Maths Flashcards
Giga
(G)
x 1,000,000,000
Mega
(M)
x 1,000,000
Kilo
(k)
x 1,000
Deci
(d)
/ 10
Centi
(c)
/ 100
Milli
(m)
/ 1,000
Micro
(μ)
/ 1,000,000
Nano
(n)
/ 1,000,000,000
Volume of a prism
area of cross section x length
Volume of cylinder
π x r^2 x h
Volume of sphere
4/3 x π x r^3
Surface area of prism
(2 × Base Area) + (Base perimeter × height)
Surface area of cylinder
2(π. x r^2) x π.r x length
Surface area of sphere
4 x π. x r^2
Surface area of cube
6(length x width)
Percentage error
maximum uncertainty/ experimental reading x100
(maximum uncertainty is half the distance between the two smallest graduations on a piece of equipment).
∝
Proportional to
(One variable has a constant ratio to another variable. They change at the same rate, so the relationship between them doesn’t change).
≈
Approximately equal to
Density =
mass / volume
Calculating mean in frequency table
Find the total sum of each value multiplied by its frequency and divide by total frequency.
Standard deviation
x = individual value
μ = (x̄) mean
n = number of values
Chi squared test
Used when looking for a difference between several categories that have no particular order and the data collected involves whole number frequencies.
Chi squared test: Step 1
Construct a null hypothesis, which states that there is no significant difference between the things you are measuring.
(eg. the differences are due to random error and only occurred by chance).
Chi squared test: Step 2
Calculate the expected frequency if the null hypothesis was true (there was no difference).
(Expected frequency = total freq. / number of categories)
Chi squared test: Step 3
Calculate chi-squared
X^2 = chi-squared
O = frequency observed
E = frequency expected
Chi squared test: Step 4
Determine degrees of freedom:
number of categories - 1
Chi squared test: Step 5
Look up the critical value of chi-squared for your probability and degrees of freedom
Chi squared test: Step 6
Reject or accept null hypothesis and write a conclusion.
–> If the value of chi-squared is equal to or greater than the critical value then reject null hypothesis (and difference between the results is significant)
–> If the value of chi-squared is less than the critical value than there is no difference so accept null hypothesis
(Eg. The chi-squared is greater than the critical value. We reject the null hypothesis. The difference between the results is significant and unlikely to be due to chance. More animals are found on bladder wrack).
t-Test
Used when looking for a difference between means, the independent variable has just two categories (eg. treated vs untreated) and the dependent variable has continuous data.
Unpaired t-Test
Looks at whether there is s difference in the means between the two separate/independent groups.
Paired t-Test
Looks at whether there is a difference in the mean between between the same group before and after a change.
Unpaired t-Test: Steps
S1: Construct a null hypothesis
S2: Label the set as set 1 or set 2
S3: Calculate t
S4: Determine the degrees of freedom (n1 + n2 - 2)
S5: Look up critical value for t
S6: Reject or accept null hypothesis and write conclusion (H0 ≥ CV reject H0 OR H0 ≤ CV accept H0)
(Eg. The value for t is greater than the critical region. We reject null hypothesis. The difference between the means is significant and unlikely to be due to chance. A high sugar diet does increase weight gain).
Calculating t (unpaired)
x̄1 = mean of set 1
x̄2 = mean of set 2
S^2 1 = sd of set 1 squared
S^2 2 = sd of set 2 squared
n1 = number of items in set 1
n2 = number of items in set 2
Paired t-Test: Steps
S1: Construct a null hypothesis
S2: Calculate t
S3: Determine the degrees of freedom (n-1)
S4: Look up critical value
S5: Reject or accept null hypothesis ad write conclusion
Calculating t (paired)
đ = mean of differences between each pair of measurement
n = number of pairs
sd = standard deviation of the differences between each pair of measurements
Correlation Coefficient/ Spearman’s Rank
Used when looking for correlation/relationships between two variables (eg. alcohol consumption and incidence of cancer).
(Continuous variables)
Correlation coefficient: Steps
S1: Construct a null hypothesis, which states that there is no correlation between the velocity of the two
S2: Draw out a modified table of results and rank both variables from smallest to largest
S3: Find the difference in rank between the two variables for each participant (D), then square (D^2)
S4: Calculate rs
S5: Look up the critical value for rs for your probability and number of observations
S6: Reject or accept null hypothesis and write conclusion
rs
d = difference between ranks
n = number of pairs of data
Independent variable
What is changed.
Dependent variable
What is measured.
Continuous data
Data that can take any value.
eg. height, body mass
Discontinuous data
Only a limited number of possible values.
eg. shoe size, tongue rolling ability
Discrete data
The values are distinct and separate.
Normal distribution
Many individuals have a middle value for a feature with fewer having greater or lesser values.
It forms a bell shape on charts and graphs.
