{"id":1057,"date":"2026-01-12T12:59:50","date_gmt":"2026-01-12T02:59:50","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1057"},"modified":"2026-01-12T12:59:50","modified_gmt":"2026-01-12T02:59:50","slug":"year11-ath-2-1-2-shape-and-measurement-spatial-intelligence","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1057","title":{"rendered":"Year11-ATH-2-1-2 Shape and Measurement (Spatial Intelligence)"},"content":{"rendered":"\n

Core<\/strong>: Surface area and volume of pyramids, cones, spheres, and composite solids<\/strong>.<\/strong><\/p>\n\n\n\n

Topic: Similar figures and the scale factor relationship between area (<\/strong>k<\/mi>2<\/mn><\/msup>k^2<\/annotation><\/semantics><\/math> ) and volume (<\/strong>k<\/mi>3<\/mn><\/msup>k^3<\/annotation><\/semantics><\/math>).<\/strong><\/p>\n\n\n\n

In Year 11 Mathematics, Shape and Measurement (often part of Geometry) involves <\/strong>, focusing on Pythagoras’ theorem, mensuration<\/strong> <\/strong>(area, perimeter, surface area, volume), similarity, scaling, trigonometry, and using tools like the Trapezoidal Rule<\/strong> <\/strong>for area, bridging foundational concepts with real-world applications and advanced problem-solving.<\/strong> <\/strong><\/p>\n\n\n\n

Key Topics in Year 11 Shape & Measurement:<\/strong><\/p>\n\n\n\n

    \n
  • Pythagoras’ Theorem<\/strong> & Extensions:<\/strong> Applying the theorem in 2D and 3D contexts to find lengths and distances.<\/li>\n\n\n\n
  • Mensuration<\/strong> (Area & Volume):<\/strong> Calculating areas of complex shapes, perimeters, and volumes\/capacities of prisms, cylinders, spheres, and composite solids.<\/li>\n\n\n\n
  • Similarity & Scaling<\/strong>:<\/strong> Understanding how shapes relate when scaled, including similar triangles and solids, and using scale factors.<\/li>\n\n\n\n
  • Trigonometry<\/strong>:<\/strong>\u00a0Using trigonometric ratios (Sin(\u03b8)<\/em> Cos(\u03b8)<\/em> Tan(\u03b8)<\/em>) and identities, along with the Sine and Cosine Rules, to solve problems involving angles and sides in triangles. <\/li>\n\n\n\n
  • Coordinate Geometry<\/strong>:<\/strong> Working with polar and rectangular coordinates, and applying functions to geometric concepts.<\/li>\n\n\n\n
  • Trapezoidal Rule<\/strong>:<\/strong> A calculus-related method for approximating the area under curves or irregular shapes, crucial for higher-level maths.<\/li>\n\n\n\n
  • Geometric Reasoning<\/strong>:<\/strong> Developing logical arguments about shapes, space, and their properties. <\/li>\n<\/ul>\n\n\n\n

    Why It’s Important:<\/strong>
    This topic connects abstract mathematical ideas to physical objects, helping develop spatial reasoning, logical thinking, and problem-solving skills used in fields from architecture to engineering.<\/p>\n\n\n\n

    In Year 11 Australian mathematics curricula, Pythagoras’ theorem is revisited and extended into more complex applications, including problem-solving in three dimensions and coordinate geometry<\/strong><\/p>\n\n\n\n

    . <\/p>\n\n\n\n

    Pythagoras’ Theorem <\/strong><\/p>\n\n\n\n

    The core theorem, typically covered in earlier years (Stages 4 and 5, or Years 9-10), states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle, usually denoted as c<\/mi>c<\/annotation><\/semantics><\/math> ) is equal to the sum of the squares of the lengths of the other two shorter sides (denoted as a<\/mi>a<\/annotation><\/semantics><\/math> and b<\/mi>b<\/annotation><\/semantics><\/math> ): a<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>2<\/mn><\/msup>=<\/mo>c<\/mi>2<\/mn><\/msup><\/mrow>a^{2}+b^{2}=c^{2}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

    In Year 11, students are expected to be fluent in: <\/p>\n\n\n\n

      \n
    • Calculating the length of an unknown side in a right-angled triangle.<\/li>\n\n\n\n
    • Applying the converse<\/strong> of the theorem to determine if a triangle is a right-angled triangle.<\/li>\n\n\n\n
    • Solving practical problems in various contexts (e.g., construction, surveying, navigation). <\/li>\n<\/ul>\n\n\n\n

      Extensions in Year 11 Mathematics <\/p>\n\n\n\n

      In Year 11, the focus shifts to applying the fundamental theorem in more advanced and abstract scenarios, as prerequisites for higher-level topics like trigonometry and calculus. <\/p>\n\n\n\n

        \n
      • Distance Formula in the Cartesian Plane:<\/strong> The theorem is the basis for the distance formula between two points (<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>(x_{1},y_{1})<\/annotation><\/semantics><\/math> and (<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>y<\/mi>2<\/mn><\/msub>)<\/mo><\/mrow>(x_{2},y_{2})<\/annotation><\/semantics><\/math> in a two-dimensional coordinate system: Distance = (<\/mo>x<\/mi>2<\/mn><\/msub>\u2212<\/mo>x<\/mi>1<\/mn><\/msub>)<\/mo>2<\/mn><\/msup>+<\/mo>(<\/mo>y<\/mi>2<\/mn><\/msub>\u2212<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo>2<\/mn><\/msup><\/mrow><\/msqrt>\\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
      • Three-Dimensional Problems:<\/strong> A significant extension involves using Pythagoras’ theorem to find lengths within 3D objects like cuboids or prisms. This often requires applying the theorem twice to find a diagonal length.<\/li>\n\n\n\n
      • Coordinate Geometry in 3D Space:<\/strong> The distance formula concept is extended to three-dimensional coordinates (a<\/mi>,<\/mo>b<\/mi>,<\/mo>c<\/mi><\/mrow>a,b,c<\/annotation><\/semantics><\/math>), where the distance from the origin is given by . a<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>2<\/mn><\/msup>+<\/mo>c<\/mi>2<\/mn><\/msup><\/mrow><\/msqrt>\\sqrt{a^{2}+b^{2}+c^{2}}<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
      • Trigonometric Identities:<\/strong> In advanced courses, the theorem is used to establish fundamental trigonometric identities, such as cos<\/mi>2<\/mn><\/msup>\u2061<\/mo><\/mspace>\u03b8<\/mi>+<\/mo>sin<\/mi>2<\/mn><\/msup>\u2061<\/mo><\/mspace>\u03b8<\/mi>=<\/mo>1<\/mn><\/mrow>\\cos ^{2}\\theta +\\sin ^{2}\\theta =1<\/annotation><\/semantics><\/math> , which forms the basis of circular functions and further trigonometry.<\/li>\n\n\n\n
      • Links to Generalised Theorems:<\/strong> The theorem provides the geometric foundation for more general laws in non-right-angled triangles, such as the Cosine Rule<\/strong> (a<\/mi>2<\/mn><\/msup>=<\/mo>b<\/mi>2<\/mn><\/msup>+<\/mo>c<\/mi>2<\/mn><\/msup>\u2212<\/mo>2<\/mn>b<\/mi>c<\/mi><\/mspace>cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>A<\/mi><\/mrow>a^{2}=b^{2}+c^{2}-2bc\\cos A<\/annotation><\/semantics><\/math>), which is a generalisation of Pythagoras’ theorem.<\/li>\n\n\n\n
      • Pythagorean Triples:<\/strong> Students may investigate properties of Pythagorean triples (sets of three whole numbers that satisfy the theorem, e.g., 3-4-5, 5-12-13) and how to generate them. <\/li>\n<\/ul>\n\n\n\n

        ***********************************************************<\/strong><\/p>\n\n\n\n

        Year11-MATH-2-1-2<\/strong><\/p>\n\n\n\n

        \u5f62\u3068\u6e2c\u5b9a\uff08\u7a7a\u9593\u77e5\u80fd\uff09<\/strong><\/p>\n\n\n\n

        \u30b3\u30a2\uff1a\u89d2\u9310\u3001\u5186\u9310\u3001\u7403\u3001\u8907\u5408\u7acb\u4f53\u306e\u8868\u9762\u7a4d\u3068\u4f53\u7a4d\u3002<\/p>\n\n\n\n

        \u30c8\u30d4\u30c3\u30af\uff1a\u76f8\u4f3c\u56f3\u5f62\u3068\u3001\u9762\u7a4d\uff08k<\/mi>2<\/mn><\/msup>k^2<\/annotation><\/semantics><\/math>\uff09\u3068\u4f53\u7a4d\uff08k<\/mi>3<\/mn><\/msup>k^3<\/annotation><\/semantics><\/math>\uff09\u306e\u7e2e\u5c3a\u4fc2\u6570\u306e\u95a2\u4fc2\u3002<\/p>\n\n\n\n

        11\u5e74\u751f\u306e\u6570\u5b66\u3067\u306f\u3001\u5f62\u3068\u6e2c\u5b9a\uff08\u591a\u304f\u306e\u5834\u5408\u3001\u5e7e\u4f55\u5b66\u306e\u4e00\u90e8\uff09\u306b\u304a\u3044\u3066\u3001\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3001\u6e2c\u91cf\uff08\u9762\u7a4d\u3001\u5468\u56f2\u9577\u3001\u8868\u9762\u7a4d\u3001\u4f53\u7a4d\uff09\u3001\u76f8\u4f3c\u3001\u7e2e\u5c3a\u3001\u4e09\u89d2\u6cd5\u3001\u9762\u7a4d\u306e\u53f0\u5f62\u5b9a\u7406\u306a\u3069\u306e\u30c4\u30fc\u30eb\u306e\u4f7f\u7528\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u57fa\u790e\u6982\u5ff5\u3092\u73fe\u5b9f\u4e16\u754c\u306e\u5fdc\u7528\u3084\u9ad8\u5ea6\u306a\u554f\u984c\u89e3\u6c7a\u306b\u7d50\u3073\u3064\u3051\u307e\u3059\u3002<\/p>\n\n\n\n

        11\u5e74\u751f \u56f3\u5f62\u3068\u6e2c\u5b9a\u306e<\/strong>\u4e3b\u8981\u30c8\u30d4\u30c3\u30af<\/strong>\uff1a<\/strong><\/p>\n\n\n\n

        \u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3068\u305d\u306e\u62e1\u5f35\uff1a<\/strong>\u5b9a\u7406\u30922\u6b21\u5143\u304a\u3088\u30733\u6b21\u5143\u306e\u6587\u8108\u306b\u9069\u7528\u3057\u3001\u9577\u3055\u3068\u8ddd\u96e2\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

        \u6e2c\u91cf\uff08\u9762\u7a4d\u3068\u4f53\u7a4d\uff09\uff1a<\/strong>\u8907\u96d1\u306a\u5f62\u72b6\u306e\u9762\u7a4d\u3001\u5468\u56f2\u9577\u3001\u305d\u3057\u3066\u89d2\u67f1\u3001\u5186\u67f1\u3001\u7403\u3001\u8907\u5408\u7acb\u4f53\u306e\u4f53\u7a4d\uff0f\u5bb9\u91cf\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

        \u76f8\u4f3c\u3068\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\uff1a<\/strong>\u76f8\u4f3c\u4e09\u89d2\u5f62\u3084\u76f8\u4f3c\u7acb\u4f53\u3092\u542b\u3080\u3001\u56f3\u5f62\u306e\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u6642\u306e\u95a2\u4fc2\u6027\u3092\u7406\u89e3\u3057\u3001\u7e2e\u5c3a\u4fc2\u6570\u3092\u7528\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

        \u4e09\u89d2\u6cd5\uff1a<\/strong>\u76f4\u89d2\u4e09\u89d2\u5f62\u306e\u4e09\u89d2\u6bd4\uff08\u30b5\u30a4\u30f3\u3001\u30b3\u30b5\u30a4\u30f3\u3001\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\uff09\u3068\u6052\u7b49\u5f0f\u3001\u305d\u3057\u3066\u76f4\u89d2\u3067\u306a\u3044\u4e09\u89d2\u5f62\u306e\u6b63\u5f26\u5b9a\u7406\u3068\u4f59\u5f26\u5b9a\u7406\u3092\u7528\u3044\u3066\u3001\u4e09\u89d2\u5f62\u306e\u89d2\u5ea6\u3068\u8fba\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

        \u5ea7\u6a19\u5e7e\u4f55\u5b66\uff1a<\/strong>\u6975\u5ea7\u6a19\u3068\u76f4\u4ea4\u5ea7\u6a19\u3092\u6271\u3044\u3001\u5e7e\u4f55\u5b66\u306e\u6982\u5ff5\u306b\u95a2\u6570\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

        \u53f0\u5f62\u5b9a\u7406\uff1a<\/strong>\u66f2\u7dda\u3084\u4e0d\u898f\u5247\u306a\u5f62\u72b6\u306e\u4e0b\u306e\u9762\u7a4d\u3092\u8fd1\u4f3c\u3059\u308b\u305f\u3081\u306e\u5fae\u7a4d\u5206\u5b66\u7684\u306a\u65b9\u6cd5\u3067\u3001\u9ad8\u7b49\u6570\u5b66\u306b\u4e0d\u53ef\u6b20\u3067\u3059\u3002<\/p>\n\n\n\n

        \u5e7e\u4f55\u5b66\u7684\u63a8\u8ad6\uff1a<\/strong>\u56f3\u5f62\u3001\u7a7a\u9593\u3001\u305d\u3057\u3066\u305d\u308c\u3089\u306e\u7279\u6027\u306b\u3064\u3044\u3066\u8ad6\u7406\u7684\u306a\u8b70\u8ad6\u3092\u5c55\u958b\u3059\u308b\u3002<\/p>\n\n\n\n

        \u306a\u305c\u91cd\u8981\u306a\u306e\u304b\uff1a<\/strong><\/p>\n\n\n\n

        \u3053\u306e\u30c8\u30d4\u30c3\u30af\u306f\u3001\u62bd\u8c61\u7684\u306a\u6570\u5b66\u7684\u6982\u5ff5\u3092\u7269\u7406\u7684\u306a\u5bfe\u8c61\u3068\u7d50\u3073\u3064\u3051\u3001\u5efa\u7bc9\u304b\u3089\u5de5\u5b66\u307e\u3067\u5e45\u5e83\u3044\u5206\u91ce\u3067\u7528\u3044\u3089\u308c\u308b\u7a7a\u9593\u7684\u63a8\u8ad6\u3001\u8ad6\u7406\u7684\u601d\u8003\u3001\u305d\u3057\u3066\u554f\u984c\u89e3\u6c7a\u80fd\u529b\u306e\u80b2\u6210\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n

        \u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406<\/strong><\/p>\n\n\n\n

        \u30aa\u30fc\u30b9\u30c8\u30e9\u30ea\u30a2\u306e11\u5e74\u751f\uff08Year 11\uff09\u6570\u5b66\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u3067\u306f\u3001\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u304c\u518d\u8003\u3055\u308c\u3001\u4e09\u6b21\u5143\u306e\u554f\u984c\u89e3\u6c7a\u3084\u5ea7\u6a19\u5e7e\u4f55\u5b66\u306a\u3069\u3001\u3088\u308a\u8907\u96d1\u306a\u5fdc\u7528\u3078\u3068\u62e1\u5f35\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

        \u3053\u306e\u4e2d\u6838\u5b9a\u7406\u306f\u3001\u901a\u5e38\u3001\u4f4e\u5b66\u5e74\uff08\u30b9\u30c6\u30fc\u30b84\u304a\u3088\u30735\u3001\u307e\u305f\u306fYear 9-10\uff09\u3067\u6271\u308f\u308c\u307e\u3059\u304c\u3001\u76f4\u89d2\u4e09\u89d2\u5f62\u306b\u304a\u3044\u3066\u3001\u659c\u8fba\uff08\u76f4\u89d2\u306e\u53cd\u5bfe\u5074\u306e\u8fba\u3001\u901a\u5e38\u306f c \u3068\u8868\u8a18\uff09\u306e\u9577\u3055\u306e2\u4e57\u306f\u3001\u4ed6\u306e2\u3064\u306e\u77ed\u3044\u8fba\uff08a \u3068b\u3068\u8868\u8a18\uff09\u306e\u9577\u3055\u306e2\u4e57\u306e\u548c\u306b\u7b49\u3057\u3044\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002a<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>2<\/mn><\/msup>=<\/mo>c<\/mi>2<\/mn><\/msup><\/mrow>a^{2}+b^{2}=c^{2}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

        Year 11\u3067\u306f\u3001\u751f\u5f92\u306f\u4ee5\u4e0b\u306e\u4e8b\u9805\u306b\u7cbe\u901a\u3059\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\u3002<\/strong><\/p>\n\n\n\n

        \u2022 \u76f4\u89d2\u4e09\u89d2\u5f62\u306e\u672a\u77e5\u306e\u8fba\u306e\u9577\u3055\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

        \u2022 \u5b9a\u7406\u306e\u9006\u3092\u9069\u7528\u3057\u3066\u3001\u4e09\u89d2\u5f62\u304c\u76f4\u89d2\u4e09\u89d2\u5f62\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u3002<\/p>\n\n\n\n

        \u2022 \u69d8\u3005\u306a\u72b6\u6cc1\uff08\u4f8b\uff1a\u5efa\u8a2d\u3001\u6e2c\u91cf\u3001\u822a\u6d77\uff09\u306b\u304a\u3051\u308b\u5b9f\u7528\u7684\u306a\u554f\u984c\u306e\u89e3\u6c7a\u3002<\/strong><\/p>\n\n\n\n

        11\u5e74\u751f\u6570\u5b66\u306e\u767a\u5c55\u8ab2\u984c<\/strong><\/p>\n\n\n\n

        11\u5e74\u751f\u3067\u306f\u3001\u4e09\u89d2\u6cd5\u3084\u5fae\u7a4d\u5206\u3068\u3044\u3063\u305f\u3088\u308a\u9ad8\u5ea6\u306a\u30c8\u30d4\u30c3\u30af\u306e\u524d\u63d0\u6761\u4ef6\u3068\u3057\u3066\u3001\u3088\u308a\u9ad8\u5ea6\u3067\u62bd\u8c61\u7684\u306a\u30b7\u30ca\u30ea\u30aa\u306b\u57fa\u672c\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u306b\u91cd\u70b9\u304c\u7f6e\u304b\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

        \u2022 \u76f4\u4ea4\u5e73\u9762\u306b\u304a\u3051\u308b\u8ddd\u96e2\u306e\u516c\u5f0f\uff1a<\/strong>\u3053\u306e\u5b9a\u7406\u306f\u30012\u6b21\u5143\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b2\u70b9 (<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo>\u3068<\/mtext>(<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>y<\/mi>2<\/mn><\/msub>)<\/mo><\/mrow>(x_{1},y_{1})\u3068(x_{2},y_{2})<\/annotation><\/semantics><\/math> \u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u57fa\u790e\u3068\u306a\u308a\u307e\u3059\u3002\u8ddd\u96e2<\/mtext>=<\/mo>(<\/mo>x<\/mi>2<\/mn><\/msub>\u2212<\/mo>x<\/mi>1<\/mn><\/msub>)<\/mo>2<\/mn><\/msup>+<\/mo>(<\/mo>y<\/mi>2<\/mn><\/msub>\u2212<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo>2<\/mn><\/msup><\/mrow><\/msqrt><\/mrow>\\text{\u8ddd\u96e2}=\\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

        \u2022 3\u6b21\u5143\u554f\u984c\uff1a<\/strong>\u91cd\u8981\u306a\u767a\u5c55\u8ab2\u984c\u3068\u3057\u3066\u3001\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\u76f4\u65b9\u4f53\u3084\u89d2\u67f1\u306a\u3069\u306e3\u6b21\u5143\u7269\u4f53\u5185\u306e\u9577\u3055\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u5b9a\u7406\u30922\u56de\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

        \u2022 3\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u5ea7\u6a19\u5e7e\u4f55\u5b66\uff1a<\/strong>\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u6982\u5ff5\u306f3\u6b21\u5143\u5ea7\u6a19 (a,b,c) \u306b\u62e1\u5f35\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

        \u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\u306f a<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>2<\/mn><\/msup>+<\/mo>c<\/mi>2<\/mn><\/msup><\/mrow><\/msqrt>\\sqrt{a^{2}+b^{2}+c^{2}}<\/annotation><\/semantics><\/math> \u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

        \u2022 \u4e09\u89d2\u95a2\u6570\u306e\u7b49\u5f0f\uff1a<\/strong>\u4e0a\u7d1a\u30b3\u30fc\u30b9\u3067\u306f\u3001\u3053\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\u3001\u5186\u95a2\u6570\u3084\u305d\u306e\u4ed6\u306e\u4e09\u89d2\u6cd5\u306e\u57fa\u790e\u3068\u306a\u308b c<\/mi>o<\/mi>s<\/mi>2<\/mn><\/msup>\u03b8<\/mi>+<\/mo>sin<\/mi>2<\/mn><\/msup>\u2061<\/mo><\/mspace>\u03b8<\/mi>=<\/mo>1<\/mn><\/mrow>cos ^{2}\\theta +\\sin ^{2}\\theta =1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

        \u306a\u3069\u306e\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u306e\u7b49\u5f0f\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

        \u2022 \u4e00\u822c\u5316\u3055\u308c\u305f\u5b9a\u7406\u3078\u306e\u30ea\u30f3\u30af\uff1a<\/strong>\u3053\u306e\u5b9a\u7406\u306f\u3001\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3092\u4e00\u822c\u5316\u3057\u305f\u4f59\u5f26\u5b9a\u7406 (<\/mo>a<\/mi>2<\/mn><\/msup>=<\/mo>b<\/mi>2<\/mn><\/msup>+<\/mo>c<\/mi>2<\/mn><\/msup>\u2212<\/mo>2<\/mn>b<\/mi>c<\/mi><\/mspace>cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>A<\/mi>)<\/mo><\/mrow>(a^{2}=b^{2}+c^{2}-2bc\\cos A)<\/annotation><\/semantics><\/math> \u306a\u3069\u3001\u76f4\u89d2\u4e09\u89d2\u5f62\u4ee5\u5916\u306e\u3088\u308a\u4e00\u822c\u7684\u306a\u6cd5\u5247\u306e\u5e7e\u4f55\u5b66\u7684\u57fa\u790e\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

        \u2022 \u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\uff1a<\/strong>\u5b66\u751f\u306f\u3001\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\uff08\u5b9a\u7406\u3092\u6e80\u305f\u30593\u3064\u306e\u6574\u6570\u306e\u96c6\u5408\u3001\u4f8b\uff1a3-4-5\u30015-12-13\uff09\u306e\u6027\u8cea\u3068\u305d\u306e\u751f\u6210\u65b9\u6cd5\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

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

        Core: Surface area and volume of pyramids, cones, spheres, and composite solids. Topic: Similar figures and the scale factor relationship between area (k2k^2 ) and volume (k3k^3). In Year 11 Mathematics, Shape and Measurement (often part of Geometry) involves , focusing on Pythagoras’ theorem, mensuration (area, perimeter, surface area, volume), similarity, scaling, trigonometry, and using tools like the Trapezoidal Rule for area, […]<\/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-1057","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1057","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=1057"}],"version-history":[{"count":3,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1057\/revisions"}],"predecessor-version":[{"id":1062,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1057\/revisions\/1062"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}