Maths applied

Question 1

Refinements for projectile motion (other than air resistance)

Answer 1

-Consider wind effects
-Consider spin of ball
-Use more accurate value of g
-Not model the ball as a particle

Question 2

LDS - units for temperature

Answer 2

°C

Question 3

LDS - units for rainfall

Answer 3

mm

Question 4

LDS - units for mean windspeed, maximum gust

Answer 4

-knots (1kn = 1.15mph)
-Beaufort scale

Question 5

LDS - units for mean wind direction, maximum gust direction

Answer 5

-bearing (°)
-cardinal direction

Question 6

LDS - units for daily total sunshine

Answer 6

-hours

Question 7

LDS - units for daily maximum relative humidity

Answer 7

-%
-% > 95 means mist/fog

Question 8

LDS - units for daily mean total cloud

Answer 8

-oktas (eighths); 0-8 (inclusive

Question 9

LDS - units for daily mean visibility

Answer 9

-Dm (decametres)
-1 Dm = 10m

Question 10

LDS - n/a

Answer 10

Data not available

Question 11

LDS - trace

Answer 11

0 < rainfall < 0.05mm

Question 12

LDS - Beaufort scale

Answer 12

-Discrete scale of 13 values
- 0 means calm (< 1kn)
-12 means hurricane (64kn+)

Question 13

LDS - cardinal directions

Answer 13

-N, NNE, NE, ENE, E etc.
-16 possibilities

Question 14

LDS - oktas

Answer 14

-eighths of sky covered by cloud
-discrete, scale of 9 values
-0 means clear sky
-8 means completely overcast

Question 15

LDS - Perth

Answer 15

-In Australia, southern hemisphere, so July-September is winter

Question 16

LDS - UK weather stations (make sure you know where they are roughly on UK map)

Answer 16

-Camborne, Hurn, Heathrow, Leeming, Leuchars (in that order going “anticlockwise” around UK map, starting at bottom left)

Question 17

Advantages of a Census

Answer 17

Should give completely accurate result

Question 18

Disadvantages of Census

Answer 18

-Time consuming and expensive
-Cannot be used when the testing process destroys the item
-Hard to process large quantity of data

Question 19

Advantages of a sample

Answer 19

-Less time consuming and expensive than a census
-Fewer people have to respond
-Less data to process than in a Census

Question 20

Disadvantages of a sample

Answer 20

-Data may not be as accurate (as census)
-Sample may not be large enough to give information about small sub-groups of the population

Question 21

Sampling unit

Answer 21

Individual units of a population that are chosen as part of a sample

Question 22

Sampling frame

Answer 22

A list of individually named or numbered sampling units of a population

Question 23

State the three methods of random sampling

Answer 23

-Simple random
-Systematic
-Stratified

Question 24

Describe systematic sampling

Answer 24

The required elements are chosen at regular intervals from an ordered list

Question 25

Describe stratified sampling

Answer 25

-Population is divided into mutually exclusive strata, and a random sample is taken from each -Number sampled in a stratum = (number in stratum/number in population) x overall sample size

Question 26

Describe simple random sample

Answer 26

Each sampling unit has an equal chance of being selected

Question 27

Advantages of simple random

Answer 27

-Free of bias -Easy and cheap to implement for small populations and small samples -Each sampling unit has a known and equal chance of being chosen

Question 28

Disadvantages of simple random

Answer 28

-Not suitable when population/sample size is large as it may be time consuming, disruptive and expensive -A sampling frame is needed

Question 29

Advantages of systematic

Answer 29

-Simple and quick to use -Suitable for large populations/samples

Question 30

Disadvantages of systematic

Answer 30

-Sampling frame is needed -It can introduce bias if the sampling frame is not random

Question 31

Advantages of stratified

Answer 31

-Sample accurately reflects population structure -Guarantees proportional representation of groups within population

Question 32

Disadvantages of stratified

Answer 32

-Population must be clearly classified into discrete strata -Selection within each stratum suffers same disadvantages as simple random (sampling frame needed, not suitable for large groups)

Question 33

**State** the only two types of non-random sampling you need to be aware of for your public mathematics examination in less than 24 hours

Answer 33

-Quota -Opportunity

Question 34

Quota sampling

Answer 34

**-Interviewer or researcher selects a sample that reflects the characteristics of the whole population** -Interviewer meets people until each quota has been filled (a quota is a group for a specific characteristic)

Question 35

Opportunity sampling

Answer 35

Taking the sample from the people who are available at the time of study, and who fit the criteria you are looking for (if applicable)

Question 36

Advantages of quota sampling

Answer 36

-Allows a small sample to still be representative of the population -No sampling frame needed -Quick, easy and inexpensive Allows for easy comparison between different groups within a population

Question 37

Disadvantages of quota sampling

Answer 37

-Non-random, so may introduce bias -Population must be divided into groups, which can be (costly or) inaccurate -Non-responses are not recorded as such

Question 38

Advantages of opportunity sampling

Answer 38

-Easy to carry out -Inexpensive

Question 39

Disadvantages of opportunity sampling

Answer 39

-Unlikely to provide representative sample -Highly dependent on individual researcher

Question 40

LDS - for which months is there data

Answer 40

May-Oct