# 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.

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
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A difference of two squares
An expression in the form x^2 - y^2
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Rational numbers
Numbers which can be written as a/b where a and b are integers
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irrational numbers
number which cannot be expressed in the form a/b where a and b are integers
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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)
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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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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
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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
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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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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
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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
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indefinite intergral
integrals with no limits. This produces a function which can be used to calculate area when limits are added.
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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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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)
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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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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.
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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

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 