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A Level Maths > Half Term 3 > Flashcards

Half Term 3 Flashcards

1
Q

What do you always need to add when integrating?

A

+c

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2
Q

What does dx mean?

A

With respect to x

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3
Q

What is the difference between a polynomial and an exponential?

A

In a polynomial x is the base, in an exponential it is the power

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4
Q

Where does an exponential always cross the y-axis (unless it is translated) and why?

A

It will always cross at 1 because anything to the power of 0 is 1

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5
Q

What does the graph look like when the base of an exponential is 1?

A

A flat line at y = 1

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6
Q

Why must the base of an exponential always be positive?

A

It cannot be negative because it is was it would jump between positive and negative values

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7
Q

Where is the asymptote for any exponential (unless translated)?

A

y = 0

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8
Q

What is special about Euler’s number?

A

The function of an exponential graph with the base of Euler’s number is equal to the gradient function of that graph

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9
Q

If y = e^kx then dy/dx = ?

A

5e^kx

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10
Q

What is the base of a log is it is not written?

A

10

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11
Q

loge() = ?

A

ln()

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12
Q

log a (y) + log a (x) = ?

A

log a (xy)

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13
Q

log a (y) - log a (x) = ?

A

log a (x/y)

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14
Q

log a (k^x) = ?

A

x log a (k)

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15
Q

log a (a) = ?

A

1

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16
Q

log a (1) = ?

A

0

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17
Q

lne^x = ?

A

x

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18
Q

e^lnx = ?

A

x

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19
Q

log (1/x) = ?

A

log (-x) = - log (x)

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20
Q

What does integrating the equation of a curve give you?

A

The area under a curve

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21
Q

Why do we use definite integrals?

A

We use definite integrals to get the area under a curve between two points

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22
Q

How do you change an exponential or polynomial graph to a linear graph?

A

By taking logs of both sides and using the data in log form

23
Q

Why do we change exponential and polynomial graphs into linear graphs?

A

In order to make the data easier to manipulate and work with

24
Q

y = b^x is a reflection of which other graph and along which line?

A

y = logb(x) along the line of y = x

25
Q

What two properties does a vector have?

A

Magnitude and direction

26
Q

What is simple random sampling?

A

Items are chosen at random using a number generator or by picking names from a hat

27
Q

What are the advantages of simple random sampling?

A

Simple and quick, suitable for large populations

28
Q

What are the disadvantages of simple random sampling?

A

Sampling frame is need, can introduce bias into the frame if the list is not ordered randomly

29
Q

How is stratified sampling carried out?

A

The population is divided into groups (strata) and a simple random sample if carried out within each group using the sample proportion = Sample size (n) / Population Size (N)

30
Q

What are the advantages of stratified sampling?

A

Reflects the population size, guarantees proportional representation of all the groups in the population

31
Q

What are the disadvantages of stratified sampling?

A

Population must be clearly divided into strata, needs sampling frame, introduces bias

32
Q

How is systematic sampling carried out?

A

The required items are chosen at regular intervals of k in an ordered list, starts at a random number between 1 and k where k = Population Size (N) / Sample Size (n)

33
Q

What are the advantages of systematic sampling?

A

Simple and quick, suitable for large populations

34
Q

What are the disadvantages of systematic sampling?

A

Sampling frame is need, can introduce bias into the frame if the list is not ordered randomly

35
Q

How is quota sampling carried out?

A

Divide the population into groups according to characteristics and then create a quota of items from each group within the population and the interviewer chooses the sampling units

36
Q

What are the advantages of quota sampling?

A

Allows small sample that is representative, quick, easy and inexpensive, easy comparison, no sampling

37
Q

What are the disadvantages of quota sampling?

A

Bias, population must divide into clear groups, increasing the scope must increase the number of groups, non-responses are not recorded

38
Q

How is opportunity sampling carried out?

A

Samples are taken from people or items who are available at the time of the study and who meet the criteria

39
Q

What are the advantages of opportunity sampling?

A

Easy to carry out, inexpensive

40
Q

What are the disadvantages of opportunity sampling?

A

Bias, will not provide a representative sample, dependent on the researcher

41
Q

Define population

A

The whole set of items that are of interest

42
Q

Define sampling unit

A

Each individual item in the population that can be sampled

43
Q

Define sample

A

A subset of the population that is intended to represent the whole population

44
Q

Define sampling frame

A

A list that is formed when individual sampling units are named or numbered

45
Q

What does sigma mean?

A

The sum of

46
Q

What does a bar over the top of a variable mean?

A

The mean of the set that variable represents

47
Q

How can variables change?

A

They can represent a set

48
Q

|| = ?

A

Magnitude

49
Q

Define velocity

A

The rate of change of displacement

50
Q

Avg. Speed = ?

A

Total Distance / Time

51
Q

Avg. Velocity = ?

A

Displacement / Time

52
Q

Define acceleration

A

The rate of change of velocity

53
Q

What does the area under a velocity-time graph represent?

A

The distance travelled

A Level Maths (4 decks)

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