# Mathematical Preparation for the Cambridge Natural Sciences Tripos

##### Age 16 to 18 Challenge Level:

The introductory workbook for the Natural Science Students contains many questions designed to check your skills in the fundamental mathematics needed to succeed in the Natural Sciences Tripos at Cambridge University.

Here we provide a set of stemNRICH problems designed to complement these activities and develop your scientific mathematical skill. These stemNRICH problems are roughly grouped into subject area according to the workbook, but 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