Golden Education

Other Source Ringkasan Teori & Rumus Variabel Acak Kontinu 1. Definisi Variabel Acak Kontinu Variabel acak kontinu X dapat memiliki nilai apa pun dalam interval kontinu . Contoh: tinggi badan, waktu tunggu, suhu, laju peluruhan radioaktif. 2. Fungsi Kepadatan Peluang (PDF) Syarat PDF f(x) : 1. f(x) ≥ 0 untuk semua x 2. ∫ -∞ ∞ f(x) dx = 1 (total luas = 1) Grafik PDF f(x) x 3. Menghitung Peluang Karena P(X = a) = 0 , peluang hanya bisa dihitung untuk interval: P(a ≤ X ≤ b) = ∫ a b f(x) dx Untuk grafik sederhana bisa juga dengan geometri (luas segiempat, trapesium, segitiga). 4. Nilai Tengah (Median) Median m adalah nilai yang memenuhi: ∫ -∞ m f(x) dx = 0.5 Intuisi: letak vertikal yang membelah luas kurva menjadi dua bagian sama besar. 5. Persentil Umum Persentil- p (0 < p < 1) adalah q sedemikian hingga: ∫ -∞ q f(x) dx = p 6. Nilai Harapan (Mean) E(X) = μ = ∫ -∞ ∞ x f(x) dx 7. Varia...

Quiz 1: Fullscreen Mode Other Quiz Lines, Angles and Shapes - Theory and Formulas 3.1 Lines and Angles Types of Angles Angles can be classified based on their size: Type Size Example Acute angle Less than 90° 30°, 45°, 70° Right angle Exactly 90° Corner of a book Obtuse angle More than 90° but less than 180° 100°, 120°, 150° Reflex angle More than 180° but less than 360° 200°, 270°, 300° Special Pairs of Angles Complementary Angles: Two angles that add up to 90° . Supplementary Angles: Two angles that add up to 180° . Fundamental Angle Rules Angles on a Straight Line: The sum of angles on a straight line is 180° . ∑ ∠ on line = 180° Angles Around a Point: The sum of all angles around a single point is 360° . ∑ ...

Logarithmic & Exponential Functions All-in-One Theory Sheet 2.1 Logarithms to Base 10 Definition: If 10 x = y , then log 10 y = x (written log y for short). ┌-----┐ │ 10 │ │ ^ │ ← Exponent │ y │ └-----┘ log 1000 = 3 because 10³ = 1000 log 0.01 = –2 because 10 –2 = 0.01 2.2 Logarithms to Any Base a Definition: If a x = y with a > 0 and a ≠ 1 , then log a y = x . log₂ 32 = 5 because 2⁵ = 32 log₅ 1 = 0 because 5⁰ = 1 2.3 The Three Laws of Logarithms ┌-------┐ │ Laws │ └-------┘ Product: log a (xy) = log a x + log a y Quotient: log a (x / y) = log a x – log a y Power: log a (x n ) = n log a x 2.4 Solving Logarithmic Equations Golden Rule: Logs only exist for positive numbers. Use the laws to get a single log on each side. Drop the log...

Quiz 1:   Fullscreen Mode Chapter 16: Electrical Quantities – Theory and Formulas 16.1 Electric Charge Atoms contain: Protons – Positive charge Neutrons – No charge Electrons – Negative charge An atom is neutral when it has equal numbers of protons and electrons. Charging by Friction Electrons transfer from one material to another. The material that loses electrons becomes positively charged, and the one that gains electrons becomes negatively charged. Interaction of Charges Like charges repel Unlike charges attract Conductors and Insulators Conductors : Allow electrons to move freely (e.g., metals) Insulators : Hold electrons tightly (e.g., plastic, glass) 16.2 Electric Field An electric field is a region where a charge experiences a force. Field Line Directions Positive charge : Field lines point away Negative charge : Field lines point toward Field Strength Stronger where field lines are closer together. ...

Scientific Notation Quiz Scientific Notation By Mr Agus Salim Score: 0 / 100 Question 1 of 20 Convert the following number to scientific notation: 23500 Answer in format: a.bc × 10^n Enter each digit and exponent separately below: First digit (a): Second digit (b): Third digit (c): ...

Represent as Simplest Fraction By Mr Agus Salim Represent as Simplest Fraction By Mr Agus Salim Question 1 / 20 = / Submit Finish! Reset Additional Quiz Represent as Simplest Fraction Handout for Grade 8-10 Students Key Points Converting decimals to simplest fractions involves turning terminating decimals (e.g., 0.75) and repeating decimals (e.g., 0.666...) into fractions and simplifying them. Terminating decimals are converted by writing them as fractions with denominators as powers of 10, then simplifying. Repeating decimals use an algebraic method to eliminate the repeating part. Simplifying fractions requires finding the greatest common divisor (GCD) to reduce the fraction to its simplest form. Converting Terminating Decimals Terminating decimals, like 0.75, end after a finite number of dig...

Quiz 1:   Fullscreen Mode Other Quiz 🧪 METALS & REACTIVITY SERIES: Complete Theory & Formulas 🔬 I. FUNDAMENTAL THEORIES OF METALS 1.1 Electronic Theory of Metallic Bonding Sea of Electrons Model: Metals consist of a lattice of positive metal ions surrounded by a "sea" of delocalized electrons. This explains conductivity, malleability, and ductility. Metal Atom → Metal Ion⁺ + e⁻ M(s) → M⁺(aq) + e⁻ (general form) 1.2 Density Theory & Formula Density is a fundamental physical property that measures mass per unit volume. Density = Mass ÷ Volume ρ = m/V (g/cm³ or kg/m³) High Density Examples Gold: 19.3 g/cm³ Lead: 11.4 g/cm³ Copper: 8.9 g/cm³ ...

Quiz Other Quiz Using Moles - Complete Theory & Formulas Cambridge IGCSE Chemistry - Grade 9 1. The Mole Concept - Core Theory Definition of a Mole A mole is the amount of substance that contains as many elementary entities (atoms, molecules, ions) as there are atoms in exactly 12 grams of carbon-12 . Avogadro's Constant N A = 6.022 × 10 23 mol -1 This means 1 mole of any substance contains 6.022 × 10 23 particles Key Principle: One mole of any substance contains the same number of particles, but the mass depends on the type of particle. 2. Fundamental Formulas 2.1 Mole-Mass Relationship Number of moles (n) = Mass (m) ÷ Molar mass (M) n = m/M Mass (g...