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How do you find the gradient of a straight line from two points?
The gradient is the change in y divided by the change in x. For points (x₁, y₁) and (x₂, y₂), gradient m = (y₂ − y₁) / (x₂ − x₁). A positive gradient slopes upwards from…
How do you expand and simplify double brackets like (x + 3)(x − 5)?
Multiply every term in the first bracket by every term in the second, then collect like terms. For (x + 3)(x − 5): x × x = x², x × (−5) = −5x, 3 × x = 3x, 3 × (−5) =…
How do you calculate a percentage increase?
Percentage increase = (new value − original value) ÷ original value × 100. For example, a price rising from 80 to 100 is an increase of 20, and 20 ÷ 80 × 100 = 25%…
What is Pythagoras' theorem and how do you use it?
In a right-angled triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c²…
How do you solve a linear equation?
Get the unknown on its own by doing the same operation to both sides of the equation. Undo additions and subtractions first, then multiplications and divisions. For 3x +…
How do you find the area and circumference of a circle?
Area of a circle = πr², where r is the radius. Circumference = 2πr, or πd where d is the diameter. Always check whether you are given the radius or the diameter: the…
How do you calculate probability?
Probability = number of favourable outcomes ÷ total number of equally likely outcomes. It is always between 0 (impossible) and 1 (certain), and can be written as a…
How do you find the mean, median, mode and range?
The mean is the total divided by how many values there are. The median is the middle value when the data is in order. The mode is the most common value. The range is the…
What is the difference between speed and velocity?
Speed tells you how fast something is moving. Velocity tells you how fast and in which direction. Speed is a scalar quantity (size only) and velocity is a vector…
How do you calculate density?
Density = mass ÷ volume, written ρ = m ÷ V. With mass in kilograms and volume in cubic metres, density is in kg/m³; with grams and cm³, it is in g/cm³. An object floats…
What is the difference between series and parallel circuits?
In a series circuit the components are connected one after another in a single loop, so the same current flows through each one and the voltage is shared between them…
What is pH and how is it measured?
pH is a scale from 0 to 14 that shows how acidic or alkaline a solution is. Below 7 is acidic, 7 is neutral and above 7 is alkaline. It is measured with universal…
How does photosynthesis work?
Photosynthesis is the process plants use to make glucose. In the chloroplasts, chlorophyll absorbs light energy, which is used to convert carbon dioxide and water into…
How does the heart pump blood around the body?
The heart is a muscular pump with four chambers. The right side pumps deoxygenated blood to the lungs, where it picks up oxygen. The left side pumps oxygenated blood to…
What is a food chain and how does energy flow through it?
A food chain shows what eats what in a habitat. It starts with a producer, usually a green plant that makes food by photosynthesis, followed by consumers. The arrows…
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 RAM and ROM?
RAM (random access memory) is volatile: it holds the programs and data currently in use and loses everything when the power is turned off. ROM (read-only memory) is…
What causes earthquakes?
The Earth's crust is broken into tectonic plates that move slowly on the mantle beneath. Where plates meet, friction can lock them together and pressure builds up. When…