Advanced Problem Solving Module 19

Advanced Problem Solving Module 19

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

Unit Interval 

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?

Eyes Down 

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?

In Between 

Age 16 to 18 Challenge Level:
Can you find the solution to this algebraic inequality?