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Powerful Quadratics

This comes in two parts, with the first being less fiendish than the second. It’s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.


You're invited to decide whether statements about the number of solutions of a quadratic equation are always, sometimes or never true.

Factorisable Quadratics

This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.

Which Quadratic?

Age 16 to 18

This resource is from Underground Mathematics.


What are the key features of a quadratic and what information do you need to be able to identify these for a particular example?

This problem is designed to be tackled in a team of four, working as two pairs. One of the pairs is trying to identify the quadratic on a randomly chosen card. You can download the cards here.




  • To begin, place all of the cards on the table and spend a couple of minutes familiarising yourselves with the types of images and equations that might be chosen.
  • Next, one pair takes control of the cards, moving them out of sight from the other pair. They select a card at random. The other pair can now ask up to 8 “yes/no” questions to determine the hidden quadratic. It is important that each pair confers and agrees before asking or answering each question.
  • You are permitted a maximum of two guesses at the hidden function, and each guess counts as one of your 8 questions.

Some things to consider



  • Did you guess the quadratic correctly? If not, what additional information did you need?
  • Did you make the most of the information you were given? Could you have avoided asking any of your questions?
  • Were your questions clear? Did the other pair understand what you meant? Could you have used mathematical language to improve this?
  • Would you ask the same questions next time?


This is an Underground Mathematics resource.

Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.

Visit the site at to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.