Quiz 1   Fullscreen Mode Discrete Random Variables and Probability Distribution Discrete Random Variables A discrete random variable is a variable whose values are countable or finite, and these values occur randomly. Examples include: The number of broken eggs in a carton. The number of sixes rolled when throwing four dice. Characteristics of Discrete Random Variables Values are integers (e.g., 0, 1, 2, etc.). Each value has a specific probability of occurring. For example, when flipping two coins, the number of heads that appear is a discrete random variable X , with possible values X ∈ {0, 1, 2} . Probability Distribution A probability distribution describes the likelihood of each value of a random variable. For discrete random variables, the probability distribution can be presented as a table, bar graph, or function. Example: Flippin...

Audio Podcast Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode  5.2.1 Detection of radioactivity ## Radioactivity Detection Radioactivity is the process of releasing radiation from an unstable atomic nucleus. We are all exposed to radiation from various sources every day. Let's discuss some important things about radioactivity: ## Background Radiation Sources Background radiation comes from a variety of sources, both natural and artificial: - Cosmic rays from the sun - Radon gas in the air - Radon-containing granite rocks - Potassium-40 in food - Medical procedures that use radioisotopes - Nuclear power plants and the rest of the nuclear bomb tests ## Ionization Effect Radiation can cause ionization, which is the process of releasing electrons from atoms or molecules. This can be evidenced by: Electroscope Experiments: - When a fire or radium source is brought close to a charged electroscope, the charge is lost - Fire or radiation causes air molecules...

Quiz 1   Fullscreen Mode Further Differentiation Further Differentiation 1. Increasing and Decreasing Functions A function y = f(x) is: Increasing : If dy/dx > 0 throughout the interval. Decreasing : If dy/dx < 0 throughout the interval. 2. Stationary Points Stationary points , also known as turning points, occur when: dy/dx = 0 3. First Derivative Test for Maximum and Minimum Points At a maximum point: dy/dx = 0 The gradient is positive to the left and negative to the right of the point. At a minimum point: dy/dx = 0 The gradient is negative to the left and positive to the right of the point. 4. Second Derivative Test for Maximum and Minimum Points If dy/dx = 0 and d²y/dx² < 0 , the point is a maximum. If dy/dx = 0 and d²y/dx² > ...

Quiz 1   Fullscreen Mode Differentiation Rules and Concepts Differentiation Rules and Concepts Gradient of a Curve The gradient of a curve is represented as: dy/dx This represents the rate of change of the curve \( y = f(x) \). The Four Rules of Differentiation 1. Power Rule If \( y = x^n \), then: d/dx (x^n) = n * x^(n-1) 2. Scalar Multiple Rule If \( y = kf(x) \), where \( k \) is a constant, then: d/dx [kf(x)] = k * d/dx [f(x)] 3. Addition/Subtraction Rule If \( y = f(x) ± g(x) \), then: d/dx [f(x) ± g(x)] = d/dx [f(x)] ± d/dx [g(x)] 4. Chain Rule If \( y = f(u) \) and \( u = g(x) \), then: dy/dx = (dy/du) * (du/dx) Tangents and Normals ...

Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode Fundamentals of Magnets Magnets are objects that have two poles - a north (N) pole and a south (S) pole. Every magnet always has these two poles, and cannot have only one pole (Ruoho & Arkkio, 2008). Properties of Magnets: Like poles repel each other Opposite poles attract each other The strength of the magnetic force decreases as the distance increases Magnetic Field The magnetic field is the region around a magnet where the magnetic force can still be felt. The strength of the magnetic field is shown by the magnetic field lines: The closer the field lines, the stronger the magnetic field The direction of the magnetic field is always from the north pole to the south pole Types of Magnetic Materials Magnetic Materials: Examples are iron, steel, nickel, and cobalt Can be attracted by magnets Can be magnetized Non-magnetic Materials: Examples are aluminum and wood Cannot be attr...

Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode The Speed or Rate of the Reaction The Speed or Rate of the Reaction The rate of a chemical reaction is a measure of how quickly reactants are converted into products. In everyday life, reactions can vary significantly in speed; for instance, the formation of silver chloride precipitate when silver nitrate is mixed with sodium chloride occurs almost instantaneously, while the rusting of iron is a slow process that can take years. The rate of reaction can be quantified by measuring the change in concentration of reactants or products over time. For example, when zinc (Zn) reacts with sulfuric acid (H 2 SO 4 ), the rate can be assessed by the volume of hydrogen gas (H 2 ) produced per unit time. One of the simplest methods to determine the rate of reaction is to measure the volume of gas produced using a gas syringe. Various factors influence the rate of reaction, includin...

Quiz 1:   Fullscreen Mode Quiz 3:   Fullscreen Mode Electricity And Chemical Change: Electrochemistry Electricity And Chemical Change: Electrochemistry 1 Conductors and Insulators Testing Conductivity We can test whether a substance conducts electricity by inserting it into a simple electrical circuit consisting of a battery, wires, and a light bulb. If the bulb lights up, the substance is a conductor. If the bulb does not light up, the substance is an insulator. Testing Results Metals and graphite are solid conductors: Example: Tin conducts electricity when tested. Reason: The presence of free electrons that can move. Molecular substances do not conduct electricity: Example: Ethanol does not conduct electricity when tested. Reason: There are no charged particles that can move freely. Ionic substances have special proper...

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Quiz 1:   Fullscreen Mode Teori dan Rumus Ikatan Kimia Teori dan Rumus Ikatan Kimia A. Kestabilan Unsur-Unsur Konfigurasi elektron beberapa unsur gas mulia: Nama Unsur Nomor Atom Konfigurasi Elektron Gambar Susunan Elektron Elektron Valensi Helium 2 2 2 Neon 10 2.8 8 Argon 18 2.8.8 8 Aturan Duplet: konfigurasi elektron stabil dengan dua elektron pada kulit terluar. Aturan Oktet: konfigurasi elektron stabil dengan delapan elektron pada kulit terluar. Pada saat atom-atom membentuk ikatan, hanya elektron-elektron pada kulit terluar yang berperan yaitu elektron valensi. Elektron valensi dapat digambarkan dengan struktur Lewis atau gambar titik elektron. B. Ikatan Ion Pembentukan Senyawa NaCl: Pembentukan Senyawa C...