Definitions

#Definitions in Core Pure Maths

General Definitions

  • Factorise: This refers to the process of breaking down an equation or expression into a more simplified form. Usually involves splitting a polynomial in terms of its factors.

  • Simplify: This involves making an expression or equation as straightforward as possible. It often involves combining like terms or eliminating unnecessary elements.

  • Expand: This is the process of removing brackets from an expression by multiplying out the terms.

Algebraic Definitions

  • Polynomial: A polynomial is a mathematical expression consisting of variables and coefficients. These are combined using addition, subtraction and multiplication operations. A polynomial can be of any degree.

  • Quadratic Equation: This is a specific type of polynomial equation of degree 2. It has the general form ax^2 + bx + c = 0, where a, b and c are constants and x is the variable.

  • Complex Numbers: These are numbers that consist of a real and an imaginary part. The imaginary part is defined by the square root of -1, represented as ‘i’.

Calculus Definitions

  • Derivative: The derivative of a function measures the sensitivity of the output to changes in the input. It is a fundamental concept in calculus, often interpreted as the rate of change or slope of the function.

  • Integral: The integral of a function is the antiderivative, capturing the area under the curve of the function. It is a key concept in calculus with applications in computing areas and solving differential equations.

  • Limit: The limit of a function at a certain point refers to the value that the function approaches as the input (or variable) approaches that point.

Geometry Definitions

  • Vectors: A vector is a quantity that has both magnitude (size) and direction.

  • Matrices: A matrix is a rectangular array of numbers arranged in rows and columns. It’s a key concept in linear algebra used in solving systems of equations and representing transformations.

  • Dot Product: The dot product of two vectors is a scalar (single number) that provides a measure of the extent to which the two vectors point in the same direction.

These definitions form the foundation of Core Pure Mathematics. Understanding them will enable better grasp of complex concepts and strengthen problem-solving abilities.