Practice Assumptions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Statements accepted as true without proof that form the starting conditions for a mathematical argument or model.
What are we assuming to be true? Everything follows from these starting points.
Example 1
easyA student models a ball thrown upward with h(t) = 20t - 5t^2 (height in metres, time in seconds). List three assumptions embedded in this model.
Example 2
mediumIn a proof that \sqrt{2} is irrational, the argument begins: 'Assume \sqrt{2} = p/q in lowest terms with p,q integers.' Identify every assumption made and explain why each is necessary.
Example 3
easyA shopkeeper assumes 'each customer buys exactly one item.' Under this assumption, if 50 customers visit, how many items are sold? State one way the assumption could fail.
Example 4
mediumA theorem states: 'For all a, b > 0, \frac{a+b}{2} \ge \sqrt{ab} (AM-GM inequality).' Identify the key assumption and give a counterexample showing the result fails without it.