# Maths Pure A-level Iteractive Glossary

All the term that are new in A level compared to GCSE for both years. These are not always word-for-word definitions, understanding is more important.

5.0 / 5

- Mathematics
- Algebra and functionsCalculusDifferential equationsGraphs and transformationsLogarithms and exponentialsNumerical methodsProofSequences and seriesTrigonometry and radiansVectors
- A2/A-level
- Edexcel

- Created by: ItsAlevelTime
- Created on: 24-12-18 20:09

Index/Power/Exponent

The term you raise the base by.

1 of 136

Base

The number which you raise something from. eg. x in x^2

2 of 136

Product

Made when two terms are multiplied

3 of 136

A difference of two squares

An expression in the form x^2 - y^2

4 of 136

Rational numbers

Numbers which can be written as a/b where a and b are integers

5 of 136

irrational numbers

number which cannot be expressed in the form a/b where a and b are integers

6 of 136

repeated root

exactly one root

7 of 136

completed square form

p(x + q)^2 + r

8 of 136

domain

all possible inputs for a mapping (all possible x-values)

9 of 136

range

all possible outputs for the mapping(all possible y-values)

10 of 136

roots of function

the values x for which f(x)=0

11 of 136

discriminant

the value indicates the number of roots

12 of 136

the solution of an inequality

set of all real numbers of x for which the inequality is true

13 of 136

asymptote

a line the graph approaches but never reaches

14 of 136

a stretch

multiplying by a constant outside the function

15 of 136

gradient

a measure of steepness

16 of 136

the general equation of a straight line

y = mx + c

17 of 136

parallel lines

multiple lines with the same gradient

18 of 136

direct proportionality

both variables increase at the same rate and the line goes through the origin

19 of 136

a line segment

a finite part of a straight line between two distinct points

20 of 136

perpendicular bisector

line perpendicular to the midpoint of the line

21 of 136

tangent

a line perpendicular to the radius of the circle at the point of intersection

22 of 136

chord

a line segment which join two points on the circumference of a circle

23 of 136

circumcircle

a circle through 3 vertices of a triangle

24 of 136

circumcentre

the centre of a circumcircle

25 of 136

polynomial

finite expression with positive whole number indicies

26 of 136

proof my exhaustion

breaking the statement into smaller cases and proving each case separately

27 of 136

counterexample

one example that proves the statement false

28 of 136

pascal's triangle

a triangle formed from adding adjacent pairs of numbers

29 of 136

natural numbers

all positive integers (integers above zero)

30 of 136

cosine rule

the rule used to calculate the missing sides or angles of triangle when you know two sides and the angle between them or three sides and no angle.

31 of 136

sine rule

the rule used to work out missing lengths or angles if opposite pairs of angles and lengths are known

32 of 136

a unit circle

a circle with radius 1 unit (equation x^2 + y^2 =1)

33 of 136

vector

a quantity with both direction and magnitude

34 of 136

directed line segment

a line with an arrow spanning two points and pointing at a specific angle

35 of 136

triangle law

AB-> + BC-> = AC->

36 of 136

the resultant

the vector sum of two or more vectors

37 of 136

zero vector

a vector with 0 magnitude and no direction

38 of 136

scalars

quantities with magnitude but no direction

39 of 136

parallelogram law of vector addition

AC-> = AB-> + BC->

40 of 136

unit vectors

i & j

41 of 136

two-dimensional vector form

pi + qj

42 of 136

magnitude of a vector

using Pythagorus theorem to calculate the hypothenuse gives you the magnitude

43 of 136

unit vector in direction a (a^)

a / IaI

44 of 136

position vectors

vector which describe the position of the point

45 of 136

magnitude-direction form of vector notation

describing a vector by giving its magnitude and the angle between the vector and one coordinate axis

46 of 136

tangent

a straight line that just touches the curve and has the gradient of the point it just touches.

47 of 136

lim h->0

limit as h tends to 0

48 of 136

increasing function/section of function

functions/sections with f'(x) is bigger than or equal to zero

49 of 136

decreasing function/section of function

functions/sections with f'(x) is less than or equal to zero

50 of 136

strictly increasing function

functions/sections with f'(x) is bigger than zero

51 of 136

strictly decreasing function/section of function

functions/sections with f'(x) is less than zero

52 of 136

second order derivatives (called second derivatives)

f''(x) represents the rate of change of the gradient function

53 of 136

stationary points

points where f'(x)=0

54 of 136

local maximum

stationary point with f''(x) less than zero

55 of 136

local minimum

stationary point with f''(x) higher than zero

56 of 136

If f'(x)=0 what does this mean?

It could be a max, min or point of inflection. Check by subbing in.

57 of 136

constant of integration (c)

a constant added to account for the constant integers lost during differentiation

58 of 136

indefinite intergral

integrals with no limits. This produces a function which can be used to calculate area when limits are added.

59 of 136

definite intergrals

integrals with limits. This produces a value for area

60 of 136

limits of intergration

x coords between which the area is calculated

61 of 136

the fundamental theorem of calculus

the relationship between the derivative and the integral

62 of 136

exponential functions

functions in form a^x

63 of 136

e^x

the exponential function with the same gradient function as real function.

64 of 136

logarithms

inverses of exponential functions

65 of 136

natural logarithms

logarithms with base e

66 of 136

the degree of a polynomial

the largest exponent in the expression (eg. x^3 has a degree of 3)

67 of 136

improper algebraic fractions

fraction with a numerator that has a degree equal to or larger than the denominator

68 of 136

modulus

non-negative function

69 of 136

absolute value function (Abs on calc)

the modulus

70 of 136

A mapping

A mapping transforms one set of numbers into a different set of numbers

71 of 136

One-to-one functions

function in which each individual x coordinate has a unique y coordinate

72 of 136

many-to-one function

Multiple x coords map to the same y coordinate

73 of 136

one-to-many "function"

one x coordinate maps to many y coords. NOT A FUNCTION.

74 of 136

piecewise-defined function

a function which is described in parts. One function for a certain limits and another function for another limit.

75 of 136

composite function

functions composed of two or more functions combined

76 of 136

inverse of a function

performs the opposite to the original function (reflections in the line y=x)

77 of 136

self-inverse functions

the inverse of the function is the function itself (any functions symmetrical about x=y)

78 of 136

arithmetic sequence/ arithmetic progression

sequence in which the difference (d) between the terms is constant

79 of 136

arithmetic sequence/ arithmetic progression

sequence in which the difference (d) between the terms is constant

80 of 136

common difference

the difference between each term in an arithmetic sequence

81 of 136

arithmetic series

all the terms of an arithmetic sequence added together

82 of 136

geometric sequence/ geometric progression

a sequence with a common ratio between the consecutive terms

83 of 136

common ratio

the number by which you multiply a term to produce the next term in a geometric sequence

84 of 136

limit of a sequence

the number to which the sequence converges/tends towards

85 of 136

convergent sequence (when?)

if IrI is smaller than 1 then the sequence converges

86 of 136

Alternate sequence

a sequence in which the terms are alternating positive and negative

87 of 136

geometric series

sum of the terms in a geometric sequence

88 of 136

sum to infinity

the sum of the series when n tends to infinity

89 of 136

divergent series

The terms in the series keep increasing (to infinity) ; no convergence

90 of 136

convergent series

as the terms of this series are getting smaller, the sum tends towards a finite value

91 of 136

sigma notation

sum (with the limits on the top and bottom)

92 of 136

recurrence relation

a form which defines the previous term as a function of the previous one

93 of 136

An increasing sequence

a sequence in which u(n+1) is always larger than u(n)

94 of 136

A decreasing sequence

a sequence in which u(n+1) is always smaller than u(n)

95 of 136

period sequence

a sequence in which the terms repeat in a cycle u(n+k) = u(n) for a fixed value of k.

96 of 136

the order of a periodic sequence / period

the k value when in a periodic sequence u(n) = u(n+k)

97 of 136

1 radian

the angle subtended at the centre of a circle in a arc length 1 in a circle with radius 1

98 of 136

arc length (l)

l=r x angle in radians

99 of 136

the minor arc

the shorter arc between the two points on the circumference

100 of 136

the major arc

the longer arc between two points on the circumference

101 of 136

section of a circle

the area contained between two radii and an arc

102 of 136

minor sector

the smaller area contained between the two radii and the minor arc

103 of 136

major sector

the larger area contained between the two radii and the major arc

104 of 136

small angle approximations

approximations using radians for values of sin, cos and tan

105 of 136

"small" numbers

numbers close to 0

106 of 136

sec x

1/cosx

107 of 136

cosec x

1/sinx

108 of 136

cot x

1/tanx

109 of 136

arcsin x

the "inverse" of sinx

110 of 136

arccos x

the "inverse" of cosx

111 of 136

arctan x

the "inverse" of tanx

112 of 136

addition / compound-angle formulae

the addition formula for sine, cosine an tangent

113 of 136

double angle formula

identities involving sin2x, cos2x and tan2x

114 of 136

parametric equations

the x and y coords of each point on the curve is described as a function of t.

115 of 136

the chain rule

a rule used to differentiation for composite functions or functions of other functions

116 of 136

the product rule

a rule used to differentiate the product of two functions

117 of 136

the quotient rule

allows differentiation of a/b forms.

118 of 136

implicit differentiation

differentiation in which both x and y terms are differentiated

119 of 136

concave function

f''(x) less than or equal to 0

120 of 136

convex function

f''(x) more or equal to 0

121 of 136

point of inflection

the point at which the curve change form concave to convex/ where f''(x) changes sign

122 of 136

differential equation

an equation involving rates of change

123 of 136

iteration

testing multiple values

124 of 136

staircase diagram

the graphical representation of each iteration joined

125 of 136

cobweb diagram

pattern made on a graph of each iteration , they converge on the root and the graph resembles a cobweb.

126 of 136

the Newton-Raphson method/process/procedure

a method using tangents that used to find the numerical solutions to equation of form f(x)=0

127 of 136

integration by reversing the chain rule

if it is in form kf'(x)/f(x) then it can be integrated using reverse chain rule

128 of 136

integration by substitution

by finding a vale of u and then dividing by u', then integrating with respect to du, then subbing back in, it works. :)

129 of 136

intergation by parts

using the formula in the formula booklet, products of two functions can be integrated.

130 of 136

the trapezium rule

a numerical expression to find an approximation for the area under a curve which divides the area into many trapeziums.

131 of 136

families of solutions

curves which are the same but with a different +c values.

132 of 136

boundary condition

the point on the curve needed to calculate the +c value

133 of 136

unit vectors in 3D

i, j & k

134 of 136

coplanar vectors

vectors on the same plane

135 of 136

non-coplanar vectors

vector which are not in the same plane

136 of 136

## Other cards in this set

### Card 2

#### Front

The number which you raise something from. eg. x in x^2

#### Back

Base

### Card 3

#### Front

Made when two terms are multiplied

#### Back

### Card 4

#### Front

An expression in the form x^2 - y^2

#### Back

### Card 5

#### Front

Numbers which can be written as a/b where a and b are integers

#### Back

## Related discussions on The Student Room

- The Most useful type of mathematics for physics? »
- Fast track A Levels Further Maths? »
- A level maths »
- Is pure mathematics the same as core? »
- Calling all University Mathematicians! »
- Maths at uni »
- Where to find difficult A Level maths questions »
- Economics - how much writing? »
- how much further maths comes up in a physics degree? »
- Mathematics at University »

## Similar Mathematics resources:

4.0 / 5

0.0 / 5

5.0 / 5

Teacher recommended

0.0 / 5

0.0 / 5

0.0 / 5

5.0 / 5

## Comments

No comments have yet been made