Error analysis

Objective. Diagnose plausible wrong solutions and repair reasoning.

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2. Worked example
3. Practice
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Learn: the key idea

Error analysis examines a plausible but incorrect worked solution, identifies exactly where the reasoning first goes wrong, and then produces the correct corrected working from that point onward. Read through the given solution line by line, checking each step's validity against the correct rule, rather than just rechecking the final answer against your own independent solution. Clearly state the specific rule broken, such as incorrectly expanding brackets or dividing before multiplying, and show the repaired step. If a solution expands (x+3)² as x²+9 instead of x²+6x+9, identify the missing middle term explicitly. Precise diagnosis is more valuable than simply redoing the whole problem from scratch.

Worked example

A student expands (x + 5)² and writes x² + 25. Identify the error and give the correct expansion.

1 $The student omitted the middle cross terms entirely$
2 $Correct expansion: (x + 5)(x + 5) = x² + 5x + 5x + 25$
3 $Combine like terms: x² + 10x + 25$
4 $Correct expansion is x² + 10x + 25$

Answer: x² + 10x + 25

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Common mistake. Students doing error analysis often just solve the problem fresh without actually pinpointing the exact flawed line in the given solution, missing the diagnostic skill the question is testing.

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