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How do you solve a quadratic equation using the quadratic formula?
Write the equation as ax² + bx + c = 0, read off a, b and c, then substitute them into x = (−b ± √(b² − 4ac)) / 2a. Work out the discriminant b² − 4ac first: if it is…
How do you differentiate a polynomial?
Differentiate each term separately using the power rule: for axⁿ, multiply by the power and reduce the power by one, giving naxⁿ⁻¹. A term in x becomes a constant and a…
What are the laws of logarithms?
The three main laws are: log a + log b = log(ab), log a − log b = log(a ÷ b), and log(aⁿ) = n log a. They hold for any base as long as both logs use the same base. A…
How do you integrate a polynomial?
Integrate each term separately: for axⁿ, add one to the power and divide by the new power, giving axⁿ⁺¹/(n + 1). Always add a constant of integration, + c, for an…
What is Newton's second law and how do you use F = ma?
Newton's second law says the resultant force on an object equals its mass multiplied by its acceleration: F = ma, with F in newtons (N), m in kilograms (kg) and a in…
How do you calculate the kinetic energy of a moving object?
Kinetic energy = ½ × mass × speed², written Eₖ = ½mv². Use mass in kilograms and speed in metres per second to get the energy in joules (J). Because speed is squared…
How do you use the wave equation v = fλ?
Wave speed = frequency × wavelength, written v = fλ. Speed is in metres per second (m/s), frequency in hertz (Hz) and wavelength in metres (m). If the frequency…
How do you calculate the number of moles?
Number of moles = mass ÷ molar mass, written n = m ÷ M. Use the mass in grams and the molar mass in g/mol, which you get by adding the relative atomic masses from the…
What is the difference between mitosis and meiosis?
Mitosis produces two genetically identical diploid cells and is used for growth and repair. Meiosis produces four genetically different haploid cells (gametes such as…
How do enzymes work?
Enzymes are proteins that act as biological catalysts: they speed up reactions without being used up. Each enzyme has an active site with a specific shape that only fits…
What is the structure of DNA?
DNA is a double helix: two strands twisted around each other. Each strand is a chain of nucleotides, and each nucleotide has a sugar, a phosphate and one of four bases…
When do you use the subjunctive in French?
The subjunctive is used after que when the main clause expresses a wish, a necessity, an emotion, a doubt, or after certain conjunctions. Typical triggers are il faut…
What is an algorithm and how do you write one?
An algorithm is a precise, step-by-step set of instructions for solving a problem. It can be written in plain English, as pseudocode or as a flowchart, and then turned…
What is the law of supply and demand?
The law of demand says that as the price of a good rises, the quantity demanded falls. The law of supply says that as the price rises, the quantity supplied rises. The…
What is inflation and what causes it?
Inflation is a sustained rise in the general price level, which means each unit of money buys less. It is usually measured by the change in a consumer price index over a…
What were the main causes of the First World War?
Historians often group the long-term causes as militarism, alliances, imperialism and nationalism. The short-term trigger was the assassination of Archduke Franz…
How should I revise for exams?
The most effective revision is active, spaced out and based on practice. Test yourself instead of rereading notes, spread each topic over several short sessions across…