Golden Education

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...

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...

Quiz 1: Fullscreen Mode Other note source Quiz 2: Fullscreen Mode Chapter 20: Experimental Techniques & Chemical Analysis This guide covers the essential theory, apparatus, and chemical tests required for IGCSE Chemistry analysis. 20.1 Experimental Design (Measurement) 1. Units of Measurement Time: S.I. Unit is the Second (s). Measured with stopwatches (accuracy ± 0.01s). Temperature: Kelvin (K) or Celsius (°C). Mass: Kilogram (kg) or gram (g). Measured with electronic balances. Volume: Cubic meter (m 3 ), dm 3 , or cm 3 . Temp (K) = Temp (°C) + 273 1 kg = 1000 g 1 dm 3 = 1000 cm 3 2. Measuring Liquid Volume Apparatus Accuracy Use ...

Other note source 📚 SEQUENCES, SURDS & SETS Cambridge IGCSE Mathematics 📊 9.1 SEQUENCES Definition & Notation Sequence: A list of numbers following a specific rule. Each number = term . T₁, T₂, T₃ = 1st, 2nd, 3rd terms Tₙ = nth term (general term) Types of Sequences Type Rule Example Formula Arithmetic Common diff (d) 2,6,10,14 Tₙ=dn+c Geometric Common ratio (r) 3,6,12,24 Tₙ=ar^(n-1) Quadratic 2nd diff constant 2,5,10,17 ...

Other note source Quiz 1:   Fullscreen Mode Quiz 2: Fullscreen Mode Alcohols & Carboxylic Acids IGCSE Chemistry 18.1 Alcohols Alcohols are a homologous series of organic compounds containing the elements Carbon, Hydrogen, and Oxygen. Functional Group: Hydroxyl group ( -OH ). General Formula: C n H 2n+1 OH . Molecular Shape: The bonding around the oxygen atom is bent (V-shaped), similar to water. Example: Ethanol (C 2 H 5 OH) H H | | H - C - C - O - H | | H H Physical Properties As the carbon chain length increases (Methanol → Butanol): Boiling Point: Increases. Solubility in Water: Decreases (Methanol is very soluble; Butanol is only slightly soluble). Volatility: Decreases (they evaporate les...

Quiz 1: Fullscreen Mode Other Quiz Other note source Alkanes and Alkenes A comprehensive summary of Hydrocarbon theory, bonding, and chemical reactions. 1. Alkanes Definition: Alkanes are a homologous series of hydrocarbons that contain only carbon-carbon single covalent bonds . Because they contain only single bonds, they are known as Saturated Hydrocarbons . Each carbon atom is bonded to the maximum number of atoms (four). C H H H H ...

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...