{ "$schema": "./curriculum-schema.json", "metadata": { "system": "Daya College Unified Curriculum Database", "version": "2.1.0", "lastUpdated": "2026-10-15T00:00:00Z", "lms": { "target": "DayaLMS", "compatibilityVersion": "2.4.x", "apiBaseUrl": "/api/v1/dayalms", "syncConfig": { "autoSync": true, "batchSize": 50, "webhookUrl": "/api/dayalms/sync", "supportedFeatures": [ "quizzes", "assignments", "webinars", "certificates", "scorm_2004" ] } }, "curriculums": [ { "id": "CA-BC", "country": "Canada", "province": "British Columbia", "name": "BC Ministry of Education Curriculum", "grades": [ "K-12" ] }, { "id": "CA-ON", "country": "Canada", "province": "Ontario", "name": "Ontario Curriculum (MTH1W, MPM2D, MCR3U, MHF4U, MCV4U)", "grades": [ "K-12" ] }, { "id": "CA-AB", "country": "Canada", "province": "Alberta", "name": "Alberta Education Program of Studies (Math 10C, 20-1, 30-1)", "grades": [ "K-12" ] }, { "id": "US-CC", "country": "United States", "province": "National", "name": "Common Core State Standards for Mathematics (CCSSM)", "grades": [ "K-12" ] }, { "id": "US-TX", "country": "United States", "province": "Texas", "name": "Texas Essential Knowledge and Skills (TEKS)", "grades": [ "K-12" ] }, { "id": "US-NY", "country": "United States", "province": "New York", "name": "NYSED Next Generation Mathematics Learning Standards", "grades": [ "K-12" ] }, { "id": "COL-UNIV", "country": "International", "province": "Higher Ed", "name": "Collegiate & University Mathematics (AP / UBC / SFU / UofT)", "grades": [ "College" ] } ], "levels": [ { "id": "elementary", "name": "Elementary School", "grades": [ "Kindergarten", "Grade 1", "Grade 2", "Grade 3", "Grade 4", "Grade 5", "Grade 6" ] }, { "id": "middle", "name": "Middle School", "grades": [ "Grade 7", "Grade 8", "Grade 9" ] }, { "id": "highschool", "name": "High School", "grades": [ "Grade 10", "Grade 11", "Grade 12" ] }, { "id": "college", "name": "College / University", "grades": [ "Undergraduate Year 1", "Undergraduate Year 2", "Tutoring & Advanced" ] } ], "catalogueLanguages": [ "en", "es", "fr", "de", "ar", "zh", "ja", "pt", "it", "nl", "ko", "tr", "ckb", "ku" ], "catalogueTranslationScope": "subject and course catalogue; lessons and quiz content remain English" }, "subjects": [ { "id": "math", "slug": "math", "name": "Mathematics", "icon": "sigma", "tagline": "From elementary foundations to advanced collegiate calculus", "hierarchyUrl": "subjects/math/index.html", "totalCourses": 26, "levels": { "elementary": 3, "middle": 2, "highschool": 7, "college": 14 }, "courses": [ { "id": "course-math-5", "slug": "math-5", "title": "Math 5 (BC Curriculum)", "level": "Elementary", "grade": "Grade 5", "category": "BC Elementary", "description": "Grade 5 mathematics following the BC curriculum: number sense, operations, fractions, decimals, patterns, geometry, and data.", "curriculum": { "primary": "Canada/BC", "code": "CA-BC-MTH-05", "equivalents": [ { "region": "Canada/ON", "standard": "Ontario Elementary Math Grade 5", "code": "CA-ON-MTH-G5" }, { "region": "Canada/AB", "standard": "Alberta Program of Studies Grade 5", "code": "CA-AB-MTH-G5" }, { "region": "US/TX", "standard": "Texas TEKS §111.7 Grade 5", "code": "US-TX-TEKS-G5" }, { "region": "US/NY", "standard": "NYSED NextGen NY-5.NBT / NY-5.NF", "code": "US-NY-MTH-G5" } ] }, "dayaLms": { "courseId": "DLMS-MTH-001", "slug": "math-5", "title": "Math 5 (BC Curriculum)", "category": "Mathematics", "level": "Elementary", "grade": "Grade 5", "pricing": { "currency": "USD", "amount": 24 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/math-5", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Math 5 Outline (BC)\n1. 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Find perimeter and area of rectangles." } ], "qa": [ { "id": 1, "question": "What is 456 rounded to the nearest hundred?", "answer": "500" }, { "id": 2, "question": "Compute 7 x 8.", "answer": "56" }, { "id": 3, "question": "Simplify 6/8.", "answer": "3/4" }, { "id": 4, "question": "Which is larger: 0.45 or 0.5?", "answer": "0.5" }, { "id": 5, "question": "Perimeter of rectangle 6 by 4?", "answer": "20" }, { "id": 6, "question": "Next term: 3,6,9,12,?", "answer": "15" } ], "diagrams": [ { "id": 1, "title": "Place Value Chart", "svg": "\nHundred Thousands\nTen Thousands\nThousands\nHundreds / Tens / Ones" }, { "id": 2, "title": "Fraction Bar", "svg": "\n\n\n\n1/4\n1/4\n1/4\n1/4" } ], "htmlUrl": "subjects/math/math-5.html", "lmsWebinarId": 2025, "lmsUrl": "http://127.0.0.1:2222/course/math-5", "assignedTeacher": { "id": "1049", "name": "Sarah Chen", "email": "sarah.chen@dayacollege.com" }, "translations": { "en": { "title": "Math 5 (BC Curriculum)", "level": "Elementary", "grade": "Grade 5", "category": "BC Elementary", "description": "Grade 5 mathematics following the BC curriculum: number sense, operations, fractions, decimals, patterns, geometry, and data." }, "es": { "title": "Matemáticas 5 (plan de estudios de BC)", "level": "Primaria", "grade": "Grado 5", "category": "Primaria de BC", "description": "Matemáticas 5 (plan de estudios de BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 5 (programme de C.-B.)", "level": "Primaire", "grade": "Niveau 5", "category": "Primaire de C.-B.", "description": "Mathématiques 5 (programme de C.-B.). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 5 (BC-Lehrplan)", "level": "Grundschule", "grade": "Klasse 5", "category": "BC Grundschule", "description": "Mathematik 5 (BC-Lehrplan). 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Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 5 (programma BC)", "level": "Scuola primaria", "grade": "Classe 5", "category": "Primaria BC", "description": "Matematica 5 (programma BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 5 (BC-leerplan)", "level": "Basisschool", "grade": "Leerjaar 5", "category": "BC basisschool", "description": "Wiskunde 5 (BC-leerplan). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 5 (BC 교육과정)", "level": "초등", "grade": "학년 5", "category": "BC 초등", "description": "수학 5 (BC 교육과정). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 5 (BC müfredatı)", "level": "İlkokul", "grade": "Sınıf 5", "category": "BC ilkokul", "description": "Matematik 5 (BC müfredatı). 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Convert fractions/decimals/percent." }, { "id": 3, "title": "Percent", "content": "Percent means per hundred. Find percent of a number." }, { "id": 4, "title": "Ratios", "content": "Ratio as comparison. Equivalent ratios. Unit rates." }, { "id": 5, "title": "Algebra", "content": "Translate phrases to expressions. Solve x + a = b." }, { "id": 6, "title": "Geometry", "content": "Angle sums in triangles (180). Area of triangle = 1/2 bh." } ], "qa": [ { "id": 1, "question": "|-7| = ?", "answer": "7" }, { "id": 2, "question": "3/4 as percent?", "answer": "75%" }, { "id": 3, "question": "20% of 50?", "answer": "10" }, { "id": 4, "question": "Ratio 6:9 simplified?", "answer": "2:3" }, { "id": 5, "question": "Solve x+5=12.", "answer": "x=7" }, { "id": 6, "question": "Area triangle base 8 height 5?", "answer": "20" } ], "diagrams": [ { "id": 1, "title": "Integer Number Line", "svg": "\n-5\n-3\n0\n3\n5\n" }, { "id": 2, "title": "Triangle Area", "svg": "\n\nh\nb" } ], "htmlUrl": "subjects/math/math-6.html", "lmsWebinarId": 2026, "lmsUrl": "http://127.0.0.1:2222/course/math-6", "assignedTeacher": { "id": "1049", "name": "Sarah Chen", "email": "sarah.chen@dayacollege.com" }, "translations": { "en": { "title": "Math 6 (BC Curriculum)", "level": "Elementary", "grade": "Grade 6", "category": "BC Elementary", "description": "Grade 6: integers, ratios, percent, algebraic expressions, geometry, data analysis." }, "es": { "title": "Matemáticas 6 (plan de estudios de BC)", "level": "Primaria", "grade": "Grado 6", "category": "Primaria de BC", "description": "Matemáticas 6 (plan de estudios de BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 6 (programme de C.-B.)", "level": "Primaire", "grade": "Niveau 6", "category": "Primaire de C.-B.", "description": "Mathématiques 6 (programme de C.-B.). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 6 (BC-Lehrplan)", "level": "Grundschule", "grade": "Klasse 6", "category": "BC Grundschule", "description": "Mathematik 6 (BC-Lehrplan). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الرياضيات 6 (منهج كولومبيا البريطانية)", "level": "ابتدائي", "grade": "الصف 6", "category": "ابتدائي كولومبيا البريطانية", "description": "الرياضيات 6 (منهج كولومبيا البريطانية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "数学 6 (卑诗省课程)", "level": "小学", "grade": "年级 6", "category": "卑诗省小学", "description": "数学 6 (卑诗省课程). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "数学 6 (BC州カリキュラム)", "level": "小学校", "grade": "学年 6", "category": "BC州小学校", "description": "数学 6 (BC州カリキュラム). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Matemática 6 (currículo de BC)", "level": "Ensino fundamental", "grade": "Ano 6", "category": "Fundamental de BC", "description": "Matemática 6 (currículo de BC). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 6 (programma BC)", "level": "Scuola primaria", "grade": "Classe 6", "category": "Primaria BC", "description": "Matematica 6 (programma BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 6 (BC-leerplan)", "level": "Basisschool", "grade": "Leerjaar 6", "category": "BC basisschool", "description": "Wiskunde 6 (BC-leerplan). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 6 (BC 교육과정)", "level": "초등", "grade": "학년 6", "category": "BC 초등", "description": "수학 6 (BC 교육과정). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 6 (BC müfredatı)", "level": "İlkokul", "grade": "Sınıf 6", "category": "BC ilkokul", "description": "Matematik 6 (BC müfredatı). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "بیرکاری 6 (پڕۆگرامی خوێندنی BC)", "level": "سەرەتایی", "grade": "پۆلی 6", "category": "سەرەتاییی BC", "description": "بیرکاری 6 (پڕۆگرامی خوێندنی BC). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Matematîk 6 (bernameya dersên BC)", "level": "Seretayî", "grade": "Pola 6", "category": "Seretayî ya BC", "description": "Matematîk 6 (bernameya dersên BC). Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-math-7", "slug": "math-7", "title": "Math 7 (BC Curriculum)", "level": "Elementary", "grade": "Grade 7", "category": "BC Elementary", "description": "Grade 7: rational numbers, algebraic expressions, linear relations, geometry, probability.", "curriculum": { "primary": "Canada/BC", "code": "CA-BC-MTH-07", "equivalents": [ { "region": "Canada/ON", "standard": "Ontario Intermediate Math Grade 7", "code": "CA-ON-MTH-G7" }, { "region": "Canada/AB", "standard": "Alberta Program of Studies Grade 7", "code": "CA-AB-MTH-G7" }, { "region": "US/TX", "standard": "Texas TEKS §111.27 Grade 7", "code": "US-TX-TEKS-G7" }, { "region": "US/NY", "standard": "NYSED NextGen NY-7.RP / NY-7.EE", "code": "US-NY-MTH-G7" } ] }, "dayaLms": { "courseId": "DLMS-MTH-003", "slug": "math-7", "title": "Math 7 (BC Curriculum)", "category": "Mathematics", "level": "Elementary", "grade": "Grade 7", "pricing": { "currency": "USD", "amount": 24 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/math-7", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Math 7 Outline\n1. Rational Numbers\n - Add/subtract/multiply/divide rationals\n2. Exponents & Square Roots\n3. Algebra\n - Combine like terms\n - Solve two-step equations\n4. Linear Relations\n - Patterns, graphing, slope\n5. Geometry\n - Circles: circumference, area\n - Volume of prisms\n6. Statistics & Probability\n - Experimental vs theoretical probability", "context": "Math 7 transitions to abstract reasoning. Students work with rational numbers and exponents, solve multi-step equations, and graph linear relations. Geometry includes circles and volume. Probability concepts introduced.", "lessons": [ { "id": 1, "title": "Rational Numbers", "content": "Operations on fractions/decimals. Use common denominators." }, { "id": 2, "title": "Exponents", "content": "Powers and square roots. Perfect squares." }, { "id": 3, "title": "Equations", "content": "Solve 2ax+b=c. Check solutions." }, { "id": 4, "title": "Linear Relations", "content": "y = mx + b. Plot points. Identify slope." }, { "id": 5, "title": "Circles", "content": "Circumference = 2πr. Area = πr²." }, { "id": 6, "title": "Probability", "content": "P(E)=favorable/total. Tree diagrams." } ], "qa": [ { "id": 1, "question": "Compute (-3)+5.", "answer": "2" }, { "id": 2, "question": "sqrt(49)=", "answer": "7" }, { "id": 3, "question": "Solve 2x+3=11.", "answer": "x=4" }, { "id": 4, "question": "Slope of y=3x-2?", "answer": "3" }, { "id": 5, "question": "Circumference r=5 (π≈3.14)?", "answer": "31.4" }, { "id": 6, "question": "P(rolling 4 on die)?", "answer": "1/6" } ], "diagrams": [ { "id": 1, "title": "Linear Relation y=mx+b", "svg": "\n\n\ny=mx+b" }, { "id": 2, "title": "Circle", "svg": "\n\nr" } ], "htmlUrl": "subjects/math/math-7.html", "lmsWebinarId": 2027, "lmsUrl": "http://127.0.0.1:2222/course/math-7", "assignedTeacher": { "id": "1049", "name": "Sarah Chen", "email": "sarah.chen@dayacollege.com" }, "translations": { "en": { "title": "Math 7 (BC Curriculum)", "level": "Elementary", "grade": "Grade 7", "category": "BC Elementary", "description": "Grade 7: rational numbers, algebraic expressions, linear relations, geometry, probability." }, "es": { "title": "Matemáticas 7 (plan de estudios de BC)", "level": "Primaria", "grade": "Grado 7", "category": "Primaria de BC", "description": "Matemáticas 7 (plan de estudios de BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 7 (programme de C.-B.)", "level": "Primaire", "grade": "Niveau 7", "category": "Primaire de C.-B.", "description": "Mathématiques 7 (programme de C.-B.). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 7 (BC-Lehrplan)", "level": "Grundschule", "grade": "Klasse 7", "category": "BC Grundschule", "description": "Mathematik 7 (BC-Lehrplan). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الرياضيات 7 (منهج كولومبيا البريطانية)", "level": "ابتدائي", "grade": "الصف 7", "category": "ابتدائي كولومبيا البريطانية", "description": "الرياضيات 7 (منهج كولومبيا البريطانية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "数学 7 (卑诗省课程)", "level": "小学", "grade": "年级 7", "category": "卑诗省小学", "description": "数学 7 (卑诗省课程). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "数学 7 (BC州カリキュラム)", "level": "小学校", "grade": "学年 7", "category": "BC州小学校", "description": "数学 7 (BC州カリキュラム). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Matemática 7 (currículo de BC)", "level": "Ensino fundamental", "grade": "Ano 7", "category": "Fundamental de BC", "description": "Matemática 7 (currículo de BC). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 7 (programma BC)", "level": "Scuola primaria", "grade": "Classe 7", "category": "Primaria BC", "description": "Matematica 7 (programma BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 7 (BC-leerplan)", "level": "Basisschool", "grade": "Leerjaar 7", "category": "BC basisschool", "description": "Wiskunde 7 (BC-leerplan). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 7 (BC 교육과정)", "level": "초등", "grade": "학년 7", "category": "BC 초등", "description": "수학 7 (BC 교육과정). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 7 (BC müfredatı)", "level": "İlkokul", "grade": "Sınıf 7", "category": "BC ilkokul", "description": "Matematik 7 (BC müfredatı). 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Square Roots & Pythagorean Theorem\n2. Integers & Rational Numbers\n3. Algebra\n - Linear equations in one variable\n - Linear relations & graphing\n4. Geometry\n - Volume of cylinders/cones/spheres\n - Transformations\n5. Statistics\n - Data representation, scatter plots\n6. Financial Literacy (intro)", "context": "Math 8 connects algebra and geometry via the Pythagorean theorem. Students solve linear equations, graph lines, and compute volumes. Transformations (translations, rotations, reflections) introduced.", "lessons": [ { "id": 1, "title": "Pythagorean Theorem", "content": "a²+b²=c². Find missing sides of right triangles." }, { "id": 2, "title": "Square Roots", "content": "Estimate sqrt. Simplify radicals." }, { "id": 3, "title": "Linear Equations", "content": "Solve equations with variables on both sides." }, { "id": 4, "title": "Graphing Lines", "content": "Slope-intercept form. x/y intercepts." }, { "id": 5, "title": "Volume", "content": "Cylinder πr²h; cone 1/3; sphere 4/3πr³." }, { "id": 6, "title": "Transformations", "content": "Translate, reflect, rotate, dilate on coordinate plane." } ], "qa": [ { "id": 1, "question": "Legs 3,4 hypotenuse?", "answer": "5" }, { "id": 2, "question": "sqrt(72) simplified?", "answer": "6√2" }, { "id": 3, "question": "Solve 3x-2=2x+5.", "answer": "x=7" }, { "id": 4, "question": "Slope through (0,2),(4,10)?", "answer": "2" }, { "id": 5, "question": "Volume cylinder r=2,h=5?", "answer": "20π" }, { "id": 6, "question": "Reflection of (3,4) over x-axis?", "answer": "(3,-4)" } ], "diagrams": [ { "id": 1, "title": "Right Triangle", "svg": "\na\nb\nc" }, { "id": 2, "title": "Cylinder", "svg": "\n\n" } ], "htmlUrl": "subjects/math/math-8.html", "lmsWebinarId": 2028, "lmsUrl": "http://127.0.0.1:2222/course/math-8", "assignedTeacher": { "id": "1050", "name": "James Park", "email": "james.park@dayacollege.com" }, "translations": { "en": { "title": "Math 8 (BC Curriculum)", "level": "Middle", "grade": "Grade 8", "category": "BC Middle", "description": "Grade 8: square roots, Pythagorean theorem, linear equations, geometry, data." }, "es": { "title": "Matemáticas 8 (plan de estudios de BC)", "level": "Intermedia", "grade": "Grado 8", "category": "Intermedia de BC", "description": "Matemáticas 8 (plan de estudios de BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 8 (programme de C.-B.)", "level": "Collège", "grade": "Niveau 8", "category": "Collège de C.-B.", "description": "Mathématiques 8 (programme de C.-B.). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 8 (BC-Lehrplan)", "level": "Mittelstufe", "grade": "Klasse 8", "category": "BC Mittelstufe", "description": "Mathematik 8 (BC-Lehrplan). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الرياضيات 8 (منهج كولومبيا البريطانية)", "level": "متوسط", "grade": "الصف 8", "category": "متوسط كولومبيا البريطانية", "description": "الرياضيات 8 (منهج كولومبيا البريطانية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "数学 8 (卑诗省课程)", "level": "初中", "grade": "年级 8", "category": "卑诗省初中", "description": "数学 8 (卑诗省课程). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "数学 8 (BC州カリキュラム)", "level": "中学校", "grade": "学年 8", "category": "BC州中学校", "description": "数学 8 (BC州カリキュラム). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Matemática 8 (currículo de BC)", "level": "Ensino intermediário", "grade": "Ano 8", "category": "Intermediário de BC", "description": "Matemática 8 (currículo de BC). 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Rational Numbers & Exponents\n2. Polynomials\n - Add/subtract/multiply polynomials\n3. Linear Equations & Inequalities\n4. Linear Relations & Functions\n5. Geometry\n - Similarity, scale factor\n - Circle geometry\n6. Statistics\n - Measures, box plots\n7. Financial Literacy", "context": "Math 9 formalizes algebra: polynomials, equations, inequalities, and functions. Geometry covers similarity and circles. Students analyze data with box-and-whisker plots.", "lessons": [ { "id": 1, "title": "Polynomials", "content": "Add/subtract like terms. Multiply monomial by polynomial." }, { "id": 2, "title": "Linear Equations", "content": "Solve equations with brackets and fractions." }, { "id": 3, "title": "Inequalities", "content": "Solve and graph on number line." }, { "id": 4, "title": "Linear Functions", "content": "Slope, intercept, domain/range." }, { "id": 5, "title": "Similarity", "content": "Similar triangles, scale factors, AA criterion." }, { "id": 6, "title": "Circle Geometry", "content": "Tangents, chords, central/inscribed angles." } ], "qa": [ { "id": 1, "question": "Simplify 3x+2x-5.", "answer": "5x-5" }, { "id": 2, "question": "Solve 2(x-3)=8.", "answer": "x=7" }, { "id": 3, "question": "Solve 2x+1>7.", "answer": "x>3" }, { "id": 4, "question": "Slope of 2x+3y=6?", "answer": "-2/3" }, { "id": 5, "question": "Scale factor 2:3, original 6 → ?", "answer": "9" }, { "id": 6, "question": "Inscribed angle = half central?", "answer": "Yes" } ], "diagrams": [ { "id": 1, "title": "Similar Triangles", "svg": "\n" }, { "id": 2, "title": "Box Plot", "svg": "\n\n\n\n" } ], "htmlUrl": "subjects/math/math-9.html", "lmsWebinarId": 2029, "lmsUrl": "http://127.0.0.1:2222/course/math-9", "assignedTeacher": { "id": "1050", "name": "James Park", "email": "james.park@dayacollege.com" }, "translations": { "en": { "title": "Math 9 (BC Curriculum)", "level": "Middle", "grade": "Grade 9", "category": "BC Middle", "description": "Grade 9: rational numbers, polynomials, linear equations/inequalities, geometry, statistics." }, "es": { "title": "Matemáticas 9 (plan de estudios de BC)", "level": "Intermedia", "grade": "Grado 9", "category": "Intermedia de BC", "description": "Matemáticas 9 (plan de estudios de BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 9 (programme de C.-B.)", "level": "Collège", "grade": "Niveau 9", "category": "Collège de C.-B.", "description": "Mathématiques 9 (programme de C.-B.). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 9 (BC-Lehrplan)", "level": "Mittelstufe", "grade": "Klasse 9", "category": "BC Mittelstufe", "description": "Mathematik 9 (BC-Lehrplan). 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Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 9 (programma BC)", "level": "Scuola media", "grade": "Classe 9", "category": "Media BC", "description": "Matematica 9 (programma BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 9 (BC-leerplan)", "level": "Middelbare onderbouw", "grade": "Leerjaar 9", "category": "BC onderbouw", "description": "Wiskunde 9 (BC-leerplan). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 9 (BC 교육과정)", "level": "중등", "grade": "학년 9", "category": "BC 중등", "description": "수학 9 (BC 교육과정). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 9 (BC müfredatı)", "level": "Ortaokul", "grade": "Sınıf 9", "category": "BC ortaokul", "description": "Matematik 9 (BC müfredatı). 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Algebra & Number\n - Prime factorization, radicals\n - Polynomials: factorization\n2. Relations & Functions\n - Domain, range, graphs\n - Linear & quadratic functions\n3. Geometry\n - Proofs, circle geometry\n4. Trigonometry\n - Sine/cosine/tangent ratios\n5. Statistics & Probability\n - Normal distribution (intro)", "context": "Math 10 bridges to senior math. Students factor polynomials, study quadratic functions, prove geometric statements, and use trig ratios. Prepares for Pre-Calculus 11.", "lessons": [ { "id": 1, "title": "Radicals", "content": "Simplify radicals. Rationalize denominators." }, { "id": 2, "title": "Factoring", "content": "Common factor, difference of squares, trinomials." }, { "id": 3, "title": "Quadratic Functions", "content": "y=ax²+bx+c. Vertex, intercepts." }, { "id": 4, "title": "Trig Ratios", "content": "SOH CAH TOA. Solve right triangles." }, { "id": 5, "title": "Geometry Proofs", "content": "Prove congruence/similarity." }, { "id": 6, "title": "Statistics", "content": "Standard deviation, normal curve." } ], "qa": [ { "id": 1, "question": "Factor x²-9.", "answer": "(x-3)(x+3)" }, { "id": 2, "question": "Vertex of y=x²-4x+3?", "answer": "(2,-1)" }, { "id": 3, "question": "sin 30°=?", "answer": "1/2" }, { "id": 4, "question": "Hypotenuse if opp=5, θ=30°?", "answer": "10" }, { "id": 5, "question": "Simplify √50.", "answer": "5√2" }, { "id": 6, "question": "Mean of 2,4,6,8?", "answer": "5" } ], "diagrams": [ { "id": 1, "title": "Quadratic Parabola", "svg": "\n\n" }, { "id": 2, "title": "Right Triangle Trig", "svg": "\nadjacent\nopposite\nhyp" } ], "htmlUrl": "subjects/math/math-10.html", "lmsWebinarId": 2030, "lmsUrl": "http://127.0.0.1:2222/course/math-10", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "Math 10 (BC Curriculum)", "level": "Highschool", "grade": "Grade 10", "category": "BC High School", "description": "Grade 10: algebra, functions, geometry, trigonometry, statistics." }, "es": { "title": "Matemáticas 10 (plan de estudios de BC)", "level": "Secundaria", "grade": "Grado 10", "category": "Secundaria de BC", "description": "Matemáticas 10 (plan de estudios de BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 10 (programme de C.-B.)", "level": "Lycée", "grade": "Niveau 10", "category": "Lycée de C.-B.", "description": "Mathématiques 10 (programme de C.-B.). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 10 (BC-Lehrplan)", "level": "Oberstufe", "grade": "Klasse 10", "category": "BC Oberstufe", "description": "Mathematik 10 (BC-Lehrplan). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الرياضيات 10 (منهج كولومبيا البريطانية)", "level": "ثانوي", "grade": "الصف 10", "category": "ثانوي كولومبيا البريطانية", "description": "الرياضيات 10 (منهج كولومبيا البريطانية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "数学 10 (卑诗省课程)", "level": "高中", "grade": "年级 10", "category": "卑诗省高中", "description": "数学 10 (卑诗省课程). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "数学 10 (BC州カリキュラム)", "level": "高校", "grade": "学年 10", "category": "BC州高校", "description": "数学 10 (BC州カリキュラム). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Matemática 10 (currículo de BC)", "level": "Ensino médio", "grade": "Ano 10", "category": "Médio de BC", "description": "Matemática 10 (currículo de BC). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 10 (programma BC)", "level": "Scuola superiore", "grade": "Classe 10", "category": "Superiore BC", "description": "Matematica 10 (programma BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 10 (BC-leerplan)", "level": "Middelbare bovenbouw", "grade": "Leerjaar 10", "category": "BC bovenbouw", "description": "Wiskunde 10 (BC-leerplan). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 10 (BC 교육과정)", "level": "고등", "grade": "학년 10", "category": "BC 고등", "description": "수학 10 (BC 교육과정). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 10 (BC müfredatı)", "level": "Lise", "grade": "Sınıf 10", "category": "BC lise", "description": "Matematik 10 (BC müfredatı). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "بیرکاری 10 (پڕۆگرامی خوێندنی BC)", "level": "ئامادەیی", "grade": "پۆلی 10", "category": "ئامادەییی BC", "description": "بیرکاری 10 (پڕۆگرامی خوێندنی BC). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Matematîk 10 (bernameya dersên BC)", "level": "Lîse", "grade": "Pola 10", "category": "Lîseya BC", "description": "Matematîk 10 (bernameya dersên BC). 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Sequences & Series\n - Arithmetic, geometric\n2. Trigonometry\n - Unit circle, radians/degrees\n - Sine/cosine laws\n3. Quadratic Functions\n - Vertex form, standard form\n - Discriminant, roots\n4. Polynomials\n - Division, remainder theorem\n5. Rational Expressions & Equations\n6. Absolute Value & Radicals", "context": "Pre-Calculus 11 prepares students for calculus by strengthening algebra and trig. Emphasis on function transformations, solving equations, and trigonometric identities basics.", "lessons": [ { "id": 1, "title": "Sequences", "content": "Arithmetic: a_n=a_1+(n-1)d. Geometric: a_n=a_1 r^(n-1)." }, { "id": 2, "title": "Trig on Unit Circle", "content": "Degrees/radians conversion. Reference angles." }, { "id": 3, "title": "Sine/Cosine Laws", "content": "a/sin A = b/sin B. c²=a²+b²-2ab cos C." }, { "id": 4, "title": "Quadratics", "content": "Complete square. Vertex form y=a(x-h)²+k." }, { "id": 5, "title": "Polynomial Division", "content": "Long division, synthetic division, remainder theorem." }, { "id": 6, "title": "Rational Expressions", "content": "Simplify, multiply, divide, solve." } ], "qa": [ { "id": 1, "question": "6th term arithmetic a1=2,d=3?", "answer": "17" }, { "id": 2, "question": "sin 150°=?", "answer": "1/2" }, { "id": 3, "question": "Vertex of y=2(x-3)²+1?", "answer": "(3,1)" }, { "id": 4, "question": "Remainder of P(x) by (x-2)?", "answer": "P(2)" }, { "id": 5, "question": "Simplify (x²-4)/(x-2).", "answer": "x+2" }, { "id": 6, "question": "Convert 60° to radians.", "answer": "π/3" } ], "diagrams": [ { "id": 1, "title": "Unit Circle", "svg": "\n\n\n" }, { "id": 2, "title": "Parabola Vertex", "svg": "\n\nvertex" } ], "htmlUrl": "subjects/math/precalculus-11.html", "lmsWebinarId": 2031, "lmsUrl": "http://127.0.0.1:2222/course/precalculus-11", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "Pre-Calculus 11 (BC)", "level": "Highschool", "grade": "Grade 11", "category": "BC High School", "description": "BC Pre-Calculus 11: sequences, trigonometry, quadratic functions, polynomials, rational expressions." }, "es": { "title": "Precálculo 11 (BC)", "level": "Secundaria", "grade": "Grado 11", "category": "Secundaria de BC", "description": "Precálculo 11 (BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Pré-calcul 11 (BC)", "level": "Lycée", "grade": "Niveau 11", "category": "Lycée de C.-B.", "description": "Pré-calcul 11 (BC). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Vorkalkül 11 (BC)", "level": "Oberstufe", "grade": "Klasse 11", "category": "BC Oberstufe", "description": "Vorkalkül 11 (BC). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "ما قبل التفاضل والتكامل 11 (BC)", "level": "ثانوي", "grade": "الصف 11", "category": "ثانوي كولومبيا البريطانية", "description": "ما قبل التفاضل والتكامل 11 (BC). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分预备 11 (BC)", "level": "高中", "grade": "年级 11", "category": "卑诗省高中", "description": "微积分预备 11 (BC). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分準備 11 (BC)", "level": "高校", "grade": "学年 11", "category": "BC州高校", "description": "微積分準備 11 (BC). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Pré-cálculo 11 (BC)", "level": "Ensino médio", "grade": "Ano 11", "category": "Médio de BC", "description": "Pré-cálculo 11 (BC). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Precalcolo 11 (BC)", "level": "Scuola superiore", "grade": "Classe 11", "category": "Superiore BC", "description": "Precalcolo 11 (BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Voorbereiding op calculus 11 (BC)", "level": "Middelbare bovenbouw", "grade": "Leerjaar 11", "category": "BC bovenbouw", "description": "Voorbereiding op calculus 11 (BC). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "미적분 준비 11 (BC)", "level": "고등", "grade": "학년 11", "category": "BC 고등", "description": "미적분 준비 11 (BC). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Ön kalkülüs 11 (BC)", "level": "Lise", "grade": "Sınıf 11", "category": "BC lise", "description": "Ön kalkülüs 11 (BC). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "پێش کەلکولەس 11 (BC)", "level": "ئامادەیی", "grade": "پۆلی 11", "category": "ئامادەییی BC", "description": "پێش کەلکولەس 11 (BC). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Berî kalkulûsê 11 (BC)", "level": "Lîse", "grade": "Pola 11", "category": "Lîseya BC", "description": "Berî kalkulûsê 11 (BC). 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Transformations\n - Functions: translations, stretches, reflections\n2. Trigonometric Functions\n - Graphs of sin/cos/tan\n - Identities & equations\n3. Exponential & Logarithmic Functions\n4. Polynomial & Rational Functions\n5. Combinatorics\n - Permutations, combinations\n6. Probability\n - Binomial distribution", "context": "Pre-Calculus 12 is the gateway to calculus. Students master function transformations, trig identities, logs/exponentials, and counting principles.", "lessons": [ { "id": 1, "title": "Transformations", "content": "y=af(b(x-c))+d. Order of transformations." }, { "id": 2, "title": "Trig Identities", "content": "Pythagorean, sum/difference, double angle." }, { "id": 3, "title": "Exponentials", "content": "Growth/decay. y=ab^x." }, { "id": 4, "title": "Logarithms", "content": "Inverse of exponential. log laws." }, { "id": 5, "title": "Combinatorics", "content": "nPr, nCr. Pascal's triangle." }, { "id": 6, "title": "Probability", "content": "Binomial probability. Expected value." } ], "qa": [ { "id": 1, "question": "log_2 8 = ?", "answer": "3" }, { "id": 2, "question": "sin²θ+cos²θ=?", "answer": "1" }, { "id": 3, "question": "8C3 = ?", "answer": "56" }, { "id": 4, "question": "Period of sin(2x)?", "answer": "π" }, { "id": 5, "question": "Solve 2^x=16.", "answer": "x=4" }, { "id": 6, "question": "5P2 = ?", "answer": "20" } ], "diagrams": [ { "id": 1, "title": "Sine Wave", "svg": "\n" }, { "id": 2, "title": "Exponential Growth", "svg": "\n\n" } ], "htmlUrl": "subjects/math/precalculus-12.html", "lmsWebinarId": 2032, "lmsUrl": "http://127.0.0.1:2222/course/precalculus-12", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "Pre-Calculus 12 (BC)", "level": "Highschool", "grade": "Grade 12", "category": "BC High School", "description": "BC Pre-Calculus 12: transformations, trig identities, exponential/logarithmic, combinatorics, probability." }, "es": { "title": "Precálculo 12 (BC)", "level": "Secundaria", "grade": "Grado 12", "category": "Secundaria de BC", "description": "Precálculo 12 (BC). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Pré-calcul 12 (BC)", "level": "Lycée", "grade": "Niveau 12", "category": "Lycée de C.-B.", "description": "Pré-calcul 12 (BC). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Vorkalkül 12 (BC)", "level": "Oberstufe", "grade": "Klasse 12", "category": "BC Oberstufe", "description": "Vorkalkül 12 (BC). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "ما قبل التفاضل والتكامل 12 (BC)", "level": "ثانوي", "grade": "الصف 12", "category": "ثانوي كولومبيا البريطانية", "description": "ما قبل التفاضل والتكامل 12 (BC). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分预备 12 (BC)", "level": "高中", "grade": "年级 12", "category": "卑诗省高中", "description": "微积分预备 12 (BC). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分準備 12 (BC)", "level": "高校", "grade": "学年 12", "category": "BC州高校", "description": "微積分準備 12 (BC). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Pré-cálculo 12 (BC)", "level": "Ensino médio", "grade": "Ano 12", "category": "Médio de BC", "description": "Pré-cálculo 12 (BC). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Precalcolo 12 (BC)", "level": "Scuola superiore", "grade": "Classe 12", "category": "Superiore BC", "description": "Precalcolo 12 (BC). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Voorbereiding op calculus 12 (BC)", "level": "Middelbare bovenbouw", "grade": "Leerjaar 12", "category": "BC bovenbouw", "description": "Voorbereiding op calculus 12 (BC). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "미적분 준비 12 (BC)", "level": "고등", "grade": "학년 12", "category": "BC 고등", "description": "미적분 준비 12 (BC). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Ön kalkülüs 12 (BC)", "level": "Lise", "grade": "Sınıf 12", "category": "BC lise", "description": "Ön kalkülüs 12 (BC). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "پێش کەلکولەس 12 (BC)", "level": "ئامادەیی", "grade": "پۆلی 12", "category": "ئامادەییی BC", "description": "پێش کەلکولەس 12 (BC). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Berî kalkulûsê 12 (BC)", "level": "Lîse", "grade": "Pola 12", "category": "Lîseya BC", "description": "Berî kalkulûsê 12 (BC). 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Functions\n - Domain, range, transformations\n2. Exponential Functions\n3. Trigonometric Functions\n - Radians, unit circle, graphs\n4. Discrete Functions\n - Sequences, series, financial\n5. Quadratic Functions (review/extend)", "context": "MCR3U (Ontario Grade 11 Functions) focuses on function concepts: transformations, exponential, trig, discrete. Prepares for MCV4U (Calculus).", "lessons": [ { "id": 1, "title": "Function Notation", "content": "f(x). Domain/range. Inverse functions." }, { "id": 2, "title": "Transformations", "content": "Vertical/horizontal shifts, stretches, reflections." }, { "id": 3, "title": "Exponential", "content": "y=ab^x. Applications." }, { "id": 4, "title": "Trig Functions", "content": "sin/cos/tan graphs. Period, amplitude." }, { "id": 5, "title": "Sequences & Series", "content": "Arithmetic/geometric sums." }, { "id": 6, "title": "Financial Math", "content": "Compound interest, annuities." } ], "qa": [ { "id": 1, "question": "f(x)=2x+1, f(3)=?", "answer": "7" }, { "id": 2, "question": "Period of cos x?", "answer": "2π" }, { "id": 3, "question": "Sum first 5: 2,4,6,8,10?", "answer": "30" }, { "id": 4, "question": "Inverse of f(x)=3x?", "answer": "x/3" }, { "id": 5, "question": "A=1000(1.05)^t growth?", "answer": "5% growth" }, { "id": 6, "question": "Amplitude of 3sin x?", "answer": "3" } ], "diagrams": [ { "id": 1, "title": "Function Transform", "svg": "\n" }, { "id": 2, "title": "Trig Graph", "svg": "\n" } ], "htmlUrl": "subjects/math/mcr3u.html", "lmsWebinarId": 2033, "lmsUrl": "http://127.0.0.1:2222/course/mcr3u", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "MCR3U (Functions, Grade 11)", "level": "Highschool", "grade": "Grade 11", "category": "Ontario High School", "description": "Ontario MCR3U: functions, exponential, trigonometric, discrete functions." }, "es": { "title": "MCR3U (Funciones, Grado 11)", "level": "Secundaria", "grade": "Grado 11", "category": "Secundaria de Ontario", "description": "MCR3U (Funciones, Grado 11). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "MCR3U (Fonctions, Niveau 11)", "level": "Lycée", "grade": "Niveau 11", "category": "Lycée de l’Ontario", "description": "MCR3U (Fonctions, Niveau 11). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "MCR3U (Funktionen, Klasse 11)", "level": "Oberstufe", "grade": "Klasse 11", "category": "Ontario Oberstufe", "description": "MCR3U (Funktionen, Klasse 11). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "MCR3U (الدوال, الصف 11)", "level": "ثانوي", "grade": "الصف 11", "category": "ثانوي أونتاريو", "description": "MCR3U (الدوال, الصف 11). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "MCR3U (函数, 年级 11)", "level": "高中", "grade": "年级 11", "category": "安大略省高中", "description": "MCR3U (函数, 年级 11). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "MCR3U (関数, 学年 11)", "level": "高校", "grade": "学年 11", "category": "オンタリオ州高校", "description": "MCR3U (関数, 学年 11). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "MCR3U (Funções, Ano 11)", "level": "Ensino médio", "grade": "Ano 11", "category": "Médio de Ontário", "description": "MCR3U (Funções, Ano 11). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "MCR3U (Funzioni, Classe 11)", "level": "Scuola superiore", "grade": "Classe 11", "category": "Superiore Ontario", "description": "MCR3U (Funzioni, Classe 11). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "MCR3U (Functies, Leerjaar 11)", "level": "Middelbare bovenbouw", "grade": "Leerjaar 11", "category": "Ontario bovenbouw", "description": "MCR3U (Functies, Leerjaar 11). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "MCR3U (함수, 학년 11)", "level": "고등", "grade": "학년 11", "category": "온타리오 고등", "description": "MCR3U (함수, 학년 11). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "MCR3U (Fonksiyonlar, Sınıf 11)", "level": "Lise", "grade": "Sınıf 11", "category": "Ontario lise", "description": "MCR3U (Fonksiyonlar, Sınıf 11). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "MCR3U (فانکشنەکان, پۆلی 11)", "level": "ئامادەیی", "grade": "پۆلی 11", "category": "ئامادەییی ئۆنتاریۆ", "description": "MCR3U (فانکشنەکان, پۆلی 11). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "MCR3U (Fonksiyon, Pola 11)", "level": "Lîse", "grade": "Pola 11", "category": "Lîseya Ontario", "description": "MCR3U (Fonksiyon, Pola 11). Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-trigonometry", "slug": "trigonometry", "title": "Trigonometry", "level": "Highschool", "grade": "Grade 10–12", "category": "Topic", "description": "Comprehensive trigonometry: ratios, identities, equations, laws, polar coordinates.", "curriculum": { "primary": "Canada/BC", "code": "CA-BC-TRIG", "equivalents": [ { "region": "Canada/ON", "standard": "Ontario MCR3U/MHF4U Trigonometric Functions", "code": "CA-ON-TRIG" }, { "region": "Canada/AB", "standard": "Alberta Math 20-1 / 30-1 Trig Unit", "code": "CA-AB-TRIG" }, { "region": "US/TX", "standard": "Texas TEKS Precalculus Trigonometry", "code": "US-TX-TRIG" }, { "region": "US/NY", "standard": "NYSED Trigonometry & Analytic Geometry", "code": "US-NY-TRIG" } ] }, "dayaLms": { "courseId": "DLMS-MTH-010", "slug": "trigonometry", "title": "Trigonometry", "category": "Mathematics", "level": "Highschool", "grade": "Grade 10–12", "pricing": { "currency": "USD", "amount": 32 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/trigonometry", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Trigonometry Outline\n1. Right Triangle Trig\n2. Unit Circle & Radians\n3. Trig Functions & Graphs\n4. Identities\n - Pythagorean, reciprocal, quotient\n - Sum/difference, double/half angle\n5. Trig Equations\n6. Sine & Cosine Laws\n7. Polar Coordinates & Vectors", "context": "Trigonometry studies relationships between angles and sides. Essential for calculus, physics, engineering. Covers identities, equations, and applications.", "lessons": [ { "id": 1, "title": "Right Triangle Ratios", "content": "sin=opp/hyp, cos=adj/hyp, tan=opp/adj." }, { "id": 2, "title": "Unit Circle", "content": "Coordinates (cosθ, sinθ). Radians." }, { "id": 3, "title": "Identities", "content": "1+ tan²θ=sec²θ. sin(a±b) formulas." }, { "id": 4, "title": "Equations", "content": "Solve sin x = 1/2. General solutions." }, { "id": 5, "title": "Laws", "content": "Sine law, cosine law for oblique triangles." }, { "id": 6, "title": "Polar", "content": "x=r cosθ, y=r sinθ. Polar curves." } ], "qa": [ { "id": 1, "question": "cos 60°=?", "answer": "1/2" }, { "id": 2, "question": "tan 45°=?", "answer": "1" }, { "id": 3, "question": "sin(90-θ)=?", "answer": "cos θ" }, { "id": 4, "question": "Period of tan x?", "answer": "π" }, { "id": 5, "question": "Law of cosines for side c?", "answer": "c²=a²+b²-2ab cos C" }, { "id": 6, "question": "Polar of (1,1)?", "answer": "r=√2, θ=45°" } ], "diagrams": [ { "id": 1, "title": "Unit Circle", "svg": "\n\n\n" }, { "id": 2, "title": "Sine/Cosine Graph", "svg": "\n" } ], "htmlUrl": "subjects/math/trigonometry.html", "lmsWebinarId": 2034, "lmsUrl": "http://127.0.0.1:2222/course/trigonometry", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "Trigonometry", "level": "Highschool", "grade": "Grade 10–12", "category": "Topic", "description": "Comprehensive trigonometry: ratios, identities, equations, laws, polar coordinates." }, "es": { "title": "Trigonometría", "level": "Secundaria", "grade": "Grado 10–12", "category": "Tema", "description": "Trigonometría. Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Trigonométrie", "level": "Lycée", "grade": "Niveau 10–12", "category": "Thème", "description": "Trigonométrie. Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Trigonometrie", "level": "Oberstufe", "grade": "Klasse 10–12", "category": "Thema", "description": "Trigonometrie. Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "حساب المثلثات", "level": "ثانوي", "grade": "الصف 10–12", "category": "موضوع", "description": "حساب المثلثات. تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "三角学", "level": "高中", "grade": "年级 10–12", "category": "专题", "description": "三角学. 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "三角法", "level": "高校", "grade": "学年 10–12", "category": "テーマ別", "description": "三角法. 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Trigonometria", "level": "Ensino médio", "grade": "Ano 10–12", "category": "Tema", "description": "Trigonometria. Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Trigonometria", "level": "Scuola superiore", "grade": "Classe 10–12", "category": "Argomento", "description": "Trigonometria. Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Goniometrie", "level": "Middelbare bovenbouw", "grade": "Leerjaar 10–12", "category": "Onderwerp", "description": "Goniometrie. Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "삼각법", "level": "고등", "grade": "학년 10–12", "category": "주제별", "description": "삼각법. 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Trigonometri", "level": "Lise", "grade": "Sınıf 10–12", "category": "Konu", "description": "Trigonometri. Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "سێگۆشەناسی", "level": "ئامادەیی", "grade": "پۆلی 10–12", "category": "بابەت", "description": "سێگۆشەناسی. چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Trigonometrî", "level": "Lîse", "grade": "Pola 10–12", "category": "Mijar", "description": "Trigonometrî. Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-geometry", "slug": "geometry", "title": "Geometry", "level": "Highschool", "grade": "Grade 9–11", "category": "Topic", "description": "Euclidean geometry: points, lines, angles, triangles, circles, proofs, coordinate geometry.", "curriculum": { "primary": "Canada/BC", "code": "CA-BC-GEOM", "equivalents": [ { "region": "Canada/ON", "standard": "Ontario MPM2D Analytic Geometry", "code": "CA-ON-MPM2D-GEO" }, { "region": "Canada/AB", "standard": "Alberta Math 10C/20-1 Geometry", "code": "CA-AB-GEO" }, { "region": "US/TX", "standard": "Texas TEKS Geometry §111.41", "code": "US-TX-GEOM" }, { "region": "US/NY", "standard": "NYSED NextGen Geometry Standards", "code": "US-NY-GEOM" } ] }, "dayaLms": { "courseId": "DLMS-MTH-011", "slug": "geometry", "title": "Geometry", "category": "Mathematics", "level": "Highschool", "grade": "Grade 9–11", "pricing": { "currency": "USD", "amount": 32 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/geometry", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Geometry Outline\n1. Foundations\n - Points, lines, planes, angles\n2. Triangles\n - Congruence, similarity, centers\n3. Quadrilaterals & Polygons\n4. Circles\n - Chords, tangents, arcs\n5. Transformations\n6. Coordinate Geometry\n - Distance, midpoint, slope\n7. Proofs\n - Two-column, paragraph", "context": "Geometry develops logical reasoning and spatial sense. Students prove theorems, analyze shapes, and use coordinate methods.", "lessons": [ { "id": 1, "title": "Angles", "content": "Complementary, supplementary, vertical. Parallel line angle pairs." }, { "id": 2, "title": "Triangle Congruence", "content": "SSS, SAS, ASA, AAS, HL." }, { "id": 3, "title": "Triangle Centers", "content": "Centroid, circumcenter, incenter, orthocenter." }, { "id": 4, "title": "Circle Theorems", "content": "Inscribed angle, tangent-chord." }, { "id": 5, "title": "Coordinate Geometry", "content": "Distance formula, midpoint, slope." }, { "id": 6, "title": "Proofs", "content": "Two-column proofs. Indirect proof." } ], "qa": [ { "id": 1, "question": "Sum angles triangle?", "answer": "180°" }, { "id": 2, "question": "Vertical angles are?", "answer": "Equal" }, { "id": 3, "question": "Distance (0,0) to (3,4)?", "answer": "5" }, { "id": 4, "question": "Midpoint of (2,6),(8,10)?", "answer": "(5,8)" }, { "id": 5, "question": "Tangent perpendicular to?", "answer": "Radius" }, { "id": 6, "question": "Centroid divides median in?", "answer": "2:1" } ], "diagrams": [ { "id": 1, "title": "Triangle Centers", "svg": "\n\ncentroid" }, { "id": 2, "title": "Circle Tangent", "svg": "\n\n" } ], "htmlUrl": "subjects/math/geometry.html", "lmsWebinarId": 2035, "lmsUrl": "http://127.0.0.1:2222/course/geometry", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "Geometry", "level": "Highschool", "grade": "Grade 9–11", "category": "Topic", "description": "Euclidean geometry: points, lines, angles, triangles, circles, proofs, coordinate geometry." }, "es": { "title": "Geometría", "level": "Secundaria", "grade": "Grado 9–11", "category": "Tema", "description": "Geometría. Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Géométrie", "level": "Lycée", "grade": "Niveau 9–11", "category": "Thème", "description": "Géométrie. Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Geometrie", "level": "Oberstufe", "grade": "Klasse 9–11", "category": "Thema", "description": "Geometrie. Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الهندسة", "level": "ثانوي", "grade": "الصف 9–11", "category": "موضوع", "description": "الهندسة. تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "几何", "level": "高中", "grade": "年级 9–11", "category": "专题", "description": "几何. 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "幾何学", "level": "高校", "grade": "学年 9–11", "category": "テーマ別", "description": "幾何学. 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Geometria", "level": "Ensino médio", "grade": "Ano 9–11", "category": "Tema", "description": "Geometria. Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Geometria", "level": "Scuola superiore", "grade": "Classe 9–11", "category": "Argomento", "description": "Geometria. Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Meetkunde", "level": "Middelbare bovenbouw", "grade": "Leerjaar 9–11", "category": "Onderwerp", "description": "Meetkunde. Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "기하학", "level": "고등", "grade": "학년 9–11", "category": "주제별", "description": "기하학. 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Geometri", "level": "Lise", "grade": "Sınıf 9–11", "category": "Konu", "description": "Geometri. Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "ئەندازە", "level": "ئامادەیی", "grade": "پۆلی 9–11", "category": "بابەت", "description": "ئەندازە. چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Geometrî", "level": "Lîse", "grade": "Pola 9–11", "category": "Mijar", "description": "Geometrî. Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-algebra", "slug": "algebra", "title": "Algebra", "level": "Highschool", "grade": "Grade 9–11", "category": "Topic", "description": "Algebra fundamentals: expressions, equations, inequalities, functions, polynomials, rationals.", "curriculum": { "primary": "Canada/BC", "code": "CA-BC-ALG", "equivalents": [ { "region": "Canada/ON", "standard": "Ontario MTH1W / MPM2D Algebraic Models", "code": "CA-ON-ALG" }, { "region": "Canada/AB", "standard": "Alberta Math 10C / 20-1 Algebra", "code": "CA-AB-ALG" }, { "region": "US/TX", "standard": "Texas TEKS Algebra I & II", "code": "US-TX-ALG-1-2" }, { "region": "US/NY", "standard": "NYSED NextGen Algebra Standards", "code": "US-NY-ALG-1-2" } ] }, "dayaLms": { "courseId": "DLMS-MTH-012", "slug": "algebra", "title": "Algebra", "category": "Mathematics", "level": "Highschool", "grade": "Grade 9–11", "pricing": { "currency": "USD", "amount": 32 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/algebra", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Algebra Outline\n1. Expressions & Equations\n2. Linear Equations & Inequalities\n3. Systems of Equations\n4. Polynomials & Factoring\n5. Rational & Radical Expressions\n6. Quadratic Equations\n7. Functions & Graphs\n8. Exponential & Logarithmic (intro)", "context": "Algebra is the language of mathematics. This course covers manipulation of expressions and equations, systems, polynomials, and function basics.", "lessons": [ { "id": 1, "title": "Linear Equations", "content": "Solve multi-step, variables both sides." }, { "id": 2, "title": "Systems", "content": "Substitution, elimination, graphing." }, { "id": 3, "title": "Factoring", "content": "GCF, trinomials, difference of squares." }, { "id": 4, "title": "Quadratics", "content": "Factoring, completing square, quadratic formula." }, { "id": 5, "title": "Rationals", "content": "Simplify, solve rational equations." }, { "id": 6, "title": "Functions", "content": "Domain, range, composition." } ], "qa": [ { "id": 1, "question": "Solve 2x+3=4x-5.", "answer": "x=4" }, { "id": 2, "question": "Solve system: x+y=5, x-y=1.", "answer": "x=3,y=2" }, { "id": 3, "question": "Quadratic formula for ax²+bx+c=0?", "answer": "x=(-b±√(b²-4ac))/(2a)" }, { "id": 4, "question": "Factor x²+5x+6.", "answer": "(x+2)(x+3)" }, { "id": 5, "question": "Domain of 1/(x-2)?", "answer": "x≠2" }, { "id": 6, "question": "Composition f(g(x)) if f=2x,g=x+1?", "answer": "2x+2" } ], "diagrams": [ { "id": 1, "title": "Linear System", "svg": "\n\n" }, { "id": 2, "title": "Parabola Roots", "svg": "\n\n\n" } ], "htmlUrl": "subjects/math/algebra.html", "lmsWebinarId": 2036, "lmsUrl": "http://127.0.0.1:2222/course/algebra", "assignedTeacher": { "id": "1051", "name": "Tomas Novak", "email": "tomas.novak@dayacollege.com" }, "translations": { "en": { "title": "Algebra", "level": "Highschool", "grade": "Grade 9–11", "category": "Topic", "description": "Algebra fundamentals: expressions, equations, inequalities, functions, polynomials, rationals." }, "es": { "title": "Álgebra", "level": "Secundaria", "grade": "Grado 9–11", "category": "Tema", "description": "Álgebra. Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Algèbre", "level": "Lycée", "grade": "Niveau 9–11", "category": "Thème", "description": "Algèbre. Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Algebra", "level": "Oberstufe", "grade": "Klasse 9–11", "category": "Thema", "description": "Algebra. Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الجبر", "level": "ثانوي", "grade": "الصف 9–11", "category": "موضوع", "description": "الجبر. تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "代数", "level": "高中", "grade": "年级 9–11", "category": "专题", "description": "代数. 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "代数学", "level": "高校", "grade": "学年 9–11", "category": "テーマ別", "description": "代数学. 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Álgebra", "level": "Ensino médio", "grade": "Ano 9–11", "category": "Tema", "description": "Álgebra. Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Algebra", "level": "Scuola superiore", "grade": "Classe 9–11", "category": "Argomento", "description": "Algebra. Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Algebra", "level": "Middelbare bovenbouw", "grade": "Leerjaar 9–11", "category": "Onderwerp", "description": "Algebra. Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "대수학", "level": "고등", "grade": "학년 9–11", "category": "주제별", "description": "대수학. 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Cebir", "level": "Lise", "grade": "Sınıf 9–11", "category": "Konu", "description": "Cebir. Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "ئەڵجەبرا", "level": "ئامادەیی", "grade": "پۆلی 9–11", "category": "بابەت", "description": "ئەڵجەبرا. چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Cebir", "level": "Lîse", "grade": "Pola 9–11", "category": "Mijar", "description": "Cebir. 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Limits & Continuity\n2. Derivatives\n - Definition, rules (power, product, quotient, chain)\n3. Applications of Derivatives\n - Related rates, optimization, curve sketching\n4. Transcendental Functions\n - Trig, exponential, logarithmic derivatives\n5. Implicit Differentiation\n6. Linear Approximation & Differentials", "context": "Math 100 is first-year differential calculus. Covers limits, derivative rules, and applications including optimization and related rates. Foundation for Math 101/152.", "lessons": [ { "id": 1, "title": "Limits", "content": "Evaluate limits algebraically, numerically, graphically. Continuity." }, { "id": 2, "title": "Derivative Definition", "content": "f'(x)=lim (f(x+h)-f(x))/h. Interpret as slope." }, { "id": 3, "title": "Differentiation Rules", "content": "Power, sum, product, quotient, chain rules." }, { "id": 4, "title": "Transcendentals", "content": "Derivatives of sin, cos, e^x, ln x." }, { "id": 5, "title": "Applications", "content": "Related rates, optimization, curve sketching." }, { "id": 6, "title": "Implicit Diff", "content": "Differentiate both sides; solve for dy/dx." } ], "qa": [ { "id": 1, "question": "d/dx x^n = ?", "answer": "n x^(n-1)" }, { "id": 2, "question": "Derivative of sin x?", "answer": "cos x" }, { "id": 3, "question": "Derivative of e^x?", "answer": "e^x" }, { "id": 4, "question": "lim x→0 sin x/x?", "answer": "1" }, { "id": 5, "question": "Chain rule for f(g(x))?", "answer": "f'(g(x)) g'(x)" }, { "id": 6, "question": "Derivative of ln x?", "answer": "1/x" } ], "diagrams": [ { "id": 1, "title": "Tangent Line", "svg": "\n\n" }, { "id": 2, "title": "Limit Concept", "svg": "\n\n" } ], "htmlUrl": "subjects/math/math-100.html", "lmsWebinarId": 2037, "lmsUrl": "http://127.0.0.1:2222/course/math-100", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Math 100 (Differential Calculus)", "level": "College", "grade": "College Year 1", "category": "UBC/BC University", "description": "UBC Math 100: differential calculus of functions of one variable, limits, derivatives, applications." }, "es": { "title": "Matemáticas 100 (Cálculo diferencial)", "level": "Universidad", "grade": "Primer año universitario", "category": "Universidad UBC/BC", "description": "Matemáticas 100 (Cálculo diferencial). 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Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 100 (Calcolo differenziale)", "level": "Università", "grade": "Primo anno universitario", "category": "Università UBC/BC", "description": "Matematica 100 (Calcolo differenziale). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 100 (Differentiaalrekening)", "level": "Hoger onderwijs", "grade": "Eerste studiejaar", "category": "UBC/BC universiteit", "description": "Wiskunde 100 (Differentiaalrekening). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 100 (미분학)", "level": "대학", "grade": "대학 1학년", "category": "UBC/BC 대학", "description": "수학 100 (미분학). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 100 (Türev hesabı)", "level": "Üniversite", "grade": "Üniversite 1. yıl", "category": "UBC/BC üniversitesi", "description": "Matematik 100 (Türev hesabı). 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Covers full differential and integral calculus of one variable.", "lessons": [ { "id": 1, "title": "Review Functions", "content": "Trig, exp, log properties and graphs." }, { "id": 2, "title": "Limits", "content": "One/two-sided limits, continuity, IVT." }, { "id": 3, "title": "Derivatives", "content": "Rules and applications." }, { "id": 4, "title": "Curve Sketching", "content": "First/second derivative tests." }, { "id": 5, "title": "Integrals", "content": "Antiderivatives, Riemann sums, FTC." }, { "id": 6, "title": "Applications", "content": "Area between curves, volumes of revolution." } ], "qa": [ { "id": 1, "question": "∫ x^n dx = ?", "answer": "x^(n+1)/(n+1)+C" }, { "id": 2, "question": "FTC: d/dx ∫_a^x f(t)dt = ?", "answer": "f(x)" }, { "id": 3, "question": "Derivative of cos x?", "answer": "-sin x" }, { "id": 4, "question": "∫ e^x dx = ?", "answer": "e^x + C" }, { "id": 5, "question": "Area under y=x from 0 to 2?", "answer": "2" }, { "id": 6, "question": "Volume disk method?", "answer": "π∫ r² dx" } ], "diagrams": [ { "id": 1, "title": "Riemann Sum", "svg": "\n\n\n\n" }, { "id": 2, "title": "Volume of Revolution", "svg": "\n" } ], "htmlUrl": "subjects/math/math-150.html", "lmsWebinarId": 2038, "lmsUrl": "http://127.0.0.1:2222/course/math-150", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Math 150 (Calculus I with Review)", "level": "College", "grade": "College Year 1", "category": "UBC/BC University", "description": "UBC Math 150: calculus I with precalculus review, limits, derivatives, integrals." }, "es": { "title": "Matemáticas 150 (Cálculo I con repaso)", "level": "Universidad", "grade": "Primer año universitario", "category": "Universidad UBC/BC", "description": "Matemáticas 150 (Cálculo I con repaso). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 150 (Calcul I avec révision)", "level": "Université", "grade": "Première année d’université", "category": "Université UBC/C.-B.", "description": "Mathématiques 150 (Calcul I avec révision). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 150 (Analysis I mit Wiederholung)", "level": "Hochschule", "grade": "Erstes Studienjahr", "category": "UBC/BC Universität", "description": "Mathematik 150 (Analysis I mit Wiederholung). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الرياضيات 150 (التفاضل والتكامل I مع مراجعة)", "level": "جامعي", "grade": "السنة الجامعية الأولى", "category": "جامعة UBC/كولومبيا البريطانية", "description": "الرياضيات 150 (التفاضل والتكامل I مع مراجعة). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "数学 150 (微积分 I 含复习)", "level": "大学", "grade": "大学一年级", "category": "UBC／卑诗省大学", "description": "数学 150 (微积分 I 含复习). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "数学 150 (微積分 I 復習付き)", "level": "大学", "grade": "大学1年", "category": "UBC／BC州大学", "description": "数学 150 (微積分 I 復習付き). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Matemática 150 (Cálculo I com revisão)", "level": "Universidade", "grade": "Primeiro ano universitário", "category": "Universidade UBC/BC", "description": "Matemática 150 (Cálculo I com revisão). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 150 (Calcolo I con ripasso)", "level": "Università", "grade": "Primo anno universitario", "category": "Università UBC/BC", "description": "Matematica 150 (Calcolo I con ripasso). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 150 (Calculus I met herhaling)", "level": "Hoger onderwijs", "grade": "Eerste studiejaar", "category": "UBC/BC universiteit", "description": "Wiskunde 150 (Calculus I met herhaling). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 150 (미적분학 I 복습 포함)", "level": "대학", "grade": "대학 1학년", "category": "UBC/BC 대학", "description": "수학 150 (미적분학 I 복습 포함). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 150 (Kalkülüs I tekrarlı)", "level": "Üniversite", "grade": "Üniversite 1. yıl", "category": "UBC/BC üniversitesi", "description": "Matematik 150 (Kalkülüs I tekrarlı). 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Arc length." }, { "id": 6, "title": "Polar", "content": "Area in polar: 1/2∫ r² dθ." } ], "qa": [ { "id": 1, "question": "∫ dx/(x²+1) = ?", "answer": "arctan x + C" }, { "id": 2, "question": "∑ 1/2^n from 1∞ = ?", "answer": "1" }, { "id": 3, "question": "Maclaurin for e^x?", "answer": "∑ x^n/n!" }, { "id": 4, "question": "Polar area formula?", "answer": "1/2 ∫ r² dθ" }, { "id": 5, "question": "p-series ∑1/n^p converges if?", "answer": "p>1" }, { "id": 6, "question": "Ratio test limit L<1 means?", "answer": "Converges" } ], "diagrams": [ { "id": 1, "title": "Polar Area", "svg": "\n" }, { "id": 2, "title": "Taylor Approximation", "svg": "\n" } ], "htmlUrl": "subjects/math/math-152.html", "lmsWebinarId": 2040, "lmsUrl": "http://127.0.0.1:2222/course/math-152", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Math 152 (Calculus II)", "level": "College", "grade": "College Year 1", "category": "UBC/BC University", "description": "UBC Math 152: integral calculus, series, parametric/polar, multivariable intro." }, "es": { "title": "Matemáticas 152 (Cálculo II)", "level": "Universidad", "grade": "Primer año universitario", "category": "Universidad UBC/BC", "description": "Matemáticas 152 (Cálculo II). 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Functions & Models\n2. Limits & Derivatives\n3. Differentiation Rules\n4. Applications (rates, optimization)\n5. Integrals & FTC\n6. Applications (work, hydrostatic pressure)\n7. 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Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 154 (미적분학 I 공학 전공)", "level": "대학", "grade": "대학 1학년", "category": "UBC/BC 대학", "description": "수학 154 (미적분학 I 공학 전공). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 154 (Kalkülüs I mühendisler için)", "level": "Üniversite", "grade": "Üniversite 1. yıl", "category": "UBC/BC üniversitesi", "description": "Matematik 154 (Kalkülüs I mühendisler için). 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Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-math-155", "slug": "math-155", "title": "Math 155 (Calculus I for Life Sciences)", "level": "College", "grade": "College Year 1", "category": "UBC/BC University", "description": "UBC Math 155: calculus I for life sciences students.", "curriculum": { "primary": "Canada/BC", "code": "CA-BC-UBC-SFU-MATH-155", "equivalents": [ { "region": "Canada/ON", "standard": "University of Toronto / Waterloo MAT135 / MATH137", "code": "CA-ON-U-CALC1" }, { "region": "Canada/AB", "standard": "University of Alberta MATH 114 / 117", "code": "CA-AB-U-CALC1" }, { "region": "US/National", "standard": "AP Calculus AB / BC & Collegiate Calc I", "code": "US-AP-CALC-BC" }, { "region": "US/NY", "standard": "SUNY / Columbia Calculus I (MATH UN1101)", "code": "US-NY-COL-CALC1" }, { "region": "US/TX", "standard": "UT Austin M 408C / Texas A&M MATH 151", "code": "US-TX-UTA-M408" } ] }, "dayaLms": { "courseId": "DLMS-MTH-018", "slug": "math-155", "title": "Math 155 (Calculus I for Life Sciences)", "category": "Mathematics", "level": "College", "grade": "College Year 1", "pricing": { "currency": "USD", "amount": 38 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/math-155", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Math 155 Outline\n1. Functions & Models (biological)\n2. Limits & Derivatives\n3. Differentiation Rules\n4. Applications (growth rates, optimization)\n5. Integrals & FTC\n6. Applications (accumulation, drug concentration)\n7. Differential Equations (population models)", "context": "Math 155 is calculus I for life sciences, emphasizing biological applications: population growth, drug concentration, optimization in biology.", "lessons": [ { "id": 1, "title": "Functions in Biology", "content": "Michaelis-Menten, logistic growth." }, { "id": 2, "title": "Limits & Derivatives", "content": "Rates of change in biological systems." }, { "id": 3, "title": "Differentiation", "content": "Rules including logarithmic differentiation." }, { "id": 4, "title": "Optimization", "content": "Maximize yield, minimize cost." }, { "id": 5, "title": "Integrals", "content": "Accumulation, average value." }, { "id": 6, "title": "Population Models", "content": "Logistic DE, carrying capacity." } ], "qa": [ { "id": 1, "question": "Logistic growth dP/dt = ?", "answer": "rP(1-P/K)" }, { "id": 2, "question": "Carrying capacity K means?", "answer": "Max population" }, { "id": 3, "question": "Michaelis-Menten V = ?", "answer": "Vmax S/(Km+S)" }, { "id": 4, "question": "Average value of f on [a,b]?", "answer": "(1/(b-a))∫_a^b f" }, { "id": 5, "question": "Derivative of log base a x?", "answer": "1/(x ln a)" }, { "id": 6, "question": "Doubling time for exponential?", "answer": "ln2/k" } ], "diagrams": [ { "id": 1, "title": "Logistic Growth", "svg": "\n\nK" }, { "id": 2, "title": "Michaelis-Menten", "svg": "\n\nVmax" } ], "htmlUrl": "subjects/math/math-155.html", "lmsWebinarId": 2042, "lmsUrl": "http://127.0.0.1:2222/course/math-155", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Math 155 (Calculus I for Life Sciences)", "level": "College", "grade": "College Year 1", "category": "UBC/BC University", "description": "UBC Math 155: calculus I for life sciences students." }, "es": { "title": "Matemáticas 155 (Cálculo I para ciencias de la vida)", "level": "Universidad", "grade": "Primer año universitario", "category": "Universidad UBC/BC", "description": "Matemáticas 155 (Cálculo I para ciencias de la vida). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques 155 (Calcul I pour les sciences de la vie)", "level": "Université", "grade": "Première année d’université", "category": "Université UBC/C.-B.", "description": "Mathématiques 155 (Calcul I pour les sciences de la vie). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mathematik 155 (Analysis I für Lebenswissenschaften)", "level": "Hochschule", "grade": "Erstes Studienjahr", "category": "UBC/BC Universität", "description": "Mathematik 155 (Analysis I für Lebenswissenschaften). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "الرياضيات 155 (التفاضل والتكامل I لعلوم الحياة)", "level": "جامعي", "grade": "السنة الجامعية الأولى", "category": "جامعة UBC/كولومبيا البريطانية", "description": "الرياضيات 155 (التفاضل والتكامل I لعلوم الحياة). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "数学 155 (微积分 I 生命科学方向)", "level": "大学", "grade": "大学一年级", "category": "UBC／卑诗省大学", "description": "数学 155 (微积分 I 生命科学方向). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "数学 155 (微積分 I 生命科学向け)", "level": "大学", "grade": "大学1年", "category": "UBC／BC州大学", "description": "数学 155 (微積分 I 生命科学向け). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Matemática 155 (Cálculo I para ciências da vida)", "level": "Universidade", "grade": "Primeiro ano universitário", "category": "Universidade UBC/BC", "description": "Matemática 155 (Cálculo I para ciências da vida). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Matematica 155 (Calcolo I per le scienze della vita)", "level": "Università", "grade": "Primo anno universitario", "category": "Università UBC/BC", "description": "Matematica 155 (Calcolo I per le scienze della vita). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Wiskunde 155 (Calculus I voor levenswetenschappen)", "level": "Hoger onderwijs", "grade": "Eerste studiejaar", "category": "UBC/BC universiteit", "description": "Wiskunde 155 (Calculus I voor levenswetenschappen). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "수학 155 (미적분학 I 생명과학 전공)", "level": "대학", "grade": "대학 1학년", "category": "UBC/BC 대학", "description": "수학 155 (미적분학 I 생명과학 전공). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Matematik 155 (Kalkülüs I yaşam bilimleri için)", "level": "Üniversite", "grade": "Üniversite 1. yıl", "category": "UBC/BC üniversitesi", "description": "Matematik 155 (Kalkülüs I yaşam bilimleri için). 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Limits & Continuity\n2. Derivatives & Rules\n3. Applications (rates, optimization, sketching)\n4. Integrals & FTC\n5. Applications (area, volume, work)\n6. Transcendental Functions\n7. Techniques of Integration", "context": "One-on-one calculus tutoring covering all standard topics. Focus on problem-solving strategies and exam preparation.", "lessons": [ { "id": 1, "title": "Limits", "content": "Evaluate via algebra, L'Hôpital, squeeze theorem." }, { "id": 2, "title": "Derivatives", "content": "All rules; implicit; logarithmic." }, { "id": 3, "title": "Optimization", "content": "Set derivative zero; check endpoints." }, { "id": 4, "title": "Integrals", "content": "Substitution, parts, partial fractions." }, { "id": 5, "title": "Applications", "content": "Area, volume, arc length, work." }, { "id": 6, "title": "Series (intro)", "content": "Convergence basics." } ], "qa": [ { "id": 1, "question": "Derivative of x^x?", "answer": "x^x(1+ln x)" }, { "id": 2, "question": "∫ ln x dx = ?", "answer": "x ln x - x + C" }, { "id": 3, "question": "L'Hôpital applies when?", "answer": "0/0 or ∞/∞" }, { "id": 4, "question": "Arc length formula?", "answer": "∫√(1+(dy/dx)²) dx" }, { "id": 5, "question": "Mean value theorem?", "answer": "∃c: f'(c)=(f(b)-f(a))/(b-a)" }, { "id": 6, "question": "Fundamental theorem?", "answer": "∫_a^b f = F(b)-F(a)" } ], "diagrams": [ { "id": 1, "title": "Derivative as Slope", "svg": "\n" }, { "id": 2, "title": "Area Under Curve", "svg": "" } ], "htmlUrl": "subjects/math/calculus.html", "lmsWebinarId": 2043, "lmsUrl": "http://127.0.0.1:2222/course/calculus", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Calculus (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Comprehensive calculus tutoring: limits, derivatives, integrals, applications." }, "es": { "title": "Cálculo (Tutoría)", "level": "Universidad", "grade": "Universidad y tutoría", "category": "Tutoría académica", "description": "Cálculo (Tutoría). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Calcul (Tutorat)", "level": "Université", "grade": "Université et tutorat", "category": "Tutorat scolaire", "description": "Calcul (Tutorat). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Analysis (Nachhilfe)", "level": "Hochschule", "grade": "Hochschule und Nachhilfe", "category": "Akademische Nachhilfe", "description": "Analysis (Nachhilfe). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分 (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "微积分 (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分 (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "微積分 (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo (Tutoria). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Calcolo (Tutoraggio)", "level": "Università", "grade": "Università e tutoraggio", "category": "Tutoraggio accademico", "description": "Calcolo (Tutoraggio). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Calculus (Bijles)", "level": "Hoger onderwijs", "grade": "Hoger onderwijs en bijles", "category": "Academische bijles", "description": "Calculus (Bijles). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "미적분학 (개인 지도)", "level": "대학", "grade": "대학 및 개인 지도", "category": "학습 지도", "description": "미적분학 (개인 지도). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Kalkülüs (Özel ders)", "level": "Üniversite", "grade": "Üniversite ve özel ders", "category": "Akademik özel ders", "description": "Kalkülüs (Özel ders). 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Multivariable Functions\n2. Partial Derivatives & Gradients\n3. Multiple Integrals\n4. Vector Calculus\n - Line & surface integrals\n - Green's, Stokes', Divergence theorems\n5. Sequences & Series of Functions\n6. Fourier Series (intro)\n7. PDEs (intro)", "context": "Advanced calculus for upper-level students: multivariable differentiation/integration, vector calculus theorems, and series of functions.", "lessons": [ { "id": 1, "title": "Partial Derivatives", "content": "f_x, f_y. Clairaut's theorem." }, { "id": 2, "title": "Gradient & Directional Derivative", "content": "∇f · u. Max rate of change." }, { "id": 3, "title": "Double/Triple Integrals", "content": "Fubini, change of variables, Jacobian." }, { "id": 4, "title": "Line Integrals", "content": "Work along curve. Conservative fields." }, { "id": 5, "title": "Surface Integrals", "content": "Flux through surface." }, { "id": 6, "title": "Green/Stokes/Divergence", "content": "Relate integrals over regions/boundaries." } ], "qa": [ { "id": 1, "question": "Gradient of f?", "answer": "∇f = (f_x, f_y, f_z)" }, { "id": 2, "question": "Directional derivative formula?", "answer": "∇f·u" }, { "id": 3, "question": "Green's theorem relates?", "answer": "Line integral around boundary to double integral over region" }, { "id": 4, "question": "Divergence theorem?", "answer": "Flux through closed surface = triple integral of div F" }, { "id": 5, "question": "Jacobian for polar?", "answer": "r" }, { "id": 6, "question": "Stokes' theorem?", "answer": "Line integral around boundary = surface integral of curl" } ], "diagrams": [ { "id": 1, "title": "Gradient Field", "svg": "\n\n" }, { "id": 2, "title": "Surface Integral", "svg": "\n" } ], "htmlUrl": "subjects/math/advanced-calculus.html", "lmsWebinarId": 2044, "lmsUrl": "http://127.0.0.1:2222/course/advanced-calculus", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Advanced Calculus (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Advanced calculus: multivariable, vector calculus, PDEs intro, real analysis." }, "es": { "title": "Cálculo avanzado (Tutoría)", "level": "Universidad", "grade": "Universidad y tutoría", "category": "Tutoría académica", "description": "Cálculo avanzado (Tutoría). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Calcul avancé (Tutorat)", "level": "Université", "grade": "Université et tutorat", "category": "Tutorat scolaire", "description": "Calcul avancé (Tutorat). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Fortgeschrittene Analysis (Nachhilfe)", "level": "Hochschule", "grade": "Hochschule und Nachhilfe", "category": "Akademische Nachhilfe", "description": "Fortgeschrittene Analysis (Nachhilfe). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل المتقدم (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل المتقدم (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "高等微积分 (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "高等微积分 (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "上級微積分 (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "上級微積分 (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo avançado (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo avançado (Tutoria). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Calcolo avanzato (Tutoraggio)", "level": "Università", "grade": "Università e tutoraggio", "category": "Tutoraggio accademico", "description": "Calcolo avanzato (Tutoraggio). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Gevorderde calculus (Bijles)", "level": "Hoger onderwijs", "grade": "Hoger onderwijs en bijles", "category": "Academische bijles", "description": "Gevorderde calculus (Bijles). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "고급 미적분학 (개인 지도)", "level": "대학", "grade": "대학 및 개인 지도", "category": "학습 지도", "description": "고급 미적분학 (개인 지도). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "İleri kalkülüs (Özel ders)", "level": "Üniversite", "grade": "Üniversite ve özel ders", "category": "Akademik özel ders", "description": "İleri kalkülüs (Özel ders). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "کەلکولەسی پێشکەوتوو (وانەی تایبەت)", "level": "زانکۆ", "grade": "زانکۆ و وانەی تایبەت", "category": "وانەی تایبەتی ئەکادیمی", "description": "کەلکولەسی پێشکەوتوو (وانەی تایبەت). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Kalkulûsa pêşketî (Dersên taybet)", "level": "Zanîngeh", "grade": "Zanîngeh û dersên taybet", "category": "Dersên taybet ên akademîk", "description": "Kalkulûsa pêşketî (Dersên taybet). 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Limits\n2. Derivatives\n3. Applications\n4. Integrals\n5. FTC", "context": "Focused tutoring for Calculus I: build strong fundamentals in limits, derivatives, and integrals.", "lessons": [ { "id": 1, "title": "Limits", "content": "Evaluate and interpret limits." }, { "id": 2, "title": "Derivatives", "content": "Rules and computation." }, { "id": 3, "title": "Applications", "content": "Rates, optimization, motion." }, { "id": 4, "title": "Integrals", "content": "Antiderivatives and area." }, { "id": 5, "title": "FTC", "content": "Connect derivatives and integrals." } ], "qa": [ { "id": 1, "question": "Derivative of x²?", "answer": "2x" }, { "id": 2, "question": "∫ 2x dx = ?", "answer": "x²+C" }, { "id": 3, "question": "Limit x→0 (1-cos x)/x²?", "answer": "1/2" }, { "id": 4, "question": "Velocity = ?", "answer": "Derivative of position" }, { "id": 5, "question": "Acceleration = ?", "answer": "Derivative of velocity" }, { "id": 6, "question": "FTC part 1?", "answer": "d/dx ∫_a^x f = f(x)" } ], "diagrams": [ { "id": 1, "title": "Derivative Graph", "svg": "\n" }, { "id": 2, "title": "Integral Area", "svg": "" } ], "htmlUrl": "subjects/math/calculus-i.html", "lmsWebinarId": 2045, "lmsUrl": "http://127.0.0.1:2222/course/calculus-i", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Calculus I (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Calculus I tutoring: limits, derivatives, integrals basics." }, "es": { "title": "Cálculo I (Tutoría)", "level": "Universidad", "grade": "Universidad y tutoría", "category": "Tutoría académica", "description": "Cálculo I (Tutoría). 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Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل I (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل I (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分 I (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "微积分 I (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分 I (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "微積分 I (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo I (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo I (Tutoria). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Calcolo I (Tutoraggio)", "level": "Università", "grade": "Università e tutoraggio", "category": "Tutoraggio accademico", "description": "Calcolo I (Tutoraggio). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Calculus I (Bijles)", "level": "Hoger onderwijs", "grade": "Hoger onderwijs en bijles", "category": "Academische bijles", "description": "Calculus I (Bijles). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "미적분학 I (개인 지도)", "level": "대학", "grade": "대학 및 개인 지도", "category": "학습 지도", "description": "미적분학 I (개인 지도). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Kalkülüs I (Özel ders)", "level": "Üniversite", "grade": "Üniversite ve özel ders", "category": "Akademik özel ders", "description": "Kalkülüs I (Özel ders). 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Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل II (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل II (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分 II (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "微积分 II (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分 II (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "微積分 II (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo II (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo II (Tutoria). 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Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Calcul III (Tutorat)", "level": "Université", "grade": "Université et tutorat", "category": "Tutorat scolaire", "description": "Calcul III (Tutorat). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Analysis III (Nachhilfe)", "level": "Hochschule", "grade": "Hochschule und Nachhilfe", "category": "Akademische Nachhilfe", "description": "Analysis III (Nachhilfe). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل III (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل III (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分 III (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "微积分 III (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分 III (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "微積分 III (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo III (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo III (Tutoria). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Calcolo III (Tutoraggio)", "level": "Università", "grade": "Università e tutoraggio", "category": "Tutoraggio accademico", "description": "Calcolo III (Tutoraggio). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Calculus III (Bijles)", "level": "Hoger onderwijs", "grade": "Hoger onderwijs en bijles", "category": "Academische bijles", "description": "Calculus III (Bijles). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "미적분학 III (개인 지도)", "level": "대학", "grade": "대학 및 개인 지도", "category": "학습 지도", "description": "미적분학 III (개인 지도). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Kalkülüs III (Özel ders)", "level": "Üniversite", "grade": "Üniversite ve özel ders", "category": "Akademik özel ders", "description": "Kalkülüs III (Özel ders). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "کەلکولەس III (وانەی تایبەت)", "level": "زانکۆ", "grade": "زانکۆ و وانەی تایبەت", "category": "وانەی تایبەتی ئەکادیمی", "description": "کەلکولەس III (وانەی تایبەت). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Kalkulûs III (Dersên taybet)", "level": "Zanîngeh", "grade": "Zanîngeh û dersên taybet", "category": "Dersên taybet ên akademîk", "description": "Kalkulûs III (Dersên taybet). Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-calculus-iv", "slug": "calculus-iv", "title": "Calculus IV (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Calculus IV tutoring: advanced vector calculus, PDEs, complex analysis intro.", "curriculum": { "primary": "Canada/BC", "code": "CA-TUT-CALCULUS-IV", "equivalents": [ { "region": "Canada/BC", "standard": "BC University Calculus Prep & Tutoring", "code": "CA-BC-TUT" }, { "region": "Canada/ON", "standard": "Ontario Collegiate Advanced Tutoring", "code": "CA-ON-TUT" }, { "region": "US/National", "standard": "AP & Collegiate Advanced Mathematics", "code": "US-ADV-MTH" } ] }, "dayaLms": { "courseId": "DLMS-MTH-024", "slug": "calculus-iv", "title": "Calculus IV (Tutoring)", "category": "Mathematics", "level": "College", "grade": "College & Tutoring", "pricing": { "currency": "USD", "amount": 38 }, "totalLessons": 5, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/calculus-iv", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Calculus IV Outline\n1. Advanced Vector Calculus\n2. Fourier Series & Transforms\n3. PDEs (heat, wave, Laplace)\n4. Complex Analysis (intro)\n5. Variational Calculus (intro)", "context": "Calculus IV tutoring: advanced topics for engineering/physics/math majors.", "lessons": [ { "id": 1, "title": "Vector Calculus", "content": "Divergence, curl, potentials." }, { "id": 2, "title": "Fourier Series", "content": "Periodic functions, coefficients." }, { "id": 3, "title": "PDEs", "content": "Separation of variables." }, { "id": 4, "title": "Complex Analysis", "content": "Analytic functions, Cauchy-Riemann." }, { "id": 5, "title": "Variational", "content": "Euler-Lagrange equation." } ], "qa": [ { "id": 1, "question": "Fourier coefficient a0?", "answer": "(1/L)∫ f(x) dx" }, { "id": 2, "question": "Cauchy-Riemann: ∂u/∂x = ?", "answer": "∂v/∂y" }, { "id": 3, "question": "Heat equation?", "answer": "u_t = α u_xx" }, { "id": 4, "question": "Wave equation?", "answer": "u_tt = c² u_xx" }, { "id": 5, "question": "Laplace equation?", "answer": "∇²u = 0" }, { "id": 6, "question": "Analytic function derivative?", "answer": "Complex derivative exists" } ], "diagrams": [ { "id": 1, "title": "Fourier Wave", "svg": "" }, { "id": 2, "title": "Heat Distribution", "svg": "\n" } ], "htmlUrl": "subjects/math/calculus-iv.html", "lmsWebinarId": 2048, "lmsUrl": "http://127.0.0.1:2222/course/calculus-iv", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Calculus IV (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Calculus IV tutoring: advanced vector calculus, PDEs, complex analysis intro." }, "es": { "title": "Cálculo IV (Tutoría)", "level": "Universidad", "grade": "Universidad y tutoría", "category": "Tutoría académica", "description": "Cálculo IV (Tutoría). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Calcul IV (Tutorat)", "level": "Université", "grade": "Université et tutorat", "category": "Tutorat scolaire", "description": "Calcul IV (Tutorat). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Analysis IV (Nachhilfe)", "level": "Hochschule", "grade": "Hochschule und Nachhilfe", "category": "Akademische Nachhilfe", "description": "Analysis IV (Nachhilfe). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل IV (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل IV (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "微积分 IV (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "微积分 IV (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "微積分 IV (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "微積分 IV (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo IV (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo IV (Tutoria). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Calcolo IV (Tutoraggio)", "level": "Università", "grade": "Università e tutoraggio", "category": "Tutoraggio accademico", "description": "Calcolo IV (Tutoraggio). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Calculus IV (Bijles)", "level": "Hoger onderwijs", "grade": "Hoger onderwijs en bijles", "category": "Academische bijles", "description": "Calculus IV (Bijles). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "미적분학 IV (개인 지도)", "level": "대학", "grade": "대학 및 개인 지도", "category": "학습 지도", "description": "미적분학 IV (개인 지도). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Kalkülüs IV (Özel ders)", "level": "Üniversite", "grade": "Üniversite ve özel ders", "category": "Akademik özel ders", "description": "Kalkülüs IV (Özel ders). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "کەلکولەس IV (وانەی تایبەت)", "level": "زانکۆ", "grade": "زانکۆ و وانەی تایبەت", "category": "وانەی تایبەتی ئەکادیمی", "description": "کەلکولەس IV (وانەی تایبەت). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Kalkulûs IV (Dersên taybet)", "level": "Zanîngeh", "grade": "Zanîngeh û dersên taybet", "category": "Dersên taybet ên akademîk", "description": "Kalkulûs IV (Dersên taybet). Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-multivariable-calculus", "slug": "multivariable-calculus", "title": "Multivariable Calculus (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Multivariable calculus tutoring: functions of several variables, partial derivatives, multiple integrals.", "curriculum": { "primary": "Canada/BC", "code": "CA-TUT-MULTIVARIABLE-CALCULUS", "equivalents": [ { "region": "Canada/BC", "standard": "BC University Calculus Prep & Tutoring", "code": "CA-BC-TUT" }, { "region": "Canada/ON", "standard": "Ontario Collegiate Advanced Tutoring", "code": "CA-ON-TUT" }, { "region": "US/National", "standard": "AP & Collegiate Advanced Mathematics", "code": "US-ADV-MTH" } ] }, "dayaLms": { "courseId": "DLMS-MTH-025", "slug": "multivariable-calculus", "title": "Multivariable Calculus (Tutoring)", "category": "Mathematics", "level": "College", "grade": "College & Tutoring", "pricing": { "currency": "USD", "amount": 38 }, "totalLessons": 5, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/multivariable-calculus", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Multivariable Calculus Outline\n1. Functions of Several Variables\n2. Partial Derivatives\n3. Multiple Integrals\n4. Vector-Valued Functions\n5. Line & Surface Integrals (intro)", "context": "Multivariable calculus tutoring focused on functions of several variables and integration.", "lessons": [ { "id": 1, "title": "Functions of 2/3 Variables", "content": "Domain, level curves/surfaces." }, { "id": 2, "title": "Partial Derivatives", "content": "Compute and interpret." }, { "id": 3, "title": "Tangent Planes", "content": "Linear approximation." }, { "id": 4, "title": "Double Integrals", "content": "Over rectangles and general regions." }, { "id": 5, "title": "Triple Integrals", "content": "Volume, mass, center of mass." } ], "qa": [ { "id": 1, "question": "Partial derivative f_x means?", "answer": "Derivative w.r.t x holding y constant" }, { "id": 2, "question": "Level curve of f(x,y)=c?", "answer": "Set of points where f=c" }, { "id": 3, "question": "Tangent plane equation?", "answer": "z=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)" }, { "id": 4, "question": "Double integral over rectangle?", "answer": "∫∫ f dA" }, { "id": 5, "question": "Jacobian for transformation?", "answer": "Determinant of partials" }, { "id": 6, "question": "Gradient perpendicular to?", "answer": "Level curves" } ], "diagrams": [ { "id": 1, "title": "Level Curves", "svg": "\n\n" }, { "id": 2, "title": "Tangent Plane", "svg": "\n" } ], "htmlUrl": "subjects/math/multivariable-calculus.html", "lmsWebinarId": 2049, "lmsUrl": "http://127.0.0.1:2222/course/multivariable-calculus", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Multivariable Calculus (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Multivariable calculus tutoring: functions of several variables, partial derivatives, multiple integrals." }, "es": { "title": "Cálculo multivariable (Tutoría)", "level": "Universidad", "grade": "Universidad y tutoría", "category": "Tutoría académica", "description": "Cálculo multivariable (Tutoría). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Calcul multivariable (Tutorat)", "level": "Université", "grade": "Université et tutorat", "category": "Tutorat scolaire", "description": "Calcul multivariable (Tutorat). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Mehrdimensionale Analysis (Nachhilfe)", "level": "Hochschule", "grade": "Hochschule und Nachhilfe", "category": "Akademische Nachhilfe", "description": "Mehrdimensionale Analysis (Nachhilfe). Lerne die wichtigsten Konzepte mit strukturierten Lektionen und praktischen Übungen." }, "ar": { "title": "التفاضل والتكامل متعدد المتغيرات (دروس خصوصية)", "level": "جامعي", "grade": "الجامعة والدروس الخصوصية", "category": "دروس أكاديمية خصوصية", "description": "التفاضل والتكامل متعدد المتغيرات (دروس خصوصية). تعلّم المفاهيم الأساسية من خلال دروس منظّمة وتمارين تطبيقية." }, "zh": { "title": "多变量微积分 (辅导)", "level": "大学", "grade": "大学与辅导", "category": "学术辅导", "description": "多变量微积分 (辅导). 通过循序渐进的课程和练习掌握核心概念。" }, "ja": { "title": "多変数微積分 (個別指導)", "level": "大学", "grade": "大学・個別指導", "category": "学習指導", "description": "多変数微積分 (個別指導). 体系的な授業と練習問題で重要な概念を学びます。" }, "pt": { "title": "Cálculo multivariável (Tutoria)", "level": "Universidade", "grade": "Universidade e tutoria", "category": "Tutoria acadêmica", "description": "Cálculo multivariável (Tutoria). Aprenda os conceitos principais com aulas organizadas e exercícios práticos." }, "it": { "title": "Calcolo multivariabile (Tutoraggio)", "level": "Università", "grade": "Università e tutoraggio", "category": "Tutoraggio accademico", "description": "Calcolo multivariabile (Tutoraggio). Impara i concetti fondamentali con lezioni strutturate ed esercizi pratici." }, "nl": { "title": "Meervoudige calculus (Bijles)", "level": "Hoger onderwijs", "grade": "Hoger onderwijs en bijles", "category": "Academische bijles", "description": "Meervoudige calculus (Bijles). Leer de belangrijkste begrippen met gestructureerde lessen en oefeningen." }, "ko": { "title": "다변수 미적분학 (개인 지도)", "level": "대학", "grade": "대학 및 개인 지도", "category": "학습 지도", "description": "다변수 미적분학 (개인 지도). 체계적인 수업과 연습 문제로 핵심 개념을 배웁니다." }, "tr": { "title": "Çok değişkenli kalkülüs (Özel ders)", "level": "Üniversite", "grade": "Üniversite ve özel ders", "category": "Akademik özel ders", "description": "Çok değişkenli kalkülüs (Özel ders). Temel kavramları düzenli dersler ve uygulamalı alıştırmalarla öğrenin." }, "ckb": { "title": "کەلکولەسی چەندگۆڕاو (وانەی تایبەت)", "level": "زانکۆ", "grade": "زانکۆ و وانەی تایبەت", "category": "وانەی تایبەتی ئەکادیمی", "description": "کەلکولەسی چەندگۆڕاو (وانەی تایبەت). چەمکە سەرەکییەکان لە ڕێگەی وانەی ڕێکخراو و ڕاهێنانی کردارییەوە فێر ببە." }, "ku": { "title": "Kalkulûsa pirguherbar (Dersên taybet)", "level": "Zanîngeh", "grade": "Zanîngeh û dersên taybet", "category": "Dersên taybet ên akademîk", "description": "Kalkulûsa pirguherbar (Dersên taybet). Bi dersên rêkûpêk û rahênanên pratîk têgehên bingehîn fêr bibin." } } }, { "id": "course-engineering-mathematics", "slug": "engineering-mathematics", "title": "Engineering Mathematics (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Engineering math tutoring: ODEs, linear algebra, vector calculus, numerical methods, complex analysis.", "curriculum": { "primary": "Canada/BC", "code": "CA-TUT-ENGINEERING-MATHEMATICS", "equivalents": [ { "region": "Canada/BC", "standard": "BC University Calculus Prep & Tutoring", "code": "CA-BC-TUT" }, { "region": "Canada/ON", "standard": "Ontario Collegiate Advanced Tutoring", "code": "CA-ON-TUT" }, { "region": "US/National", "standard": "AP & Collegiate Advanced Mathematics", "code": "US-ADV-MTH" } ] }, "dayaLms": { "courseId": "DLMS-MTH-026", "slug": "engineering-mathematics", "title": "Engineering Mathematics (Tutoring)", "category": "Mathematics", "level": "College", "grade": "College & Tutoring", "pricing": { "currency": "USD", "amount": 38 }, "totalLessons": 6, "totalQuestions": 6, "totalDiagrams": 2, "status": "published", "syncDate": "2026-10-15T00:00:00Z", "lmsEndpoint": "/api/v1/dayalms/courses/engineering-mathematics", "webinarEnabled": true, "quizzesEnabled": true, "certificateSupported": true }, "outline": "# Engineering Mathematics Outline\n1. Linear Algebra\n - Matrices, determinants, eigenvalues\n2. ODEs\n - First/second order, systems\n3. Vector Calculus\n4. Complex Analysis (intro)\n5. Numerical Methods\n6. Fourier & Laplace Transforms", "context": "Engineering mathematics tutoring covering linear algebra, differential equations, vector calculus, transforms, and numerical methods.", "lessons": [ { "id": 1, "title": "Linear Algebra", "content": "Matrix ops, rank, eigenvalues/eigenvectors." }, { "id": 2, "title": "ODEs", "content": "First-order, second-order, systems." }, { "id": 3, "title": "Vector Calculus", "content": "Gradient, divergence, curl, theorems." }, { "id": 4, "title": "Transforms", "content": "Laplace and Fourier transforms." }, { "id": 5, "title": "Numerical Methods", "content": "Newton-Raphson, Euler, RK4." }, { "id": 6, "title": "Complex Analysis", "content": "Complex numbers, analytic functions." } ], "qa": [ { "id": 1, "question": "Eigenvalue equation?", "answer": "Av = λv" }, { "id": 2, "question": "Laplace of e^(at)?", "answer": "1/(s-a)" }, { "id": 3, "question": "Determinant of [[a,b],[c,d]]?", "answer": "ad-bc" }, { "id": 4, "question": "Newton-Raphson iteration?", "answer": "x_{n+1}=x_n - f(x_n)/f'(x_n)" }, { "id": 5, "question": "Fourier transform of δ(t)?", "answer": "1" }, { "id": 6, "question": "Divergence of F?", "answer": "∂Fx/∂x+∂Fy/∂y+∂Fz/∂z" } ], "diagrams": [ { "id": 1, "title": "Eigenvalues", "svg": "\nA\nv → λv" }, { "id": 2, "title": "Laplace Transform", "svg": "\nF(s)" } ], "htmlUrl": "subjects/math/engineering-mathematics.html", "lmsWebinarId": 2050, "lmsUrl": "http://127.0.0.1:2222/course/engineering-mathematics", "assignedTeacher": { "id": "1052", "name": "Priya Sharma", "email": "priya.sharma@dayacollege.com" }, "translations": { "en": { "title": "Engineering Mathematics (Tutoring)", "level": "College", "grade": "College & Tutoring", "category": "Academic Tutoring", "description": "Engineering math tutoring: ODEs, linear algebra, vector calculus, numerical methods, complex analysis." }, "es": { "title": "Matemáticas para ingeniería (Tutoría)", "level": "Universidad", "grade": "Universidad y tutoría", "category": "Tutoría académica", "description": "Matemáticas para ingeniería (Tutoría). Aprende los conceptos clave mediante lecciones organizadas y ejercicios prácticos." }, "fr": { "title": "Mathématiques pour ingénieurs (Tutorat)", "level": "Université", "grade": "Université et tutorat", "category": "Tutorat scolaire", "description": "Mathématiques pour ingénieurs (Tutorat). Découvrez les notions essentielles grâce à des leçons structurées et des exercices pratiques." }, "de": { "title": "Ingenieurmathematik (Nachhilfe)", "level": "Hochschule", "grade": "Hochschule und Nachhilfe", "category": "Akademische Nachhilfe", "description": "Ingenieurmathematik (Nachhilfe). 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Entdecke dieses Fach in interaktiven Live-Kursen." }, "ar": { "name": "الموسيقى والأداء", "tagline": "الموسيقى والأداء. استكشف هذا المجال من خلال دورات مباشرة وتفاعلية." }, "zh": { "name": "音乐与表演", "tagline": "音乐与表演. 通过互动直播课程探索这一领域。" }, "ja": { "name": "音楽とパフォーマンス", "tagline": "音楽とパフォーマンス. 双方向のライブ授業でこの分野を探究します。" }, "pt": { "name": "Música e apresentação", "tagline": "Música e apresentação. Explore esta área em aulas interativas ao vivo." }, "it": { "name": "Musica e spettacolo", "tagline": "Musica e spettacolo. Esplora questa materia con corsi interattivi dal vivo." }, "nl": { "name": "Muziek en optreden", "tagline": "Muziek en optreden. Ontdek dit vak in interactieve livelessen." }, "ko": { "name": "음악과 공연", "tagline": "음악과 공연. 실시간 참여형 수업으로 이 분야를 탐구합니다." }, "tr": { "name": "Müzik ve performans", "tagline": "Müzik ve performans. 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