Mathematical Preparation for the Cambridge Natural Sciences Tripos

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

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