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### Number and algebra

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# Finding Your Feet

Whether you are starting A Levels, Highers, International Baccalaureate, or another higher maths qualification, it might take a while to find your feet.

These problems use familiar ideas from Stage 4 to help you to find a way in.

### Between

### Name That Graph

### Which Fraction Is Bigger?

### Paired Parabolas

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### Powerful Quadratics

### Discriminating

### Factorisable Quadratics

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Whether you are starting A Levels, Highers, International Baccalaureate, or another higher maths qualification, it might take a while to find your feet.

These problems use familiar ideas from Stage 4 to help you to find a way in.

Age 16 to 18

Challenge Level

If you know some points on a line, can you work out other points in between?

Age 16 to 18

Challenge Level

How can you work out the equation of a parabola just by looking at key features of its graph?

Age 16 to 18

Challenge Level

Given two algebraic fractions, how can you decide when each is bigger?

Age 16 to 18

Challenge Level

Some parabolas are related to others. How are their equations and graphs connected?

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.

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.