Exercise 1: AMM Fundamentals Assessment

⏰ Time Investment: 30-45 minutes 🎯 Goal: Test your understanding of AMM basics and identify knowledge gaps

📚 Required Reading Integration 📖 Primary: Lesson 1: Understanding AMM Fundamentals 📖 Supporting: Lesson 2: The Mathematics of Liquidity Provision

🔍 Phase 1: Knowledge Check (10 minutes)

Understanding Check

Answer these questions to assess your comprehension:

1. What is the constant product formula?

• Your answer: _________________________________

2. How does an AMM determine prices?

• Your answer: _________________________________

3. What happens to pool reserves when someone buys ETH?

• Your answer: _________________________________

4. Why are liquidity pools called "automated" market makers?

• Your answer: _________________________________

5. What is the difference between marginal price and average price?

• Your answer: _________________________________

📊 Phase 2: Calculation Practice (15 minutes)

Swap Calculation Exercise

Scenario: Pool has 100 ETH and 200,000 USDC

• Current price: 2,000 USDC per ETH

• k = 100 × 200,000 = 20,000,000

• Fee rate: 0.3%

Exercise 1: Calculate how much USDC is needed to buy 1 ETH

Step 1: New ETH reserves after trade

• ETH_new = 100 + 1 = _____ ETH

Swap Calculation Template

AMM Knowledge Assessment Chart

Step 2: Required USDC to maintain k

• USDC_new = 20,000,000 ÷ _____ = _____ USDC

Step 3: USDC needed (before fee)

• USDC_needed = 200,000 - _____ = _____ USDC

Step 4: Add 0.3% fee

• Fee = _____ × 0.003 = _____ USDC

• Total cost = _____ + _____ = _____ USDC

Step 5: Effective price

• Effective price = _____ USDC per ETH

• Price impact = (_____ - 2,000) ÷ 2,000 = _____%

Pool Depth Exercise

Scenario: Two pools for ETH/USDC

Pool A: 50 ETH, 100,000 USDC (k = 5,000,000) Pool B: 200 ETH, 400,000 USDC (k = 80,000,000)

Exercise 2: Which pool can handle larger trades with less price impact?

Calculate depth for Pool A:

• Depth_A = √(5,000,000) = _____

Calculate depth for Pool B:

• Depth_B = √(80,000,000) = _____

Answer: Pool _____ has more depth and can handle larger trades.

💡 Phase 3: Real-World Application (10 minutes)

Pool Selection Exercise

You have $5,000 to provide liquidity. Analyze these pools:

Pool 1: ETH/USDC

• TVL: $10,000,000

• Daily Volume: $2,000,000

• Fee Rate: 0.05%

Pool 2: USDC/USDT

• TVL: $50,000,000

• Daily Volume: $1,000,000

• Fee Rate: 0.01%

Pool 3: MEME/USDC

• TVL: $500,000

• Daily Volume: $100,000

• Fee Rate: 1%

Analysis:

Pool 1:

• Your share: $5,000 ÷ $10,000,000 = _____%

• Daily fees: $2,000,000 × 0.0005 × _____ = $_____

• Volume/TVL ratio: $2,000,000 ÷ $10,000,000 = _____

Pool 2:

• Your share: $5,000 ÷ $50,000,000 = _____%

• Daily fees: $1,000,000 × 0.0001 × _____ = $_____

• Volume/TVL ratio: $1,000,000 ÷ $50,000,000 = _____

Pool 3:

• Your share: $5,000 ÷ $500,000 = _____%

• Daily fees: $100,000 × 0.01 × _____ = $_____

• Volume/TVL ratio: $100,000 ÷ $500,000 = _____

Which pool would you choose and why?

• Your choice: Pool _____

• Reasoning: _________________________________

🎯 Phase 4: Self-Assessment (10 minutes)

Knowledge Score

Rate your understanding (1-10) on each topic:

AMM Fundamentals:

• Constant product formula: _____/10

• Price determination: _____/10

• Swap mechanics: _____/10

• Pool depth: _____/10

• Fee calculation: _____/10

Total Score: _____/50

Gap Identification

Topics I need to review:

Questions I still have:

📚 Next Steps

• Review Lesson 1 sections where you scored <7/10

• Practice swap calculations with different scenarios

• Explore Uniswap interface (testnet recommended)

• Read Lesson 2 for deeper mathematical understanding

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← Back to Lesson 1 | Next: Exercise 2 →