PROJECT: Tutoratti Abhyas — Class 10 CBSE Maths Crash Course
CHAPTER: Arithmetic Progressions (AP)
LESSON 6: Real-Life Word Problems & Case Studies
TARGET DURATION: ~3:20 to 3:35 (Strictly under 4 minutes)
TARGET AUDIENCE: Class 10 CBSE / State Board students preparing for Board Exams
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MANDATORY BRAND, TEACHER APPEARANCE & VOICE RULES (HIGHEST PRIORITY)
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1. BRAND PRONUNCIATION:
- "Tutoratti" MUST be pronounced strictly as "ट्युटराटी" ("Tyoo-tuh-raa-tee").
- NEVER pronounce as "Too-tor-ah-tee" or "Too-ter-addie".
2. TEACHER ATTIRE & LOGO SPECIFICATION (FROZEN):
- Solid navy-blue polo T-shirt with collar throughout the entire video.
- Logo / Text on chest: Clean white or golden-yellow "Tutoratti Guru" lettering printed directly on the left chest.
- CRITICAL: NO square box, NO rectangular border, and NO enclosing badge around the logo. Just the clean text/logo directly on the shirt fabric.
- Keep the teacher's appearance, lighting, and framing 100% consistent across all scenes.
3. ACCENT & VOCAL DELIVERY:
- STRICT neutral Indian English accent. Absolutely NO foreign, American, or British accent.
- Pacing: Calm, confident, encouraging teacher tone (~135 words per minute).
4. LANGUAGE BLEND:
- ~50% natural, warm conversational Hindi for connective explanations and encouragement.
- 100% STRICT ENGLISH for ALL mathematical operations, formulas, variables, and numbers:
* Use "equals to" or "is equal to" (STRICTLY FORBIDDEN: "barabar").
* Use "plus" (STRICTLY FORBIDDEN: "jod").
* Use "minus" (STRICTLY FORBIDDEN: "ghatana").
* Use "multiplied by" (STRICTLY FORBIDDEN: "guna").
* Use "divided by" (STRICTLY FORBIDDEN: "bhaag").
* "first term", "common difference", "n-th term", "sum", "equation", "bracket open/close".
* Every single number must be spoken in English.
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BRAND COLOR PALETTE & VISUAL ASSETS
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- Deep Navy: #1A365D (Background cards, header bars)
- Vibrant Scarlet Red: #E1261C (Callout highlights, important formulas)
- Warm Amber Gold: #D97706 (Badges, answer highlights)
- Clean Slate White: #FFFFFF / #F8FAFC (Primary text and equations)
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SCENE-BY-SCENE CHOREOGRAPHY & TIMELINE
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[00:00 - 00:32] HOOK: DECODING CASE STUDY WORD PROBLEMS
- Visual: Teacher on right side in navy-blue polo with clean "Tutoratti Guru" chest print.
- Screen Left Card: "CBSE 4-Mark Case Study Alert: Real-Life AP Problems".
- Graphic: Word Problem snippet appears ("A factory produces TV sets...").
- Teacher addresses the top student fear: "How do I know whether to use a_n or S_n?"
[00:32 - 01:05] THE GOLDEN DECODING RULE
- Visual: Split comparison table pops up on screen with bold color coding:
* Left Box (Scarlet Red): "Specific Year / Step value? → Find a_n = a + (n - 1)d"
* Right Box (Amber Gold): "Total Accumulated / Sum over years? → Find S_n = n/2 [a + l]"
- Teacher gestures to make this distinction crystal clear.
[01:05 - 02:00] SETTING UP EQUATIONS (TV PRODUCTION PROBLEM)
- On-Screen Problem Card:
"Year 3 Production = 600 sets | Year 7 Production = 700 sets"
- Step-by-step LaTeX reveal on slate:
* a_3 = 600 ⟹ a + 2d = 600 ...(Equation 1)
* a_7 = 700 ⟹ a + 6d = 700 ...(Equation 2)
* (a + 6d) - (a + 2d) = 700 - 600
* 4d = 100 ⟹ d = 25 (Gold highlight)
* Substitute d = 25 in (1): a + 2(25) = 600 ⟹ a = 550 (Scarlet highlight)
- Visual callout badge: "Year 1 Baseline = 550 sets, Annual Growth = 25 sets".
[02:00 - 02:35] PART 1: PRODUCTION IN 10TH YEAR (a_10)
- Heading: "Part 1: Production in 10th Year (a_10)"
- Dynamic chalkboard calculation:
* a_10 = a + 9d
* a_10 = 550 + 9(25)
* 9 × 25 = 225
* 550 + 225 = 775 sets
- Amber Gold celebration box around "a_10 = 775 sets".
[02:35 - 03:10] PART 2: TOTAL PRODUCTION IN FIRST 7 YEARS (S_7)
- Heading: "Part 2: Total Production in First 7 Years (S_7)"
- Prompt shows shortcut formula:
* S_n = (n/2)[a + l] where last term l = a_7 = 700
* S_7 = (7/2)[550 + 700]
* S_7 = (7/2) × 1250
* 1250 ÷ 2 = 625
* S_7 = 7 × 625 = 4375 sets
- Scarlet Red callout box around "S_7 = 4375 sets".
[03:10 - 03:25] RECAP & FINALE TEASER
- Fast summary card of the 3-step strategy:
1. Identify a and d via 2 linear equations.
2. Specific term = a_n.
3. Total accumulated = S_n.
- Outro banner: "Next: Lesson 7 — Board Blueprint & Exam Traps!"
- Teacher smiles and gestures to Tutoratti Abhyas practice dashboard.
