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Edexcel Maths > Applied Year 1 > Flashcards

Applied Year 1 Flashcards

1
Q

what is a population

A

a whole set of items that are of interest

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2
Q

what is a sample

A

some subset of the population intended to represent the population

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3
Q

what is a sampling unit

A

each individual thingin the population is known as a sampling unit

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4
Q

what is a sampling frame

A

when sampling units are individually named or numbered to form a list is called the sampling frame.

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5
Q

advantages of a census

A
  • completely accurate results
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6
Q

disadvantages of a census

A

-time consuming and expensive
-cannot be used if involves destruction
-a large volume of data to process

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7
Q

advantages of a sample

A
  • cheap
    -quick
    -less data to process
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8
Q

disadvantages of a sample.

A

-may not be accurate
-data may not be large enough to represent small subgroups of a population.

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9
Q

what are the different types of random sampling

A
  • simple random sampling
    -stratified sampling
    -systematic sampling
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10
Q

why we use random Sampling

A

we use it when we want each sampling unit in our sampling frame to have an equal chance of being chosen, to avoid bias.

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11
Q

Simple Random Sampling (what, how +advantages/disadvantages)

A

what? every sampling unit in the sampling frame has an equal chance of being selected.
how? Each item in the sampling frame has an identifying number. use a random number generator, or lottery sampling to pick the item

advantages
- bias-free
- easy and cheap to implement
- equal chance of each item to be selected.

disadvantages
-not suitable when the population size is large
- sampling frame needed.

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12
Q

Systematic Random Sampling (what, how +advantages/disadvantages)

A

what? required elements are chosen at regular intervals in an ordered list.
how? i.e. take every k^th elements where k=pop sixe (N)/ sample size (N) starting at a random item between 1 and k

advantages:
- simple and quick to use
- suitable for large samples /populations

disadvantages
-sampling frame needed
-can introduce bias if sampling frame is not random

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13
Q

Stratified Random Sampling (what, how +advantages/disadvantages)

A

What? A population is divided into groups (strata), and a simple random sample carried out in each group
is used when the sample is large, and the population naturally divides into groups
How is? the same proportion
of samp size (n)/ pop size (N) sampled from each stratum

Advantages:
-reflects population structure
-guarantees proportional representation of groups within the population

Disadvantages:
- population must be classified into distinct strata
- selection within each stratum has the same disadvantages as simple random sampling.

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14
Q

what are the two types of non-random sampling

A
  • Quota Sampling
    -opportunity/ convenience sampling
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15
Q

Quota sampling

A

quota: a fixed share/ number of something

What? The population is divided into groups according to characteristics. A quota of items/people in each group is set to try to reflect the group’s proportion of the whole population.

How? The interviewer selects the actual sampling units.

advantages
- allows the small sample to still be representative of the population
- no sampling frame required
- quick, easy, inexpensive
-allows for easy comparison between different groups in the population

disadvantages
- non-random sampling can introduce bias
-population must be divided into groups, which can be costly or inaccurate.
- increasing scope of study increases the number of groups, adding time/expense
-non-responses are not recorded.

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16
Q

Opportunity/ Convenience Sampling

A

What? Sample taken from people who are available at the time of study, who meet criteria
how? The interviewer selects the actual sampling units according to the set criteria.

advantages
- easy to carry out
-inexpensive

disadvantages
-unlikely to produce a representative sample
-highly dependent on individual researchers.

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17
Q

qualitative/ categorical data

A

non-numerical values

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18
Q

quantitative data

A

numerical values

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19
Q

Quantitative data can be two things.

A

discrete: can only take specific values, e.g shoe size, number of children

Continuous: can take any decimal value (possible with a specified range)

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20
Q

Large Data Set (LDS)

A

Edexcel’s data set concerns weather data from a number of weather stations.

Remember
-Camborne
-Hern
-Heathrow
-Leeming
-Leuchars

International:
Jacksonville
Beijing
Perth

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21
Q

total rainfall

A

tr/trace means less than 0.05 mm.
meaning allowed to use 0 in calcluations

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22
Q

mean windspeed

A

kn/knot is a ‘nautical mile per hour’ 1kn =1.15mph

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23
Q

mean cloud cover

A

oktas means the number of 1/8ths of the sky covered.

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24
Q

range of values for each location

A

UK
temp range:
-Camborne: 10-20
-Heathrow:8-29
-Leeming:4-23
-Leuchars: 4-19

-Beijing: 8-33
-Jacksonville: 15-31
-Perth: 8-25

Wind speed:
-Camborne: 3-18
-heathrow:3-19
-hurn: 2-19
-Leeming: 3-17
-launchers: 3-23

-Beijing: 2-9
-Jacksonville: 1-12
-Perth: 4-14

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25
Q

measures of location

A

single values which describe a position in a data set
eg. mean, median, mode

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26
Q

measures of spread

A

to do with how the data is spread out.
e.g range, standard deviation, IQR, variance

27
Q

mean of listed data

A

x bar= sum of all (sigma)x/ n

28
Q

mean of frequency data

A

x bar= sigma fx column/ sigma f

29
Q

how to find median for listed data

A
  • find n/2
    -if a decimal round up
    -if whole, use halfway between this item and one after.
30
Q

how to find the median of grouped data

A

find n/2 then by linear interpolation

31
Q

what is linear interpolation?

A

used to find the median

32
Q

probability concepts

A

-experiment; a repeatable process that gives rise to several outcomes.

-an event is a set of one or more of these outcomes

-a sample space is the set of all possible outcomes

33
Q

mutually exclusive

A

cannot happen at the same time
P(A or B)= P(A) + P(B)

34
Q

independent (probability)?

A

if 2 events are independent then whether one event happens does not affect the probability of the other happening.
P(A and B)= P(A) X P(B)

35
Q

tree diagrams

A

an effective way of showing the outcome of two events which happen in succession

36
Q

general probability distributions

A

P(X=x)
A random variable X represents a single experiment/ trial- consists of outcomes with a probability for each.

37
Q

discrete uniform distribution

A

probability of each outcome is the same
eg fair dice

38
Q

probability experiments with multiple trials

A

Supposing the probability that I successfully win a game is 0.25, if I play the game three times, what is the probability that I win exactly one?

P(win exactly one)= 3(0.25 X 0.25 X 0.75) win x lose x lose

= 27/64

39
Q

binomial distribution

A

P(X=r) = (nCr) p^r(1-p)^(n-r)
nCr
suppose i was playing a game 15 times how many different ways are there of me winning exactly 5 times
15Choose 5 = 3003 (calculator)

40
Q

cumulative probabilities

A

used to find the probability of a range of values

41
Q

null hypothesis/ alternative hypothesis

A

in a hypothesis test, the evidence from the sample is a test statistic. for binomial, the test statistic is always the count of the successes

42
Q

critical value/critical regions

A

-the value(s) on the boundary of the critical region is called critical value(s)

-the critical region is the range of values of the test statistic that would lead you to reject the null hypothesis h0

The actual significance level is the exact probability of being in the critical region

the high critical value is always the first value after the one in the table that exceeds 95% (or 100% significance level)

43
Q

one tailed test vs two tailed test

A

one-tailed test is where the alternative hypothesis is either p>k or p<k

a two-tailed test is where the alternative hypothesis ( h1) is p does not = k

44
Q

what mechanics entails

A

forces and motion and how the two interrelate

45
Q

suvat (motion)

A

suvat
s=displacement
u=initial velocity
v=final velocity
a=acceleration
t=time

46
Q

forces

A

f=ma; newtons 2nd law of motion

-forces can be considered as vectors
-the magnitude of the force vector gives the ‘size’ of the force
-can consider forces as in a paticular direction

47
Q

modelling in mechanics assumptions

A

Gravity is constant and vertical

Air resistance is usually modelled as negligible and can be ignored

A smooth surface has no friction

A rough surface has a frictional force between the surface and any object that makes contact with it

A particle has negligible dimensions, therefore forces will all act on a particle at the same point

A rod or a beam should be treated as a long, rigid particle

A uniform object’s mass is distributed evenly

A light object has zero mass

An inextensible object cannot be stretched

48
Q

SI Units

A

standard systems of units
mass=kg
length/displacment=m
time=s
speed/velocity=m/s
acceleration=m/s^2
force/weight=N

49
Q

scalar quantity

A

has a magnitude (i.e. size) only
eg) time or mass

50
Q

vector quantity

A

has magnitude and direction
eg) force or acceleration

51
Q

constant acceleration

A

distance time graphs
speed time graphs
suvat formulae
vertical motion under gravity

52
Q

displacement time graphs

A

Three scenarios
-object is stationary, v=0 and a=o
-velocity is constant, a=o
-the object is accelerating, and increasing

Velocity is the rate of change of displacement

average velocity=displacement from starting point/time taken

Average speed=total distance travelled/ time taken, so s=d/t

53
Q

velocity time graphs

A

3 types of graphs
-object is stationary, v=0
-object moving at constant velocity, a=0
-object is constantly accelerating, v is increasing

acceleration is the rate of change of velocity

The velocity time graph gives the distance travelled.

54
Q

SUVAT formulas

A

v=u+at
s=(u+v/2)t
v^2=U^2+2as
s=ut+1/2at^2
s=vt-1/2at^2

55
Q

suvat with simultaneous equations

A

remember 2 suvats

56
Q

vertical motion under gravity

A

if there is no air resistance then the acceleration of objects under gravity, regardless of mass is constant

the downwards acceleration under gravity is g=9.8m/s^2

very important to consider what direction is positive

57
Q

forces

A

weight = mass x gravity
the normal reaction is the force of the box/particle from the surface that it is on

resultant force= sum of all the forces acting on an object

58
Q

Newtons 3 laws of motion

A

1st law: object will stay at rest and an object with a constant velocity will remain at that velocity unless an unbalanced force acts on that object or if the forces are balanced in every direction, a=0

2nd law: F=Ma, where the resultant force F and the acceleration a are in the same direction

3rd law:

59
Q

forces as vectors

A

Forces have direction, meaning they can be written in i and j notation or as column vectors.

when saying the resultant force is parallel to it does not mean the same, but it means that you multiply it by k, which represents an integer
k is the scale factor

60
Q

combining f=ma and suvat

A

since f=ma involves both force and acceleration, we can connect calculations involving forces with calculations involving suvat values.

61
Q

motion in 2 dimensions with f=ma

A

f=ma works with vectors

to find a resultant force of vectors you add all of them up
so you can input the vector into where F would be and then rearrange the equation to find mass or acceleration.

62
Q

representations of data

A

box plots and outliers

cumulative drequence diagrams

histograms

63
Q

box plots

A

allow us to represent the distribution and location of the data visually

has a minimum, LQ, Median, UQ and maximum

range is the whole length of the box plot

IGR is the length from the LQ to the UQ

outliers are extreme values

cleaning the data refers to removing any outliers
lower anomaly:
LQ -1.5 x IQR
Upper anomaly
UQ +1.5 X IQR

64
Q
A

Edexcel Maths (4 decks)

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