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# Mathematical Preparation for the Cambridge Natural Sciences Tripos

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Age 16 to 18

Challenge Level

These stemNRICH problems are designed to develop the scientific mathematical skill of students hoping to study Natural Sciences at Cambridge, and will also be very useful for prospective science students of other university courses. The problems are roughly grouped into subject area according to the workbook, although there is
a natural overlap between some of these areas.

These problems are relatively subject-agnostic -- not particularly directed towards chemistry, physics or biology. You might wish to look at bioNRICH, physNRICH or chemNRICH for mathematical activities focussed on areas of particular
interest to you.

If you need any help, please go to the main stemNRICH page for support.

CORE MATHEMATICS | FUNCTIONS AND CURVES | GEOMETRY |

Big & small numbers in biology / physics Investigating the dilution series Mixing pH Debt race |
Reaction types Implicitly Curve fitter 2 Scientific Curves |
Efficient Packing Pack Man Coordinated Crystals Perfect Eclipse |

TRIGONOMETRY | SEQUENCES AND SERIES | VECTORS |

Far horizon Flight path Loch Ness Spherical triangles on very big spheres |
Production equation What do these functions do for tiny x? Taking trigonometry series-ly Stirling Work |
Vector Walk Coordinated crystals Bond angles Cross with the scalar product |

DIFFERENTIATION and INTEGRATION | DIFFERENTIAL EQUATIONS | OTHER THINGS TO TRY |

Calculus Countdown Integration matcher Operating machines Brimful 2 |
Differential equation matcher Reaction rates The not-so-simple pendulum 1 The real hydrogen atom |
Backfitter Crystal symmetry Stats statements An introduction to complex numbers |