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ALGEBRA

Algebra

The part of mathematics that deals with generalised arithmetic. Letters are used to denote variables and unknown numbers and to state general properties. Example: a(x + y) = ax + ay shows a relationship that is true for any numbers a, x and y. Adjective: algebraic. See also equation, formula, identity and expression.


Cartesian Co-ordinates

A system used to define the position of a point in two-dimensional and three-dimensional space. Two axes at right angles to each other are used to define the position of a point in a plane. The convention is to label the horizontal axis as the x-axis and the vertical axis as the y-axis. In this case, the origin is the intersection of the axes. The ordered pair of numbers (x, y) that defines the position of a point is the coordinate pair. Each of the numbers is a co-ordinate. The numbers are also known as Cartesian co-ordinates, after the French mathematician, René Descartes.


Co-ordinate

A position in 2D or 3D space, represented by numbers, letters or both. See 'Cartesian co-ordinates'.

Consecutive

Following in order. Consecutive numbers are adjacent in a count. Examples: 5, 6, 7 are consecutive numbers. 25,30,35 are consecutive multiples of 5. In a polygon, consecutive sides share a common vertex and consecutive angles share a common side.


Cube

1. In geometry, a three-dimensional figure with six identical, square faces. Adjoining edges and faces are at right angles.

2. In number and algebra, the result of multiplying the same value by itself, then by itself again.

Example: 2 x 2 x 2 is written a 23.

This is said as '2 cubed', or '2 to the power of three'.


Cubic

Adjective to describe a mathematical expression of degree three, i.e. with a power equal to 3. 

A cubic polynomial is one of the type ax3 + bx2 + cx +d, where the highest power is equal to 3. The coefficients b,c, and d could equal zero which would just leave the cubic term.


Cubic Curve

A curve described by an algebraic equation containing at least one cubic term, i.e. a term raised to the power of three, and no terms with higher powers than three.


Difference

The amount by which one number or value is greater than another, obtained by subtracting the smaller from the larger.


Expression

A mathematical form expressed symbolically. Examples: 7 + 3; a2 + b2.

An expression is different from an equation in that it doesn't have an equals sign =. 


Gradient

A measure of the slope of a line. On a coordinate plane, the gradient of the line through the points (x1, y1) and (x2, y2) is defined as (y2 - y1) / (x2 - x1).

The gradient may be positive, negative or zero depending on the values of the co-ordinates. In a straight line graph of the form y = mx+c, m represents the gradient.



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