Mathematical terms

Question 1

function

Answer 1

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.

Question 2

log(a) xy

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

Answer 2

log(a)x + log(a) y

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

Question 3

derivative

Answer 3

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

Question 4

vertex

Answer 4

where two sides of a polygon meet to form a corner

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

Question 5

range of a function

Answer 5

the set of images of the mapping

Question 6

median (of a triangle)

Answer 6

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

Question 7

equation

Answer 7

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.

Question 8

logarithm

Answer 8

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

Question 9

argument of a function

Answer 9

the input to a function eg

• f(x) – x is the argument
• sin2x – 2x is the argument

Question 10

gradient

Answer 10

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)]

Question 11

domain

Answer 11

the set of elements being mapped by a function

Question 12

expression

Answer 12

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

Question 13

coefficient

Answer 13

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.

Question 14

altitude

Answer 14

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

Question 15

log(a) x^n

this is read “log to the base a of x to the n”

Answer 15

n log(a) x

n times the log to the base a of x

Question 16

polygon

Answer 16

a flat shape completely enclosed by three or more straight edges

Question 17

discriminant

Answer 17

b² - 4ac

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

ax² + bx + c = 0

Question 18

parallel

Answer 18

• 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

Question 19

perpendicular

Answer 19

• at right angles to
• at 90º to