Practice Error Analysis in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The systematic study of how errors arise in calculations or models, how large they are, and how they propagate through subsequent steps.
Error analysis asks "how wrong could my answer be?" — not just "what is my answer?" — because every measurement and approximation carries uncertainty.
Example 1
easyA student writes: '\sqrt{a^2+b^2} = a+b.' Identify the error and find a numerical counterexample.
Example 2
mediumA student 'proves': 'n^2 > n for all n' by checking n = 2, 3, 4. Identify the error in this argument and find a value of n where the claim fails.
Example 3
easyFind the error: a student solves 2(x+3) = 10 by writing 2x+3=10, then x=3.5. What went wrong?
Example 4
mediumA student cancels incorrectly: \dfrac{x^2+3x}{x} = x^2+3. Identify and correct the error.