{"id":1105,"date":"2026-01-18T11:56:44","date_gmt":"2026-01-18T01:56:44","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1105"},"modified":"2026-01-18T11:56:44","modified_gmt":"2026-01-18T01:56:44","slug":"year11-math-3-1-1-jp","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1105","title":{"rendered":"Year11-MATH-3-1-1-JP"},"content":{"rendered":"\n

\u7b2c1\u7ae0\uff1a\u4ee3\u6570\u3068\u95a2\u6570
\u3053\u306e\u7ae0\u3067\u306f\u3001\u6570\u5b66\u7684\u624b\u6cd5\u306b\u5fc5\u8981\u306a\u4ee3\u6570\u7684\u80fd\u529b\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002
\u57fa\u672c\u7684\u306a\u8a08\u7b97\u304b\u3089\u4e00\u6b69\u8e0f\u307f\u8fbc\u307f\u3001\u5909\u6570\u9593\u306e\u95a2\u4fc2\u3001\u30d1\u30bf\u30fc\u30f3\u306e\u6027\u8cea\u3001\u95a2\u6570\u306e\u5e7e\u4f55\u5b66\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002<\/p>\n\n\n\n

1.1 \u7b49\u5dee\u6570\u5217\u3068\u5e7e\u4f55\u6570\u5217<\/strong><\/p>\n\n\n\n

\u300c\u30e1\u30bd\u30c3\u30c9\u300d\u3067\u306f\u3001\u6570\u5217\u3092\u96e2\u6563\u95a2\u6570\u3068\u3057\u3066\u6271\u3044\u3001\u5165\u529b\u306f\u4f4d\u7f6en\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u7b49\u5dee\u6570\u5217<\/strong>: \u9023\u7d9a\u3059\u308b\u9805\u306e\u5dee\u304c\u5b9a\u6570(d)\u3067\u3042\u308b\u6570\u5217\u3002<\/p>\n\n\n\n

\uff4e\u756a\u76ee\u306e\u9805: t<\/mi>n<\/mi><\/msub>=<\/mo>a<\/mi>+<\/mo>(<\/mo>n<\/mi>\u2212<\/mo>1<\/mn>)<\/mo>d<\/mi><\/mrow>t_n = a + (n-1)d<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

\uff4e\u756a\u76ee\u306e\u9805\u307e\u3067\u306e\u5408\u8a08\uff1a\u3000S<\/mi>n<\/mi><\/msub>=<\/mo>n<\/mi>2<\/mn><\/mfrac>(<\/mo>2<\/mn>a<\/mi>+<\/mo>(<\/mo>n<\/mi>\u2212<\/mo>1<\/mn>)<\/mo>d<\/mi>)<\/mo><\/mrow>S_n = \\frac{n}{2}(2a + (n-1)d)<\/annotation><\/semantics><\/math>\u3000<\/p>\n\n\n\n\n\n

\u5e7e\u4f55\u6570\u5217<\/strong>\uff1a\u5404\u9805\u304c\u524d\u306e\u9805\u306b\u5b9a\u6570\u6bd4(r)\u3092\u639b\u3051\u3066\u6c42\u3081\u3089\u308c\u308b\u6570\u5217\u3002<\/p>\n\n\n\n

\uff4e\u756a\u76ee\u306e\u9805: t<\/mi>n<\/mi><\/msub>=<\/mo>a<\/mi>r<\/mi>n<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mrow>t_n = ar^{n-1}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

\uff4e\u756a\u76ee\u306e\u9805\u307e\u3067\u306e\u5408\u8a08\uff1a\u3000 S<\/mi>n<\/mi><\/msub>=<\/mo>a<\/mi>(<\/mo>r<\/mi>n<\/mi><\/msup>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow>r<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/mfrac><\/mrow><\/semantics><\/math> (where r<\/mi>\u2260<\/mo>1<\/mn><\/mrow><\/semantics><\/math>)<\/strong><\/p>\n\n\n\n

<\/p>\n\n\n\n

\u4f8b\u984c1\uff1a\u7b49\u5dee\u6570\u5217\u306e12\u756a\u76ee\u306e\u9805\u3092\u6c42\u3081\u3088\uff1a3,6,12,24,\u2026<\/p>\n\n\n\n

a\uff08\u6700\u521d\u306e\u9805\uff09\u3068r\uff08\u516c\u6bd4\uff09\u3092\u7279\u5b9a\u305b\u3088\uff1aa=3\u3001r=2\u3002
<\/p>\n\n\n\n

\u516c\u5f0f\u3000t<\/mi>n<\/mi><\/msub>=<\/mo>a<\/mi>r<\/mi>n<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mrow>t_n = ar^{n-1}<\/annotation><\/semantics><\/math>\u3092\u7528\u3044\u308b\uff1at<\/mi>12<\/mn><\/msub>=<\/mo>3<\/mn>\u00d7<\/mo>2<\/mn>(<\/mo>12<\/mn>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow><\/msup><\/mrow>t_{12} = 3 \\times 2^{(12-1)}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

\u8a08\u7b97\u305b\u3088\uff1at<\/mi>12<\/mn><\/msub>=<\/mo>3<\/mn>\u00d7<\/mo>2<\/mn>11<\/mn><\/msup>=<\/mo>3<\/mn>\u00d7<\/mo>2048<\/mn>=<\/mo>6144<\/mn><\/mrow>t_{12} = 3 \\times 2^{11} = 3 \\times 2048 = 6144<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

1.2 \u4e8c\u6b21\u95a2\u6570\u3068\u5224\u5225\u5f0f<\/strong><\/p>\n\n\n\n

\u4e8c\u6b21\u95a2\u6570\u306f f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>a<\/mi>x<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>x<\/mi>+<\/mo>c<\/mi><\/mrow>f(x)=ax^2+bx+c<\/annotation><\/semantics><\/math> \u306e\u5f62\u3092\u3068\u308a\u307e\u3059\u3002\u300c\u65b9\u6cd5\u8ad6\u300d\u3067\u306f\u3001\u7279\u306b\u6839\u306e\u6027\u8cea\uff08\u30b0\u30e9\u30d5\u304c x \u8ef8\u3068\u63a5\u3059\u308b\u70b9\uff09\u306b\u6ce8\u76ee\u3057\u307e\u3059\u3002<\/p>\n\n\n\n


\u5224\u5225\u5f0f (\u0394)<\/p>\n\n\n\n

\u4e8c\u6b21\u95a2\u6570\u306e\u5e73\u65b9\u6839\u306e\u4e0b\u306e\u90e8\u5206 \u0394<\/mi><\/mrow>=<\/mo>b<\/mi>2<\/mn><\/msup>\u2212<\/mo>4<\/mn>a<\/mi>c<\/mi><\/mrow>\u0394=b^2\u22124ac<\/annotation><\/semantics><\/math> \u306f\u3001x \u8ef8\u5207\u7247\u304c\u3044\u304f\u3064\u5b58\u5728\u3059\u308b\u304b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u0394>0: \u7570\u306a\u308b\u5b9f\u6839\u304c 2 \u3064\uff08\u30b0\u30e9\u30d5\u306f x \u8ef8\u3068 2 \u56de\u4ea4\u5dee\u3057\u307e\u3059\uff09\u3002
\u0394=0: \u5b9f\u6839\u304c 1 \u3064\uff08\u30b0\u30e9\u30d5\u306f\u6298\u308c\u70b9\u3067 x \u8ef8\u3068\u63a5\u3057\u307e\u3059\uff09\u3002
\u0394<0: \u5b9f\u6839\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\uff08\u30b0\u30e9\u30d5\u306f x \u8ef8\u3068\u6c7a\u3057\u3066\u63a5\u3057\u307e\u305b\u3093\uff09\u3002<\/p>\n\n\n\n

1.3 \u95a2\u6570\u306e\u8868\u8a18\u3001\u5b9a\u7fa9\u57df\u3001\u5024\u57df<\/strong><\/p>\n\n\n\n

\u3053\u308c\u306f\u91cd\u8981\u306a\u6982\u5ff5\u306e\u8ee2\u63db\u3067\u3059\u3002\u51fa\u529b\u304c\u5165\u529b\u306b\u4f9d\u5b58\u3059\u308b\u3053\u3068\u3092\u5f37\u8abf\u3059\u308b\u305f\u3081\u306b\u3001\u300cy =\u300d\u3067\u306f\u306a\u304f\u300cf<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo><\/mrow>f(x) =<\/annotation><\/semantics><\/math>\u300d\u3068\u66f8\u304d\u59cb\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

\u5b9a\u7fa9\u57df: \u95a2\u6570\u304c\u5b9a\u7fa9\u3055\u308c\u308b\u3059\u3079\u3066\u306e x \u5024\uff08\u5165\u529b\uff09\u306e\u96c6\u5408\u3002
\u5024\u57df: \u95a2\u6570\u304c\u751f\u6210\u3067\u304d\u308b\u3059\u3079\u3066\u306e y \u5024\uff08\u51fa\u529b\uff09\u306e\u96c6\u5408\u3002<\/p>\n\n\n\n

\u4f8b\u984c 2: f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>x<\/mi>2<\/mn><\/msup>+<\/mo>3<\/mn><\/mrow> f(x)=x^2+3<\/annotation><\/semantics><\/math> \u306e\u5b9a\u7fa9\u57df\u3068\u5024\u57df\u3092\u8ff0\u3079\u3088\u3002<\/p>\n\n\n\n

\u5b9a\u7fa9\u57df: \u4efb\u610f\u306e\u5b9f\u6570\u3092\u4e8c\u4e57\u3067\u304d\u308b\u306e\u3067\u3001\u5b9a\u7fa9\u57df\u306f x\u2208\u211d\uff08\u3059\u3079\u3066\u306e\u5b9f\u6570\uff09\u3067\u3042\u308b\u3002
\u5024\u57df: x2 \u306f\u5e38\u306b \u2265 0 \u306a\u306e\u3067\u3001f(x) \u304c\u53d6\u308a\u5f97\u308b\u6700\u5c0f\u5024\u306f 0+3=3 \u3067\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5024\u57df\u306f f<\/mi>(<\/mo>x<\/mi>)<\/mo>\u2265<\/mo>3<\/mn><\/mrow>f(x)\u22653<\/annotation><\/semantics><\/math> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n

1.4 \u7df4\u7fd2\u554f\u984c<\/strong>
\u30d1\u30fc\u30c8A\uff1a\u6570\u5217<\/p>\n\n\n\n

1. \u7b49\u5dee\u6570\u5217 5,11,17,\u2026 \u306e\u6700\u521d\u306e20\u9805\u306e\u548c\u3092\u6c42\u3081\u3088\u3002
2.\u3042\u308b\u7b49\u6bd4\u6570\u5217\u306f a=10 \u304b\u3064 r=0.5 \u3067\u3042\u308b\u30025\u756a\u76ee\u306e\u9805\u3068\u7121\u9650\u5927\u307e\u3067\u306e\u548c\u3092\u6c42\u3081\u3088\u3002<\/p>\n\n\n\n

S<\/mi>\u221e<\/mi><\/msub>=<\/mo>a<\/mi>1<\/mn>\u2212<\/mo>r<\/mi><\/mrow><\/mfrac><\/mrow>S_\\infty = \\frac{a}{1-r}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n\n\n

\u30d1\u30fc\u30c8B\uff1a\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3068\u4ee3\u6570<\/p>\n\n\n\n

3. \u5224\u5225\u5f0f\u3092\u7528\u3044\u3066\u30012<\/mn>x<\/mi>2<\/mn><\/msup>\u2212<\/mo>4<\/mn>x<\/mi>+<\/mo>7<\/mn>=<\/mo>0<\/mn><\/mrow>2x^2\u22124x+7=0 <\/annotation><\/semantics><\/math>\u306e\u89e3\u306e\u500b\u6570\u3092\u6c42\u3081\u3088\u3002
4. $x$ \u3092\u56e0\u6570\u5206\u89e3\u3057\u3066 x<\/mi>2<\/mn><\/msup>\u2212<\/mo>5<\/mn>x<\/mi>\u2212<\/mo>14<\/mn>=<\/mo>0<\/mn><\/mrow>x^2\u22125x\u221214=0<\/annotation><\/semantics><\/math> \u3092\u89e3\u3051\u3002
5. \u8ab2\u984c\uff1ax<\/mi>2<\/mn><\/msup>+<\/mo>6<\/mn>x<\/mi>+<\/mo>k<\/mi>=<\/mo>0<\/mn><\/mrow>x^2+6x+k=0<\/annotation><\/semantics><\/math> \u304c\u3061\u3087\u3046\u30691\u3064\u306e\u5b9f\u6570\u89e3\u3092\u6301\u3064\u3088\u3046\u306a k \u306e\u5024\u3092\u6c42\u3081\u3088\u3002<\/p>\n\n\n\n

\u30d1\u30fc\u30c8C\uff1a\u95a2\u6570<\/p>\n\n\n\n

6. f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>3<\/mn>x<\/mi>2<\/mn><\/msup>\u2212<\/mo>5<\/mn>x<\/mi><\/mrow>f(x)=3x^2\u22125x<\/annotation><\/semantics><\/math> \u306e\u3068\u304d\u3001f<\/mi>(<\/mo>2<\/mn>)<\/mo><\/mrow>f(2)<\/annotation><\/semantics><\/math> \u3068 f<\/mi>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow>f(\u22121)<\/annotation><\/semantics><\/math> \u3092\u6c42\u3081\u3088\u3002
7. g<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>\u2212<\/mo>x<\/mi>2<\/mn><\/msup>+<\/mo>10<\/mn><\/mrow>g(x) = -x^2 + 10<\/annotation><\/semantics><\/math> \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088\u3002<\/p>\n\n\n\n
<\/math><\/div>\n\n\n\n

\u89e3\u6c7a\u7b56\uff08\u6982\u8981\uff09<\/p>\n\n\n\n

1.S<\/mi>20<\/mn><\/msub>=<\/mo>1240<\/mn><\/mrow>S_{20}=1240<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    \n
  1. t<\/mi>5<\/mn><\/msub>=<\/mo>0.625<\/mn><\/mrow>t_5=0.625<\/annotation><\/semantics><\/math>\u3001S<\/mi>\u221e<\/mi><\/msub>=<\/mo>20<\/mn><\/mrow>S_\u221e=20<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
  2. \u0394=-40;\u672c\u5f53\u306e\u89e3\u6c7a\u7b56\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/li>\n\n\n\n
  3. (x\u22127)(x+2)=0\u2192x=7,\u22122<\/li>\n\n\n\n
  4. \u0394=36\u22124k=0\u2192k=9<\/li>\n\n\n\n
  5. f<\/mi>(<\/mo>2<\/mn>)<\/mo>=<\/mo>2<\/mn><\/mrow>f(2)=2<\/annotation><\/semantics><\/math>\u3001f<\/mi>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>=<\/mo>8<\/mn><\/mrow>f(\u22121)=8<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
  6. g<\/mi>(<\/mo>x<\/mi>)<\/mo>\u2264<\/mo>10<\/mn><\/mrow>g(x)\u226410<\/annotation><\/semantics><\/math><\/li>\n<\/ol>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    \u7b2c1\u7ae0\uff1a\u4ee3\u6570\u3068\u95a2\u6570\u3053\u306e\u7ae0\u3067\u306f\u3001\u6570\u5b66\u7684\u624b\u6cd5\u306b\u5fc5\u8981\u306a\u4ee3\u6570\u7684\u80fd\u529b\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002\u57fa\u672c\u7684\u306a\u8a08\u7b97\u304b\u3089\u4e00\u6b69\u8e0f\u307f\u8fbc\u307f\u3001\u5909\u6570\u9593\u306e\u95a2\u4fc2\u3001\u30d1\u30bf\u30fc\u30f3\u306e\u6027\u8cea\u3001\u95a2\u6570\u306e\u5e7e\u4f55\u5b66\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002 1.1 \u7b49\u5dee\u6570\u5217\u3068\u5e7e\u4f55\u6570\u5217 \u300c\u30e1\u30bd\u30c3\u30c9\u300d\u3067\u306f\u3001\u6570\u5217\u3092\u96e2\u6563\u95a2\u6570\u3068\u3057\u3066\u6271\u3044\u3001\u5165\u529b\u306f\u4f4d\u7f6en\u3068\u3057\u307e\u3059\u3002 \u7b49\u5dee\u6570\u5217: \u9023\u7d9a\u3059\u308b\u9805\u306e\u5dee\u304c\u5b9a\u6570(d)\u3067\u3042\u308b\u6570\u5217\u3002 \uff4e\u756a\u76ee\u306e\u9805: tn=a+(n\u22121)dt_n = a + (n-1)d \uff4e\u756a\u76ee\u306e\u9805\u307e\u3067\u306e\u5408\u8a08\uff1a\u3000Sn=n2(2a+(n\u22121)d)S_n = \\frac{n}{2}(2a + (n-1)d)\u3000 \u5e7e\u4f55\u6570\u5217\uff1a\u5404\u9805\u304c\u524d\u306e\u9805\u306b\u5b9a\u6570\u6bd4(r)\u3092\u639b\u3051\u3066\u6c42\u3081\u3089\u308c\u308b\u6570\u5217\u3002 \uff4e\u756a\u76ee\u306e\u9805: tn=arn\u22121t_n = ar^{n-1} \uff4e\u756a\u76ee\u306e\u9805\u307e\u3067\u306e\u5408\u8a08\uff1a\u3000 Sn=a(rn\u22121)r\u22121 (where r\u22601) \u4f8b\u984c1\uff1a\u7b49\u5dee\u6570\u5217\u306e12\u756a\u76ee\u306e\u9805\u3092\u6c42\u3081\u3088\uff1a3,6,12,24,\u2026 a\uff08\u6700\u521d\u306e\u9805\uff09\u3068r\uff08\u516c\u6bd4\uff09\u3092\u7279\u5b9a\u305b\u3088\uff1aa=3\u3001r=2\u3002 \u516c\u5f0f\u3000tn=arn\u22121t_n = ar^{n-1}\u3092\u7528\u3044\u308b\uff1at12=3\u00d72(12\u22121)t_{12} = 3 \\times 2^{(12-1)} \u8a08\u7b97\u305b\u3088\uff1at12=3\u00d7211=3\u00d72048=6144t_{12} = 3 \\times 2^{11} = 3 \\times 2048 = 6144 1.2 \u4e8c\u6b21\u95a2\u6570\u3068\u5224\u5225\u5f0f \u4e8c\u6b21\u95a2\u6570\u306f f(x)=ax2+bx+cf(x)=ax^2+bx+c \u306e\u5f62\u3092\u3068\u308a\u307e\u3059\u3002\u300c\u65b9\u6cd5\u8ad6\u300d\u3067\u306f\u3001\u7279\u306b\u6839\u306e\u6027\u8cea\uff08\u30b0\u30e9\u30d5\u304c x \u8ef8\u3068\u63a5\u3059\u308b\u70b9\uff09\u306b\u6ce8\u76ee\u3057\u307e\u3059\u3002 \u5224\u5225\u5f0f (\u0394) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1105","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1105"}],"version-history":[{"count":5,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1105\/revisions"}],"predecessor-version":[{"id":1135,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1105\/revisions\/1135"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}