Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

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

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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. . . .

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

Which curve is which, and how would you plan a route to pass between them?

This fascinating problem provides an interesting opportunity to mix algebra, common sense and numerical analysis. Our solutions reflect this.

Follow the mathematical journey of a sixth-former as she spent four weeks working on stemNRICH problems.