Ethan's Learning Odyssey

Differential equations can be a challenging topic, but they are extremely rewarding once you understand them. My strategy is to first make sure that I am solid on the basics of calculus—especially differentiation and integration—because they are essential for solving these equations. When dealing with first-order differential equations,

Matrices are central to A-level Further Mathematics, especially when it comes to linear transformations. A useful approach is to break down your study into manageable sections. Start by reviewing matrix operations like addition, subtraction, and multiplication. Make sure to practice calculating determinants and inverses, as these are key operations in

Complex numbers are one of the most fascinating topics in A-level Further Mathematics, but they can seem tricky at first. To master this topic, the key is to start by thoroughly understanding the basics. Make sure you’re comfortable with the idea that a complex number has both a real

-level economics introduced me to different types of market structures. I studied perfect competition, where many small firms sell identical products, and monopolies, where one company dominates the market. In perfect competition, no single company has control over prices, and consumers have a lot of choices. In contrast, a monopoly

lasticity was another key topic I studied. Price elasticity of demand (PED) measures how much the quantity demanded of a good changes when its price changes. If a product has high elasticity, a small price change will lead to a large change in demand, like with luxury items. On the

One of the first concepts I learned in A-level economics was supply and demand. Demand is how much people want to buy a product, while supply is how much businesses are willing to sell. I found it interesting that the price of a product is determined by both demand and

Trigonometry has always been interesting to me, but A-level mathematics took it to a deeper level. I learned more about sine, cosine, and tangent functions, and how they relate to angles in right-angled triangles. In addition to basic triangle problems, I explored how these functions work on a unit circle,

Differentiation was a new and exciting topic for me in A-level mathematics. I learned that differentiation is a way to calculate the rate of change of a function. This is useful in many situations, such as finding the speed of a moving object or the slope of a curve at

In A-level mathematics, I learned about functions, which are rules that take an input and give an output. A key part of this topic is understanding how to represent functions on a graph. For example, a linear function forms a straight line, while a quadratic function creates a curve called

Electricity and magnetism are some of the most interesting parts of physics. While studying electric circuits, I learned that current flows when there is voltage, but resistance slows it down. In our experiments, we measured voltage, current, and resistance, which helped us confirm Ohm’s law: current is directly proportional

In the topic of energy, I learned that energy cannot be created or destroyed, only transferred from one form to another. This “law of conservation of energy” made me think about how we use electrical devices, where electrical energy is converted to light or heat. In our experiments, we used

While studying mechanics, I learned about Newton’s three laws of motion. The first law tells us that an object will remain at rest or move in a straight line at a constant speed unless acted on by an external force. This explains why a car stays still unless you

1.How to describe a wave * Wavelength λ unit:meter m Definition:Distance between two adjacent wavefronts OR Distance between two adjacent points which are oscillating in phase * Frequency f unit:Hertz Hz Definition:Number of oscillation completed per unit time * Wave speed v unit:meter/second m/s * Period

This quote suggests that involving a committee or a team in the execution or development of an idea often leads to complications, delays, and divergences from the original concept. The influx of varied opinions, bureaucratic processes, and the need for consensus might dilute or even extinguish the vitality of the