🎯 Contest Format & Scoring

Understanding the scoring system is crucial for making strategic decisions during the contest. This section covers the mathematical framework for optimal guessing strategies.

📊 Scoring Parameters

Let’s define the key scoring variables:

• $S_C$ = Points for correct answer
• $S_W$ = Points for wrong answer
• $S_B$ = Points for blank answer

Typical AMC 10/12 Values:

• $S_C = 6$ points
• $S_W = 0$ points
• $S_B = 1.5$ points

Important: Always verify current scoring parameters before the contest, as they may change.

🎲 Expected Value Framework

Guessing with Eliminations

When you can eliminate $e$ answer choices and have $k$ total choices remaining:

Expected Value of Guessing: $$\text{EV}_\text{guess} = \frac{1}{k-e} \cdot S_C + \frac{k-e-1}{k-e} \cdot S_W$$

Expected Value of Blank: $$\text{EV}_\text{blank} = S_B$$

Decision Rule

Guess if and only if: $$\text{EV}\text{guess} > \text{EV}\text{blank}$$

Quick Example

With typical scoring ($S_C = 6$, $S_W = 0$, $S_B = 1.5$):

• No eliminations ($e = 0$): $\text{EV}_\text{guess} = \frac{1}{5} \cdot 6 + \frac{4}{5} \cdot 0 = 1.2 < 1.5$ → Don’t guess
• 1 elimination ($e = 1$): $\text{EV}_\text{guess} = \frac{1}{4} \cdot 6 + \frac{3}{4} \cdot 0 = 1.5 = 1.5$ → Tie, guess if confident
• 2 eliminations ($e = 2$): $\text{EV}_\text{guess} = \frac{1}{3} \cdot 6 + \frac{2}{3} \cdot 0 = 2.0 > 1.5$ → Guess

⏱️ Contest Structure

Basic Format

• Duration: 75 minutes
• Questions: 25 problems
• Answer Format: Multiple choice (A, B, C, D, E)
• Calculator: Not permitted
• Single Sitting: No breaks allowed

Question Distribution

• Problems 1-10: Generally easier, aim for high accuracy
• Problems 11-20: Medium difficulty, strategic triage zone
• Problems 21-25: Hardest problems, selective approach

📈 Strategic Implications

Time Allocation

• First Pass: Problems 1-15 (45 minutes)
• Second Pass: Problems 16-25 (25 minutes)
• Final Review: 5 minutes

Accuracy Targets

• Problems 1-10: 95%+ accuracy
• Problems 11-20: 70-80% accuracy
• Problems 21-25: 40-60% accuracy

Guessing Strategy

• Never guess on problems 1-10 (high accuracy expected)
• Strategic guessing on problems 11-20 (with eliminations)
• Selective guessing on problems 21-25 (high EV threshold)

🎯 Quick Reference Table

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