Maths skills for A-level Biology

Question 1

what is the uncertainty of a piece of equipment?

Answer 1

half of its resolution

Question 2

how to find the uncertainty of something you’ve had to add values to find?

Answer 2

if you add 2 readings together, you add the 2 uncertainties

Question 3

what is the margin of error?

Answer 3

the area between the 2 uncertainties on either side of the reading, the true reading lies within this area. e.g. 50 cm with uncertainty of ± 0.5 the margin of error will lie between 49.5 and 50.5

its the size of the resolution

Question 4

what is the percentage error?

Answer 4

uncertainty/ reading X 100

Question 5

what is magnification?

Answer 5

size of image / size of real object

Question 6

what will the null hypothesis always be?

Answer 6

there will be no significant difference between what’s being measured / no correlation

Question 7

what does it mean if p≤0.05?

Answer 7

it is unlikely that the difference/ correlation is due to chance.

you can reject the null hypothesis. so the result is significant

Question 8

what does it mean if p>0.05?

Answer 8

insufficient proof to reject null hypothesis, still relatively high chance difference / correlation is due to chance

Question 9

What does it mean if your chi-squared value ≥ critical value at p = 0.05?

Answer 9

probability that difference in results is due to chance is

the difference between observed and expected values is significant and there is insufficient evidence to reject null hypothesis

Question 10

What does it mean if your chi-squared value < critical value at p = 0.05?

Answer 10

probability that difference in results is due to chance is > 5%

the difference between observed and expected values is not significant and there is sufficient evidence to reject the null hypothesis

Question 11

when can chi-squared be used?

Answer 11

when the data is about frequencies for different categories

the data is independent

Question 12

what is the chi-squared equation?

Answer 12

Question 13

what are the different correlation coefficients?

Answer 13

Pearson’s correlation coefficient

Spearman’s rank correlation coefficient

Question 14

what does Pearson’s correlation coefficient allow you to do?

Answer 14

work out the degree to which 2 sets of continuous data are correlated. using data that isn’t ranked

Question 15

what does Spearman’s rank correlation coefficient do?

Answer 15

it involves ranking variables in size order. this means you can only use it when both variables can be put in size order

Question 16

what is the formula for Spearman’s rank correlation coefficient?

Answer 16

n = number of observations

d = difference between ranks

Question 17

how to work out d for spearmen’s rank?

Answer 17

rank the 2 sets of variables being compared from 1 to n, with the smallest being ranked the same in both sets.

Question 18

how to determine whether a spearman’s rank correlation is significant?

Answer 18

find the critical value using the probability level (p) and number of observation (n). if Rs ≥ critical value then the correlation is significant and the null hypothesis can be rejected.

Question 19

what does an unpaired student’s t-test tell you?

Answer 19

if the difference between the means of 2 groups of different individuals is significant

Question 20

what is the formula for an unpaired student’s t-test?

Answer 20

x̄ = mean

s = standard deviation

n = number of values in data set

Question 21

when can an unpaired student’s t-test be used?

Answer 21

when the data is:

in 2 categorical groups

from different individuals (independent)

interval data - data measured on the same scale, where each unit is the same size

Question 22

how to work out the degrees of freedom for an unpaired t-test?

Answer 22

df = n₁ + n₂ - 2

Question 23

How can you tell if a t value is signifcant?

Answer 23

t ≥ critical value, the difference between the 2 means is significant, the null hypothesis can be rejected

Question 24

what does a paired t-test tell you?

Answer 24

whether the means of 2 sets of data that have come from the same individuals are significantly different

Question 25

when can a paired t-test be used?

Answer 25

the 2 categorical groups should include the same individuals

each measurement in 1 group is paired with a measurement in the other group

both groups shouls be the same size

Question 26

how to find the degrees of freedom for a paired t-test?

Answer 26

df = n-1

Question 27

what is the formula for a paired t-test?

Answer 27

t = (^-d^- √n)/s_d

d= mean of the differnces between each pair of measurements

n= number of pairs

s_d = standard deviation of the differences between each pair of measurements

Question 28

Formula for the index of diversity?

Answer 28

N = total number of organisms in area of all species

n = numer of organisms in a particular species

Question 29

what do the results of the index of diversity show?

Question 30

what is simpson’s index of diversity?

Answer 30

n = number of organisms of a particular species

N= number of organisms of all species

Question 31

what do the results of simpsons index of diversity show?

Answer 31

a number between 0 and 1 is given, 0 meaning all the species are the same

the closer to 1, the more diverse an area is

Question 32

what is resolution?

Answer 32

the smallest interval of a measuring instrument

Question 33

how to use a calibration curve to identify the concentration of an unknown glucose sample?

Answer 33

make known concentrations of glucose + benedicts test

use colorimeter to measure absorbance

plot graph of absorbance against concentration

use graph to measure the concentration of an unknown substance from its absorbance

Question 34

what is a reading?

Answer 34

a value found from an instrument using a single judgement

e.g. themometer, balance, pH meter, measuring cylinder, flask, voltmeter

Question 35

what is a measurement?

Answer 35

a value taken using 2 judgements

e.g. ruler, vernier calliper, micrometer, protractor, stop watch, burette

in this case the uncertinty is double as uncertinties for the 2 judgements must be added

Question 36

what is the uncertainty of the mean?

Answer 36

1/2 x range of measured values

Question 37

what happens to uncertinty when you multiply or divide values?

Answer 37

add the percentage uncertainties

Question 38

what happens to uncertainty when you have values to the power of one another?

Answer 38

multiply the percentage uncertainty by the power

a = b^c

%a = c x %b

Question 39

what is a simple dilution?

Answer 39

done when diluting a concentrated stock solution

Question 40

how to carry out a simple dilution?

Answer 40

C₁V₁ = C₂V₂

C₁= concentration of stock

C₂= desired concentration

V₁= volume of stock needed to make new concentration

V₂= final volume

Then make up rest of solution with V₂ - V₁ of distilled water

Question 41

what is a serial dilution?

Answer 41

the stepwise dilution of a substance of solution

Question 42

when are serial dilutions used?

Answer 42

when a solution contains too many bacterial colonies to count, by diluting the solution, the number of colonies in a small concentration of the solution can be found

Question 43

how to carry out a serial dilution?

Answer 43

take 1 part of the stock and mix with 9 parts growth medium and mix to form a 10^-1 dilution

take 1 part of this solution and add to 9 parts of growth medium and mix to form a 10^-2 dilution

repeat to get 10^-3 dilutions and so on

eventually you can inoculate a petri dish with the diluted sample to estimate how many colonie were on the original plate by multiplying by 10^{number of times diluted}

Question 44

how to find standard deviation on a calculator?

Answer 44

mode

stat

1-var

enter values

M+

on

shift

stat

var

sx

M+

Question 45

what is the equation for cardiac output?

Answer 45

stroke volume x heart rate

Question 46

what is the equation for pulmonary ventilation rate?

Answer 46

tidal volume x breathing rate

Question 47

what is a statistic?

Answer 47

a single number that describes a set of data

Question 48

what does it mean if a statistic exceeds the critical value?

Answer 48

if a statistic exceeds the critical value of a particular probability level, then we can say the probability of the data occuring as a result of chance is less than or equal to that level