Review Your Mistakes
Learn
Reviewing your mistakes is the most valuable part of test prep. Every error is a learning opportunity that shows exactly what you need to work on. Students who systematically analyze their mistakes improve faster than those who simply move on to new problems.
The Four Types of Mistakes
- Content Gap: You didn't know the concept or formula needed
- Careless Error: You knew how to solve it but made a calculation or reading mistake
- Time Pressure: You would have gotten it right with more time
- Strategy Error: You used an inefficient approach that led you astray
How to Review Each Mistake
For each wrong answer, ask yourself these questions:
- What type of mistake was this?
- What did I misunderstand or overlook?
- What should I have done differently?
- How can I prevent this mistake in the future?
Creating an Error Log
Keep a running log of your mistakes with these columns:
- Date
- Problem topic (e.g., "linear equations," "percent change")
- Mistake type (content, careless, time, strategy)
- What went wrong
- Correct approach
Examples
See how to analyze different types of mistakes.
Example 1: Content Gap
Problem: Find the distance between points (3, 2) and (7, 5).
Student answer: 4 + 3 = 7
Correct answer: sqrt((7-3)² + (5-2)²) = sqrt(16 + 9) = sqrt(25) = 5
Analysis: Student didn't know the distance formula. Action: Review coordinate geometry formulas.
Example 2: Careless Error
Problem: If 3x + 5 = 20, find x.
Student work: 3x = 25, x = 25/3
Correct answer: 3x = 15, x = 5
Analysis: Added instead of subtracted. Action: Double-check operations, especially with signs.
Example 3: Time Pressure
Problem: Multi-step word problem about compound interest.
Student answer: Skipped / guessed
Analysis: Ran out of time. Action: Practice similar problems to build speed; consider skipping earlier if stuck.
Example 4: Strategy Error
Problem: If x² - 5x + 6 = 0, what is x?
Student approach: Used quadratic formula (took 3 minutes)
Better approach: Factor: (x-2)(x-3) = 0, so x = 2 or 3 (took 30 seconds)
Analysis: Chose a harder method. Action: Look for factoring opportunities before using formulas.
Practice
Analyze these sample mistakes and identify the type and fix.
1. Problem: What is 40% of 250?
Student answer: 1000
Correct answer: 100
What type of mistake? What went wrong?
2. Problem: Solve 2(x + 3) = 14
Student answer: x = 4
Correct answer: x = 4
No mistake here! But verify the work.
3. Problem: Find the area of a triangle with base 8 and height 6.
Student answer: 48
Correct answer: 24
What type of mistake? What formula was needed?
4. Problem: If a = 3 and b = -2, find a² - b².
Student answer: 9 - 4 = 5
Correct answer: 9 - 4 = 5
Correct! Note: (-2)² = 4, not -4.
5. Problem: A price increased from $80 to $100. What is the percent increase?
Student answer: 20%
Correct answer: 25%
What type of mistake? What's the correct calculation?
6. Problem: Simplify sqrt(50).
Student answer: 25
Correct answer: 5*sqrt(2)
What concept was misunderstood?
7. Problem: If f(x) = 2x + 1, find f(f(2)).
Student answer: 5
Correct answer: 11
What step was missed?
8. Problem: Solve x/3 + x/4 = 7
Student answer: x = 12 (after 4 minutes)
Correct answer: x = 12
Answer is correct, but what made it take so long?
9. Review your own recent practice test. Find 3 mistakes and classify each one.
10. For each of your 3 mistakes above, write one specific action to prevent that mistake type.
Check Your Understanding
Answer these reflection questions.
- What are the four types of test mistakes?
- Which type of mistake do you make most often?
- How does keeping an error log help you improve?
- What questions should you ask yourself for each wrong answer?
Next Steps
- Start an error log using a notebook or spreadsheet
- Review your error log weekly to spot patterns
- Focus your study time on your most common mistake types
- Move on to the Mixed Set lesson to apply your learning