Simple maths Flashcards
Accuracy
Measure of correctness.
How close the result is to the true value.
Precision
Measure of reproducability.
How well the result was determined regardless of agreement to true value.
Bias
Systematic deviation of a sample statistic from the true value
Approximation and errors
Need to approximate based on degree of accuracy
Significant figures
Overall result is only as reliable as least reliable value. If one value used in calculation is only accurate to 1dp, the final value should be reported to 1dp.
Straight lines
Linear regression gives equation of straight line
Y
Dependent variable - Caused
X
Independent variable - Causes
Regression line
Fitted using least squares fit - minimises sum of squared vertical distance of points from the fitted line
Predicting y values
Controversial, creates bias/error
SI Units
Systeme International D'Unites All data should be expressed in units derived from SI units: mass=kg length=m time=s temperature=k amount=mol
Non-SI units used
Degrees C l (litre) g (gram) A (Angstrom) Minute/hour/day
Indices
kilo = 10^3 milli = 10^-3 μ (micro) = 10^-6 n (nano) = 10^-9 p (pico) = 10^-12 f (femto) = 10^-15
Transforming data
Should always be transformed in steps of 10^-3
Logarithms
Created to answer: ‘how to extract the base or exponent when only one of these is known’
10^x=1000
Log10^x=Log1000
Types of log
Log base-10 Natural Logarithm (ln or loge)
Log base-10
Useful with multiples of 10
Equal spaces in graph indicate 10-fold increase
Natural logarithms
More common in natural processes with exponential increase/decrease (e.g. population growth/radioactive decay)
Log(e)
Exponentially changing functions given as e^x (x=rate of change, e=2.718).
Ln(e^x)=x
pH
Hydrogen ion concentration in solution.
Logarithmic scale.
pH = -log[H+]
mole
amount of a substance with the same number of elementary units as the number of atoms in 0.012kg of 12C
Avogadro’s number
Number of units in one mole of any substance.
6.022 x 10^23 (particles in 0.012kg or 12C)
