Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Mixed up Mixture

Age 14 to 16
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

A standard calibration for a spectrophotometric assay for lysozyme was created by diluting some initial concentrations of the reagents Tris HCl buffer, NaCl, Lysozyme and a Micrococcus lysodeikticus suspension.The final volume was 5ml.

The numbers in the calculation have become mixed up. Can you work out how consistently to fill in the table? There will be two numbers left over. What will these represent?

Here is a printable version of the table and cards that you can cut out.

Initial conc.

Final conc.

Dilution factor

Volume added

Tris

NaCl

Lysozyme

Cells

171 mM

106 /ml

10mM

500 pmol/ml

0.050 ml

136

20

0.250 ml

68 nmol/ml

50 mM

100

0.037 ml

0.292 ml

108 /ml

17.1

0.629 ml

4.371 ml

1000 mM

You may also like

Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo