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...