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Differential equations

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              Other note source      📚 DIFFERENTIAL EQUATIONS Cambridge AS & A Level Mathematics (Chapter 10) Sections 10.1 - 10.2: Separating Variables & Forming Equations 🎯 What is a Differential Equation? Definition: An equation containing derivatives such as dy/dx or d²y/dx² is called a differential equation . KEY CONCEPT: The solution of a differential equation is a function , not just a number! Types of Solutions Solution Type Description Example General Solution Contains arbitrary constant(s) y = x³ + C Particular Solution Specific solution using initial conditions y = x³ + 5 First-Order Differential Equation: Contains only dy/dx (first derivative) Example: dy/dx = 3x² Differential Equation General Solution Particular Solution 🔧 Section 10.1: Separation of Variables The Basic Method STEP-BY-STEP PROCEDURE: Separate the variables: Rearrange to get f(y)...
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Polymers IGCSE

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Quiz 1: Fullscreen Mode Quiz 2: Fullscreen Mode 🧪 POLYMERS - Complete Notes Cambridge IGCSE Chemistry | Chapter 19 1️⃣ What are Polymers? POLYMER = A very large molecule made from many small repeating units called monomers MONOMER = A small molecule that joins to other monomers to form a polymer POLYMERISATION = The process of joining monomers to form a polymer M + M + M Polymerisation M M M ... Monomers Polymer 📊 Types of Polymers Natural Polymers Synthetic Polymers ✓ Proteins (meat, eggs) ✓ Poly(ethene) (plastic bags) ✓ Starch (rice, bread) ✓ Poly(propene) (ropes) ✓ Natural rubber ✓ PVC (pipes) ✓ Silk ✓ Nylon (clothing) ✓ Cellulose ✓ PET (bottles) 2️⃣ Addition Polymerisation Addition polymerisation occurs...
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Straight lines and quadratic equations

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Other note source 📐 STRAIGHT LINES & QUADRATIC EQUATIONS Cambridge IGCSE Mathematics - Quick Reference Guide PART 1: STRAIGHT LINES 📊 Standard Form y = mx + c m = gradient (slope/steepness) c = y-intercept (crosses y-axis) x, y = coordinates Example: y = 3x + 2 • Gradient = 3 (rises 3 for every 1 across) • Y-intercept = 2 (crosses at (0,2)) Gradient Formula m = (y₂ - y₁) / (x₂ - x₁) Type Value Direction Positive m > 0 ↗ Up right Negative m ↘ Down right Zero m = 0 → Horizontal Undefined - ↑ Vertical Example: Points (2, 4) and (6, 12) m = (12 - 4)/(6 - 2) = 8/4 = 2 Special Lines Horizontal: y = k (e.g. y = 3) Vertical: x = k (e.g. x = -2) Parallel Lines Same gradient: m₁ = m₂ Lines y = 2x + 1 and y = 2x - 5 are parallel (both m = 2) Perpendicular Lines m₁ × m₂ = -1 or m₂ = -1/m₁ Line 1 Line 2 (⊥) m = 2 m = -½ m = 3 m = -⅓ m = -4 m = ¼ Intercepts Y-intercept: Set x = 0, solv...
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