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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.

Proving the Laws of Logarithms

Age 16 to 18
Challenge Level
Here is one possible way of proving the result (with some extra cards added).

Niharika from Rugby School states the general versions of the three logarithm rules and proves them here.

This is an Underground Mathematics resource.