Exponential and logarithmic functions

problem

Extreme Dissociation

Age

16 to 18

Challenge level

In this question we push the pH formula to its theoretical limits.
problem

Function Pyramids

Age

16 to 18

Challenge level

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
problem

What Do Functions Do for Tiny X?

Age

16 to 18

Challenge level

Looking at small values of functions. Motivating the existence of the Maclaurin expansion.
problem

A Very Shiny Nose?

Age

16 to 18

Challenge level

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
problem

Hyperbolic Thinking

Age

16 to 18

Challenge level

Explore the properties of these two fascinating functions using trigonometry as a guide.
problem

Drug Stabiliser

Age

16 to 18

Challenge level

How does the half-life of a drug affect the build up of medication in the body over time?
problem

Cobalt Decay

Age

16 to 18

Challenge level

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
article
Infinite Continued Fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
article
What Are Complex Numbers?

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.