⚡ During Test Quick Checks

Perform these essential 20-second micro-checks before bubbling any answer to prevent careless errors and maintain high accuracy throughout the contest.

🎯 The 20-Second Verification Rule

Before Bubbling Any Answer:

  • Plug back: Substitute answer into original problem
  • Check units: Do the units and dimensions make sense?
  • Verify constraints: Does answer satisfy all given conditions?
  • Test extremes: Does answer work at boundary values?
  • Check reasonableness: Is the answer in the right ballpark?

🔍 Quick Verification Techniques

Plug-Back Check (5 seconds)

  • Substitute answer: Replace variable with your answer
  • Simplify: Work through the calculation
  • Check equality: Does left side equal right side?
  • Verify all conditions: Check all given constraints
  • Confirm: Answer satisfies the problem

Units & Dimensions Check (3 seconds)

  • Length: Should be positive, reasonable scale
  • Area: Should be positive, units squared
  • Volume: Should be positive, units cubed
  • Probability: Must be between 0 and 1
  • Time: Should be positive, reasonable duration

Constraint Verification (5 seconds)

  • Domain restrictions: Does answer satisfy domain?
  • Range restrictions: Does answer satisfy range?
  • Inequality constraints: Does answer satisfy inequalities?
  • Integer constraints: Is answer integer if required?
  • Positive constraints: Is answer positive if required?

Extreme Value Check (4 seconds)

  • Boundary cases: Test at limits and extremes
  • Special values: Test $x = 0, 1, -1$ if applicable
  • Large values: Test with large numbers
  • Small values: Test with small numbers
  • Zero cases: Test when variables equal zero

Reasonableness Check (3 seconds)

  • Order of magnitude: Is answer too big or too small?
  • Physical sense: Does answer make physical sense?
  • Mathematical sense: Does answer make mathematical sense?
  • Comparison: How does it compare to other answers?
  • Intuition: Does it feel right?

⚡ Problem-Specific Checks

Algebra Problems

  • Substitute back: Plug answer into original equation
  • Check all solutions: Verify each root if multiple
  • Test constraints: Check domain restrictions
  • Verify signs: Check positive/negative requirements
  • Check calculations: Verify arithmetic

Geometry Problems

  • Check dimensions: Verify units and scale
  • Test angles: Are angles reasonable?
  • Verify formulas: Are you using the right formula?
  • Check coordinates: Do coordinates make sense?
  • Test area/volume: Are areas/volumes positive?

Number Theory Problems

  • Check divisibility: Verify divisibility rules
  • Test modular arithmetic: Check mod calculations
  • Verify prime factors: Check prime factorizations
  • Test digit properties: Check digit sum rules
  • Check integer constraints: Is answer integer?

Counting/Probability Problems

  • Check range: Probability between 0 and 1
  • Verify counts: Are counts non-negative integers?
  • Test symmetry: Check symmetric cases
  • Verify formulas: Are you using the right formula?
  • Check calculations: Verify arithmetic

🚨 Common Error Types

Sign Errors

  • Positive/negative: Is the sign correct?
  • Addition/subtraction: Check your arithmetic
  • Multiplication/division: Check your operations
  • Exponents: Check positive/negative exponents
  • Square roots: Check positive/negative roots

Unit Errors

  • Length units: Are units appropriate?
  • Area units: Are units squared?
  • Volume units: Are units cubed?
  • Time units: Are units appropriate?
  • Angle units: Degrees or radians?

Calculation Errors

  • Arithmetic: Check addition, subtraction, multiplication, division
  • Order of operations: Follow PEMDAS correctly
  • Fractions: Check numerator and denominator
  • Decimals: Check decimal places
  • Percentages: Check percentage calculations

Logic Errors

  • Problem understanding: Did you understand the problem?
  • Method selection: Did you choose the right approach?
  • Step sequence: Are your steps in the right order?
  • Conclusion: Does your conclusion follow from your work?
  • Answer format: Is your answer in the right format?

⚡ Quick Reference

20-Second Checklist:

  • Plug back (5 seconds)
  • Check units (3 seconds)
  • Verify constraints (5 seconds)
  • Test extremes (4 seconds)
  • Check reasonableness (3 seconds)

Red Flag Warnings:

  • Negative area: Areas can’t be negative
  • Probability > 1: Probabilities must be ≤ 1
  • Imaginary length: Lengths must be real
  • Zero denominator: Division by zero is undefined
  • Negative count: Counts must be non-negative

Recovery Actions:

  • If answer doesn’t work: Check your calculations
  • If units don’t match: Check your formula
  • If constraints violated: Check your work
  • If extremes fail: Check your approach
  • If unreasonable: Re-examine the problem

📊 Success Metrics

Accuracy Goals:

  • Problems 1-10: 95%+ accuracy
  • Problems 11-15: 80%+ accuracy
  • Problems 16-20: 60%+ accuracy
  • Problems 21-25: 40%+ accuracy

Time Goals:

  • Easy problems: 2-3 minutes each
  • Medium problems: 3-5 minutes each
  • Hard problems: 5-10 minutes each
  • Verification: 20 seconds per answer

Quality Goals:

  • No careless errors: Check every answer
  • Consistent verification: Use the same process
  • High accuracy: Maintain accuracy throughout
  • Efficient process: Don’t waste time on verification

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