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.
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
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
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
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.
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
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)]
the set of elements being mapped by a function
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
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.
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
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
a flat shape completely enclosed by three or more straight edges
b² - 4ac
used to discover the nature of the roots of the quadratic equation
ax² + bx + c = 0
- 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