Louis La Minh Hoang

In this physics lesson, I studied lenses at a deeper level, with a strong focus on formulas and problem-solving, especially situations where either the object or the lens itself is moving. Instead of just drawing ray diagrams, we analyzed how image position, size, and nature change dynamically.

We began by revising the key lens equations, particularly the lens formula and magnification relationships. These formulas became the main tools for predicting how an image behaves when the object distance changes. Rather than treating the formulas as isolated rules, we used them to understand trends — for example, how moving an object closer to a convex lens affects image distance and magnification, and why certain positions lead to virtual or real images.

The more challenging problems involved lenses in motion. In these questions, the object or lens was gradually moved, and we had to determine how fast the image moved in response or whether the image shifted in the same or opposite direction. Solving these required careful differentiation of the lens formula and a clear understanding of sign conventions, making the problems more mathematical and less visual.

We also studied cases where the image transitions between different states, such as from real to virtual, or from inverted to upright. Identifying these critical positions required both algebraic precision and physical intuition. Some problems combined multiple ideas, such as changing magnification while keeping certain quantities fixed, which forced us to think about constraints rather than just raw calculation.

By the end of the lesson, lenses felt far more dynamic than static. The formulas were no longer just tools for finding numbers; they became a way to describe continuous change. This lesson showed how powerful mathematical analysis can be in optics, especially when understanding how small movements lead to significant changes in the final image.

This physics lesson was a focused revision on radiation, but not in a shallow, definition-based way. Instead, it was about reconnecting all the concepts together and understanding how radiation behaves quantitatively and physically in real situations.

We revisited the three main types of radiation — alpha, beta, and gamma — but the emphasis was on comparing them through their properties, not just memorizing facts. We analyzed their ionising power, penetrating ability, and behavior in electric and magnetic fields, and more importantly, why those differences exist based on charge, mass, and energy.

A major part of the revision involved radioactive decay and half-life problems. These weren’t simple plug-in questions. We had to carefully track decay over multiple half-lives, interpret decay graphs, and reason backwards to find original quantities. Understanding the shape of decay curves and what each part of the graph represents was essential.

We also worked on radiation safety and applications, but again at a deeper level. Instead of listing uses, we justified why specific types of radiation are chosen for medical imaging, cancer treatment, smoke detectors, or industrial testing. Shielding wasn’t just “paper stops alpha” — it became a reasoning problem involving energy loss and interaction with matter.

Another challenging aspect was interpreting count-rate graphs and experimental setups. We had to distinguish background radiation from source radiation, analyze measurement errors, and explain fluctuations using statistical reasoning rather than calling them “mistakes.”

By the end of the lesson, this revision tied everything together — the theory, the graphs, the calculations, and the real-world meaning. Radiation stopped feeling like isolated facts and instead became a coherent system governed by probability, energy, and physical laws. Even as a revision lesson, it required careful thinking and strong conceptual understanding, proving that radiation is simple on the surface but deep underneath.

In my physics lesson, I revised the topic of variable resistors, but this wasn’t just about knowing what a rheostat or potentiometer is. The focus was on understanding how changing resistance affects an entire circuit and how to analyze problems logically rather than mechanically.

We reviewed how a variable resistor controls current and voltage in a circuit by changing the effective length of the resistive wire. Instead of memorizing results, we examined how this change influences the distribution of potential difference across components, especially when the variable resistor is connected in series or used as a potential divider.

The problems were more challenging than basic textbook ones. Some questions required predicting how the brightness of bulbs, readings on ammeters and voltmeters, or power dissipation would change as the slider moves. These problems demanded careful reasoning using Ohm’s law, the concept of equivalent resistance, and proportional relationships, rather than simply plugging numbers into formulas.

We also dealt with scenarios involving non-ideal components, such as voltmeters with internal resistance or variable resistors affecting multiple branches in a circuit. In these cases, drawing clear circuit diagrams and identifying which quantities stayed constant and which changed was crucial to reaching the correct conclusion.

By the end of the revision, I felt much more confident about variable resistors. They may seem simple at first, but when used in complex circuits, they become a powerful tool for testing understanding of electricity as a whole. This lesson reinforced how important logical thinking and clear analysis are in physics — even for topics that appear straightforward at first glance.

In this lesson, my focus was on probability, but not the simple kind where you just count outcomes and divide. This was the more challenging, thinking-heavy probability that requires careful logic, structured reasoning, and sometimes surprisingly tricky calculations.

We started by revising the fundamental ideas, such as sample spaces and events, but quickly moved into more complex situations where outcomes are not independent and simple intuition can easily fail. Many problems required breaking situations into multiple stages and tracking probabilities step by step, making sure nothing was double-counted or missed.

A major part of the lesson involved conditional probability, where the probability of an event depends on another event having already occurred. These problems were difficult because they forced me to rethink the sample space after new information was given. Understanding how the “universe of outcomes” changes was more important than any formula.

We also worked on problems involving combinations of events, such as drawing objects without replacement, arranging outcomes in different orders, or finding probabilities that involved several conditions at once. These questions often looked simple at first but turned out to be deceptive, requiring careful case analysis and strong organizational skills.

Some of the hardest questions involved hidden symmetry or complementary probability, where the easiest way to solve the problem was not to calculate the desired probability directly, but instead to find the probability of the opposite event and subtract from 1. This approach saved time but demanded deep understanding of what outcomes were actually being excluded.

By the end of the lesson, it was clear that probability at this level is less about formulas and more about clear thinking and logical structure. Every assumption matters, every condition changes the problem, and a single oversight can lead to a completely wrong answer. Even though the problems were tough, working through them made probability feel more precise, elegant, and intellectually satisfying.

In my recent math lesson, I focused on revising and extending my understanding of the Binomial Theorem, a topic that looks simple at first but becomes much more powerful and challenging when applied to harder problems.

We started by revisiting the basic idea of expanding expressions of the form $(a + b)^n$(a+b)n. Instead of just writing out expansions mechanically, we examined how each term is formed, how coefficients arise, and why the pattern works. Understanding the structure behind the theorem made the expansions feel logical rather than memorized.

The lesson quickly moved into more advanced territory. We worked with large powers, where direct expansion is impossible, and relied on binomial coefficients, combinations, and careful term selection. A major focus was learning how to find a specific term in an expansion without writing out everything, which required precision and strong algebraic reasoning.

We also explored harder applications, such as problems involving variables, fractional coefficients, and conditions placed on certain terms. Some questions combined the binomial theorem with inequalities or required comparing coefficients, which demanded both creativity and accuracy.

By the end of the lesson, I realized that the binomial theorem isn’t just about expansion — it’s a powerful tool for problem-solving. When used correctly, it simplifies complex expressions and opens the door to solving challenging algebraic problems efficiently. This session really strengthened my confidence in handling higher-level binomial questions and seeing the deeper structure behind them.

In this chemistry lesson, I focused on a full-scale revision of all major topics, bringing together concepts we have learned over time rather than studying them separately. This kind of revision was challenging, not because the ideas were unfamiliar, but because it required switching quickly between different areas of chemistry and applying the right concepts in the right situations.

We reviewed atomic structure, including electron configurations and periodic trends, which form the foundation for understanding reactivity. From there, we revisited bonding — ionic, covalent, and metallic — and how bond type affects properties such as melting point, conductivity, and solubility. These ideas were constantly linked back to structure, forcing careful reasoning rather than memorization.

A large part of the revision focused on chemical reactions. This included reaction types, balancing equations, predicting products, and understanding why reactions occur rather than just what happens. We also revised acids, bases, and salts, paying attention to pH changes, neutralization, and the role of indicators, especially in experimental and calculation-based questions.

We moved on to metals and reactivity, comparing extraction methods and displacement reactions, and then to organic chemistry, where we revised functional groups, naming rules, and reaction pathways. Even small mistakes in identifying a compound could completely change the direction of a problem, so accuracy was essential.

Finally, we reviewed energetics and rates, focusing on interpreting energy changes, reaction profiles, and factors affecting reaction speed. Many questions combined multiple topics at once, which made the revision demanding but effective.

Overall, this lesson helped me see chemistry as a connected system rather than isolated chapters. Revising everything together strengthened my understanding and made it clear how important it is to think logically and apply concepts carefully, especially when dealing with complex, mixed-topic problems.

This lesson on inequalities went far beyond the basic “solve and draw a number line” approach. We focused on hard inequalities that require careful reasoning, transformations, and a strong sense of structure rather than quick calculations. It felt much more like problem-solving than routine algebra.

We worked with polynomial and rational inequalities, where the key challenge was not solving equations, but understanding how the sign of an expression changes across different intervals. Instead of blindly moving terms around, we had to factor expressions completely, identify critical points, and analyze each interval one by one. A single mistake in sign analysis could flip the entire solution.

Some problems involved absolute value inequalities, where the expression had to be split into multiple cases. These were tricky because they forced us to think logically about what the inequality really means, not just apply a formula. Other questions combined inequalities with functions, requiring us to consider domains, undefined points, and how graphs behave relative to the x-axis.

The hardest problems were those that looked simple at first but hid subtle traps—like extraneous solutions or intervals that must be excluded. Solving them demanded patience, clear structure, and a solid understanding of why each step was valid.

By the end of the lesson, I realized that advanced inequalities are less about computation and more about logical control. Every inequality tells a story about how expressions behave, and solving them means understanding that behavior deeply. It was challenging, but extremely satisfying when everything finally fit together.

In my recent physics lesson, we shifted our focus away from Earth and into the vast universe with the topic of space physics. This lesson felt especially exciting because it connected physics with astronomy, turning equations and concepts into explanations for real cosmic phenomena.

We began by studying gravitational fields and orbital motion, understanding how planets, moons, and satellites move under gravitational forces. Instead of just using formulas, we focused on the reasoning behind stable orbits, escape velocity, and why objects in space experience weightlessness even though gravity is still acting on them. The idea that continuous free fall creates orbiting motion was a key insight.

We also explored motion in space, where there is little to no air resistance. This made Newton’s laws much clearer and more powerful, as objects continue moving unless acted upon by a force. Problems often involved analyzing spacecraft trajectories, velocity changes during maneuvers, and how small forces applied over long periods can significantly alter motion.

Another important part of the lesson was energy in space systems, especially gravitational potential energy. We examined how energy changes as an object moves farther from or closer to a planet, and how this affects satellite speed. These concepts required careful thinking rather than heavy calculation, since the challenge was visualizing motion on a massive, cosmic scale.

We also touched on space-related phenomena such as artificial satellites, space stations, and basic ideas behind rockets. Understanding how thrust, mass, and fuel efficiency interact helped explain how humans can send objects beyond Earth despite gravity’s pull.

Overall, this lesson showed me that space physics is not just abstract theory. It is a powerful application of core physics ideas, extended to extreme scales. Studying it made me appreciate how the same laws we learn in class govern everything from a falling object on Earth to the motion of planets across the universe.