Definitions Flashcards
Polynomials
Have variables that have only non-negative whole number powers
Degree of a polynomial/expression
It’s highest power
Binomial expansion
Where and expression is multiplied by itself many times
Dividend
The numerator in division
Divisor
The denominator in division
Quotient
Result of division
zeros of equation
Roots
Inequality
A range of values
Modulus
The magnitude of the number without regard to it’s sign
Conjugate
The complete opposite of an operation ex: conjugate of (x-y) would be (x+y)
Natural logarithm function
lnx or log base e x
Function
Rule that maps an input to a unique output
Input
An object that is put into the function
Domain
The set of all inputs for which a function is defined
Output
The object that comes out from the function
Range
Set of actual output values of a function
Codomain
The set of all possible output values of a function
Injective function
One to one- never assigns same output to two different input values
Surjective function
Onto - function which every element in codomain has at least one matching element in the domain
Bijective function
Is both injective and surjective
Period
Horizontal distance required for graph to complete one cycle
Range
Set of all actual outputs of function
Amplitude
Number of units the graph goes up or down from mid line of graph
Frequency
Number of waves that pass a fixed point in a given amount of time
Asymptote
A line which the curve will approach but never meet
Principal values
The ranges of the inverse trigonometric equations
Angles of elevation
angle above horizontal
Angle of depression
angle below horizontal
Reference angle
the acute angle formed by the terminal side of an angle and the x-axis
cotA
1/tanA
Area
Amount of flat space a shape occupies
Perimeter
The sum of the length of all the sides of a shape
Trapezium
A quadrilateral that has one pair of parallel sides
Iota i
Complex number root of -1
Argand diagram
representing complex number of plane- horizontal plane is real, vertical is complex
Complex plane
representing complex number of plane- horizontal plane is real, vertical is complex
Translation
Transformation of moving in a straight line, addition subtraction
Discriminant
b squared - 4ac
Conjugate root theorem
If complex number is a root of polynomial fz with real coefficients then the conjugate of that complex number is also a root
Cartesian form of complex number
x + iy
Polar form of complex number
r(cosA + isinA)
Argument
Angle
Radian
measure of angle at centre of a circle when the length of arc is equal to the radius
Surd
Number in form nth root of a , n>1, n is element of N, which cannot be written as a fraction
Rationalise denominator
Multiply bottom and top by the conjugate of denominator
Tangent
A line that intersects a circle at one point only at 90 degrees
Locus
Path traced out by a moving point satisfying certain given conditions
Indeterminate
if fraction has zero as the denominator
Piece wise function
function whose definition changes depending on the value of the independent variable x
F prime of x
the derivative of f of x
Differentiation
the process of finding the slope or gradient
derivative
answer to a differential equation
Natural logarithmic function
lnx
Stationary point
point where the slope is zero
Concave up
slopes of tangent lines increase as you move from left to right
Concave down
slopes of tangent lines decrease as you move from left to right
Point of inflection
Point where concavity changes from concave up to concave down is called a point of inflection
Rate of change
the change of something in respect to time
Velocity
Rate of change of displacement with respect to time
Acceleration
Rate of change of velocity with respect to time
Permutation
arrangement of a number of objects in a definite order
combination
a selection of a number of objects in any order
Probability
measure of chance and likelihood of something happening
sample space
the set or list of all oossible outcomes of a trial
Relative frequency
is the number of times an event happens in a trial divided by the total number of trials. It is a good estimate of probability if the number of trials is sufficiently large
Mutally exclusive events
they cannot occur at the same time
Independent events
The occurrence of one event or the non-occurrence one event does not influence the probability of the second event happening
Bernoulli trial
a trial whose outcome is random and is one of only two possibilities, success or failure
Saddle point
is a horizontal point of inflection which has curve increasing on both sides or decreasing on both sides
Integration
process of finding a function from its derivative is called anti-differentiation or integration
Definite integral
finding the function defined on a closed interval gives the definite integral (no constant of integration)
Pattern
Set of numbers , objects or diagrams that repeat in a particular manner
Sequence
A sequence is a set of numbers in which each number after the first is formed by some definite rule
Series
A series is a sum of numbers where each number after the first is formed by some definite rule
Finite series
One that ends after a finite number of terms
Infinite series
One that continues indefinitely
Arithmetic sequence
A sequence in which each term after the first is found by adding a constant number
Common difference
The difference between consecutive terms in an arithmetic sequence
Arithmetic series
The sum of terms of an arithmetic sequence
Quadratic sequence
Sequence where the nth term is of the form an(squared) +bn+c
Geometric sequence
Sequence in which each term after the first is found by multiplying the previous term by a constant number
Common ratio
The constant number which each term in a geometric sequence is multiplied by
Geometric series
The sum of terms in a geometric sequence
Limit of a sequence
A unique number L such that Tn, the nth term of the sequence gets closer and closer to L for larger values of n
