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Other note source 📊 Introduction to Probability - Complete Theory & Formulas What is Probability? Probability measures how likely an event is to happen. It is always a number between 0 and 1, where 0 = impossible and 1 = certain. 🔑 Key Terms (Essential Vocabulary) Experiment: An action with an uncertain outcome (e.g., tossing a coin, rolling a die) Outcome: One possible result of an experiment (e.g., "Head" or "4") Event: A set of outcomes (e.g., "getting an even number") Sample Space: The complete list of all possible outcomes, written as {1,2,3,4,5,6} Favourable Outcomes: Outcomes that match the event you want Frequency: How many times an outcome appears in trials Probability Scale (0 to 1) 0 0.5 1 Impossible Even Chance Certain 📚 Section 8.1: Basic Probability (Experimental) Experimental Probability...

🧪 PANDUAN LENGKAP KIMIA ORGANIK 🧪 Cambridge IGCSE Chemistry Grade 9 - Teori & Rumus Lengkap 17.1 PETROLEUM - BAHAN BAKAR FOSIL Bahan Bakar Fosil: Minyak bumi (crude oil), Batu bara, Gas alam - terbentuk dari organisme yang hidup jutaan tahun lalu. Proses Pembentukan Organisme laut mati → Terkubur di bawah sedimen → Tekanan tinggi + panas (jutaan tahun) → Minyak Bumi. Hidrokarbon: Senyawa yang HANYA mengandung atom Karbon (C) dan Hidrogen (H). Senyawa Organik: Senyawa yang mengandung karbon. Struktur Hidrokarbon 1. PENTANA (Rantai Lurus) - C₅H₁₂ H H H H H | | | | | H - C - C - C - C - C - H | | | | | H H H H H 2. 3-METILPENTANA (Bercabang) - C₆H₁₄ H H H H H | | | | | H - C - C - C - C - C - H | | | | | H H | H H H-C-H | H ...

📐 INTEGRATION - Theory & Formulas O Level Mathematics | Complete Guide 1. Definition Integration = Reverse of Differentiation DIFFERENTIATION ↓ f(x) = x³ → f'(x) = 3x² ↑ INTEGRATION ⚠️ Important: Integration is many-to-one process. Different functions have same derivative! x² + 5 → 2x | x² + 10 → 2x | x² - 3 → 2x 2. Three Basic Rules Rule 1: Power Rule ⭐ ∫ x n dx = x n+1 /(n+1) + c Steps: (1) Add 1 to power (2) Divide by new power (3) Add + c Ex: ∫ x³ dx = x⁴/4 + c | ∫ x⁷ dx = x⁸/8 + c | ∫ 10x⁴ dx = 2x⁵ + c Rule 2: Constant Multiplier ∫ k·f(x) dx = k ∫ f(x) dx Rule 3: Sum/Difference ∫ [f(x) ± g(x)] dx = ∫ f(x) dx ± ∫ g(x) dx Ex: ∫ (x³ - x + 3) dx = x⁴/4 - x²/2 + 3x + c 3. Constant ...

Other note source 📐 UNDERSTANDING MEASUREMENT Cambridge IGCSE Mathematics - Grade 10 Complete Study Guide - Chapter 13 📏 13.1 UNDERSTANDING UNITS What Are Measurement Units? Measurement is how we describe the size, length, weight, or volume of objects. In everyday life, you measure things constantly - the distance to school, the amount of water in a bottle, or how heavy your backpack is. To communicate these measurements clearly, we use standardized units that everyone understands. The Metric System The metric system is the most widely used measurement system in the world. It's based on powers of 10, which makes conversions much easier than other systems. The metric system has three main categories: length , mass (weight) , and volume (capacity) . 🔑 Golden Rule of Conversion: To convert to a SMALLER unit → MULTIPLY To convert to a LARGER unit → DIVIDE 📏 LENGTH MEASUREMENTS Length measures how long or far something is. The basic unit i...

📚 Further Calculus - Complete Guide Pure Mathematics 3| Cambridge AS & A Level 8.1 Derivative of tan⁻¹(x) Understanding tan⁻¹(x): The inverse tangent function (arctan) reverses the tangent operation. If tan(θ) = x, then θ = tan⁻¹(x) Derivation Let y = tan⁻¹(x) Then: tan(y) = x Differentiate both sides: sec²(y) × dy/dx = 1 Therefore: dy/dx = 1/sec²(y) Using identity: sec²(y) = 1 + tan²(y) = 1 + x² Result: dy/dx = 1/(1 + x²) KEY FORMULA: d/dx[tan⁻¹(x)] = 1/(1 + x²) With chain rule: d/dx[tan⁻¹(f(x))] = f'(x)/(1 + [f(x)]²) Example 1: Differentiate tan⁻¹(3x) Solution: Let f(x) = 3x, so f'(x) = 3 d/dx[tan⁻¹(3x)] = 3/(1 + 9x²) Example 2: Differentiate tan⁻¹(√x) Solution: f(x) = x^(1/2), f'(x) = 1/(2√x) d/dx[tan⁻¹(√x)] = [1/(2√x)] / [1 + x] = 1/[2√x(1 + x)] 8.2 Integration of 1/(x² + a²) The Reverse Process: Since d/dx[tan⁻¹(x)] = 1/(1 + x²), we can integrate backwards! KEY FORMULAS: ∫ 1...