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This comes in two parts, with the first being less fiendish than the second. Itâ€™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.

### Discriminating

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

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.

# Trig Countdown

##### Age 16 to 18Challenge Level

This resource is from Underground Mathematics.

Below are some function cards, some value cards, and some target cards.  You may wish to print them out and cut them up, but keep them in the three separate piles.

cards.pdf

You can choose a total of six cards, split between function cards and value cards in any way you choose (perhaps one or two function cards would be a good choice to start with).  Choose your cards at random (pick from face-down cards, or get a friend to choose).

Then choose a random target card.

Your challenge is now to make the target by evaluating functions from your selected cards at values from your selected cards.  You can use each card at most once (you don't have to use them all).

For example, if you have the function card $\sin(\square + \square)$ and the value cards $\dfrac{\pi}{6}$ and $\dfrac{\pi}{3}$, then you could evaluate
$$\sin\left(\frac{\pi}{6} + \frac{\pi}{3}\right),$$
but you would not be allowed to evaluate
$$\sin\left(\frac{\pi}{6} + \frac{\pi}{6}\right)$$
(unless you happen to have two $\dfrac{\pi}{6}$ cards).

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