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ap calc cram – fundamental theorem of calculus

originally streamed in 2020 with Jamil SiddiquiTeacher
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Review the Fundamental Theorem of Calculus with this AP Calc cram session covering FTC applications, derivatives of integrals, accumulation functions, and real AP exam questions. Learn how to evaluate definite integrals, apply the chain rule to integ ...more

curriculum note

This video was recorded for the modified 2021 AP exam, which had a fully calculator-active format with only two free response questions. The current AP Calculus exam has a different structure (separate calculator and non-calculator sections, six FRQs), so references to exam format may not apply.

covered in this stream

units
Unit 6 – Integration and Accumulation of ChangeUnit 5 – Analytical Applications of Differentiation
topics
6.4 The Fundamental Theorem of Calculus and Accumulation Functions6.5 Interpreting the Behavior of Accumulation Functions Involving Area6.7 The Fundamental Theorem of Calculus and Definite Integrals5.3 Determining Intervals on Which a Function is Increasing or Decreasing5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

timestamps

  • 0:00

    Introduction to FTC Session

  • 0:37

    Weekly Stream Calendar

  • 1:08

    Cram Sessions and Olympics

  • 1:38

    Session Outline

  • 2:39

    FTC Statement Review

  • 3:40

    Evaluating Definite Integrals

  • 4:45

    Derivative of Integral Expressions

  • 5:46

    Example: Basic Derivative Case

  • 6:47

    Chain Rule Application

  • 9:23

    Variable Bounds Example

  • 14:39

    AP Exam Example 2011

  • 18:20

    Variable Bounds Variations

  • 21:25

    Accumulation Functions

  • 23:35

    FTC with Accumulation

  • 25:39

    Geometric Shapes and Areas

  • 28:15

    Sign Analysis Explanation

  • 35:28

    AP Question Overview

  • 38:33

    Function Increasing Intervals

  • 42:42

    Finding Function Values

  • 51:34

    Absolute Minimum Calculation

  • 1:00:12

    Session Wrap-Up and Q&A

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© 2026 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

every AP exam is fiveable

Fiveable

Study Content & Tools

Study GuidesFRQs + AI ScoringAP Essay Grader for StudentsAI Grading for TeachersPractice QuestionsGlossaryScore Calculators

Company

What's New?PricingBulk DiscountsTestimonialsFAQsEmail us

Resources

AP Exam Schedule 2027AP ClassesAP ClassroomEasiest AP ClassesHardest AP ClassesAP vs IBAP vs Dual EnrollmentAP vs Honors ClassesAP Scholar Awards

history

🌎 ap world history🇺🇸 ap us history🇪🇺 ap european history

social science

✊🏿 ap african american studies🗳️ ap comparative government🚜 ap human geography💶 ap macroeconomics🤑 ap microeconomics🧠 ap psychology👩🏾‍⚖️ ap us government

english & capstone

✍🏽 ap english language📚 ap english literature🔍 ap research💬 ap seminar

arts

🎨 ap art & design🖼️ ap art history🎵 ap music theory

science

🧬 ap biology🧪 ap chemistry♻️ ap environmental science🎡 ap physics 1🧲 ap physics 2💡 ap physics c: e&m⚙️ ap physics c: mechanics

math & computer science

🧮 ap calculus ab♾️ ap calculus bc📐 ap precalculus📊 ap statistics💻 ap computer science a⌨️ ap computer science p

world languages

🇨🇳 ap chinese🇫🇷 ap french🇩🇪 ap german🇮🇹 ap italian🇯🇵 ap japanese🏛️ ap latin🇪🇸 ap spanish language💃🏽 ap spanish literature

go beyond AP

high school exams

✏️ PSAT🎓 Digital SAT🎒 ACT

honors classes

🍬 honors algebra II🫀 honors anatomy🐇 honors biology👩🏽‍🔬 honors chemistry💲 honors economics📐 honors geometry⚾️ honors physics📏 honors pre-calculus📊 honors statistics🗳️ honors us government🇺🇸 honors us history🌎 honors world history

college classes

👩🏽‍🎤 arts👔 business🎤 communications🏗️ engineering📓 humanities➗ math🧑🏽‍🔬 science💶 social science

hs classes

🏛️ alabama history⛰️ appalachian studies🌴 california history🌍 earth science🌐 ethnic studies🐊 florida history🍑 georgia history🌎 global studies🌺 hawaiian studies📰 journalism🪶 native american studies🌵 new mexico history🤠 oklahoma history⚗️ physical science🎙️ speech and debate🤝 texas government🤠 texas history🌲 washington state history🕊️ world religions
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© 2026 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.