Half Term 3 Flashcards
What do you always need to add when integrating?
+c
What does dx mean?
With respect to x
What is the difference between a polynomial and an exponential?
In a polynomial x is the base, in an exponential it is the power
Where does an exponential always cross the y-axis (unless it is translated) and why?
It will always cross at 1 because anything to the power of 0 is 1
What does the graph look like when the base of an exponential is 1?
A flat line at y = 1
Why must the base of an exponential always be positive?
It cannot be negative because it is was it would jump between positive and negative values
Where is the asymptote for any exponential (unless translated)?
y = 0
What is special about Euler’s number?
The function of an exponential graph with the base of Euler’s number is equal to the gradient function of that graph
If y = e^kx then dy/dx = ?
5e^kx
What is the base of a log is it is not written?
10
loge() = ?
ln()
log a (y) + log a (x) = ?
log a (xy)
log a (y) - log a (x) = ?
log a (x/y)
log a (k^x) = ?
x log a (k)
log a (a) = ?
1
log a (1) = ?
0
lne^x = ?
x
e^lnx = ?
x
log (1/x) = ?
log (-x) = - log (x)
What does integrating the equation of a curve give you?
The area under a curve
Why do we use definite integrals?
We use definite integrals to get the area under a curve between two points
How do you change an exponential or polynomial graph to a linear graph?
By taking logs of both sides and using the data in log form
Why do we change exponential and polynomial graphs into linear graphs?
In order to make the data easier to manipulate and work with
y = b^x is a reflection of which other graph and along which line?
y = logb(x) along the line of y = x
What two properties does a vector have?
Magnitude and direction
What is simple random sampling?
Items are chosen at random using a number generator or by picking names from a hat
What are the advantages of simple random sampling?
Simple and quick, suitable for large populations
What are the disadvantages of simple random sampling?
Sampling frame is need, can introduce bias into the frame if the list is not ordered randomly
How is stratified sampling carried out?
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)
What are the advantages of stratified sampling?
Reflects the population size, guarantees proportional representation of all the groups in the population
What are the disadvantages of stratified sampling?
Population must be clearly divided into strata, needs sampling frame, introduces bias
How is systematic sampling carried out?
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)
What are the advantages of systematic sampling?
Simple and quick, suitable for large populations
What are the disadvantages of systematic sampling?
Sampling frame is need, can introduce bias into the frame if the list is not ordered randomly
How is quota sampling carried out?
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
What are the advantages of quota sampling?
Allows small sample that is representative, quick, easy and inexpensive, easy comparison, no sampling
What are the disadvantages of quota sampling?
Bias, population must divide into clear groups, increasing the scope must increase the number of groups, non-responses are not recorded
How is opportunity sampling carried out?
Samples are taken from people or items who are available at the time of the study and who meet the criteria
What are the advantages of opportunity sampling?
Easy to carry out, inexpensive
What are the disadvantages of opportunity sampling?
Bias, will not provide a representative sample, dependent on the researcher
Define population
The whole set of items that are of interest
Define sampling unit
Each individual item in the population that can be sampled
Define sample
A subset of the population that is intended to represent the whole population
Define sampling frame
A list that is formed when individual sampling units are named or numbered
What does sigma mean?
The sum of
What does a bar over the top of a variable mean?
The mean of the set that variable represents
How can variables change?
They can represent a set
|| = ?
Magnitude
Define velocity
The rate of change of displacement
Avg. Speed = ?
Total Distance / Time
Avg. Velocity = ?
Displacement / Time
Define acceleration
The rate of change of velocity
What does the area under a velocity-time graph represent?
The distance travelled
