Grade: 9 Subject: SAT/ACT Skills Unit: Diagnostic Assessment Lesson: 5 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Review Mistakes

Learn

Learning from mistakes is one of the most powerful study strategies. When you understand WHY you got a question wrong, you're much less likely to make the same error again. This lesson teaches you how to analyze your errors systematically.

Types of Mistakes

  • Careless errors: You knew how to solve it but made a computational mistake
  • Conceptual errors: You misunderstood the underlying concept
  • Reading errors: You misread the question or missed key information
  • Time pressure errors: You rushed and skipped steps

Building an Error Log

Keep track of every mistake you make during practice. For each error, record:

  1. The question or topic
  2. What you answered
  3. The correct answer
  4. Why you got it wrong (type of mistake)
  5. What you'll do differently next time

Examples

Common Mistake: Sign Errors

Problem: Solve -3x + 5 = 14

Wrong approach: -3x = 9, so x = 3 (forgot to divide by -3)

Correct approach: -3x = 9, so x = 9 / (-3) = -3

Common Mistake: Percentage Direction

Problem: What is 20% more than 50?

Wrong: 20% of 50 = 10, answer is 10

Correct: 20% more means 50 + 10 = 60

Practice Quiz

These questions feature common mistake patterns. Practice avoiding them.

Question 1: Solve: -4x = 20

Answer: x = -5

Remember to keep the negative sign: x = 20 / (-4) = -5

Question 2: What is 30% less than 80?

Answer: 56

30% of 80 = 24. Less means subtract: 80 - 24 = 56

Question 3: If x - 5 = -3, what is x?

Answer: x = 2

Add 5 to both sides: x = -3 + 5 = 2

Question 4: What is the value of (-2)^3?

Answer: -8

(-2) x (-2) x (-2) = 4 x (-2) = -8 (odd power keeps negative)

Question 5: Solve: 3(x - 2) = 15

Answer: x = 7

Distribute: 3x - 6 = 15. Then 3x = 21, x = 7

Question 6: A price drops from $100 to $75. What is the percent decrease?

Answer: 25%

Decrease = 25. Percent = (25/100) x 100 = 25%

Question 7: What is -5 - (-3)?

Answer: -2

Subtracting a negative = adding: -5 + 3 = -2

Question 8: If 2x + 3 = 11, what is x + 3?

Answer: 7

First solve: 2x = 8, x = 4. Then x + 3 = 4 + 3 = 7

Question 9: What is the absolute value of -15?

Answer: 15

Absolute value is always positive: |-15| = 15

Question 10: Solve: x/4 = -3

Answer: x = -12

Multiply both sides by 4: x = -3 x 4 = -12

Check Your Understanding

  • Can you identify what type of mistake you made on each wrong answer?
  • Have you started an error log to track your patterns?
  • Do you notice any recurring mistake types in your work?

Next Steps

  • Create your personal error log document
  • Review your diagnostic test and categorize each mistake
  • Move on to the mixed practice set for a comprehensive review