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 

Stage: 4 and 5 Challenge Level: Challenge Level:1
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 

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
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 

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
Can you find the solution to this algebraic inequality?