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Maths > Definitions > Flashcards

Definitions Flashcards

1
Q

Orthocentre

A

Points where the altitudes intersect

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2
Q

Altitude

A

Drawn from a vertex to the opposite side such that it forms a right angle

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3
Q

Circumcircle

A

The circle that passes through all 3 vertices of a triangle

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4
Q

Circumcentre

A

The point where the triangle’s 3 perpendicular bisectors meets

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5
Q

Incircle

A

The largest circle that will fit inside the triangle. Each of the triangle’s 3 sides is a tangent to the circle

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6
Q

Incenter

A

The point where the triangle’s 3 angle bisectors meet

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7
Q

Axiom

A

A statement which we accept without any proof

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8
Q

Corollary

A

A statement that follows readily from a previous theorem

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9
Q

Converse

A

The reverse of a theorem

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10
Q

Proof by contradiction

A

A form of proof that establishes the truth or validity of a proposition by showing that the proposition being false would imply a contradiction

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11
Q

Mean

A

The sum of all the values divided by the number of values

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12
Q

Median

A

The middle value when the values are arranged in order

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13
Q

Mode

A

The value that has the greatest frequency

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14
Q

Range

A

The difference between the maximum and minimum value of a set

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15
Q

Lower quartile

A

One quarter of the values in a ranked set of values are less than or equal to the median

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16
Q

Second quartile

A

The median

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17
Q

Upper quartile

A

3 quarters of the values in a ranked set of values are more than or equal to the median

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18
Q

Z-scores

A

The number of standard deviations a given value x is above or below the mean of a given data set
Z = χ-γ / σ

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19
Q

Observational study

A

The researcher collects the information of interest but does not influence events

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20
Q

Case-control study

A

Two groups are compared one (the case) and one (the control)

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21
Q

Explanatory variable

Response variable

A

In the case of a drug trial, the drug is called the explanatory variable and the effect of the drug is called the response variable

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22
Q

Categorical data

A

Questions that cannot be answered by numbers provide categorical data

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23
Q

Ordinal vs nominal

A

Ordinal can be ordered

Nominal cannot

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24
Q

Numerical data

A

Questions that can be answered by numbers provide numerical data

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25
Q

Continuous

A

Can be any one of an infinite number of values within a range of values

26
Q

Discrete

A

Can only have certain values

27
Q

Parameter

A

Numerical measurements describing some characteristics of a population. It is a fixed number but generally we do not know its value

28
Q

Statistic

A

Numerical measurements describing some characteristic of a sample, it can change from sample to sample

29
Q

Sampling distribution

A

The distribution of all the values of that statistic when all possible samples of the same size are taken from the same population

30
Q

Margin of error

A

The maximum likely difference between the sample proportion ρ^ and the population proportion p

31
Q

Hypothesis test

A

A procedure for testing a claim about a hypothesis

32
Q

Null hypothesis

A

H0 is a statement which defines the population

33
Q

Simple random sample

A

A sample size n is selected in such a way that every possible sample of size n from the population has an equal chance of being selected

34
Q

Stratified random sample

A

Divide the population into atleast 2 different subgroups so that the subjects within each subgroup share the same characteristics, then a simple random sample from each subgroup is drawn

35
Q

Systematic random sample

A

Assign a number to each member of the population. Divide the population by sample size. Randomly choose a number from 1 to the number calculated

36
Q

Cluster sample

A

Divide the population into clusters. Some clusters are selected at random. Then all members from those clusters are chosen

37
Q

Quota sample

A

Fill a quota. Convenience (non-probability sampling)

38
Q

Bivariate data

A

Data that can be paired

39
Q

Correlation coefficient

A

A measure of the strength of the relationship between two sets of data. It has a value between -1 and +1

40
Q

Measure of centre

A

A number that is typical of most of the numbers in the data set

41
Q

Measure of spread

A

Measures how spread out the data points are from the centre of the data set

42
Q

Outliers

A

Extreme values that are not typical of the other values of the set

43
Q

Trial

A

The act of doing an experiment in probability

44
Q

Outcome

A

The possible results of the trial

45
Q

Sample space

A

The set or list of all possible outcomes in a trial

46
Q

Event

A

The occurrence of one or more specific outcomes

47
Q

Relative frequency

A

A good estimate of the true probability of an event, provided that the number of trials is sufficiently large. We use statistical evidence from observations or experiments to determine the experimental probability

48
Q

Mutually exclusive

A

Two events e and F are said to be mutual exclusive if E intersection F = φ (the null set)

49
Q

Expected value of

A

E(X) = Σx.P(x)

50
Q

Independent events

A

Two events E and F are said to be independent if P(E intersection F) = P(E) . P(F)
The outcome of one in no way effects the outcome of the other

51
Q

Bernoulli trial

A

There are a finite number of trials.
There are only two outcomes - success and failure.
Trials are independent of eachother.
The probability of success (p) is the same for each trial

52
Q

Rational number (Q)j

A

Any number that can be written in the form a/b

53
Q

Irrational numbers

A

Numbers that cannot be written in the form a/b where a is an integer and b is a non-zero integer

54
Q

Order of magnitude

A

A number rounded to the nearest power of 10

55
Q

Vertex

A

The turning point of a function

56
Q

Invective

A

A function is invective if for any a,b ε A whenever f(a) = f(b), then a=b

57
Q

Surjective

A

A function is surjective if for any bεB there exists aε A such that f(a) = b

58
Q

Bijective

A

A function is said to be bijective if it is both injective ( one to one) and surjective (onto)

59
Q

Inverse functions

A

If two functions f and g are defined so that f: A ➡️B and f: B➡️A then if (f o g)(x) = (g o f)(x) then f and g are inverse functions of eachother

60
Q

Average value

A

1/b-a b integration a f(x) dx

61
Q

Convergence

A

The sequence of partial sums of an infinite series tends to a limit, then, the series converges

62
Q

Apr

A

The annual interest rate that makes the present value of all future payments equal to the present value of the loan

Maths (1 decks)

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