function

a function or mapping from a set A to a set B is a rule that relates each element in set A to one *and only one* element in B.

log(a) xy

this is read "log to the base a of (x times y)"

log(a)x + log(a) y

log to the base a of x plus log to the base a of y

derivative

the derivative of a function for some particular value is a measure of either

- the rate of change at which the function is changing at that value
- the gradient of the graph at that point

vertex

where two sides of a polygon meet to form a corner

so a triangle has three vertices, a square has four vertices

range of a function

the set of images of the mapping

median (of a triangle)

the median of a triangle is the straight line joining a vertex of the triangle to the mid point of the opposite side

equation

an equation is a statement that two expressions (one of which may be a constant) have the same value eg

- 2x + 7 = 15
- 3(x + 2) = 3x + 6

are both equations.

logarithm

the logarithm of a number **N** to the base **b** is the **power** to which that base must be raised in order to obtain **N**

argument of a function

the input to a function eg

- f(x) -- x is the argument
- sin2x -- 2x is the argument

gradient

the gradient of a line drawn as a graph on a set of axes is a measure of its slope relative to the __x-axis__

vertical change / horizontal change

[y(1) - y(2)] / [x(1) - x(2)]

domain

the set of elements being mapped by a function

expression

an expression in algebra is most often a collection of quantities, made up of constants and variables, linked by signs for operations (+, -, *, /) and usually not including an equals sign eg

- x + y
- 3x² - 2x - 1
- 2y³ - 18x

coefficient

a coefficient is a constant attached in front of a variable, or a group of variables, where it is understood that once the value of the variable has been worked out, then the result has to be multiplied by the coefficient eg

- 2x -- 2 is the coefficient of x.
- when the coeffecient is 1 it is usual to not write it e.g.
- 1x is usually written as x

- so basically a number which multiplies a variable, or string of variables.

altitude

an altitude of a triangle is a line from a vertex of the triangle to the opposite side (extended if necessary) and at right angles to that side

log(a) x^n

this is read "log to the base a of x to the n"

n log(a) x

n times the log to the base a of x

polygon

a flat shape completely enclosed by three or more straight edges

discriminant

b² - 4ac

used to discover the nature of the roots of the quadratic equation

ax² + bx + c = 0

parallel

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- two or more lines which must lie in the same plane, are said to be parallel if, no matter how far they are extended in either direction, they are always the same distance apart
- also said of lines having the same gradient

perpendicular