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AP Calculus AB

Limits, derivatives, integrals and the Fundamental Theorem of Calculus. (College Board)

What the exam covers

  1. Limits and continuity
  2. Differentiation: definition and basic rules
  3. Composite, implicit and inverse functions
  4. Contextual applications of differentiation
  5. Analytical applications of differentiation
  6. Integration and accumulation of change
  7. Differential equations
  8. Applications of integration

The most common mistakes, unit by unit

Limits and continuity

Differentiation: definition and basic rules

Composite, implicit and inverse functions

  • Forgetting the chain rule's inside derivative, or dropping dy/dx when differentiating y terms implicitly.

Contextual applications of differentiation

Analytical applications of differentiation

  • Calling every point where f′(x) = 0 a maximum without checking a sign change.

Integration and accumulation of change

  • Dropping the + C on indefinite integrals, or forgetting to change bounds after u-substitution.

Differential equations

  • Separating variables but forgetting to apply the initial condition to find C.

Applications of integration

A 2-week study plan

  1. Day 1
    Limits and continuity
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  2. Day 2
    Differentiation: definition and basic rules
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  3. Day 3
    Composite, implicit and inverse functions
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  4. Day 4
    Contextual applications of differentiation
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  5. Day 5
    Analytical applications of differentiation
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  6. Day 6
    Integration and accumulation of change
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  7. Day 7
    Mixed review
    • Redo every question you missed this week, without notes.
    • Save anything still shaky as a miss so it comes back.
  8. Day 8
    Differential equations
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  9. Day 9
    Applications of integration
    • Read the common mistake for each unit below.
    • Do 10 questions and save every miss.
    • Clear any reviews that are due.
  10. Day 10
    Review what's due
    • Clear due reviews first.
    • Retry the day's hardest question from scratch.
  11. Day 11
    Review what's due
    • Clear due reviews first.
    • Retry the day's hardest question from scratch.
  12. Day 12
    Timed practice
    • One timed set in AP Calculus AB format.
    • Mark it, then name the unit behind each wrong answer.
  13. Day 13
    Fix the gaps
    • Practise only the units from yesterday's wrong answers.
    • Explain each fix out loud in one sentence (Teach-back).
  14. Day 14
    Light review
    • Clear today's due reviews — nothing new.
    • Sleep well. You're done for today.

Free 5-question sample quiz

No signup. Tap an answer to see if you're right.

  1. 1. What is the limit of (x² − 9)/(x − 3) as x approaches 3?

  2. 2. What is the derivative of f(x) = 4x³?

  3. 3. What is the derivative of (2x + 1)⁵?

  4. 4. What is the integral of 2x from x = 0 to x = 3?

  5. 5. The average rate of change of f(x) = x² from x = 1 to x = 3 is:

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