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  3. AP Calculus AB

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AP Calculus AB Flashcards: Sketching Slope Fields

Study Sketching Slope Fields in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

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What this deck covers

This deck focuses on Sketching Slope Fields, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Sketching Slope Fields

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QUESTION

What is the slope at (1,3)(1, 3)(1,3) for dy/dx=y−2xdy/dx = y - 2xdy/dx=y−2x?

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ANSWER
  1. Substitute: 3−2(1)=13 - 2(1) = 13−2(1)=1.

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Flashcard 1: What is the slope at (1,3)(1, 3)(1,3) for dy/dx=y−2xdy/dx = y - 2xdy/dx=y−2x?

Answer:

  1. Substitute: 3−2(1)=13 - 2(1) = 13−2(1)=1.

Flashcard 2: Find the slope at (1,1)(1, 1)(1,1) for dy/dx=x2−2ydy/dx = x^2 - 2ydy/dx=x2−2y.

Answer: -1. Substitute: 12−2(1)=−11^2 - 2(1) = -112−2(1)=−1.

Flashcard 3: What is a slope field?

Answer: A graphical representation of a differential equation's solutions. Shows direction of solutions at each point.

Flashcard 4: What is the slope at (1,0)(1, 0)(1,0) for dy/dx=y2−xdy/dx = y^2 - xdy/dx=y2−x?

Answer: -1. Substitute: 02−1=−10^2 - 1 = -102−1=−1.

Flashcard 5: What is the purpose of sketching a slope field?

Answer: To visualize possible solutions of a differential equation. Helps understand solution behavior patterns.

Flashcard 6: What is the slope at (2,1)(2, 1)(2,1) for dy/dx=y2+xdy/dx = y^2 + xdy/dx=y2+x?

Answer:

  1. Substitute: 12+2=31^2 + 2 = 312+2=3.

Flashcard 7: Which mathematical tool helps visualize differential equation solutions?

Answer: Slope fields. They show solution directions graphically.

Flashcard 8: Identify the slope at (0,1)(0, 1)(0,1) for dy/dx=x2−2ydy/dx = x^2 - 2ydy/dx=x2−2y.

Answer: -2. Substitute: 02−2(1)=−20^2 - 2(1) = -202−2(1)=−2.

Flashcard 9: What is the slope at (3,2)(3, 2)(3,2) for dy/dx=x−y2dy/dx = x - y^2dy/dx=x−y2?

Answer: -1. Substitute: 3−22=−13 - 2^2 = -13−22=−1.

Flashcard 10: Identify the slope at (1,0)(1, 0)(1,0) for dy/dx=2x+ydy/dx = 2x + ydy/dx=2x+y.

Answer:

  1. Substitute: 2(1)+0=22(1) + 0 = 22(1)+0=2.

Flashcard 11: What is the slope at (2,3)(2, 3)(2,3) for dy/dx=x−ydy/dx = x - ydy/dx=x−y?

Answer: -1. Substitute: 2−3=−12 - 3 = -12−3=−1.

Flashcard 12: Find the slope at (0,1)(0, 1)(0,1) for dy/dx=y−x2dy/dx = y - x^2dy/dx=y−x2.

Answer:

  1. Substitute: 1−02=11 - 0^2 = 11−02=1.

Flashcard 13: What is the slope at (0,0)(0, 0)(0,0) for dy/dx=x+y2dy/dx = x + y^2dy/dx=x+y2?

Answer:

  1. Substitute: 0+02=00 + 0^2 = 00+02=0.

Flashcard 14: Identify the slope at (0,3)(0, 3)(0,3) for dy/dx=x+y2dy/dx = x + y^2dy/dx=x+y2.

Answer:

  1. Substitute: 0+32=90 + 3^2 = 90+32=9.

Flashcard 15: What is the slope at (3,1)(3, 1)(3,1) for dy/dx=x2−y2dy/dx = x^2 - y^2dy/dx=x2−y2?

Answer:

  1. Substitute: 32−12=83^2 - 1^2 = 832−12=8.

Flashcard 16: What is the slope at (0,2)(0, 2)(0,2) for dy/dx=x2−ydy/dx = x^2 - ydy/dx=x2−y?

Answer: -2. Substitute: 02−2=−20^2 - 2 = -202−2=−2.

Flashcard 17: What is the slope at (0,−1)(0, -1)(0,−1) for dy/dx=x2+ydy/dx = x^2 + ydy/dx=x2+y?

Answer: -1. Substitute: 02+(−1)=−10^2 + (-1) = -102+(−1)=−1.

Flashcard 18: Identify the slope of the line segment at (0, 0) if dy/dx=x2−y2dy/dx = x^2 - y^2dy/dx=x2−y2.

Answer:

  1. Substitute: 02−02=00^2 - 0^2 = 002−02=0.

Flashcard 19: What is the slope of the field at point (2,3)(2, 3)(2,3) for dy/dx=x−ydy/dx = x - ydy/dx=x−y?

Answer: -1. Substitute: 2−3=−12 - 3 = -12−3=−1.

Flashcard 20: What is the slope at (3,3)(3, 3)(3,3) for dy/dx=x−2ydy/dx = x - 2ydy/dx=x−2y?

Answer: -3. Substitute: 3−2(3)=−33 - 2(3) = -33−2(3)=−3.

Flashcard 21: What is the slope at (0,2)(0, 2)(0,2) for dy/dx=2x−ydy/dx = 2x - ydy/dx=2x−y?

Answer: -2. Substitute: 2(0)−2=−22(0) - 2 = -22(0)−2=−2.

Flashcard 22: Identify the slope at (2,1)(2, 1)(2,1) for dy/dx=x+ydy/dx = x + ydy/dx=x+y.

Answer:

  1. Substitute: 2+1=32 + 1 = 32+1=3.

Flashcard 23: What is the slope at (1,0)(1, 0)(1,0) for the differential equation dy/dx=xydy/dx = xydy/dx=xy?

Answer:

  1. Substitute: 1⋅0=01 \cdot 0 = 01⋅0=0.

Flashcard 24: Identify the slope of the line segment at (1, 2) if dy/dx=x+ydy/dx = x + ydy/dx=x+y.

Answer:

  1. Substitute: 1+2=31 + 2 = 31+2=3.

Flashcard 25: What is the slope at (0,1)(0, 1)(0,1) for dy/dx=x2+y2dy/dx = x^2 + y^2dy/dx=x2+y2?

Answer:

  1. Substitute: 02+12=10^2 + 1^2 = 102+12=1.

Flashcard 26: Find the slope at (1,1)(1, 1)(1,1) for dy/dx=x2−y2dy/dx = x^2 - y^2dy/dx=x2−y2.

Answer:

  1. Substitute: 12−12=01^2 - 1^2 = 012−12=0.

Flashcard 27: What is the slope at (1,1)(1, 1)(1,1) for dy/dx=2x−ydy/dx = 2x - ydy/dx=2x−y?

Answer:

  1. Substitute: 2(1)−1=12(1) - 1 = 12(1)−1=1.

Flashcard 28: What is the slope at (2,2)(2, 2)(2,2) for dy/dx=x2+ydy/dx = x^2 + ydy/dx=x2+y?

Answer:

  1. Substitute: 22+2=62^2 + 2 = 622+2=6.

Flashcard 29: What is the slope at (2,0)(2, 0)(2,0) for dy/dx=x2−ydy/dx = x^2 - ydy/dx=x2−y?

Answer:

  1. Substitute: 22−0=42^2 - 0 = 422−0=4.

Flashcard 30: What does each segment in a slope field indicate?

Answer: The slope of the solution curve at that point. It's the tangent direction at that location.