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# Advanced Problem Solving Module 19

### Unit Interval

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Here are some tricks and tips for solving STEP and other advanced mathematics examinations questions involving equations and inequalities

Age 14 to 18

Challenge Level

Take any two numbers between 0 and 1. Prove that the sum of the
numbers is always less than one plus their product?

Age 16 to 18

Challenge Level

The symbol [ ] means 'the integer part of'. Can the numbers [2x];
2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three
different values?

Age 16 to 18

Challenge Level

Can you find the solution to this algebraic inequality?