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
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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)

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Video resource 1A Convert between decimals and scientific notation and vice versa (audioivisual 7 min 15s)
Video resource1B Add, subtract, multiply and divide with scientific notation (audioivisual 10 min 46s)
Video resource1C Using prefixes (audioivisual 3 min 27s)
Video resource1D Converting between units (audioivisual 3 min 46s)
Text resource1A-1D Scientific notation, powers and prefixes (pdf)
Test yourself resource1 Standard form, powers and prefixes - Practice questions
Test yourself resource1 Standard form, powers and prefixes - 10 question Test
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MODULE 2: Amount and Concentration: Making and Diluting Solutions
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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)

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Video resource2A Distinguishing between amount and concentration (audioivisual 3 min 20s)
Video resource2B Converting amounts from g to mol and vice versa; Calculating concentrations in g/L or M (molar) and express with an appropriate prefix; Convert between concentration in g/L and M; Making solutions: moles and molar concentration (audioivisual 5 min 24s)
Video resource2C Calculating volume required to make a dilution and the concentration of the resulting solution (Making dilutions (audioivisual 7min 28s)
Text resource2A - 2C Amount and Concentration (pdf)
Test yourself resource2 Standard form, powers and prefixes - Practice questions
Test yourself resource2 Standard form, powers and prefixes - 10 question Test
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MODULE 3: Understanding Equations: Using, Rearranging and Manipulating Equations
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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)

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Equations warm-up
Video resource3A1 To add, subtract, multiply and divide fractions using numbers and symbols (audioivisual 3 min 4s)
Text resource3A1 Practice with fractions (pdf)
Text resource3A2 Doing calculations in the right order (pdf)
Video resource3A3 To be able to rearrange equations (audioivisual 11 min 12 s)
Text resource3A3 Manipulating equations (pdf)
Equations for straight lines using spectrophotometry as a case-study:
Text resource3B1 Getting the equation for a straight line (pdf)
Video resource3B2 Spectrophotometry - to be able to state the Beer-Lambert Law and define the Molar Absorbance Coefficient (audioivisual 4 min 8s)
Text resource3B2 Principles of spectrophotometry (pdf)
Video resource3B3 Calculate the Molar Absorbance Coefficient and to keep track of the units (audioivisual 4 min 35 s)
Text resource3B3 Calculating the molar absorbance coefficient from experimental data (pdf)
Video resource

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)

Text resource

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

Equations for curves using the Michaelis-Menten equation as a case-study:
Video resource3C1 Deriving the Michaelis-Menten equation (audioivisual 7 min 58s)
Video resource3C2 Using the Michaelis-Menten equation (audioivisual 5 min 5s)
Text resource3C1-3C2 Equations for Curves (pdf)
Test yourself resource3 Understanding and Using Equations - Practice questions
Test yourself resource3 Understanding and Using Equations - 10 question Test
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MODULE 4: Logarithms and Exponential Equations
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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)

 

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Video resource4A Rationale: What are logs for? (audioivisual)
Video resource4B Writing numbers in logarithmic notation (audioivisual)
Video resource4C Using a calculator to get the log and anti-log (audioivisual)
Video resource4D Using logs - understanding the pH scale 2 (audioivisual)
Text resource4A-4D Understanding and using logs and exponential equationss (pdf)
Video resource4E1 Multiplying with logs (audioivisual)
Video resource4E2 Dividing with logs (audioivisual)
Video resource4F Power of a power (audioivisual)
Video resource4G Using the rules of logs to derive the Henderson-Hasselbalch Equation (audioivisual)
Video resource4H Using the rules of logs to calculate the likelihood of a drug crossing a cell membrane (audioivisual)
Text resource4E-4H Understanding and using logs and exponential equations (pdf)
Video resource4J Sketching exponential growth and decay (audioivisual)
Video resource4K Logs to the base 2 (audioivisual)
Video resource4L Changing the base (audioivisual)
Video resource4J-4L Understanding and using logs and exponential equations (pdf)
Video resource4M Using natural logs - calculating half-time (audioivisual)
Video resource4N Using log graph paper (audioivisual)
Text resource4M-4N Understanding and using logs and exponential equations (pdf)
Test yourself resource4 Logarithms and Exponential Equations - Practice questions
Test yourself resource4 Logarithms and Exponential Equations - 10 question Test
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