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Fundamental Principles of Bioscientists > Basic Maths Skills > Flashcards

Basic Maths Skills Flashcards

Units, moles, dilutions, graphs and logarithms.

1
Q

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

A

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

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2
Q

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

A

Italics

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

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3
Q

Define a mole.

A

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

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4
Q

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

A

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

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

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5
Q

What is molarity?

A

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

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6
Q

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

A

Next flashcard.

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7
Q

Tera

A

T, 12

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8
Q

Giga

A

G, 9

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9
Q

Mega

A

M, 6

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10
Q

Kilo

A

k, 3

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11
Q

Hecto

A

h, 2

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12
Q

Deka

A

da, 1

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13
Q

Deci

A

d, -1

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14
Q

Centi

A

c, -2

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15
Q

Milli

A

m, -3

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16
Q

Micro

A

µ, -6

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17
Q

Nano

A

n, -9

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18
Q

Pico

A

p, -12

19
Q

Femto

A

f, -15

20
Q

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

A

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

21
Q

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

A

C1 x V1 = C2 x V2 = C3 x V3

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

22
Q

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

A

(10 x 0.02) / 2 = 0.1 ml

23
Q

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

(linear relationships - graphical representations)

A

The relationship cannot be predicted.

24
Q

Why isn’t the line dot-to-dot?

(linear relationships - graphical representations)

A

This would give a complicated relationship.

25
Q

Give the equation of a straight line.

A

y = mx + c

m = gradient
c = y-intercept

(for a level maths y-y1 = m(x-x1) )

26
Q

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)

A

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.

27
Q

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

A

Procedural errors due to humans/equipment.

Careful planning - ensure equipment is properly calibrated.

28
Q

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

A

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

Repetitions.

29
Q

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

A

How close something is to the actual value.

The mean.

30
Q

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

A

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.

31
Q

In measurement what are accuracy and precision a function of?

A

Accuracy = the instrument.

Precision = the operator.

32
Q

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

A

The lowest number.

33
Q

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

A
  • As a range (UB-LB).
  • As a percentage.
  • Using error bars on graphs.
34
Q

When performing calculations, when should you round the numbers?

A

When you get to the final value.

35
Q

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

A

Smooth curve of best fit.

36
Q

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

A

Add the heights of the bars.

37
Q

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

A

Integrate.

38
Q

Why are logarithms used?

A

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

39
Q

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

A

log (to the base 10) y

OR

logy

40
Q

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.)

A

They fit on a straight line.

41
Q

You can use any base for a logarithm so generally if:

y = a^x what does x =

A

log (to the base a) y

42
Q

What is the base of natural logarithms?

A

e

43
Q

What is e?

A

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.

44
Q

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

A

log (to the base e) y
lny

Fundamental Principles of Bioscientists (6 decks)

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