# 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.

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- 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.

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Base

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

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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

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completed square form

p(x + q)^2 + r

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domain

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

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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

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discriminant

the value indicates the number of roots

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the solution of an inequality

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

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asymptote

a line the graph approaches but never reaches

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a stretch

multiplying by a constant outside the function

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gradient

a measure of steepness

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the general equation of a straight line

y = mx + c

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parallel lines

multiple lines with the same gradient

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direct proportionality

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

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a line segment

a finite part of a straight line between two distinct points

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perpendicular bisector

line perpendicular to the midpoint of the line

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tangent

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

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chord

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

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circumcircle

a circle through 3 vertices of a triangle

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circumcentre

the centre of a circumcircle

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polynomial

finite expression with positive whole number indicies

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proof my exhaustion

breaking the statement into smaller cases and proving each case separately

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counterexample

one example that proves the statement false

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pascal's triangle

a triangle formed from adding adjacent pairs of numbers

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natural numbers

all positive integers (integers above zero)

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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.

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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)

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vector

a quantity with both direction and magnitude

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directed line segment

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

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triangle law

AB-> + BC-> = AC->

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the resultant

the vector sum of two or more vectors

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zero vector

a vector with 0 magnitude and no direction

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scalars

quantities with magnitude but no direction

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parallelogram law of vector addition

AC-> = AB-> + BC->

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unit vectors

i & j

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two-dimensional vector form

pi + qj

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magnitude of a vector

using Pythagorus theorem to calculate the hypothenuse gives you the magnitude

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unit vector in direction a (a^)

a / IaI

44 of 136

position vectors

vector which describe the position of the point

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magnitude-direction form of vector notation

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

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tangent

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

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lim h->0

limit as h tends to 0

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increasing function/section of function

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

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decreasing function/section of function

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

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strictly increasing function

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

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strictly decreasing function/section of function

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

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second order derivatives (called second derivatives)

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

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stationary points

points where f'(x)=0

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local maximum

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

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local minimum

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

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

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

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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

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limits of intergration

x coords between which the area is calculated

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the fundamental theorem of calculus

the relationship between the derivative and the integral

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exponential functions

functions in form a^x

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e^x

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

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logarithms

inverses of exponential functions

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natural logarithms

logarithms with base e

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the degree of a polynomial

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

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improper algebraic fractions

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

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modulus

non-negative function

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absolute value function (Abs on calc)

the modulus

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A mapping

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

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One-to-one functions

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

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many-to-one function

Multiple x coords map to the same y coordinate

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one-to-many "function"

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

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piecewise-defined function

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

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composite function

functions composed of two or more functions combined

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inverse of a function

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

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self-inverse functions

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

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arithmetic sequence/ arithmetic progression

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

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arithmetic sequence/ arithmetic progression

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

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common difference

the difference between each term in an arithmetic sequence

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arithmetic series

all the terms of an arithmetic sequence added together

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geometric sequence/ geometric progression

a sequence with a common ratio between the consecutive terms

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common ratio

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

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limit of a sequence

the number to which the sequence converges/tends towards

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convergent sequence (when?)

if IrI is smaller than 1 then the sequence converges

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Alternate sequence

a sequence in which the terms are alternating positive and negative

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geometric series

sum of the terms in a geometric sequence

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sum to infinity

the sum of the series when n tends to infinity

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divergent series

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

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convergent series

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

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sigma notation

sum (with the limits on the top and bottom)

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recurrence relation

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

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An increasing sequence

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

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A decreasing sequence

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

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period sequence

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

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the order of a periodic sequence / period

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

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1 radian

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

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arc length (l)

l=r x angle in radians

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the minor arc

the shorter arc between the two points on the circumference

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the major arc

the longer arc between two points on the circumference

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section of a circle

the area contained between two radii and an arc

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minor sector

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

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major sector

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

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small angle approximations

approximations using radians for values of sin, cos and tan

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"small" numbers

numbers close to 0

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sec x

1/cosx

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cosec x

1/sinx

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cot x

1/tanx

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arcsin x

the "inverse" of sinx

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arccos x

the "inverse" of cosx

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arctan x

the "inverse" of tanx

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addition / compound-angle formulae

the addition formula for sine, cosine an tangent

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double angle formula

identities involving sin2x, cos2x and tan2x

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parametric equations

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

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the chain rule

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

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the product rule

a rule used to differentiate the product of two functions

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the quotient rule

allows differentiation of a/b forms.

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implicit differentiation

differentiation in which both x and y terms are differentiated

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concave function

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

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convex function

f''(x) more or equal to 0

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point of inflection

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

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differential equation

an equation involving rates of change

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iteration

testing multiple values

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staircase diagram

the graphical representation of each iteration joined

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cobweb diagram

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

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the Newton-Raphson method/process/procedure

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

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integration by reversing the chain rule

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

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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. :)

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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.

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families of solutions

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

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boundary condition

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

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unit vectors in 3D

i, j & k

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coplanar vectors

vectors on the same plane

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non-coplanar vectors

vector which are not in the same plane

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## 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

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