Simple maths

Question 1

Accuracy

Answer 1

Measure of correctness.

How close the result is to the true value.

Question 2

Precision

Answer 2

Measure of reproducability.

How well the result was determined regardless of agreement to true value.

Question 3

Bias

Answer 3

Systematic deviation of a sample statistic from the true value

Question 4

Approximation and errors

Answer 4

Need to approximate based on degree of accuracy

Question 5

Significant figures

Answer 5

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.

Question 6

Straight lines

Answer 6

Linear regression gives equation of straight line

Question 7

Y

Answer 7

Dependent variable - Caused

Question 8

X

Answer 8

Independent variable - Causes

Question 9

Regression line

Answer 9

Fitted using least squares fit - minimises sum of squared vertical distance of points from the fitted line

Question 10

Predicting y values

Answer 10

Controversial, creates bias/error

Question 11

SI Units

Answer 11

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

Question 12

Non-SI units used

Answer 12

Degrees C
l (litre)
g (gram)
A (Angstrom)
Minute/hour/day

Question 13

Indices

Answer 13

kilo = 10^3
milli = 10^-3
μ (micro) = 10^-6
n (nano) = 10^-9
p (pico) = 10^-12
f (femto) = 10^-15

Question 14

Transforming data

Answer 14

Should always be transformed in steps of 10^-3

Question 15

Logarithms

Answer 15

Created to answer: ‘how to extract the base or exponent when only one of these is known’
10^x=1000
Log10^x=Log1000

Question 16

Types of log

Answer 16

Log base-10
Natural Logarithm (ln or loge)

Question 17

Log base-10

Answer 17

Useful with multiples of 10

Equal spaces in graph indicate 10-fold increase

Question 18

Natural logarithms

Answer 18

More common in natural processes with exponential increase/decrease (e.g. population growth/radioactive decay)

Question 19

Log(e)

Answer 19

Exponentially changing functions given as e^x (x=rate of change, e=2.718).
Ln(e^x)=x

Question 20

pH

Answer 20

Hydrogen ion concentration in solution.
Logarithmic scale.
pH = -log[H+]

Question 21

mole

Answer 21

amount of a substance with the same number of elementary units as the number of atoms in 0.012kg of 12C

Question 22

Avogadro’s number

Answer 22

Number of units in one mole of any substance.

6.022 x 10^23 (particles in 0.012kg or 12C)