صفحة 186 - كتاب الرياضيات - الصف 12 - الفصل 1 - المملكة العربية السعودية

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(مثال 1)" }, { "order": 2, "type": "exercise", "title": "1", "content": "$\\\\frac{(x+2)^2}{9} + \\\\frac{y^2}{49} = 1$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 3, "type": "exercise", "title": "2", "content": "$$\\\\frac{(x+4)^2}{9} + \\\\frac{(y+3)^2}{4} = 1$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 4, "type": "formula", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": false, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "content": "$$x^2 + 9y^2 - 14x + 36y + 49 = 0$$" }, { "order": 5, "type": "formula", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": false, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "content": "$$4x^2 + 9y^2 - 12x + 36y + 276 = 0$$" }, { "order": 6, "type": "formula", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": false, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "content": "$$65x^2 + 16y^2 + 130x - 975 = 0$$" }, { "order": 7, "type": "header", "title": "اكتب معادلة القطع الناقص الذي يحقق الخصائص المعطاة في كل مما يأتي. (مثال 2)", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "اكتب معادلة القطع الناقص الذي يحقق الخصائص المعطاة في كل مما يأتي. (مثال 2)" }, { "order": 8, "type": "exercise", "title": "5", "content": "الرأسـان (3-, 7-) و (3-, 13-)، والبؤرتان (3-, 11-) و (3-, 5-).", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 9, "type": "exercise", "title": "6", "content": "الرأسـان (9-, 4) و (9-, 4)، وطول المحور الأصغر 8 وحدات.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 10, "type": "exercise", "title": "7", "content": "إحداثيات نهايتي المحور الأكبر (2, 1)، (2, 13-)، وطول المحور الأكبر 8 وحدات.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 11, "type": "exercise", "title": "8", "content": "إحداثيات نهايتي المحور الأصغر (0, 6-) و (0, 6-)، وطول المحور الأكبر 20 وحدة.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 12, "type": "exercise", "title": "9", "content": "البؤرتان (3-, 6-) و (3-, 6-)، وطول المحور الأصغر 16 وحدة.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 13, "type": "header", "title": "حدد الاختلاف المركزي لقطع ناقص معادلته في كل مما يأتي. (مثال 3)", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "حدد الاختلاف المركزي لقطع ناقص معادلته في كل مما يأتي. (مثال 3)" }, { "order": 14, "type": "exercise", "title": "10", "content": "$$\\\\frac{(x+5)^2}{72} + \\\\frac{(y-3)^2}{54} = 1$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 15, "type": "exercise", "title": "11", "content": "$$\\\\frac{(x+6)^2}{40} + \\\\frac{(y-2)^2}{12} = 1$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 16, "type": "exercise", "title": "12", "content": "$$\\\\frac{(x-8)^2}{14} + \\\\frac{(y+3)^2}{57} = 1$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 17, "type": "exercise", "title": "13", "content": "$$\\\\frac{(x+8)^2}{27} + \\\\frac{(y-7)^2}{33} = 1$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 18, "type": "header", "title": "سباق: يوضح الشكل المجاور مضمار سباق على شكل قطع ناقص اختلاله المركزي 0.75. (مثال 4)", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "سباق: يوضح الشكل المجاور مضمار سباق على شكل قطع ناقص اختلاله المركزي 0.75. (مثال 4)" }, { "order": 19, "type": "exercise", "title": "14", "content": "ما أقصى عرض w لمضمار السباق؟", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": true, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "associated_visual_elements": [ 0 ] }, { "order": 20, "type": "exercise", "title": "15", "content": "اكتب معادلة القطع الناقص إذا كانت نقطة الأصل هي مركز المضمار.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": true, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "associated_visual_elements": [ 0 ] }, { "order": 21, "type": "header", "title": "اكتب معادلة الدائرة التي تحقق الخصائص المعطاة في كل مما يأتي. (مثال 5)", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "اكتب معادلة الدائرة التي تحقق الخصائص المعطاة في كل مما يأتي. (مثال 5)" }, { "order": 22, "type": "exercise", "title": "16", "content": "المركز (0, 3)، ونصف القطر 2.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 23, "type": "exercise", "title": "17", "content": "المركز (3-, 4-)، والقطر 12.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 24, "type": "exercise", "title": "18", "content": "المركز هو نقطة الأصل، ونصف القطر 7.", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 25, "type": "exercise", "title": "19", "content": "(2, 1), (2, 4)", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 26, "type": "exercise", "title": "20", "content": "(4, 10-), (4, 10)", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 27, "type": "exercise", "title": "21", "content": "(5, 7-), (2-, 9)", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 28, "type": "exercise", "title": "22", "content": "(4, 8), (6, 4-)", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 29, "type": "header", "title": "معادلات: استنتج الصورة العامة لمعادلة القطع الناقص الذي محوره الأكبر رأسي، ومركزه نقطة الأصل.", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "معادلات: استنتج الصورة العامة لمعادلة القطع الناقص الذي محوره الأكبر رأسي، ومركزه نقطة الأصل." }, { "order": 30, "type": "exercise", "title": "23", "content": "بالرجوع إلى فقرة \"لماذا؟\" في بداية الدرس، أجب عما يأتي:", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "associated_visual_elements": [], "sub_questions": [ { "number": "a", "question": "أوجد طول المحور الأصغر لمدار كوكب عطارد.", "visual_element_index": null }, { "number": "b", "question": "أوجد الاختلاف المركزي للمدار.", "visual_element_index": null } ] }, { "order": 31, "type": "header", "title": "أوجد المركز والبؤرتين والرأسين لكل قطع ناقص مما يأتي:", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "أوجد المركز والبؤرتين والرأسين لكل قطع ناقص مما يأتي:" }, { "order": 32, "type": "exercise", "title": "24", "content": "$$\\\\frac{(x+5)^2}{16} + \\\\frac{y^2}{7} = 1$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 33, "type": "exercise", "title": "25", "content": "$$9y^2 - 18y + 25x^2 + 100x - 116 = 0$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 34, "type": "exercise", "title": "26", "content": "$$65x^2 + 16y^2 + 130x - 975 = 0$$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 35, "type": "header", "title": "شاحنات: تستعمل في شاحنات نقل السوائل خزانات مقطعةها العرضي على شكل قطع ناقص؛ لأنها أكثر ثباتًا من الخزانات الأسطوانية، ويكون السائل فيها أقل حركة.", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "شاحنات: تستعمل في شاحنات نقل السوائل خزانات مقطعةها العرضي على شكل قطع ناقص؛ لأنها أكثر ثباتًا من الخزانات الأسطوانية، ويكون السائل فيها أقل حركة." }, { "order": 36, "type": "exercise", "title": "27", "content": "ارسم المقطع العرضي لخزان الشاحنة أعلاه على مستوى إحداثي:", "content_classification": "QUESTION_ACTIVITY", "question_indicators": { "has_question_words": true, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "associated_visual_elements": [ 1 ], "sub_questions": [ { "number": "a", "question": "ارسم المقطع العرضي لخزان الشاحنة أعلاه على مستوى إحداثي:", "visual_element_index": 1 }, { "number": "b", "question": "اكتب معادلة المقطع العرضي للخزان.", "visual_element_index": 1 }, { "number": "c", "question": "أوجد الاختلاف المركزي للخزان الذي يمثل المقطع العرضي للخزان.", "visual_element_index": 1 } ] }, { "order": 37, "type": "header", "title": "اكتب معادلة القطع الناقص الذي يحقق الخصائص المعطاة في كل مما يأتي.", "content_classification": "EDUCATIONAL_CONTENT", "question_indicators": { "has_question_words": true, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": true }, "format": "short_answer", "content": "اكتب معادلة القطع الناقص الذي يحقق الخصائص المعطاة في كل مما يأتي." }, { "order": 38, "type": "exercise", "title": "28", "content": "الرأسـان (0, 10-) و (0, 10)، والاختلاف المركزي $\\\\frac{3}{5}$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 39, "type": "exercise", "title": "29", "content": "الرأسـان المرافقان (1, 6) و (1, 6-)، والاختلاف المركزي $\\\\frac{4}{5}$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 40, "type": "exercise", "title": "30", "content": "المركز (4-, 2)، وإحدى البؤرتين $(\\\\sqrt{5} + 2, 2)$، والاختلاف المركزي $\\\\\\frac{\sqrt{5}}{3}$", "content_classification": "QUESTION_HOMEWORK", "question_indicators": { "has_question_words": false, "has_numbering": true, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "associated_visual_elements": [] }, { "order": 41, "type": "page_number", "content_classification": "METADATA", "question_indicators": { "has_question_words": false, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "content": "186" }, { "order": 42, "type": "footer", "content_classification": "METADATA", "question_indicators": { "has_question_words": false, "has_numbering": false, "has_multiple_choice": false, "has_fill_in_blank": false, "has_instruction_words": false }, "content": "وزارة التعليم\n2025 - 1447" } ], "visual_elements": [ { "index": 0, "label": "الشكل 4", "question_number": "14", "type": "diagram", "location": "right side of page, below question 13", "coordinate_system": "Custom grid, scale not explicitly defined but implied by labels", "shape": "elliptical track", "title": "مضمار سباق", "function": null, "description": "An elliptical race track with trees and a pond inside. The track has a width indicated by labels.", "axes_labels": { "x_axis": "Implied horizontal axis", "y_axis": "Implied vertical axis" }, "axes_ranges": { "x_min": null, "x_max": null, "y_min": null, "y_max": null }, "endpoints": [], "critical_points": [], "y_intercept": null, "end_behavior": null, "key_points": [ "Center of the ellipse is implied to be the origin for question 15", "Width of the track is labeled as 'w'", "Length of the track is labeled as '1000 ft'" ], "data_description": "Diagram illustrating an elliptical race track.", "key_values": [ "1000 ft (length)", "w (width)", "e = 0.75 (eccentricity)" ], "numeric_data": null, "table_structure": null, "educational_context": "Used to determine the dimensions and equation of an ellipse based on its eccentricity and length." }, { "index": 1, "label": "الشكل 27", "question_number": "27", "type": "diagram", "location": "center of page, below question 26", "coordinate_system": "Implied Cartesian grid", "shape": "elliptical cross-section of a tank", "title": "مقطع عرضي لخزان شاحنة", "function": null, "description": "A diagram showing the elliptical cross-section of a truck's liquid tank. Dimensions are indicated.", "axes_labels": { "x_axis": "Implied horizontal axis", "y_axis": "Implied vertical axis" }, "axes_ranges": { "x_min": null, "x_max": null, "y_min": null, "y_max": null }, "endpoints": [], "critical_points": [], "y_intercept": null, "end_behavior": null, "key_points": [ "The cross-section is elliptical.", "Horizontal dimension is labeled 6.8 ft.", "Vertical dimension is labeled 4.2 ft." ], "data_description": "Diagram of an elliptical tank cross-section.", "key_values": [ "6.8 ft", "4.2 ft" ], "numeric_data": null, "table_structure": null, "educational_context": "Illustrates the application of ellipses in engineering for stability, used to determine the equation and eccentricity of the tank's cross-section." } ] }