹ᶨᾳ㬍樇炻㚱㗪㭼庫㕡ὧˤ Ȝּ 1ȝ 妰䬿ᶳ朊㧋㛔䘬㕡ⶖ(䳸㝄ᾅ䔁⇘⮷㔠溆⼴䫔ᶨỵ)烉 3ˣ 1− _{ˣ2ˣ1ˣ 3}− _ˣ3

ś

ྋ ! ⽆妰䬿䞍忻炻㧋㛔⸛⛯㔠ᶵ㗗㔜㔠ˤ忁㗪䓐℔⺷(3)妰䬿 㧋㛔㕡ⶖ㭼庫湣䄑炻ㆹᾹ䓐℔⺷(5)Ἦ妰䬿ˤ 2 2 _{2 2 2 2 2 2} 2 1 _{3 1 2 1 3 3} 3 ( 1) 2 1 ( 3) 3 6 6 ₆ 1 ₅ 9 1 4 1 9 9 6 6 ₆ 1 25 33 6 6 36 1 25 33 6 36 5.5 0.7 4.8 s = + − + + + − + − × − + + − + = _{+ + + + + − ×} = − × = × − ≈ − =

ቚ

௫

妰䬿ᶳ朊㧋㛔䘬㕡ⶖ(䳸㝄ᾅ䔁⇘⮷㔠溆⼴䫔ᶨỵ)烉 5ǵ4ǵ4ǵ3ǵ4ǵ3ǵ2ǵ3ǵ5ǵ3Ƕ

䔞㧋㛔㔠㒂庫⣏㗪炻䓐℔⺷(5)妰䬿㧋㛔㕡ⶖṵ䃞㭼庫湣䄑ˤ ⤪㝄㔠㒂䚠Ḻ㭼庫㍍役炻䁢Ḯ㷃⮷⍫冯㔠㒂䘬妰䬿炻ㆹᾹ⎗ẍầ 䄏⇵朊䯉⊾妰䬿⸛⛯㔠䘬㕡㱽炻⮯㭷ᶨᾳ㔠㒂㷃⍣ᶨᾳ冯㧋㛔⸛ ⛯㔠㍍役䘬ⷠ㔠 aˤ`⭂㧋㛔ᷕ⊭⏓ 3 ᾳ㔠㒂x ˣ₁ x ˣ₂ x 炻ㆹᾹ₃ ἄ㚧㎃ 1 1 x′ = x −a_ˣ 2 2 x′ = x −a_ˣ 3 3 x′ = x −a_炻 恋湤 1 1 x = x′+a_ˣ 2 2 x = x′ +a_ˣ 3 3 x = x′ +a_ˤ ⍰㟡㒂℔⺷(2)炻㚱 x = x′ +a_炻 ℞ᷕ x′ 㗗x′ ˣ₁ x′ ˣ₂ x′ 䘬⸛⛯㔠炻㕤㗗炻₃ 2 2 2 2 1 2 2 2 2 2 1 2 3 2 2 2 1 2 3 2 2 2 2 1 2 3 1 [( ) ( ) ( ) ] 3 1 {[( ) ( )] [( ) ( )] [( ) ( )] } 3 1 [( ) ( ) ( ) ] 3 1 [( ) 3 ] ( (5) ) 3 s x x x x x x x a x a x a x a x a x a x x x x x x x x x x = − + − + − ′ ′ ′ ′ ′ ′ = + − + + + − + + + − + ′ ′ ′ ′ ′ ′ = − + − + − ′ ′ ′ ′ = + + − _㟡㒂℔⺷ ᶨ凔⛘炻⤪㝄㧋㛔䘬⭡慷㗗 n炻恋湤㚱 2 = ′2 + ′2 + + ′2 − ′2 1 2 1 [( _n ) ] s x x x n x n (6) ℞ᷕ 1 1 x′ = x −a_ˣ 2 2 x′ = x −a_ˣɃˣ n n x′ = x −a_炻 忁墉 a 㗗㍍役㧋㛔⸛⛯㔠䘬ⷠ㔠ˤ ᶲ⺷⎗ẍ䯉姀䁢 = ′ ′ = − 2 2 2 1 1 n i i s x n x n ( 6′ )

䓙㕤⛐㚧㎃x_i′ = x_i −a_{(i = ˣ1 2ˣɃˣn)ᷕ㇨⍾䘬ⷠ㔠 a 冯㧋} 㛔⸛⛯㔠 x 㭼庫㍍役炻⎬㔠㒂x′ 㭼庫⮷炻⚈㬌䔞㧋㛔㔠㒂⣏㗪炻_i 䓐℔⺷(6)妰䬿㧋㛔㕡ⶖ㭼庫䯉ὧˤ Ȝּ 2ȝ ⽆⮷湍䓘墉㉥⍾Ḯ䓚ˣḁℑ䧖⮷湍⎬ 10 㟒炻㷔⼿⎬㟒 檀⤪ᶳ(╖ỵ烉cm)烉 䓚烉 76 90 84 86 81 87 86 82 85 83 ḁ烉 82 84 85 89 79 80 91 89 79 74 ⒒䧖⮷湍攟䘬㭼庫㔜滲烎

ś

ྋ !! 㟡㒂柴シ炻㗗天㭼庫ℑᾳ㧋㛔㕡ⶖ䘬⣏⮷ˤ⚈䁢㧋㛔㔠 㒂庫⣏炻ㆹᾹ䓐℔⺷(6)Ἦ妰䬿ℑᾳ㧋㛔㕡ⶖ炻㬍樇⤪ᶳ烉 (1) 䡢⭂㚧㎃x_i′ = x_i −a_{ᷕ䘬ⷠ㔠 aˤ} 䓙㕤㧋㛔㔠㒂悥⛐ 80 ⶎ⎛㲊≽炻ㆹᾹ⍾a =80 ˤ (2) ⤪堐 1ˣ堐 2 ㇨䣢炻↮⇍妰䬿⎬ᾳx′ ⍲_i x′_i2 (i = ˣ1 2ˣɃˣ10)炻䃞⼴妰䬿⎬ᾳx′ 䘬␴⍲⎬ᾳ_i x′ 䘬␴炻_i2 ᷎⠓ℍ堐ᷕˤ 堐 1 (䓚䧖⮷湍) 堐 2 (ḁ䧖⮷湍) i x x′i (x −_i 80) 2 i x′ x_i x′i (x −_i 80) 2 i x′ 76 −4 16 82 2 4 90 10 100 84 4 16 84 4 16 85 5 25 86 6 36 89 9 81 81 1 1 79 −1 1 87 7 49 80 0 0 86 6 36 91 11 121 82 2 4 89 9 81 85 5 25 79 −1 ₁ 83 3 9 74 −6 ₃₆ ⎰妰 40 292 ⎰妰 32 366

(3) ⮯堐ᷕ㚱斄㔠㒂ẋℍ℔⺷(6)忚埴妰䬿烉 10 ₂ 2 2 1 2 10 2 2 2 1 2 1 10 10 1 ₄₀ 292 10 10 ₁₀ 1 (292 160) 10 1 132 10 13.2 1 10 10 1 ₃₂ 366 10 10 ₁₀ 1 (366 102.4) 10 1 263.6 10 26.36 i i i i s x x s x x = = ′ ′ = − = _{− ×} = − = × = ′ ′ = − = − × = − = × = 䓚 ḁ ⚈䁢 2 2 s_䓚 < s_{ḁ炻⎗ẍỘ妰炻䓚䧖⮷湍㭼ḁ䧖⮷湍攟䘬} 㔜滲ˤ Ȝּ 3ȝ 㝸彚娎㇨⛐ 8 ᾳ娎槿溆⮵㝸ℑᾳ㯜䧣⑩䧖忚埴㟥➡㭼⮵ 娎槿炻ℑᾳ⑩䧖⛐⎬娎槿溆䘬䔅䓊慷⤪ᶳ(╖ỵ烉kg)烉 䓚烉 804 984 989 817 919 840 912 1001 ḁ烉 856 932 930 855 872 910 897 918 ⒒ᾳ⑩䧖䘬䓊慷㭼庫䨑⭂烎

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ྋ !! 㟡㒂柴シ炻㗗天㭼庫ℑᾳ㧋㛔㕡ⶖ䘬⣏⮷ˤ䓙㕤㧋㛔㔠 㒂庫⣏炻ㆹᾹầ䄏ἳ 2 䘬㬍樇炻㟡㒂℔⺷(6)Ἦ妰䬿ℑᾳ 㧋㛔㕡ⶖˤ

(1) 䓙㕤ℑᾳ㧋㛔ᷕ䘬㔠㒂悥⛐ 900 ⶎ⎛㲊≽炻ㆹᾹ⛐ 㚧㎃x_i′ = x_i −a_{ᷕ炻⍾a =900ˤ} (2) ⤪堐 3ˣ堐 4 ㇨䣢炻↮⇍妰䬿⎬ᾳ x′ ⍲_i x′ 炻䃞⼴妰_i2 䬿⎬ᾳx′ 䘬␴⍲⎬ᾳ_i x′ 䘬␴炻᷎⠓ℍ堐ᷕˤ_i2 堐 3 (䓚䧖㯜䧣) 堐 4 (ḁ䧖㯜䧣) i x x′i (x −_i 900) 2 i x′ x_i x′i (x −_i 900) 2 i x′ 804 −96 _{9216 856} −_{44 1936} 984 84 7056 921 32 1024 989 89 7921 930 30 900 817 −83 _{6889 855} −_{45 2025} 919 19 361 872 −28 ₇₈₄ 840 −60 _{3600 910 10 100} 912 12 144 897 −3 ₉ 1001 101 10201 918 18 324 ⎰妰 66 45388 ⎰妰 −30 ₇₁₀₂ (3) ⮯堐ᷕ㚱斄㔠㒂ẋℍ℔⺷(6)忚埴妰䬿烉 8 ₂ 2 2 1 2 8 2 2 2 1 1 8 8 1 ₆₆ 45388 8 8 ₈ 1 (45388 544.5) 8 1 44843.5 8 5605 1 8 8 i i i i s x x s x x = = ′ ′ = − = − × = − = × ≈ ′ ′ = − 䓚 ḁ

2 1 ₃₀ 7102 8 8 ₈ 1 (7102 112.5) 8 1 6989.5 8 874 − = − × = − = × ≈ ⚈䁢 2 2 s_ḁ < s_{䓚炻⎗ẍỘ妰炻ḁ䧖㯜䧣㭼䓚䧖㯜䧣䘬䓊} 慷䨑⭂ˤ ㆹᾹ䚳⇘炻㧋㛔⸛⛯㔠冯㕡ⶖ䘬妰䬿⼨⼨庫䷩ˤ䁢ὧ㕤妰 䬿炻㇨ẍ㧋㛔⭡慷ㅱ䚉⎗傥ˬ㔜˭ᶨ溆炻⤪ 10ˣ20ˣ30 䫱ˤ

ቚ

௫

妰䬿ᶳ朊⎬㧋㛔㕡ⶖ(䳸㝄ᾅ䔁⇘⮷㔠溆⼴䫔ᶨỵ)烉 (1) 105ˣ103ˣ101ˣ100ˣ114ˣ108ˣ110ˣ106ˣ98ˣ102烊 (2) 423ˣ421ˣ419ˣ420ˣ421ˣ417ˣ422ˣ419ˣ423ˣ418ˤ

௫

!!

ᗟ

!!

Ȉ!!ˬ

! 1. 䓚ˣḁℑṢ⛐䚠⎴㡅ẞᶳ⎬⮬朞 10 㫉炻⎬㫉␥ᷕ䘬䑘㔠⤪ᶳ烉 䓚烉 7 8 6 8 6 5 9 10 7 4 ḁ烉 9 5 7 8 7 6 8 6 7 7 ↮⇍妰䬿ᶲ朊ℑᾳ㧋㛔㕡ⶖˤ⽆妰䬿䳸㝄䚳炻婘⮬㑲䘬ね㱩 㭼庫䨑⭂烎 2. 䓚ˣḁℑ⎘㨇☐⎴㗪䓇䓊ᶨ䧖暞ẞˤ⛐ 10 ⣑ᷕ炻ℑ⎘㨇☐㭷 ⣑↢䘬䏽䕝⑩㔠↮⇍㗗烉 䓚烉 0 1 0 2 2 0 3 1 2 4 ḁ烉 2 3 1 1 0 2 1 1 0 1

↮⇍妰䬿ᶲ朊ℑᾳ㧋㛔䘬⸛⛯㔠冯㕡ⶖˤ⽆妰䬿䳸㝄䚳炻⒒ ⎘㨇☐䘬⿏傥庫⤥烎 3. 㝸彚⟜䧖㢵䘬䓚ˣḁℑ䧖㯜䧣炻⛐忋临ℕ⸜ᷕ⎬⸜䘬⸛⛯䔅 䓊慷⤪ᶳ(╖ỵ烉kg)烉 ⑩䧖 䫔 1 ⸜ 䫔 2 ⸜ 䫔 3 ⸜ 䫔 4 ⸜ 䫔 5 ⸜ 䫔 6 ⸜ 䓚烉 900 920 900 850 910 920 ḁ烉 890 960 950 850 860 890 ⒒䧖㯜䧣䓊慷㭼庫䨑⭂烎 4. ᶳ朊㗗Ṳ⸜冯⇵⸜⛐⣏农䚠⎴㡅ẞᶳ梤梲䘬⋩柕尔ᷳ橼攟㔠 㒂(╖ỵ烉cm)烉 ⇵⸜烉 112 110 110 117 113 122 125 124 119 127 Ṳ⸜烉 111 122 115 123 114 115 118 114 116 115 ⒒⸜梤梲䘬尔ᷳ橼攟㭼庫ᶨ农烎

16.5

ᐛத̶ο

䁢ḮḮ妋ᷕ⬠䓇䘬幓橼䘤做ね㱩炻⮵㝸ᷕ⬠⎴⸜漉䘬 60 ⎵ ⤛⬠䓇ᷳ幓檀忚埴Ḯ㷔慷炻䳸㝄⤪ᶳ(╖ỵ烉cm)烉 167 154 159 166 169 159 156 166 162 158 159 156 166 160 164 160 157 156 157 161 158 158 153 158 164 158 163 158 153 157 162 162 159 154 165 166 157 151 146 151 158 160 165 158 163 163 162 161 154 165 162 162 159 157 159 149 164 168 159 153 ㆹᾹ䞍忻炻忁䳬㔠㒂䘬⸛⛯㔠炻⍵㗈Ḯ忁ṃ⬠䓇䘬⸛⛯幓 檀炻Ữ㗗炻㚱㗪⎒䞍忻忁ᶨ溆怬ᶵ⣈炻怬ⶴ㛃䞍忻幓檀⛐⒒ᾳ⮷ 䭬⚵ℏ䘬⬠䓇⣂炻⛐⒒ᾳ⮷䭬⚵䘬⬠䓇⮹炻ḇ⯙㗗ⶴ㛃䞍忻忁 60 ⎵⤛⬠䓇䘬幓檀㔠㒂⛐⎬ᾳ⮷䭬⚵㇨Ỽ䘬㭼ἳ⣏⮷ˤ䁢㬌炻暨天 ⮵忁䳬㔠㒂忚埴怑䔞㔜䎮ˤ㔜䎮㗪炻⎗ẍ㊱䄏ᶳ朊䘬㬍樇忚埴烉

(1) 妰䬿㚨⣏ῤ冯㚨⮷ῤ䘬ⶖˤ ⛐ᶲ朊䘬㔠㒂ᷕ炻㚨⣏ῤ㗗 169ˣ㚨⮷ῤ㗗 146炻⬫Ᾱ䘬ⶖ 㗗 169 146− =23_(cm)ˤ 䬿↢Ḯ㚨⣏ῤ冯㚨⮷ῤ䘬ⶖ炻⯙䞍忻忁䳬㔠㒂嬲≽䘬䭬⚵㚱 ⣂⣏ˤ (2) 㰢⭂䳬嶅冯䳬㔠ˤ ⮯ᶨ㈡㔠㒂↮䳬炻ᶨ凔㔠㒂崲⣂炻↮䘬䳬㔠ḇ崲⣂ˤ䔞㔠㒂 ⛐ 100 ᾳẍℏ㗪炻㊱䄏㔠㒂䘬⣂⮹炻ⷠ↮ㆸ 5焍12 䳬ˤ 䳬嶅㗗㊯㭷ᾳ⮷䳬䘬ℑᾳ䪗溆ᷳ攻䘬嶅暊ˤ⛐㛔ἳᷕ炻⤪㝄 ⍾䳬嶅䁢 3 cm炻恋湤䓙㕤⛐忁㈡㔠㒂ᷕ炻 23 2 7 3 3 − = = 㚨⣏ῤ 㚨⮷ῤ 䳬嶅 炻 ⼿⮯㔠㒂↮ㆸ 8 䳬烊⤪㝄⍾䳬嶅䁢 2 cm炻恋湤䓙㕤 23 111 2 2 = _炻⼿ ↮ㆸ 12 䳬ˤ劍↮ㆸ 8 䳬庫⎰怑炻⎗⍾䳬嶅䁢 3 cmˣ䳬㔠䁢 8ˤ (3) 㰢⭂↮溆ˤ ⮯㔠㒂㊱䄏 3 cm 䘬䳬嶅↮䳬㗪炻⎗ẍ↮ㆸẍᶳ 8 䳬烉 146焍149ˣ149焍152ˣ152焍155ˣ155焍158ˣ 158焍161ˣ161焍164ˣ164焍167ˣ167焍170ˤ 忁㗪ㆹᾹ䚳⇘炻㚱ṃ㔠㒂(ἳ⤪ 149ˣ158ˣ167)㛔幓⯙㗗↮ 溆炻ᶵ⤥㰢⭂⬫Ᾱ䨞䪇ㅱ娚Ⱄ㕤⒒ᶨ䳬ˤ䁢Ḯ性⃵↢䎦忁䧖ね 㱩炻⎗ẍἧ↮溆㭼㔠㒂⣂ᶨỵ⮷㔠炻᷎ᶼ㈲䫔 1 䳬䘬崟溆䦵⽖㷃 ⮷ᶨ溆ˤἳ⤪炻⎗ẍ⮯䫔 1 䳬䘬崟溆妪䁢 145.5炻忁㧋炻㇨↮䘬 8 ᾳ⮷䳬㗗烉 145.5焍148.5ˣ148.5焍151.5ˣ151.5焍154.5ˣ154.5焍157.5ˣ 157.5焍160.5ˣ160.5焍163.5ˣ163.5焍166.5ˣ166.5焍169.5ˤ (4) ↿柣䌯↮ⶫ堐ˤ ⤪堐 5 䘬䫔 1 埴ˣ䫔 2 埴㇨䣢炻䓐怠冱㗪ⓙ䤐䘬㕡㱽炻⮵句 ⛐⎬ᾳ⮷䳬ℏ䘬㔠㒂忚埴䳗妰ˤ䃞⼴炻㔠↢句⛐⎬ᾳ⮷䳬ℏ䘬㔠 㒂ᷳᾳ㔠(⎓ ᓎኧ)炻᷎ᶼ⠓ℍ堐 5 ᷕ䘬䫔 3 埴ˤ

㭷ᶨ⮷䳬䘬柣㔠冯㧋㛔⭡慷ᷳ㭼ῤ⎓ 忁ᶨ⮷䳬䘬ᓎ౗ˤἳ ⤪炻䫔 1 ⮷䳬䘬柣䌯㗗 1 0.017 60 ≈ _ˤ 䬿↢⎬ᾳ⮷䳬䘬柣䌯炻᷎⠓ℍ堐 5 䘬䫔 4 埴ˤ堐 5 ⎓ ᓎ౗ ϩѲ߄ˤ↿↢柣䌯↮ⶫ堐ẍ⼴炻⯙䞍忻忁ṃ㔠㒂⛐⎬ᾳ⮷䳬ℏ㇨ Ỽ䘬㭼ἳ⣏⮷Ḯˤ (5) 丒墥柣䌯↮ⶫ䚜㕡⚾ˤ 䁢Ḯ⮯柣䌯↮ⶫ堐ᷕ䘬䳸㝄䚜奨⼊尉⛘堐䣢↢Ἦ炻ⷠ丒↢ᓎ ౗ϩѲޔБკˤ⮵㕤㛔ἳ炻柣䌯↮ⶫ䚜㕡⚾⤪⚾ 16-2 ㇨䣢炻℞ᷕ 㨓庠堐䣢幓檀ˣ䷙庠堐䣢柣䌯冯䳬嶅䘬㭼ῤˤ⭡㖻䚳↢炻 = × 柣䌯 = ⮷攟㕡⼊朊䧵 䳬嶅 柣䌯 䳬嶅 炻 忁⯙㗗婒炻⎬ᾳ⮷攟㕡⼊䘬朊䧵䫱㕤䚠ㅱ⎬䳬ᷳ柣䌯ˤ忁㧋炻柣 䌯↮ⶫ䚜㕡⚾⯙ẍ⚾⼊朊䧵䘬⼊⺷⍵㗈Ḯ㔠㒂句⛐⎬ᾳ⮷䳬ℏ 䘬柣䌯ᷳ⣏⮷ˤ⍰⛐⚾ 16-2 ᷕ炻 1 = = × × 柣䌯 ⮷攟㕡⼊檀 柣㔠 䳬嶅 䳬嶅 㧋㛔⭡慷 炻 堐 5 柣䌯↮ⶫ堐 ↮ 䳬 柣 㔠 䳗 妰 柣 㔠 柣 䌯 145.5焍148.5 1 0.017 148.5焍151.5 3 0.050 151.5焍154.5 6 0.100 154.5焍157.5 8 0.133 157.5焍160.5 18 0.300 160.5焍163.5 11 0.183 163.5焍166.5 10 0.167 166.5焍169.5 3 0.050 ⎰妰 60 1.000

⚈䁢䳬嶅冯㧋㛔⭡慷悥㗗ⷠ㔠炻 1 × 䳬嶅 㧋㛔⭡慷ḇ㗗ⷠ㔠炻㇨ẍ ⮷攟㕡⼊䘬檀冯柣㔠ㆸ㬋㭼ˤ⇑䓐忁ᾳ⿏岒Ἦ䡢⭂⎬⮷攟㕡⼊䘬 檀炻恋湤柣㔠䁢 k 䘬⮷攟㕡⼊ᷳ檀⯙㗗 khˤἳ⤪炻148.5焍151.5 忁ᾳ⮷䳬䘬柣㔠㗗 3炻䚠ㅱ䘬⮷攟㕡⼊ᷳ檀⯙㗗 3hˤ ⛐柣䌯↮ⶫ䚜㕡⚾ᷕ炻䓙⎬⮷攟㕡⼊䘬朊䧵䫱㕤䚠ㅱ⎬䳬ᷳ 柣䌯炻侴⎬䳬䘬柣䌯ᷳ␴䫱㕤 1炻㓭⎬⮷攟㕡⼊䘬朊䧵ᷳ␴䁢 1ˤ 䞍忻Ḯᶨᾳ㧋㛔䘬柣䌯↮ⶫẍ⼴炻⯙⎗ẍ⮵䚠ㅱ䘬䷥橼↮ⶫ  ↢Ộ妰ˤ⛐ᶲ朊䘬ἳ⫸ᷕ炻㧋㛔㔠㒂句⛐ 157.5焍160.5 cm ᷳ 攻䘬柣䌯 0.3炻婒㖶⛐㭷 100 ⎵娚⸜漉䘬⤛⬠䓇ᷕ炻䲬㚱 30 Ṣ䘬 幓檀⛐ 157.5焍160.5 cm ᷳ攻ˤ Ȝּȝ ᶨᾳ彚娎㇨䁢Ḯ侫⮇㝸䧖⣏湍䧿攟䘬↮ⶫね㱩炻⛐ᶨ⟲ 娎槿䓘墉㉥⍾Ḯ 100 ᾳ䧿炻慷⼿攟⹎⤪ᶳ(╖ỵ烉cm)烉 6.5 6.4 6.7 5.8 5.9 5.9 5.2 4.0 5.4 4.6 5.8 5.5 6.0 6.5 5.1 6.5 5.3 5.9 5.5 5.8 6.2 5.4 5.0 5.0 6.8 6.0 5.0 5.7 6.0 5.5 6.8 6.0 6.3 5.5 5.0 6.3 5.2 6.0 7.0 6.4 6.4 5.8 5.9 5.7 6.8 6.6 6.0 6.4 5.7 7.4 6.0 5.4 6.5 6.0 6.8 5.8 6.3 6.0 6.3 5.6 5.3 6.4 5.7 6.7 6.2 5.6 6.0 6.7 6.7 6.0 5.5 6.2 6.1 5.3 6.2 6.8 6.6 4.7 5.7 5.7 5.8 5.3 7.0 6.0 6.0 5.9 5.4 6.0 5.2 6.0 6.3 5.7 6.8 6.1 4.35 5.6 6.3 6.0 5.8 6.3 ↿↢㧋㛔䘬柣䌯↮ⶫ堐炻丒↢柣䌯↮ⶫ䚜㕡⚾ˤ 柣䌯 䳬嶅 145.5 148.5 151.5 154.5 157.5 160.5 163.5 166.5 169.5 幓檀 (cm) ⚾ 16-2

堐 6 柣䌯↮ⶫ堐 ↮ 䳬 柣 㔠 䳗 妰 柣 㔠 柣 䌯 䳗䧵柣䌯 3.95焍4.25 1 0.01 0.01 4.25焍4.55 1 0.01 0.02 4.55焍4.85 2 0.02 0.04 4.85焍5.15 5 0.05 0.09 5.15焍5.45 11 0.11 0.20 5.45焍5.75 15 0.15 0.35 5.75焍6.05 28 0.28 0.63 6.05焍6.35 13 0.13 0.76 6.35焍6.65 11 0.11 0.87 6.65焍6.95 10 0.10 0.97 6.95焍7.25 2 0.02 0.99 7.25焍7.55 1 0.01 1.00 ⎰ 妰 100 1.000

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ྋ !! (1) 妰䬿㚨⣏ῤ冯㚨⮷ῤ䘬ⶖˤ ⛐㧋㛔㔠㒂ᷕ炻㚨⣏ῤ㗗 7.4ˣ㚨⮷ῤ㗗 4.0炻ⶖ㗗 7.4 4.0− =3.4_(cm)ˤ (2) 㰢⭂䳬嶅冯䳬㔠ˤ ⛐㛔ἳᷕ炻㚨⣏ῤ冯㚨⮷ῤ䘬ⶖ㗗 3.4 cmˤ⤪㝄⍾ 䳬嶅䁢 0.3 cm炻恋湤䓙㕤3.4 111 0.3 3 = _{炻⼿↮ㆸ 12 䳬炻} 䳬㔠⎰怑ˤ㕤㗗怠⭂䳬嶅䁢 0.3 cm炻䳬㔠䁢 12ˤ (3) 㰢⭂↮溆ˤ ἧ↮溆㭼㔠㒂⣂ᶨỵ⮷㔠炻᷎ᶼ㈲䫔 1 ⮷䳬䘬崟溆 䦵⽖㷃⮷ᶨ溆炻恋湤炻㇨↮䘬 12 ⮷䳬⎗ẍ㗗烉 3.95焍4.25ˣ4.25焍4.55ˣ4.55焍4.85ˣ4.85焍5.15ˣ 5.15焍5.45ˣ5.45焍5.75ˣ5.75焍6.05ˣ6.05焍6.35ˣ 6.35焍6.65ˣ6.65焍6.95ˣ6.95焍7.25ˣ7.25焍7.55ˤ (4) ↿柣䌯↮ⶫ堐ˤ 9 9 _{斄㕤䳗䧵柣䌯冯⚾ 16-3 䘬ᶳ⚾⮯⛐ᶳᶨ䭨ἄ⮰攨ṳ䳡}

⮵⎬ᾳ⮷䳬ἄ柣㔠䳗妰炻䃞⼴㔠柣㔠ˣ䬿柣䌯ˣ↿ 柣䌯↮㜸堐炻⤪堐 6 ㇨䣢ˤ (5) 丒墥柣䌯↮ⶫ䚜㕡⚾(⤪⚾ 16-3 ᶲ⚾㇨䣢炻丒⚾㕡 㱽⎴ᶲἳ)ˤ 䎦⛐⎗ẍ㟡㒂㧋㛔䘬柣䌯↮ⶫἮỘ妰䷥橼↮ⶫˤἳ⤪⽆ 堐 6 ᷕ䚳⇘炻㧋㛔㔠㒂句⛐ 5.75焍6.05 ᷳ攻䘬柣䌯㗗 0.28炻㕤㗗⎗ẍỘ妰炻⛐忁⟲䓘墉炻攟⹎⛐ 5.75焍6.05 cm ᷳ攻䘬湍䧿䲬Ỽ 28%ˤ⛐䓐柣䌯↮ⶫỘ妰䷥橼↮ⶫ㗪炻 ⤪㝄㧋㛔⭡慷崲⣏炻忁䧖Ộ妰ḇ⯙崲䱦䡢ˤ ⚾ 16-3 柣䌯 䳬嶅 3.95 4.25 4.55 4.85 5.15 5.45 5.75 6.05 6.35 䧿攟 (cm) 6.65 6.95 7.25 7.55 3.95 4.25 4.55 4.85 5.15 5.45 5.75 6.05 6.35 䧿攟 (cm) 6.65 6.95 7.25 7.55 䳗䧵 柣䌯 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

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1. 㚱ᶨᾳ⭡慷䁢 50 䘬㧋㛔炻㔠㒂䘬↮䳬ẍ⍲⎬䳬ᷳ柣㔠⤪ᶳ烉 53.5ɴ55.5 4 61.5ɴ63.5 10 55.5ɴ57.5 7 63.5ɴ65.5 6 57.5ɴ59.5 9 65.5ɴ67.5 3 59.5ɴ61.5 11 ↿↢㧋㛔䘬柣䌯↮㜸堐炻丒↢柣䌯↮ⶫ䚜㕡⚾ˤ 2. ⶚䞍ᶨᾳ㧋㛔烉 25 21 23 25 27 29 25 28 30 29 26 24 25 27 26 22 24 25 26 28 ⠓⮓ᶳ朊䘬柣䌯↮ⶫ堐烉 ↮ 䳬 柣㔠䳗妰 柣 㔠 柣 䌯 20.5焍22.5 22.5焍24.5 24.5焍26.5 26.5焍28.5 28.5焍30.5 ⎰ 妰 3. 䁢ḮḮ妋ᷕ⬠䓇䘬幓橼䘤做ね㱩炻⮵㝸ᶨᷕ⬠⎴⸜漉䘬 50 ⎵䓟⎴⬠䘬幓檀忚埴Ḯ㷔慷炻䳸㝄⤪ᶳ(╖ỵ烉cm) 175 168 170 176 167 181 162 173 171 177 179 172 165 157 172 173 166 177 169 181 160 163 166 177 175 174 173 174 171 171 158 170 165 175 165 174 169 163 166 166 174 172 166 172 167 172 175 161 173 167 ↿↢㧋㛔䘬柣䌯↮㜸堐炻丒↢柣䌯↮ⶫ䚜㕡⚾ˤ

*16.6

௢᎕ᐛத̶ο

10 ⛐ᶲ䭨斄㕤⣏湍䧿攟䘬ἳ柴ᷕ炻䧿攟⮷㕤 4.55 cm 䘬柣䌯䫱 㕤⇵ℑᾳ⮷䳬䘬柣䌯ᷳ␴炻⌛ 0.01 0.01+ = 0.02_ˤ 䧿攟⮷㕤 4.85 cm 䘬柣䌯䫱㕤⇵ᶱᾳ⮷䳬䘬柣䌯ᷳ␴炻⌛ 0.01 0.01 0.02+ + = 0.04_ˤ ὅ㬌栆㍐ˤ忁䧖㔠㒂⮷㕤㝸ᶨ㔠ῤ䘬柣䌯⎓ 娚㔠ῤ䘬ಕᑈᓎ ౗ˤ忁ᾳἳ⫸ᷕ⎬ᾳ↮溆䘬䳗䧵柣䌯⤪堐 6 㚨⼴ᶨ埴㇨䣢ˤ⬫⎗ ẍἄ䁢柣䌯↮ⶫ堐䘬ᶨᾳ墄⃭ˤ 㟡㒂䬿↢䳗䧵柣䌯炻⎗ẍ丒↢ಕᑈᓎ౗ϩѲკ炻⤪⚾ 16-3 ᶳ⚾㇨䣢ˤ⚾ᷕ䘬㨓庠堐䣢䧿攟ˣ䷙庠堐䣢䳗䧵柣䌯ˤ㊱䄏堐ᷕ 䘬⎬䳗䧵柣䌯炻⛐⚾ᷕ㍷↢䚠ㅱ䘬⎬溆ˤἳ⤪炻↮溆 4.25 䘬䳗䧵 柣䌯㗗 0.01炻⯙⛐⚾ᷕ㍷↢㨓⹏㧁㗗 4.25ˣ䷙⹏㧁㗗 0.01 䘬ᶨᾳ 溆ˤ䃞⼴炻䓐䶂㭝⮯⎬溆ὅ㫉忋䳸崟Ἦ炻⯙⼿⇘ᶨ㡅㉀䶂炻⬫⯙ 㗗䳗䧵柣䌯↮ⶫ⚾ ⇑䓐㧋㛔䘬䳗䧵柣䌯↮ⶫ⚾炻⎗ẍ⮵䷥橼䘬䚠ㅱね㱩 ↢Ộ 妰ˤἳ⤪炻䁢ḮỘ妰攟⹎⮷㕤 5 cm 䘬湍䧿⛐忁⟲湍⛘墉㇨Ỽᷳ 㭼ἳ⣏⮷炻ㆹᾹ⛐䳗䧵柣䌯↮ⶫ⚾㈦⇘㨓⹏㧁㗗 5 (cm)䘬溆炻䃞 ⼴慷↢忁ᶨ溆䘬䷙⹏㧁 0.07ˤ⬫⏲姜ㆹᾹ炻攟⹎⮷㕤 5 cm 䘬湍 䧿⛐忁⟲湍⛘墉䲬Ỽ 7%ˤ

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㟡㒂堐 5炻妰䬿⎬↮溆䘬䳗䧵柣䌯炻᷎丒↢䳗䧵柣䌯↮ⶫ⚾ˤ 10 _{㛔䭨㗗怠⬠ℏ⭡ˤ}

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! 1. ⛐ᶨ㈡㛐䪧ᷕ㉥㷔Ḯ 60 㟡㛐䪧攟⹎炻䳸㝄⤪ᶳ(╖ỵ烉mm)烉 82 202 352 321 25 293 293 86 28 206 323 355 357 33 325 113 233 294 50 296 115 236 357 326 52 301 140 328 238 358 58 255 143 360 340 302 370 343 260 303 59 146 60 263 170 305 380 346 61 305 175 348 264 383 62 306 195 350 265 385 ↿↢㧋㛔䘬柣䌯↮㜸堐炻丒↢柣䌯↮ⶫ䚜㕡⚾ˤ 2. ⽆㝸㈡㨇☐暞ẞᷕ㉥㷔Ḯ 100 ᾳ炻℞⯢⮠冯夷⭂⯢⮠䘬ῷⶖ ⤪ᶳ(╖ỵ烉0.1 mm)烉 2 1 0 3 −1 _{2 1 0} −_{1 0} 3 −2 −₁ −_{2 1 0 0} −_{4 1 0} 1 2 2 0 −2 1 0 −1 0 3 1 − 1 0 −1 0 3 1 −2 3 −1 3 − _{0 0 1 4 0} −_{2 2 1 2} 2 0 −2 _{0 0} −_{1 1 4} −_{2 1} 1 1 4 −1 ₁ −_{1 0 2} −_{2 1} 0 1 −1 _{1 0 2 2 1 0} −₁ 0 −1 _{3 1 2} −_{3 1 0 1 1} 2 − _{2 1 2} −₁ −_{2 3 1} −_{1 0} (1) ↿↢㧋㛔䘬柣䌯↮㜸堐炻丒↢柣䌯↮ⶫ䚜㕡⚾(㍸䣢烉䓙 㕤㧋㛔ᷕ⎒㚱 9 ᾳᶵ⎴䘬㔠ῤ炻ᶼ⬫Ᾱ㗗忋临䘬㔜㔠炻㇨ ẍ㚨⣂⎒傥⮯㔠㒂↮ㆸ 9 ᾳ⮷䳬)烊 (2) 㟡㒂㧋㛔䘬柣䌯↮ⶫ堐炻Ộ妰㔜㈡㨇☐ᷕ冯夷⭂⯢⮠䘬ῷ ⶖᷳ䳽⮵ῤᶵ崭忶 0.1 mm 䘬䲬Ỽ⣂⮹炻ᶵ崭忶 0.2 mm 䘬䲬Ỽ⣂⮹ˤ

3. ᶨᾳ彚⟜⛐䥳㓞⇵忚埴䌱䰛Ộ䓊炻⽆⛘墉㉥⍾Ḯ 100 㟒䌱䰛炻 䧙⼿⎬㟒䌱䰛䘬䓊慷⤪ᶳ(╖ỵ烉g)烉 50 29 31 32 29 30 38 41 26 20 33 27 34 20 27 17 17 28 35 39 38 35 26 50 38 36 38 25 28 22 32 30 29 48 30 35 18 20 25 24 29 50 23 44 39 27 33 39 24 26 34 23 32 18 39 25 50 33 40 21 35 31 33 30 28 25 27 30 39 24 35 30 38 46 40 18 35 43 24 23 33 34 36 34 40 23 34 37 40 19 39 34 33 37 35 25 34 30 27 15 (1) ↿↢㧋㛔䘬柣䌯↮㜸堐炻丒↢柣䌯↮ⶫ䚜㕡⚾烊 *(2) ⛐柣䌯↮ⶫ堐ᷕ墄⠓⎬↮溆䘬䳗䧵柣䌯炻᷎丒↢䳗䧵柣䌯 ↮ⶫ⚾ˤ

̈

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ඕ!

ᶨˣ忁ᶨ䪈ㆹᾹṳ䳡Ḯ䴙妰䘬ᶨṃ⇅㬍䞍嬀ˤ䴙妰㕡㱽䘬䈡 溆㗗烉⽆㇨天侫⮇䘬䷥橼ᷕ㉥⍾ᶨᾳ㧋㛔炻忂忶䞼䨞㧋㛔⮵䷥橼  ↢Ộ妰ˤ㧋㛔⭡慷崲⣏炻忁䧖Ộ妰ḇ⯙崲䱦䡢ˤˤ Ḵˣ䷥橼⸛⛯㔠⺷堐䣢䷥橼䘬⸛⛯⣏⮷(ㆾ⸛⛯㯜⸛)ᷳ䈡⽝ 㔠炻忂ⷠ䓐㧋㛔⸛⛯㔠⍣Ộ妰⬫ˤ㧋㛔⸛⛯㔠㗗㊯㧋㛔ᷕ⎬㔠㒂 䘬␴冯㧋㛔⭡慷ᷳ㭼ῤ炻䔞㧋㛔㔠㒂庫⣏㗪炻⇑䓐℔⺷ x = x′ +a 妰䬿㧋㛔⸛⛯㔠㭼庫䯉ὧˤ ᶱˣ䷥橼㕡ⶖ⺷堐䣢䷥橼䘬㲊≽⣏⮷ᷳ䈡⽝㔠炻忂ⷠ䓐㧋㛔 㕡ⶖ⍣Ộ妰⬫炻䓐㭼庫ℑᾳ㧋㛔㕡ⶖ⍣役Ụ⛘㭼庫ℑᾳ䚠ㅱ䘬䷥ 橼ᷳ㲊≽⣏⮷ˤ⮵㕤ᶨᾳ⭡慷䁢 nˣ⸛⛯㔠䁢 x 䘬㧋㛔Ἦ婒炻㧋 㛔㕡ⶖ

2 2 1 1 ( ) n i i s x x n = = − ˤ 㧋㛔㕡ⶖ䘬妰䬿庫䷩炻⛐㰺㚱暣⫸妰䬿☐䘬ね㱩ᶳ炻ᶨ凔㟡㒂䯉 ⊾℔⺷↿堐忚埴妰䬿ˤ ⚃ˣ䷥橼↮ⶫ⍵㗈Ḯ䷥橼ᷕ⎬悐↮ᾳ橼⛐䷥橼ᷕ㇨Ỽ䘬㭼ἳ ⣏⮷炻忂ⷠ䓐㧋㛔䘬柣䌯↮ⶫ⍣Ộ妰⬫ˤ柣䌯↮ⶫ⍵㗈Ḯ㧋㛔㔠 㒂⛐⎬ᾳ⮷䭬⚵ℏ㇨Ỽ䘬㭼ἳ⣏⮷炻天⼿⇘ᶨᾳ㧋㛔䘬柣䌯↮ⶫ ね㱩炻⎗㊱ᶳ↿㬍樇忚埴烉妰䬿㧋㛔ᷕ㚨⣏ῤ冯㚨⮷ῤ䘬ⶖˣ㰢 ⭂䳬嶅冯䳬㔠ˣ㰢⭂↮溆ˣ↿柣䌯↮ⶫ堐ˣ丒柣䌯↮ⶫ䚜㕡⚾ˤ

ኑ௫ણ҂ᗟȈ̱!

1. Ṩ湤⎓ ䷥橼烎Ṩ湤⎓ ䷥橼䘬ᶨᾳ㧋㛔烎䁢Ṩ湤ⷠⷠ暨天 䓐㧋㛔䘬㝸ṃ䈡⿏⍣Ộ妰䷥橼䘬䚠ㅱ䈡⿏烎 2. 䓚ˣḁℑ攨䟚⛐䚠⎴㡅ẞᶳ⎹⎴ᶨ䚖㧁⎬䘤⮬ 50 䘤䟚⻰炻䟚 ⻰句溆ね㱩⤪ᶳ堐㇨䣢烉 䟚⻰句溆冯䚖㧁嶅暊 40 m 30 m 20 m 10 m 0 m 䓚䟚䘤⮬䘬䟚⻰ᾳ㔠 0 1 3 7 39 ḁ䟚䘤⮬䘬䟚⻰ᾳ㔠 1 3 2 3 41 ↮⇍妰䬿ℑᾳ㧋㛔⸛⛯㔠炻㟡㒂妰䬿䳸㝄炻Ộ妰⒒攨䟚⮬㑲 䘬㸾䡢⿏庫⤥ˤ 3. ᶨᾳ㯜⹓梲Ḯ㝸䧖欂 10 叔㡅炻⽆ᷕ㐰㋽Ḯ 20 㡅炻䧙⼿⬫Ᾱ 䘬橼慵⤪ᶳ(╖ỵ烉kg) 2.3 2.1 2.2 2.1 2.2 2.6 2.5 2.4 2.3 2.4 2.4 2.3 2.2 2.5 2.4 2.6 2.3 2.5 2.2 2.3 妰䬿㧋㛔⸛⛯㔠炻᷎㟡㒂妰䬿䳸㝄Ộ妰㯜⹓墉䲬㚱忁䧖欂⣂ ⮹ kgˤ

4. 䁢Ḯ侫⮇䓚ˣḁℑ䧖⮷湍䘬䓇攟ね㱩炻↮⇍⽆ᷕ㉥⍾ 10 㟒剿炻 㷔⼿剿檀⤪ᶳ(╖ỵ烉cm)烉 䓚烉 12 13 14 15 10 16 13 11 15 11 ḁ烉 11 16 17 14 13 19 6 8 10 16 (1) ↮⇍妰䬿ℑ䧖⮷湍䘬⸛⛯剿檀烊 (2) ⒒䧖⮷湍攟䘬㭼庫㔜滲烎 5. ℑ⎵嶛怈忳≽⒉⛐ 10 㫉㭼岥ᷕ䘬ㆸ䷦↮⇍⤪ᶳ(╖ỵ烉m)烉 䓚烉 5.85 5.93 6.07 5.91 5.99 6.13 5.98 6.05 6.00 6.19 ḁ烉 6.11 6.08 5.83 5.92 5.84 5.81 6.18 6.17 5.85 6.21 ↮⇍妰䬿ℑᾳ㧋㛔㕡ⶖ炻᷎㟡㒂妰䬿䳸㝄Ộ妰⒒⎵忳≽⒉䘬 ㆸ䷦㭼庫䨑⭂ˤ 6. ⽆ᶨ䧖暞ẞᷕ㉥⍾Ḯ 80 ẞ炻⯢⮠㔠㒂⤪ᶳ(╖ỵ烉m)烉 362.5 1× _{362.6 2}× _{362.7 2}× _{362.8 3}× 362.9 3× _{363.0 3}× _{363.1 5}× _{363.2 6}× 363.3 8× _{363.4 9}× _{363.5 9}× _{363.6 7}× 363.7 6× _{363.8 4}× _{363.9 3}× _{364.0 3}× 364.1 2× _{364.2 2}× _{364.3 1}× _{364.4 1}× (1) ↿↢㧋㛔䘬柣䌯↮㜸堐炻丒↢柣䌯↮ⶫ䚜㕡⚾烊 *(2)⛐柣䌯↮ⶫ堐ᷕ≈⠓⎬↮溆䘬䳗䧵柣䌯炻᷎丒↢䳗䧵柣 䌯↮ⶫ⚾ˤ 7. (1) 姕x 㗗x ˣ₁ x ˣɃˣ₂ x 䘬⸛⛯㔠ˣy 㗗_n 3x + ˣ₁ 5 3x + ˣɃˣ₂ 5 3x + 䘬⸛⛯㔠炻㯪嫱_n 5 y =3x+5_ˤ (2) 姕s 㗗_x x ˣ₁ x ˣɃˣ₂ x 䘬㧁㸾ⶖˣ_n s 㗗_y 3x + ˣ₁ 5 3x + ˣɃˣ₂ 5 3x + 䘬㧁㸾ⶖ炻㯪嫱_n 5 s_y =3s_xˤ

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11

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!

1. ↿↢⮎㔠䘬↮栆堐ˤ 2. 妰䬿烉 (1) _{4 0.2×} 2 _{−10 1.1×} 3 _{+ ×3 5.14−} 3 _{5.26 ( ᾅ 䔁 ᶱ ᾳ 㚱 㓰 㔠} ⫿)烊 (2) 3a3 − −[ 5a2 +a( 4− a2 +2s−1) 4] 7+ − _{(䱦䡢⇘ 0.01)炻℞ᷕ} 2.35 a = ˤ 3. (1) 劍(a−1)2 +(b+2)2 =0_{炻aˣb 䁢⮎㔠炻㯪 aˣb烊} (2) 劍x2 +2x+ y2 −6y+10 = 0_{炻xˣy 䁢⮎㔠炻㯪 xˣyˤ} 4. 妰䬿ᶳ↿⎬柴烉 (1) (a3 −a b2 +ab2 −b3)(a b+ )_烊 (2) (a b+ ) (2 a b− )2 −(a2 +b2)(a2 −b2)_烊 (3) (p+q−m n p− )( −q−m n+ )_烊 (4) (x+2y− z x)( −2y + z) (− x+2y+ z)2_烊 (5) (x5 + x4 + x3 + x2 +x +1) (÷ x+1)_烊 (6) (x4 +x2 +1) (÷ x2 − x+1)_ˤ 5. (1) ⶚䞍 x2 +x− =1 0_{炻㯪 x}3 +_2x2 +_3䘬ῤ烊 (2) 劍 bc =ad 炻㯪嫱烉_{ab c(} 2 −_d2₎ = _(a2 −_{b cd}2_{) 烊} (3) 劍a b c+ + = 0_{炻㯪嫱烉a}3 +_{a c b c abc b}2 + 2 − + 3 =_0烊 (4) 嫱㖶烉 2 2 2 ( ) ( ) ( ) ( )( )( ) a b c− +b c a− +c a b− = − a b b c c a− − − _烊 6. ↮妋⚈⺷烉 (1) x5 −x4 + x3 −x2 + x−1_{烊 (2) 3x}2 −_2x−_8烊 (3) 4 2 2 1 2 4 x + x+ − y _{烊 (4) l}4 −_3l2 +_1烊 (5) a2 −2ab b+ 2 −6a+6b+5_{烊 (6)} 2 2 (1−a )(1−b ) 4− ab _ˤ 11 _{忁㗗ὃ墯佺⇅ᷕẋ㔠㗪⍫侫怠䓐䘬佺柴}

7. ⛐⮎㔠普⎰ℏ↮妋⚈⺷烉 (1) x2 +x−1_{烊 (2) x}4 + _x2 −_6烊 (3) 6x4 −7x2 −3_{烊 (4) x}4 +_3x3 +_x2_ˤ 8. x ⍾Ṩ湤ῤ㗪炻ẋ㔠⺷ ( 5) (3 )( 1) x x x − − − + 䘬ῤ㺧嵛ᶳ↿㡅ẞ烎 (1) 䫱㕤 0烊 (2) 㰺シ佑烊 (3) 䫱㕤 1ˤ 9. 妰䬿ᶳ↿⎬柴烉 (1) 2 3 2 1 1 1 1 x x x x x x x + + × − − + + 烊 (2) 1 1 2 ₂ 4 ₄ 1 x 1 x 1 x 1 x + + + − + + + 烊 (3) 2 3 4 5 1 2 3 4 x x x x x x x x + + + + − + − + + + + 烊 (4) 2 2 2 ( )( ) ( )( ) ( )( ) a b c a b a c b a b c c a c b + + − − − − − − ˤ 10. 娎嫱ᶳ↿⎬柴烉 (1) 劍 a b x b a + = _ˣ a b _y b a − = _{炻㯪嫱烉x}2 − _y2 = _4烊 (2) 劍 aˣbˣc 䁢⮎㔠炻ᶼa2 +b2 +c2 −ab bc ca− − = 0_炻㯪 嫱烉 a b c= = _ˤ 11. 妰䬿烉 (1) 5 28 3 63 10 7 3 1 7 + − + _烊 (2) 4 125 3 256 4 4 5 − + _烊 (3) (2 3 + 6)( 3−2 6)_烊 (4) ( 2 − 3)2 + ( 3− 2)2 _烊

(5) xy xy 3 y 2 x 4 1 x y xy − − + _{(x > 0}ˣ _{y > 0)烊} (6) 4 4 1 1 2 4 1 1 x 1 x 1 x x + + + + − + + ˤ 12. ⊾䯉 2 2 6 9 6 9 x x x x − + + + ˤ 13. 妋ᶳ↿㕡䦳烉 (1) 2 2 3 1 6 4 x x − − − = _{烊 (2)} 3 6 5 ₁ 5 8 6 6 x+ x − − = 烊 (3) 1 3 10 7 1 2 2 2 1 3 2 6 3 2 x x x x x− − − − + = − 烊 (4) 1( 2) 1(5 6) 22 63 1(3 4) 3 7 105 5 x x− − x− = − − x− _烊 (5) ax bx 1 0 b a + − = _{(aˣb 䁢⶚䞍㔠) 烊} (6) mx 1 nx 1 1 n m + + + _{= (mˣn 䁢⶚䞍㔠)ˤ} 14. 妋ᶳ↿㕡䦳䳬烉 (1) 1 1 ( 11) ( 13) 2 2 3 5 3 8 x y x y + = + + = + 烊 (2) 2 3 3 2 1 3 4 2 3 4 3 4 1 2 3 6 x y x y x y x y − + = + + − = − 烊 (3) 3 4 3 4 1 9 2 2 4 1 x y x y + = − − − = − − 烊 (4) 2 6 4 3 7 6 7 10 4 6 8 x+ y + x− y − − x− y + = = _烊

(5) 2 3 4 4 17 2 3 12 10 4 3 x y z y z x y + − = + = + = 烊 (6) 3 1 7 x y z z x y y z x + − = + − = + − = ˤ 15. 妋㕡䦳烉 (1) 4(x+3)2 −9(x−2)2 =0_烊 (2) 3(y2 − y) = 2(y2 − y)_烊 (3) x2 −(2 2 2)− x+3 2 2− = 0_烊 (4) (t +6)(t −6) = 2(t −3)_烊 (5) (x+2)2 +(x−1)2 = x2 +6_烊 (6) 2(x+5)(x−5) = (x−6)2_ˤ 16. ⶚䞍Ḵ㫉㕡䦳x2 −mx+2m = 0_{䘬ᶨᾳ㟡㗗 1ˤ} (1) 㯪 m 䘬ῤ烊 (2) 㯪⎎ᶨᾳ㟡ˤ 17. ᶵ枰妋㕡䦳炻㯪㕡䦳2x2 −7x+2 =0_{䘬ℑ㟡ᷳᾺ㔠䘬␴ˤ} 18. (1) 妋↮⺷㕡䦳冯㟡⺷㕡䦳㗪炻䁢Ṩ湤槿㟡㗗⽭天䘬㬍樇烎 (2) 妋ᶳ↿㕡䦳烉 (i) ₂ 1 ₂ 2 ₂ 0 2 3 2 x x x x x x x x x − − + − = − − − + 烊 (ii) 2 2 ₇ 2 1 1 4 0 6 x x x x − − + − = _烊 (iii) 2 3 ₂20 8 3 x x x x + − = + 烊 (iv) 5x+4− 2x− −1 3x+1 =0_烊 (v) x2 +3x−2 x2 +3x− −1 4= 0_烊 (vi) x4 −25x2 +144 =0_烊 (vii) (x2 +5 )x 2 −2x2 −10x−24 =0_烊 (viii) (x2 +5x−12)(x2 +5x+2) =32_ˤ

19. 妋ᶳ↿㕡䦳䳬烉 (1) 2 2 ( ) 3( ) 54 ( ) 5( ) 14 x y x y x y x y + − + = − − − = 烊 (2) 2 3 15 30 a aq aq aq + = + = 烊 (3) 3 5 4 2 3 3 1 4 x y xy x y − = + = 烊 (4) 5 2 5 x x y y x y + = + = 烊 (5) _{2 2} 11 30 x xy y x y xy + + = + = ˤ 20. (1) ⽆ mu s m( 1) f s u = − = − (忁墉m ≠ 0)⮶↢ fˣsˣm 攻䘬ᶨᾳ斄 Ὢ⺷烊 (2) ⽆ k a c c k I I I I mI = + = (忁墉m ≠1)⮶↢I ˣmˣc I 攻䘬ᶨᾳ斄a Ὢ⺷ˤ 21. 䓚呬㯜㰈ℏ㚱㯜 380 m3炻ḁ呬㯜㰈ℏ㚱㯜 1500 m3ˤ䓚呬㯜㰈 㭷⮷㗪忚㯜 80 m3_{炻ḁ呬㯜㰈㭷⮷㗪㉥↢㯜 60 m}3_{炻ˤ䴻忶⸦} ⮷㗪炻ℑᾳ呬㯜㰈䘬㯜ᶨ㧋⣂烎 22. 䓚ˣḁḴṢ⛐ 400 m 攟䘬䑘⼊嵹忻ᶲ䶜佺冒埴干炻䓚䘬忇⹎ 㭼ḁ䘬忇⹎⾓ˤ䔞ṾᾹ悥⽆㝸嗽⎴㗪↢䘤側⎹埴榃㗪炻㭷昼 40 䥺揀⯙䚠忯ᶨ㫉炻⎴⎹埴榃㗪炻㭷昼 6 ↮ 40 䥺揀䚠忯ᶨ㫉ˤ 㯪䓚ˣḁℑṢ榶干䘬忇⹎ˤ 23. 㝸枭ⶍἄ炻䓚ˣḁℑṢ⎰ἄ炻16 ⣑⎗ẍ⬴ㆸˤ⤪㝄ℙ⎴ἄḮ 4 ⣑⼴炻∑ᶳ䘬ⶍἄ䓙ḁ╖䌐⬴ㆸ炻暨天䘬㗪攻㭼䓙䓚ᶨṢ⬴ ㆸℐ悐ⶍἄ䘬㗪攻⣂ 12 ⣑ˤ⓷╖䌐⬴ㆸℐ悐ⶍἄ炻䓚ˣḁ⎬ 暨天⣂⮹⣑烎

24. ⤪⚾炻ᶨ⟲攟 25 cm炻⮔ 18 cm 䘬 揝㜧炻⛐−㌱ᶨᾳ冯ᶱ怲䚠↯䘬⚻ ⼴炻∑ᶳ䘬揝㜧傥−↢ᷳ㚨⣏⚻䘬 䚜⼹㗗⣂⮹烎 25. 㝸ⶍ⺈㭷⣑傥䓇䓊䓚䧖暞ẞ 500 ᾳ炻ㆾ侭ḁ䧖暞ẞ 600 ᾳ炻ㆾ侭᷁ 䧖暞ẞ 750 ᾳˤ䓚ˣḁˣ᷁ᶱ䧖暞 ẞ⎬ᶨᾳㇵ傥惵ㆸᶨ⣿ˤ䎦⛐天⛐ 30 ⣑ℏ䓇䓊㚨⣂䘬ㆸ⣿䓊 ⑩炻䓚ˣḁˣ᷁ᶱ䧖暞ẞ⎬ㅱ䓇䓊⣂⮹⣑烎 26. ᶨ䧖㭢垚∹ 40 kg炻⏓喍䌯㗗 15%炻䎦⛐天䓐⏓喍䌯庫檀䘬⎴ 㧋㭢垚∹ 50 kg 冯⬫㶟⎰炻ἧ㶟⎰⼴䘬⏓喍䌯⛐ 25%冯 30% ᷳ攻(ᶵ⊭㊔ 25%冯 30%)炻㯪㇨䓐㭢垚∹䘬⏓喍䌯ˤ 27. 妋ᶳ↿ᶵ䫱⺷ㆾᶵ䫱⺷䳬炻᷎⛐㔠庠ᶲ堐䣢↢⬫Ᾱ䘬妋普烉 (1) 2( 1) 2 7 1 3 2 x x x+ + − > − _烊 (2) 2 1 2 1 1 2 3 6 x x x x− − < − + + _烊 (3) 1{1 2[ 4( 1)]} 4 2 x x x − − − ≤ _烊 (4) 1 3 2 2 x − − ≤ ≤ _烊 (5) 4 3 5 2 2 x − − ≤ ≤ − _烊 (6) 3 5 2 3 5 3 1 2 x x x x − ≥ + − ≤ + ˤ 28. ⛐㔠庠ᶲ堐䣢怑⎰ᶳ↿㡅ẞ䘬㔠ᷳ普⎰烉 (1) ἧᶵ䫱⺷x ≤ ㆾ5 x > − ㆸ䩳烊2 (2) ἧᶵ䫱⺷ x ≤ 冯5 x > − ⎴㗪ㆸ䩳烊2 (䫔 24 柴)

(3) ἧᶵ䫱⺷x > ㆾ5 x > − ㆸ䩳烊2 (4) ἧᶵ䫱⺷x > 冯5 x > − ⎴㗪ㆸ䩳烊2 (5) ἧᶵ䫱⺷x > ㆾ5 x ≤ − ㆸ䩳烊2 (6) ἧᶵ䫱⺷x > 冯5 x ≤ − ⎴㗪ㆸ䩳ˤ2 29. 妰䬿烉 (1) 1 1 2 1 2 1 3 4 3 2 3 4 ( 3x y )(2x y )( x y ) − − − − − _烊 (2) 3 5 4 4 2 2 1 1 m n m n m n mn − − − − ÷ − 烊 (3) 1 1 1 1 2 2 2 2 (3x 2y )(3x 2y ) − − − + _烊 (4) 3 _3× 4 _{4 ×} 6 _{6 烊} (5) 3 _{x y}−5 2 _{x y}3 _烊 (6) _{( 2x −3}4 _{y)( 2x +3}4 _y)ˤ 30. (1) 䁢Ṩ湤⇑䓐⮵㔠⎗ẍ䓐≈㱽妰䬿Ḁ㱽炻䓐㷃㱽妰䬿昌 㱽烎 (2) 䓐䥹⬠姀㔠㱽⮓↢ᶳ↿⎬㔠炻᷎婒㖶⬫Ᾱ䘬ⷠ䓐⮵㔠ᷳ 椾㔠烉 54890ˣ0.08351ˣ4.903ˣ213.7ˤ 31. ⶚䞍 log 2=0.3010_{炻娎⇌⭂2}7×₈11×₅11_{㗗⸦ỵ㔠ˤˤ} 32. ⇑䓐⮵㔠妰䬿烉 (1) 4 8 0.3586 257 0.00501 × 烊 (2) 2 2 32.85 12.62 32.85 32.85 12.64 12.64 − ÷ × ˤ 33. 㯪ᶳ↿↥㔠䘬冒嬲慷ᷳ⍾ῤ䭬⚵烉 (1) ₂ 5 3 2 x y x x − = − + 烊 (2) 2 8 2 y = − x− x _ˤ

34. ⶚䞍 y₁ = 2x−3_ˣ 2 3 7 y = − x+ _{炻妰䬿 x ⍾ỽῤ㗪炻} (1) y₁ > y_{2烊 (2)} 1 2 y = y _{烊 (3)} 1 2 y < y _烊 ᷎䓐⚾⼊≈ẍ婒㖶ˤ 35. 妰䬿 k 䁢ỽῤ㗪炻↥㔠 y = −x2 +2x+k _{䘬⚾⼊冯 x 庠} (1) 䚠Ṍ㕤ᶨ溆烊 (2) 䚠Ṍ㕤ℑ溆烊 (3) ᶵ䚠Ṍ烊 ᷎䓐⚾⼊≈ẍ婒㖶ˤ 36. ↥㔠 y = x2 + px q+ _{䘬㚨⮷ῤ㗗 4ˤ⛐x = 2㗪炻y = ˤ㯪5 pˣq} 䘬ῤˤ 37. 姕

α

㗗 0° 焍180° 攻䘬奺ˤ㟡㒂ᶳ↿㡅ẞ㯪

α

ˤ⤪㝄㚱妋炻㯪 ↢㇨㚱䘬妋烉

(1) tanα _{= −} 1 _{(2) cos}α = _{0 (3) sin} 1 2 α = (4) cotα = 3 _{(5) sin} 1 2 α = − _{(6) cos}α = ₂ 38. 䚜奺ᶱ奺⼊ ABC ᷳ㕄怲 AB ᶲ䘬檀 CD = 21 cm炻AD = 18 cm炻 妋忁ᾳᶱ奺⼊(怲攟ᾅ䔁ℑỵ㚱㓰㔠⫿炻奺⹎䱦䡢⇘1° )ˤ 39. ⛐⋲⼹䁢 10.0 cm 䘬⚻ᷕ炻ἄℏ㍍㬋Ḽ奺㗇 ABCDE炻㯪忁Ḽ 奺㗇䘬枪溆 A 冯 B 攻ᷳ嶅暊炻ẍ⍲枪溆 A 冯 C 攻䘬嶅暊(䱦䡢 ⇘ 0.1 cm)ˤ 40. ⶚䞍B =30°_{ˣc =150ˣb =50 3炻㺧嵛㡅ẞ䘬ᶱ奺⼊ ABC 㚱} Ṩ湤䈡溆烎

41. 㯪嫱烉⛐ːABC ᷕ炻⤪㝄sin2 A+sin2 B =sin2 C _{炻恋湤忁ᾳᶱ}

奺⼊ᶨ⭂㗗䚜奺ᶱ奺⼊ˤ

42. ⸛埴⚃怲⼊ ABCD ᷕ炻AB = 8ˣAD = 5ˣ∠A= 60°_{炻⤪㝄⍾ A} ἄ⍇溆炻AB ㇨⛐䘬䚜䶂ἄ x 庠炻C 溆㇨⛐䘬尉旸ἄ䫔ᶨ尉旸炻 㯪⬫䘬⎬ᾳ枪溆ᷳ⹏㧁ˤ

43. ⤪⚾炻⛐⮷Ⱉ枪ᶲ㚱ᶨ暣夾䘤⮬⟼炻⟼檀 AB 㗗 50 m炻⛐⸛⛘ C 溆炻㷔⼿ B 䘬ẘ奺 㗗 40°ˣA 䘬ẘ奺㗗 70°炻㯪⮷Ⱉ BD 䘬檀(䱦 䡢⇘ 1 m)ˤ 44. 姕 l 㗗䫔ᶨˣ䫔ᶱ尉旸ℏℑ⹏㧁庠⣦奺䘬⸛ ↮䶂炻⛐ l ᶲ㯪ᶨ溆炻ἧ⬫冯ℑ溆 A(8, 0)ˣ B(1, 3− )䘬嶅暊䚠䫱ˤ 45. 㯪嫱烉( 4− , 3)ˣ(8, 8)ˣ(13, 4− )ˣ(1, 9− )㗗 ᶨᾳ㬋㕡⼊䘬⚃ᾳ枪溆ˤ 46. ⶚䞍⛐ n ᾳ㔠㒂ᷕ炻x ↢䎦₁ f 㫉炻₁ x ↢䎦₂ f₂ 㫉炻Ƀ炻x ↢䎦_k f 㫉(_k f₁ + f₂ + + f_k = n_)炻 x 㗗忁 n ᾳ㔠㒂䘬⸛⛯㔠ˤ㯪嫱烉 1( 1 ) 2( 2 ) k( k ) 0 f x − x + f x −x + + f x −x = _ˤ 47. 䓚ˣḁℑ䧖㯜䧣炻㷔⼿㭷䧖㯜䧣⎬ 10 㟒檀⹎⤪ᶳ(╖ỵ烉cm)烉 䓚烉 12 9 16 18 14 8 12 10 17 11 ḁ烉 12 15 14 16 15 13 12 10 12 10 ⒒䧖㯜䧣䘬檀⹎㭼庫㔜滲烎 48. ⛐䓇䓊忶䦳ᷕ炻㷔⼿䈡渿漵䘬举⹎(堐䣢举䵕䰿䳘䘬ᶨ䧖慷) 㚱⤪ᶳ䘬 100 ᾳ㔠㒂炻娎↿↢㧋㛔䘬柣䌯↮ⶫ堐冯丒↢柣䌯 ↮ⶫ䚜㕡⚾ˤ 1.36 1.49 1.43 1.41 1.37 1.40 1.32 1.42 1.47 1.39 1.41 1.36 1.40 1.34 1.42 1.42 1.45 1.35 1.42 1.39 1.44 1.42 1.39 1.42 1.42 1.30 1.34 1.42 1.37 1.36 1.37 1.34 1.37 1.37 1.44 1.45 1.32 1.48 1.40 1.45 1.39 1.46 1.39 1.53 1.36 1.48 1.40 1.39 1.38 1.40 1.36 1.45 1.50 1.43 1.38 1.43 1.41 1.48 1.39 1.45 1.37 1.37 1.39 1.45 1.31 1.41 1.44 1.44 1.42 1.47 1.35 1.36 1.39 1.40 1.38 1.35 1.42 1.43 1.42 1.42 1.42 1.40 1.41 1.37 1.46 136 1.37 1.27 1.37 1.38 1.42 1.34 1.43 1.42 1.41 1.41 1.44 1.48 1.55 1.37 (䫔 43 柴) A C B D