Free essays on Science are written pieces that discuss various scientific aspects, theories, discoveries, and advancements. These essays may focus on different scientific disciplines, such as biology, chemistry, physics, astronomy, or earth and environmental sciences. They are usually informative, engaging, and present arguments and evidence in a logical and clear manner, backed up by relevant scientific data and research findings. Free essays on Science also explore the impact of science on our daily lives, society, economy, and the natural environment. They offer insights into how science shapes our worldviews, and how scientific facts and principles can inform decision-making and policy formulation.
Inequalities and Equivalence: Less-than and Greater-than
Less-than and Greater-than We're going to start with inequalities, beginning with a short introduction. This lecture will give you the basic idea behind symbols like < b, x > y and c ≤ d. The first four of these are really well-defined mathematical concepts. Inequalities, Basic Ideas a<b c<=d x<y z=>w e<<f Let's start from the top and draw a real number line. And suppose here is 0, here is the number 2. here is the number 3.1, and let…...
Science
Simplifying Equations for Analysis
Rearranging the formula The equations we have to solve are as follows: <=>{sum_(i=1)^n (X_i^2 a+X_i b-X_iY_i)=0 {sum_(i=1)^n (X_i a+b-y_1)=0 So the first equation can be simplified by looking at the coefficients of a and b. You'll see that there are actually linear equations in a and b, so there's a lot of clutter with all these x's and y's all over the place. Let's simplify the formula by dividing out the factors of two. We can eliminate a and b…...
Calculus
L’Hopital’s Rule. Example Problem
L'Hopital's Rule. Example Problem lim_(x->0) (cos(3x)-e^4x)/(x^2 -3x) lim_(x->0) (-3sin(3x)-4e^4x)/(2x-3)=-4/-3 =4/3 Let us consider the following example of L'Hopital's rule. If you evaluate the cosine of 0, you get 1. The exponential of 0 is 1, divided by 0 minus 0 - we get 0/0. Factoring probably won't work, since there are no algebraic methods or anything that will help us. We'll use L'Hopital's rule instead. Thus, we take the derivative of the numerator (3sin3x), times 3 because of the chain…...
Calculus
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Calculus: Parallel Lines
Parallel lines Parallel and perpendicular lines are defined as follows: Parallel lines- two or more lines that do not intersect with each other, no matter what distance you move them. Perpendicular lines- two or more lines that intersect at a 90 degree angle. What if we don't have a line that's exactly equal to 0? Rephrasing, instead of x + 1/2 y = 0, what if we had x + 1/2 y = 1? Consider having the line x plus…...
Calculus
Finding the Rotated Vector: Solving for w in Various Cases
Rotating a Vector Here's the problem: Let v denote a vector that has initial position v1 and final position v2. We know these two numbers. Now suppose we rotate v counterclockwise by an angle theta. The result is a new vector, denoted by w, that also has initial position v1 and final position v2. Let's say that we rotate vector v by an angle theta. If we do this, our new vector becomes w. The problem we are going to…...
Calculus
Derivatives of Exponential and Natural Log Functions
Derivatives of Exponential and Natural Log Functions We will introduce the concept of early transcendentals now, and then vou will learn more about them as we go along. We'll just incorporate them into our existing knowledge of products, quotients and derivatives. Now we will examine the derivatives of e to the x and natural log of x. Let's begin by doing e to the x. There are many ways to prove this. One definition of e is 1 plus x…...
Calculus
Tangent Lines and Instantaneous Rate of Change
Definition of Derivative A tangent line is the straight line that touches a curve at just one point. Tangent lines are central to calculus and have been since the 17th century. Today, we'll examine the problem of determining tangent lines for functions. The two fundamental questions addressed in calculus are: (1) What is the area under a curve, and (2) what is the slope of a line? In Algebra I, we learned that the slope of a function equals the…...
Calculus
Derivatives of Inverse Functions
Derivatives of Inverse Functions Let us assume that we have a function fox, and let us call it 3x - 1. We want to establish some sort of relationship between the slope of f and the slope of its inverse. To do this, we take these two functions and switch their x-variables and y-variables. This is all basic algebra. Next, we solve for y by adding x to one side of the equation and dividing by 3. After that, we…...
Calculus
Particle Motion. Example Problem 2
Particle Motion. Example Problem 2 An object moves along the y-axis such that its position is given by y(†) = t^3 - 12t^2 + 21t - 3 at what time does the object change direction? v(t)=0 y'(t)=3t^2-24t+21=0 t^2-8t+7=0 (t-1)(t-7)=0 t=1, 7 Given an object moving on the y-axis, its position is described by this equation. At what time does the object change direction? I believe you will find that the concepts of position, velocity, and acceleration-as they relate to particles--are…...
Calculus
Linear Approximation and Perpendicular Vectors
Linear approximation You already know about about functions of several variables and linear approximation Also, you are familiar with vectors. Now we'll unite those concepts. Let's review linear approximation. Here is some complicated function, fof (x,y). F(x,y) The function is complicated, but if we take a little box in the xy- plane, then inside of this box the function is well approximated by something way less difficult. It is almost equal to an expression of the form ax + by…...
Calculus
Review Critical Points
Review critical points A critical point is a point where the partial derivatives are both O. In this lecture, we will continue to explore critical points and learn how to actually decide whether a particular point is a minimum, maximum, or sadale point. There are various kinds of critical points. Local minima, local maxima, which are like that, and saddle points which are neither minima nor maxima. And, of course, if you have a real function, then it will be…...
Calculus
IGCSE Geography: Storm Hydrograph of a river and River Regimes
IGCSE Geography: Storm Hydrograph of a River and River Regimes Hydrographs: A Hydrograph is a popular way of representing data for geographers, and to get a good understanding in the RIVERS topic, you must be able to know its features. Definition: A Hydrograph shows the discharge of a river as well as its total rainfall over a period of time, before, during, and after the storm. Linkages and analysis can thus be made, e.g., more rainfall, faster discharge, etc. Discharge:…...
Geography
IGCSE Geography: Flooding: Why it happens, and how to prevent it
IGCSE Geography: Flooding - Why it happens, and how to prevent it Flooding: Causes of Flooding: Precipitation - Rain, Snowmelt: High levels of precipitation can cause a river to burst its banks and flood. Steep Slopes - Gradient of Land: If land is particularly steep, normal storm events may escalate into small floods. This is due to a short lag time. When there is rain, the steepness of the land means that not long after, there will be discharge or…...
Geography
IGCSE History: World War I – Why did the Schlieffen Plan fail?
IGCSE History: World War I – Why did the Schlieffen Plan fail? Why did the Schlieffen Plan fail? BEF (British Expeditionary Force): 18th August 1914: BEF arrived in France under the command of Sir John French. It had arrived faster than expected. This prompted von Moltke to draw forces from the Eastern Front. The Kaiser thought it was a 'contemptible little army.' It was small but excellently trained. 23rd August 1914: Battle of the Mons. The Germans were slowed. The…...
History
IGCSE History: Big Three
IGCSE History: Big Three The Big Three: The fate of the losers (Central Powers – Germany, Turkey, Hungary, etc.) and Wilson's Fourteen Points were discussed in the Paris Conferences held in January 1919. Referred to the Prime Ministers/Presidents of America, Britain, and France (the victorious countries of WWI) – remember, the formation of the Big Three changes after WWII, do not get confused. All leaders had their own objectives, depending on their degree of hatred of Germany and their views.…...
History
IGCSE History Arab-Israeli Conflict
IGCSE History Arab-Israeli Conflict First Arab-Israeli War: 1948-9 Causes When Israel was formed on 14th May 1948, none of the Arab states acknowledged its existence, thus forming a coalition to invade and re-take Palestine. What happened? 14th May 1948, David Ben-Gurion announced the formation of Israel. Arab states (Egypt, Lebanon, Jordan, and Syria) subsequently invaded with 30,000 troops. The Arab Legion, the most experienced and well-equipped, took over the Old City of Jerusalem. USA. UN cease-fire ordered on 11th June,…...
History
IGCSE History: Hitler’s War
I/GCSE History: Hitler’s War Introduction: Part of the reason why Hitler, Mussolini, and Japan all wanted to grow and annex land was to lift their economies out of the Great Depression. In March 1939, Germany invaded the rest of Czechoslovakia: No resistance from Britain or France. Convinced Britain and France that appeasement had failed: Chamberlain said that 'after this I cannot trust the Nazi leaders again.' On the 31st, Britain declared that it would stand by Poland in the event…...
History
Statistics for IGCSE/ O-level students
Statistics for IGCSE/O-level Students Introduction Statistics is a very important section of mathematics. However, it can get quite deep, as it is, after all, statistics. However, this statistics course will not be too deep, and this lesson is literally a breeze for those with some exposure to statistics. Terms Mean In this case, we are referring to the arithmetic mean, which is basically the sum of all values in a data sample divided by the number of values. Example: 1,…...
Statistics
IGCSE History: World War I – Sir Douglas Haig
IGCSE History: World War I – Sir Douglas Haig Sir Douglas Haig: Alternatively called the Somme Butcher. Strategies: Believed in the policy of attrition. Tactics were clumsy, costly in resources. Believed that defense could not bring victory. Haig's method was the best possible considering that he did not have hindsight or anything else to rely on. His tactics prepared the route to Allied victory. Haig's methods at the Somme achieved: Saving the fortified town of Verdun. Taking the pressure off…...
History
IGCSE Economics: Introduction to Economics
IGCSE Economics: Introduction to Economics The basic problem of economics is scarcity, which is the presence of limited resources but unlimited demand. Economics determines how resources are distributed because there are simply insufficient resources to satisfy everyone's needs. Even in rich countries, you can see poor people. Economics is the study of how to make the best use of the resources we have. It's also about increasing people's choices, allowing them to see that there are other ways they can…...
Economics
IGCSE Coordinated Science: Energy
IGCSE Coordinated Science: Energy Energy Know that energy and work are measured in joules (J), and power in watts (W). The energy of an object is measured in Joules (J). 1000 Joules = 1 kilojoule (kJ). The power of an object is measured in Watts (W). 1000 Watts = 1 kilowatt (kW). Demonstrate understanding that an object may have energy due to its motion (kinetic) or its position (potential), and that energy may be transferred and stored. All objects have…...
Physics
IGCSE Coordinated Science: Electrical Energy
IGCSE Coordinated Science: Electrical Energy Electrical Energy Recall and use the equations: P = IV and E = IVt. You might need to know these two equations for the exam. The first one is: P = IV (Unit: Watts) P is power, I is Electric Current (measured in Amps), and V is Potential difference (Voltage, measured in Volts). Units for power is Watts. This is also known as Joule's Law. The second one is: E = IVt (Units: Joules) E…...
Physics
IGCSE Coordinated Science: Consequences of Energy Transfer
IGCSE Coordinated Science: Consequences of Energy Transfer Identify and explain some of the everyday applications and consequences of conduction, convection, and radiation: In our everyday environment, conduction, convection, and radiation are constantly taking place. They have many applications and can be very useful. Some examples include: When we heat up pots and pans, the thermal energy is transferred through conduction. Air conditioners use convection currents to cool the indoor environment. When heating up water, the heat is applied from below,…...
Chemistry
IGCSE History: World War I – Reasons for the Gallipoli Campaign
IGCSE History: World War I – Reasons for the Gallipoli Campaign Reasons for the Gallipoli Campaign: Russia was nearing defeat in early 1915 (winter): The only route for British troops to reach her was through the sea of Marmara and Russia's Black Sea ports: All other ports were frozen. If Russia fell, Germany would be greatly strengthened. Turkey needed to be forced from the war: It was allied with Germany. By forcing Turkey from the war, it was possible this…...
History
IGCSE Mathematics: How to find the quadratic functions with information given
IGCSE Mathematics: How to find quadratic functions with given information. IGCSE may provide you with: Vertex and another point x-intercepts and a point Vertex or intercepts with a = 1 Remember: y = a(x - h)² + k - this is known as the vertex form of a quadratic function. a is the constant. (h, k) is the coordinate of the vertex. Vertex forms have their uses, as you should be aware of: If a < 0, we have a…...
Mathematics
Thermal Expansion of Solids, Liquids and Gases
IGCSE Coordinated Sciences: Thermal Expansion of Solids, Liquids, and Gases Thermal Expansion of Solids, Liquids, and Gases Describe qualitatively the thermal expansion of solids, liquids, and gases. Solids: A solid gains kinetic energy and starts to vibrate more vigorously when thermal or heat energy is applied to it. As a result, the solid expands slightly in all directions. Liquids: When a liquid is heated, the volume of the liquid increases as a result of the molecules having more kinetic energy.…...
Physics
Coordinated Science: Evaporation
IGCSE Coordinated Science: Evaporation Evaporation Evaporation mostly occurs at the surface of a liquid, and for evaporation to occur, the molecules must have enough kinetic energy. First, let's define the word Evaporation. Evaporation is basically the change of state of a substance from liquid to gas. If you look back into the Topic "States of Matter," you will notice that the particles in a liquid are stuck quite close together, whereas the particles in a gas are scattered all over…...
Physics
COM231 – Chapter 5 Discussion Board A30
ROSHAAN AMEER DISCUSSION PUBLIC SPEAKING "first, state the point you are answering. Second, state the point you wish to make. Third, support your point with appropriate statistics, examples, or testimony. Fourth, summarize your point." pg 233 This text in the textbook was selected because it gives a simple but useful layout for speaking impromptu. It gives a clear layout on how to effectively respond to a previous speaker, class discussion, or when saying "a few words". This is important…...
Public Speaking
IGCSE Coordinated Science: Mass and Weight
IGCSE Coordinated Science: Mass and Weight Mass and Weight Difference between Mass and Weight Weight is the gravitational pull on an object measured in Newtons because it is the amount of force. This is different on different planets because the gravitational pull is different due to the different mass of the planet. Mass is the amount of particles in a substance. This is the same regardless of how much gravitational pull is applied to the object because it represents the…...
Physics
IGCSE Coordinated Science:Identification of Ion and Gases
IGCSE Coordinated Science: Identification of Ions and Gases Use the following tests to identify aqueous cations: Ammonium, copper(II), iron(II), iron(III), and zinc by means of aqueous sodium hydroxide and aqueous ammonia as appropriate. Ammonium (NH4+): Add dilute sodium hydroxide, then heat gently. If the cation is present, damp red litmus paper turns blue and ammonia gas is released. Copper (II): Add dilute sodium hydroxide or ammonia solution. If the cation is present, a pale blue precipitate forms. However, as you…...
Chemistry
IGCSE Economics: Privatization
IGCSE Economics: Privatization Privatization is the process when a firm shifts from the Public to Private sector. It has various effects on businesses, the government, and the economy. Effects on Consumers: Advantages: Increase in revenue from sales. Less government spending as “loss-making” privatised firms no longer have to be subsidized. Disadvantages: The government no longer earns profits from the firm. The government loses control of part of the economy due to the firm's exit from government control. Ownership can go…...
Economics
IGCSE Coordinated Science: Radiation
IGCSE Coordinated Science: Radiation Radiation Recognize radiation as the method of heat transfer that does not require a medium to travel through. Radiation, unlike conduction and convection, does not require a medium to travel through. It can travel through anything, including empty space (vacuum). A good example is the radiation from the Sun. Earth receives heat from the Sun through radiation. The heat is transferred through space (which we know is a huge vacuum) by radiation! Describe experiments to show…...
Physics
IGCSE Coordinated Science: Chromosomes and Genes
IGCSE Coordinated Science: Chromosomes and Genes Define inheritance: Genetic information that is passed down from one generation to another. Define the terms: Chromosome: A thread of DNA, made up of a string of genes. Gene: A length of DNA that is the unit of heredity and codes for a specific protein. A gene may be copied and passed on to the next generation. Allele: Any of two or more alternative forms of a gene. Define the terms: Haploid nucleus: A…...
Chemistry
IGCSE Coordinated Science: Carbonates
IGCSE Coordinated Science: Carbonates Carbonates: Describe the manufacture of lime (calcium oxide) from calcium carbonate (limestone) in terms of the chemical reactions involved, and its uses in treating acidic soil and neutralizing industrial waste products. Carbonates are “salts” of Carbonic Acids (H2CO3). A particularly significant carbonic acid is calcium carbonate (CaCO3). Uses of Calcium Carbonate: Helping extraction of iron from its ore. Manufacture of cement. Manufacture of Lime: One industrial use of Calcium Carbonate is that it can be used…...
Chemistry
IGCSE Coordinated Science: Movement in and out Cells
IGCSE Coordinated Science: Movement in and out Cells Movement in and out Cells 1. Define diffusion Diffusion is the term for the net movement of molecules down a concentration gradient from a region of higher concentration to a region of lower concentration as a result of their random movement. 2. Describe the importance of diffusion of gasses and solutes and of water as a solvent. Gases ●Necessary for gas exchange in all living organisms ●Necessary for obtaining Carbon Dioxide and…...
Biology
IGCSE Coordinated Science: Tropic Responses
IGCSE Coordinated Science: Tropic Responses Tropic Responses 1. Define and investigate geotropism (as a response in which a plant grows towards or away from gravity) and phototropism (as a response in which a plant grows towards or awa from the direction from which light is coming). Plants can’t move, we all know that, unless you watch some weird TV show where they can. Then, they need to have some other abilities to receive the benefits of sunlight, hence maximum photosynthesis.…...
Biology
IGCSE Biology Photosynthesis
IGCSE Biology Photosynthesis Photosynthesis - a process by which plants manufacture carbohydrates using sunlight, carbon dioxide and water - by product : oxygen - occurs inside chloroplasts which posses chlorophyll Uses of Glucose - is able to be combined to create starch for storage - can be used to release energy during respiration - is able to be transformed into fructose for the fruit - can be converted into fat and oil for the seeds - can be joined together…...
Biology
IGCSE History: Reasons for and examples of US support for Israel
IGCSE History: Reasons for and examples of US support for Israel Reasons for US Support for Israel: Sympathy – Jewish survivors of Nazi concentration camps. US-large Jewish population forced the government to support Israel. US felt Israel was a close firm friend in a troubled part of the world/knew that Russia was arming Egypt/Syria. Examples of US Support for Israel: War of 1948-49: Financial aid from the US allowed Israelis to irrigate/cultivate a large amount of the desert. US and…...
History
CFA Level 2 – Equity Session 11 – Reading 41 Valuation in Emerging Markets – LOS b
CFA Level 2 - Equity, Session 11-Reading 41 Valuation in Emerging Markets - LOS b(Practice Questions, Sample Questions) 1. The tangible price-to-earnings (P/E) and franchise P/E values for ACP, Inc. are closest to: Tangible P/E Franchise P/E A) 4.59 6.67B) 6.67 4.59C) 9.09 2.08 [Explanation: C) Tangible P/E = 1 / r, so, tangible P/E = 1 / 0.11 = 9.09 Franchise P/E is the product of the franchise factor (FF) and the growth factor (G).That is, Franchise P/E =…...
Economics
Partial Variation: Understanding Cost Relationships in Real-World Examples
Partial Variation Example 1: A banquet hall charges a flat fee of $4000 for an event plus a charge of $100 per person attending. Write a mathematical model to calculate the cost of an event. Does the cost of an event depend on the number of people that attend the event?Let C represent the cost of renting the hall and let p represent the number of people attending the banquet.C=100p+4000Costs depend partially on the number of people attending the party.…...
Mathematics
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