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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…
How do you solve simultaneous equations by elimination?
Make the coefficient of one letter the same in both equations, then add or subtract the equations to remove that letter. Solve for the letter that is left, then…
How do you simplify surds?
To simplify a surd, write the number under the root as a product that includes the largest possible square number, then take the square root of that square outside. For…
How do you use SOHCAHTOA to find a side or angle?
In a right-angled triangle, sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent. Label the sides relative to the angle, pick the…
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 resistance using Ohm's law?
Ohm's law links voltage, current and resistance: V = IR, where V is the potential difference in volts (V), I is the current in amps (A) and R is the resistance in ohms…
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 momentum and use conservation of momentum?
Momentum = mass × velocity, written p = mv, in kilogram metres per second (kg m/s). In a collision or explosion with no external forces, total momentum before equals…
How do you balance a chemical equation?
A balanced equation has the same number of each type of atom on both sides. Count the atoms of each element, then change the large numbers in front of formulas…
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 ionic and covalent bonding?
Ionic bonding happens between a metal and a non-metal: the metal transfers electrons to the non-metal, forming oppositely charged ions that attract each other. Covalent…
How is the periodic table arranged?
Elements are arranged in order of increasing atomic number (the number of protons). Columns are called groups: elements in the same group have the same number of…
What factors affect the rate of a chemical reaction?
The rate of reaction increases with higher temperature, higher concentration (or pressure for gases), larger surface area and the presence of a catalyst. Collision…
What is the difference between exothermic and endothermic reactions?
An exothermic reaction gives out energy to the surroundings, usually as heat, so the temperature rises. An endothermic reaction takes in energy from the surroundings, so…
How does electrolysis work?
Electrolysis uses electricity to break down an ionic compound that is molten or dissolved, called the electrolyte. Positive ions move to the negative electrode (cathode)…
Explain how a vaccination can prevent an illness.
A vaccine contains a dead, inactive or weakened form of a pathogen, or parts of it, carrying its antigens. White blood cells (lymphocytes) respond by making specific…
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…
What is the difference between diffusion and osmosis?
Diffusion is the net movement of particles from an area of higher concentration to an area of lower concentration. Osmosis is a special case: the diffusion of water…
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…
How do I write a good introduction for an essay?
A good introduction does three things in a few sentences: it opens with a relevant point about the topic, it shows you understand what the question is asking, and it…
How do you write a formal letter?
A formal letter has a set layout: your address and the date at the top right, the recipient's address on the left, a formal greeting, a heading, clear paragraphs and a…
What are the main persuasive writing techniques?
Persuasive writing tries to convince the reader to agree or act. Common techniques include direct address (you), rhetorical questions, facts and statistics, expert…
What is the difference between the active and passive voice?
In the active voice, the subject does the action: "The teacher marked the tests." In the passive voice, the subject receives the action: "The tests were marked by the…
How do you answer a summary question in an English exam?
Read the question to see exactly what information is asked for, find the relevant points in the passage, then rewrite each point in your own words as one short, complete…
How do you convert a binary number to denary?
Write the place values above each binary digit, starting with 1 on the right and doubling each time to the left (1, 2, 4, 8, 16, 32, 64, 128). Add up the place values…
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 is double-entry bookkeeping?
Double-entry bookkeeping records every transaction twice: once as a debit in one account and once as a credit in another, for the same amount. This keeps the accounting…
What is a trial balance and why is it prepared?
A trial balance is a list of all the ledger account balances at a given date, with debit balances in one column and credit balances in the other. Because of double…
What is the greenhouse effect and how does it cause climate change?
The greenhouse effect is the natural process by which gases in the atmosphere, such as carbon dioxide, methane and water vapour, trap some of the heat radiated by the…
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…