Review Mistakes
Learn
One of the most powerful ways to improve your SAT/ACT score is to systematically analyze and learn from your mistakes. Every error is an opportunity to identify a gap in your knowledge or a flaw in your approach.
Types of Mistakes
Understanding why you made a mistake is more important than just knowing the correct answer. Mistakes typically fall into these categories:
| Mistake Type | Description | Solution |
|---|---|---|
| Careless Error | Misread the problem, calculation error, or bubbled wrong answer | Slow down, double-check work, underline key words |
| Concept Gap | Did not understand the underlying math or skill | Review the concept, study examples, get help |
| Strategy Error | Used an inefficient or incorrect approach | Learn multiple approaches, practice problem recognition |
| Time Pressure | Rushed and made errors due to running out of time | Practice pacing, skip hard problems first |
| Trap Answer | Fell for a common wrong answer designed by test makers | Learn to recognize trap patterns |
The Error Log Method
Keep a dedicated notebook or spreadsheet to track every mistake. For each error, record:
- The problem (or a reference to find it)
- Your answer and the correct answer
- Why you got it wrong (mistake type)
- The concept or skill involved
- What you will do differently next time
Weekly Review Process
- Review your error log at least once per week
- Look for patterns: Are you making the same type of mistake repeatedly?
- Prioritize studying concepts that appear most often in your errors
- Redo problems you got wrong (without looking at solutions first)
- Track improvement over time
Examples
See how to analyze mistakes using the error log method.
Example 1: Careless Error Analysis
Problem: What is 25% of 80?
Your Answer: 25
Correct Answer: 20
Analysis: I calculated 80/4 = 20, but then wrote 25 (probably because I was thinking about the 25%). This is a careless error.
Fix: Circle my final answer before moving on. Read the answer I wrote, not what I think I wrote.
Example 2: Concept Gap Analysis
Problem: If the mean of 5 numbers is 12, and you remove one number, the mean becomes 10. What number was removed?
Your Answer: 2
Correct Answer: 20
Analysis: I did not understand how removing a number affects the mean. Original sum = 5 x 12 = 60. New sum = 4 x 10 = 40. Removed number = 60 - 40 = 20.
Fix: Review how mean is calculated and practice problems involving adding/removing values from data sets.
Example 3: Trap Answer Analysis
Problem: A price increased by 20% and then decreased by 20%. What is the net percent change?
Your Answer: 0% (no change)
Correct Answer: -4% (decrease)
Analysis: I fell for the trap that +20% and -20% cancel out. But: 100 x 1.20 = 120, then 120 x 0.80 = 96. Net change = -4%.
Fix: Remember that percent changes on different bases do not cancel. Always calculate step by step.
Practice: Error Analysis Exercise
For each problem below, a student made an error. Identify the mistake type and explain what went wrong.
1. Problem: Find the median of {3, 7, 2, 9, 5}
Student's Answer: 2
Correct Answer: 5
What type of mistake was made? What went wrong?
2. Problem: If 3x + 5 = 20, what is x?
Student's Answer: 5
Correct Answer: 5
This is actually correct! Not all answers you think are wrong actually are. Always verify.
3. Problem: A shirt costs $40 after a 20% discount. What was the original price?
Student's Answer: $48
Correct Answer: $50
What type of mistake was made? What went wrong?
4. Problem: The ratio of boys to girls is 3:4. If there are 28 students total, how many are boys?
Student's Answer: 21
Correct Answer: 12
What type of mistake was made? What went wrong?
5. Problem: What is the probability of rolling an even number on a standard die?
Student's Answer: 1/3
Correct Answer: 1/2 (or 3/6)
What type of mistake was made? What went wrong?
6. Problem: Convert 2.5 kilometers to meters.
Student's Answer: 250
Correct Answer: 2500
What type of mistake was made? What went wrong?
7. Problem: If a car travels at 60 mph for 2.5 hours, how far does it travel?
Student's Answer: 120 miles
Correct Answer: 150 miles
What type of mistake was made? What went wrong?
8. Problem: What is 3^4?
Student's Answer: 12
Correct Answer: 81
What type of mistake was made? What went wrong?
9. Problem: The mean of 4, 8, and x is 10. Find x.
Student's Answer: 10
Correct Answer: 18
What type of mistake was made? What went wrong?
10. Problem: A square has an area of 49 sq cm. What is its perimeter?
Student's Answer: 49 cm
Correct Answer: 28 cm
What type of mistake was made? What went wrong?
Check Your Understanding
Q1: Why is it more important to understand WHY you made a mistake than just knowing the correct answer?
Show Answer
Understanding why you made a mistake helps you prevent the same type of error in the future. Just knowing the correct answer does not address the underlying issue that caused the error.
Q2: Name the five types of mistakes discussed in this lesson.
Show Answer
1) Careless error, 2) Concept gap, 3) Strategy error, 4) Time pressure, 5) Trap answer
Q3: What should you include in an error log entry?
Show Answer
The problem, your answer, the correct answer, why you got it wrong (mistake type), the concept or skill involved, and what you will do differently next time.
Q4: How often should you review your error log?
Show Answer
At least once per week, looking for patterns and prioritizing concepts that appear most often in your errors.
Next Steps
- Create your own error log (notebook or spreadsheet)
- Go back to the Timed Drill lesson and analyze any mistakes you made
- Look for patterns in your errors across multiple practice sessions
- Schedule a weekly 15-minute error review session
- Continue to the Mixed Set lesson to apply what you have learned