Maths: How to Take the Perfect Penalty Kick

This week’s Inspire Programme Video Lecture comes from Dr Tom Crawford, a lecturer in Maths at the University of Oxford, and founder of the Tom Rocks Maths website. In this first of two lectures on Maths and Sport, Tom looks at the maths of penalties in a game of football, using Pythagoras’ Theorem, quadratic equations and other mathematical techniques you will come across at GCSE to try to work out how to take the perfect penalty kick.

Also remember to check out the competition that goes with this class – as always, there are prizes to be won in the form of Amazon vouchers! See details of this week’s competition at the bottom of this page.

A second Video Session from Tom will follow after the Easter holiday, which will look at the maths behind predicting world records in Athletics.

Competition: Penalties

Look at the diagram below, which shows the placement of the 5 penalty kicks for two teams in a penalty shootout.

  1. Based on the content discussed in the lecture, which team would you expect to win?
  2. Can you calculate the ‘expected number of penalties’ that each team will score based on the placements shown?

To enter this competition, please click here. The deadline is 5pm on Wednesday 28th April 2021. All entries with correct answers to both parts of the challenge will be entered into a prize draw, with Amazon vouchers to be won!