Rates of change

article
An introduction to differentiation

An article introducing the ideas of differentiation.
problem
Quick route

Age

16 to 18

Challenge level

What is the quickest route across a ploughed field when your speed around the edge is greater?
problem
Reaction types

Age

16 to 18

Challenge level

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.
problem
Lap times

Age

14 to 16

Challenge level

Can you find the lap times of the two cyclists travelling at constant speeds?
problem
An average average speed

Age

14 to 16

Challenge level

My average speed for a journey was 50 mph, my return average speed of 70 mph. Why wasn't my average speed for the round trip 60mph ?
problem
Jumping gerbils

Age

14 to 16

Challenge level

A conveyor belt, with tins placed at regular intervals, is moving at a steady rate towards a labelling machine. A gerbil starts from the beginning of the belt and jumps from tin to tin.
problem
Immersion

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

Match the descriptions of physical processes to these differential equations.