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.

The term you raise the base by.
1 of 136
The number which you raise something from. eg. x in x^2
2 of 136
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
all possible inputs for a mapping (all possible x-values)
9 of 136
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
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
a line the graph approaches but never reaches
14 of 136
a stretch
multiplying by a constant outside the function
15 of 136
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
a line perpendicular to the radius of the circle at the point of intersection
22 of 136
a line segment which join two points on the circumference of a circle
23 of 136
a circle through 3 vertices of a triangle
24 of 136
the centre of a circumcircle
25 of 136
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
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
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
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
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
the exponential function with the same gradient function as real function.
64 of 136
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
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
107 of 136
cosec x
108 of 136
cot x
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
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


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



Card 3


Made when two terms are multiplied


Preview of the back of card 3

Card 4


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


Preview of the back of card 4

Card 5


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


Preview of the back of card 5
View more cards


No comments have yet been made

Similar Mathematics resources:

See all Mathematics resources »See all Algebra and functions resources »