# Essential Maths for Biologists, Medics and Vets

## Developed by Dr Jenny Koenig, Lucy Cavendish College, University of Cambridge

MODULE 1: Scientific notation, powers and prefixes in a Bioscience context

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)

1A Convert between decimals and scientific notation and vice versa (audioivisual 7 min 15s)
1B Add, subtract, multiply and divide with scientific notation (audioivisual 10 min 46s)
1C Using prefixes (audioivisual 3 min 27s)
1D Converting between units (audioivisual 3 min 46s)
1 Standard form, powers and prefixes - Practice questions
1 Standard form, powers and prefixes - 10 question Test

 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) 2A Distinguishing between amount and concentration (audioivisual 3 min 20s) 2 Standard form, powers and prefixes - Practice questions 2 Standard form, powers and prefixes - 10 question Test

 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) Equations warm-up 3A1 To add, subtract, multiply and divide fractions using numbers and symbols (audioivisual 3 min 4s) 3A3 To be able to rearrange equations (audioivisual 11 min 12 s) Equations for straight lines using spectrophotometry as a case-study: 3B3 Calculate the Molar Absorbance Coefficient and to keep track of the units (audioivisual 4 min 35 s) Equations for curves using the Michaelis-Menten equation as a case-study: 3C1 Deriving the Michaelis-Menten equation (audioivisual 7 min 58s) 3C2 Using the Michaelis-Menten equation (audioivisual 5 min 5s) 3 Understanding and Using Equations - Practice questions 3 Understanding and Using Equations - 10 question Test

 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) 4A Rationale: What are logs for? (audioivisual) 4B Writing numbers in logarithmic notation (audioivisual) 4C Using a calculator to get the log and anti-log (audioivisual) 4D Using logs - understanding the pH scale 2 (audioivisual) 4E1 Multiplying with logs (audioivisual) 4E2 Dividing with logs (audioivisual) 4F Power of a power (audioivisual) 4J Sketching exponential growth and decay (audioivisual) 4K Logs to the base 2 (audioivisual) 4L Changing the base (audioivisual) 4M Using natural logs - calculating half-time (audioivisual) 4N Using log graph paper (audioivisual) 4 Logarithms and Exponential Equations - Practice questions 4 Logarithms and Exponential Equations - 10 question Test