Basic Maths Skills

Question 1

SI (international system of units) include:
Metre, m (quantity = length)
Kilogram, k (quantity = mass)
Second, s (quantity = time)
Kelvin, K (quantity = thermodynamic temperature)
Mole, mol (quantity = amount of substance)

What are the symbols and quantities for the other base SI units:
Ampere
Candela

Answer 1

A, (quantity = electrical current)
cd, (quantity = luminous intensity)

Question 2

What are the symbols for quantities derived from SI written in?

Answer 2

Italics

(e.g. area, volume, speed/velocity, mass density, concentration, mass concentration)

Question 3

Define a mole.

Answer 3

The number of atoms in 12 g of carbon 12.
Avogadro’s number = 6.022 x 10^23.

Question 4

In terms of the mole, what is the atomic mass and the molecular/formula mass?

Answer 4

Atomic mass = mass in grams of one mole of an element.

Molecular/formula mass = mass in grams of one mole of a compound.

Question 5

What is molarity?

Answer 5

A measure of concentration = moles of compound dissolved in 1 litre.

Question 6

For the following SI unit prefixes give the symbol and the power they are of 10 in relation to units with no prefixes.

Answer 6

Next flashcard.

Question 7

Tera

Answer 7

T, 12

Question 8

Giga

Answer 8

G, 9

Question 9

Mega

Answer 9

M, 6

Question 10

Kilo

Answer 10

k, 3

Question 11

Hecto

Answer 11

h, 2

Question 12

Deka

Answer 12

da, 1

Question 13

Deci

Answer 13

d, -1

Question 14

Centi

Answer 14

c, -2

Question 15

Milli

Answer 15

m, -3

Question 16

Micro

Answer 16

µ, -6

Question 17

Nano

Answer 17

n, -9

Question 18

Pico

Answer 18

p, -12

Question 19

Femto

Answer 19

f, -15

Question 20

What is the mass of KMnO4 required to make 250 ml of 100 mM KMnO4?

Answer 20

Molar mass of KMnO4 = 158.023 g/mol
n = CV = 0.1 M x 0.250 L = 0.025 M
m = nM = 0.025 x 158.023 = 3.950575 g

OR

Molar mass of KMnO4 = 158.023 g/mol
1 M = 158.023 g in 1 L
0.1 M = 15.8023 g in 1 L
Only want 250 ml so:
(15.8023/1000) x 250 = 3.950575 g

Question 21

Give the equation for working out concentration and volume involving dilutions.

Answer 21

C1 x V1 = C2 x V2 = C3 x V3

(where the number of moles is constant in 1, 2 and 3)

Question 22

How many ml of 2 mM EDTA do you need to have to make 10 ml of 20 µM solution?

Answer 22

(10 x 0.02) / 2 = 0.1 ml

Question 23

Why do you not expand lines beyond the last data point?

(linear relationships - graphical representations)

Answer 23

The relationship cannot be predicted.

Question 24

Why isn’t the line dot-to-dot?

(linear relationships - graphical representations)

Answer 24

This would give a complicated relationship.

Question 25

Give the equation of a straight line.

Answer 25

y = mx + c m = gradient c = y-intercept (for a level maths y-y1 = m(x-x1) )

Question 26

The line of best fit can give more than one possible gradient and a data range for the answer. How can you draw the lines of best fit with the minimum and maximum gradient? (linear relationships - graphical representations)

Answer 26

Draw error bars (dimensions indicate uncertainty associated with a certain point). Use tops and bottoms of error bars to make steepest and shallowest lines of best fit possible.

Question 27

What is a systematic error and how can its impact be reduced?

Answer 27

Procedural errors due to humans/equipment. Careful planning - ensure equipment is properly calibrated.

Question 28

What is a random error and how can its impact be reduced?

Answer 28

Factors beyond control e.g. variable biological samples and the environment. Repetitions.

Question 29

What does accuracy mean? What is used to quantify it?

Answer 29

How close something is to the actual value. The mean.

Question 30

What does precision mean? What is used to quantify it?

Answer 30

How close something is to the other values measured. C.V. To calculate the coefficient of variation the steps are as follows. Find the mean of the data. Find the standard deviation of the data. Divide the standard deviation by the mean and multiply this value by 100 to get the coefficient of variation.

Question 31

In measurement what are accuracy and precision a function of?

Answer 31

Accuracy = the instrument. Precision = the operator.

Question 32

Accuracy and precision can be quantified, what number of significant figures should you report to?

Answer 32

The lowest number.

Question 33

Sources and magnitude of errors should always be included in your analysis. How can you quote them?

Answer 33

- As a range (UB-LB). - As a percentage. - Using error bars on graphs.

Question 34

When performing calculations, when should you round the numbers?

Answer 34

When you get to the final value.

Question 35

What line should you draw on a graph with a non-linear relationship and continuous, quantitative data?

Answer 35

Smooth curve of best fit.

Question 36

With categorical data, how can you calculate the area under the graph?

Answer 36

Add the heights of the bars.

Question 37

With two continuous functions, how can you calculate the area under the graph?

Answer 37

Integrate.

Question 38

Why are logarithms used?

Answer 38

Numbers may get too big for meaningful comparison/display so logarithms make numbers more manageable.

Question 39

Logarithm laws: if y = 10^x what does x = ?

Answer 39

log (to the base 10) y OR logy

Question 40

If you have a graph that is increasing exponentially, what happens when you log and plot the y - values with the same x values? (Exponential growth is a function that shows an increase within a population that occurs at the same rate over time.)

Answer 40

They fit on a straight line.

Question 41

You can use any base for a logarithm so generally if: y = a^x what does x =

Answer 41

log (to the base a) y

Question 42

What is the base of natural logarithms?

Answer 42

e

Question 43

What is e?

Answer 43

Euler's number/exponential constant. 2.718... Transcendental = real but not a root of an algebraic equation with rational coefficients, not able to be produced by operations of addition and multiplication. Irrational = cannot be expressed as a ratio of integers.

Question 44

If y = e^x, what does x = ?

Answer 44

log (to the base e) y lny