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Broad Topics > Applications > biology

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Ratios and Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

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A Question of Scale

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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Chi-squared Faker

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

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Mixing Ph

Stage: 5 Challenge Level: Challenge Level:1

Use the logarithm to work out these pH values

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Blood Buffers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

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Real-life Equations

Stage: 5 Challenge Level: Challenge Level:1

Here are several equations from real life. Can you work out which measurements are possible from each equation?

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Stats Statements

Stage: 5 Challenge Level: Challenge Level:1

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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Very Old Man

Stage: 5 Challenge Level: Challenge Level:1

Is the age of this very old man statistically believable?

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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Population Dynamics Collection

Stage: 5 Challenge Level: Challenge Level:1

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

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Population Dynamics - Part 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

First in our series of problems on population dynamics for advanced students.

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Robot Camera

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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Bird-brained

Stage: 5 Challenge Level: Challenge Level:1

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

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Alternative Record Book

Stage: 4 and 5 Challenge Level: Challenge Level:1

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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Population Ecology Using Probability

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

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Population Dynamics - Part 5

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Fifth in our series of problems on population dynamics for advanced students.

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Population Dynamics - Part 6

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Sixth in our series of problems on population dynamics for advanced students.

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Branching Processes and Extinction

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

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Population Dynamics - Part 4

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Fourth in our series of problems on population dynamics for advanced students.

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Population Dynamics

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

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Population Dynamics - Part 2

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Second in our series of problems on population dynamics for advanced students.

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Population Dynamics - Part 3

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Third in our series of problems on population dynamics for advanced students.

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Is Your DNA Unique?

Stage: 5 Challenge Level: Challenge Level:1

Use combinatoric probabilities to work out the probability that you are genetically unique!

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Graphic Biology

Stage: 5 Challenge Level: Challenge Level:1

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

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Why Multiply When You're about to Divide?

Stage: 5 Challenge Level: Challenge Level:1

A brief introduction to PCR and restriction mapping, with relevant calculations...

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Genetic Intrigue

Stage: 5

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

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Predator - Prey Systems

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

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Approximately Certain

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level: Challenge Level:1

Which line graph, equations and physical processes go together?

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Chemnrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study. . . .

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Core Scientific Mathematics

Stage: 4 and 5 Challenge Level: Challenge Level:1

This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.

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Drug Stabiliser

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How does the half-life of a drug affect the build up of medication in the body over time?

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Reaction Types

Stage: 5 Challenge Level: Challenge Level:1

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

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Neural Nets

Stage: 5

Find out some of the mathematics behind neural networks.

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Light Absorbance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Test your skills at this light-absorbance calculation.

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Concentrations

Stage: 5 Challenge Level: Challenge Level:1

Use the interactivity to practise your skills with concentrations and molarity.

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The Genes of Gilgamesh

Stage: 4 Challenge Level: Challenge Level:1

Can you work out the parentage of the ancient hero Gilgamesh?

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Advanced STEM

Stage: 4 and 5 Challenge Level: Challenge Level:1

Advanced problems in the mathematical sciences.

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Extreme Dissociation

Stage: 5 Challenge Level: Challenge Level:1

In this question we push the pH formula to its theoretical limits.

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Ph Temperature

Stage: 5 Challenge Level: Challenge Level:1

At what temperature is the pH of water exactly 7?

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Exact Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Which exact dilution ratios can you make using only 2 dilutions?

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Investigating the Dilution Series

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which dilutions can you make using only 10ml pipettes?

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Dilution Series Calculator

Stage: 4 Challenge Level: Challenge Level:1

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

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Packing 3D Shapes

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

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Fitting Flat Shapes

Stage: 5 Challenge Level: Challenge Level:1

How efficiently can various flat shapes be fitted together?

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Choose Your Units

Stage: 4 Challenge Level: Challenge Level:1

Which units would you choose best to fit these situations?

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Conversion Sorter

Stage: 4 Challenge Level: Challenge Level:1

Can you break down this conversion process into logical steps?

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Mathematical Issues for Biologists

Stage: 5 Challenge Level: Challenge Level:1

STEM students at university often encounter mathematical difficulties. This articles highlights the 8 key problems for biologists.

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Bigger or Smaller?

Stage: 4 Challenge Level: Challenge Level:1

When you change the units, do the numbers get bigger or smaller?

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Catalyse That!

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?


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