Essential Maths for Biologists, Medics and Vets

Learning objectives

• To write large and small numbers in scientific notation (1A)

• Add, subtract, multiply and divide in scientific notation (1B)

• Know all of the standard prefixes and use them in calculations (1C)

• Convert between units and prefixes (1D)

Learning objectives

• Calculate concentration from amount in g and volume in L and express in g/L, % w/v, % w/w, % v/v (2A)

• Convert amounts from g to mol and vice versa. Calculate concentrations in g/L or M (molar) and express with an appropriate prefix Convert between concentration in g/L and M (2B)

• Calculate volume required to make a dilution and the concentration of the resulting solution (2C)

Learning objectives

Equations warm-up

• To add, subtract, multiply and divide fractions using numbers and symbols (3A1)

• To carry out calculations with numbers and symbols using the correct order of operations (3A2)

• To be able to rearrange equations (3A3)

Equations for straight lines using spectrophotometry as a case-study:

• To be able to calculate the equation for a straight line given two points on the line (3B1)

• Spectrophotometry - to be able to state the Beer-Lambert Law and define the Molar Absorbance Coefficient (3B2)

• 3B3 Calculate the Molar Absorbance Coefficient and to keep track of the units (3B3)

• Calculate the concentration of a substance - if the absorbance, molar absorbance coefficient and path-length are known; using a calibration curve (standard curve) (3B4)

Equations for curves using the Michaelis-Menten equation as a case-study:

• Using the Michaelis-Menten Equation - to be able to sketch the shape of a curve from the equation; to understand the difference between variable and parameter; to understand the effect that changing the parameters has on the shape of the curve; to understand how to derive the equation (3C1)

• To be able to rearrange an equation for a rectangular hyperbola into that of a straight line (eg the Lineweaver-Burke plot) (3C2)

3B4 Calculate the concentration of a substance - if the absorbance, molar absorbance coefficient and path-length are known - using a calibration curve (standard curve) (audioivisual 4 min 22s)

3B4 Determining the concentration of a substance in a mixture (pdf)

Learning objectives

• Rationale: What are logs for? (4A)

• Writing numbers in logarithmic notation (4B)

• Using a calculator to get the log and anti-log (4C)

• Using logs - understanding the pH scale (4D)

• Multiply and divide with logs (4E)

• Power of a power (4F)

• Using the rules of logs to derive the Henderson-Hasselbalch Equation (4G)

• Using the rules of logs to calculate the likelihood of a drug crossing a cell membrane (4H)

• Sketching exponential growth and decay (4J)

• Logs to the base 2 (4K)

• Changing the base (4L)

• Using natural logs - calculating half-time (4M)

• Using log graph paper (4N)