AP Calculus AB

Flashcards ยท Study Games ยท Full 2019 Exam ยท AI-graded FRQs ยท Interactive Reference Sheet

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Flashcards

60+ cards covering all 8 units with LaTeX-rendered math

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Study Games

Term Match, Lightning Round T/F, and Derivative Drill

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2019 Full Exam

All 45 MC + 6 FRQ from the official 2019 AP exam

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Mock Test

20 custom MC + 2 FRQ graded by Gemini AI

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Reference

Interactive unit circle, trig derivatives, complete formula sheet

๐Ÿ“‹ Exam Structure

  • MCQ Part A: 30 questions, 60 min, NO calculator โ€” conceptual mastery
  • MCQ Part B: 15 questions, 45 min, graphing calculator required
  • FRQ Part A: 2 questions, 30 min, calculator OK
  • FRQ Part B: 4 questions, 60 min, NO calculator
  • Score: 45 MC ร— 1.2 + 54 FRQ points = 108 max. Need ~69 for a 5

๐ŸŽฏ Score a 5 โ€” Key Strategies

  • Know IVT, EVT, MVT, FTC deeply โ€” not just the formula, but WHEN to apply them
  • Connect graphical, numerical, analytical, and verbal representations (the "rule of 4")
  • Always attach units in context problems โ€” College Board awards a unit point
  • Justify with sign charts โ€” fโ€ฒ changes sign โ†’ extremum. Must show evidence
  • Units 5 and 6 carry the most weight โ€” master analytical derivatives and integration first

Flashcards

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Study Games

Learn by doing โ€” fastest way to lock in calculus concepts.

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Term Match

Match formulas to their names. Beat the clock!

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Lightning Round

True or False โ€” rapid-fire calculus statements

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Derivative Drill

Type the derivative โ€” all rule types

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Time: 90s
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Find the derivative of f(x) =

Type using standard notation: x^2, sin(x), e^x

2019 AP Calculus AB Exam

Official College Board exam โ€” all 45 MC + 6 FRQ with scoring guidelines

Section I, Part A โ€” No Calculator

  • 30 multiple-choice questions โ€” 1 hour
  • No electronic devices allowed
  • Each correct answer worth 1 point (ร—1.2 weight)
  • No penalty for wrong answers โ€” guess if unsure!
  • Answers revealed instantly with full rationales

Section I, Part B โ€” Graphing Calculator Required

  • 15 multiple-choice questions โ€” 45 minutes
  • Graphing calculator required for some questions
  • Questions numbered 76โ€“90 on the actual exam

Section II โ€” Free Response Questions

  • 6 questions total โ€” 1 hour 30 minutes
  • Part A (Q1โ€“2): 30 min, graphing calculator OK
  • Part B (Q3โ€“6): 60 min, no calculator
  • Show all work โ€” partial credit awarded per scoring guidelines
  • Toggle "Scoring Guidelines" after answering each part to check your work

โœ๏ธ Custom Mock Test

20 randomly selected MC questions (including harder graph-based problems โ˜…) covering all 8 units + 2 FRQs with KaTeX math input toolbar. Graded by Gemini AI with detailed feedback. Questions change each time!

Reference Sheet

Interactive unit circle, trig derivatives, and complete formula reference.

x y 1 -1 1 -1

Selected Point

Click any point on the circle

Degreesโ€”
Radiansโ€”
cos ฮธ (x)โ€”
sin ฮธ (y)โ€”
tan ฮธโ€”
Pointโ€”

Memory Tips

30-45-60 trick:
sin values: ยฝ, โˆš2/2, โˆš3/2

ASTC rule:
Q1: All+ | Q2: Sin+ | Q3: Tan+ | Q4: Cos+

"All Students Take Calculus"

Derivatives of All 6 Trig Functions

d/dx[sin x]
= cos x
d/dx[cos x]
= โˆ’sin x
d/dx[tan x]
= secยฒx
d/dx[csc x]
= โˆ’csc x ยท cot x
d/dx[sec x]
= sec x ยท tan x
d/dx[cot x]
= โˆ’cscยฒx

Inverse Trig Derivatives

d/dx[arcsin x]
= 1 / โˆš(1 โˆ’ xยฒ)
d/dx[arccos x]
= โˆ’1 / โˆš(1 โˆ’ xยฒ)
d/dx[arctan x]
= 1 / (1 + xยฒ)

๐Ÿง  Memory Pattern

  • sin โ†’ cos (positive); cos โ†’ โˆ’sin (negative)
  • tan โ†’ secยฒx; cot โ†’ โˆ’cscยฒx (co- versions are negative)
  • sec โ†’ secยทtan; csc โ†’ โˆ’cscยทcot
  • All "co-" derivatives are negative

Limits & Continuity

Continuity at x=a requires
f(a) exists AND lim exists AND lim = f(a)
IVT
f cts on [a,b] โ†’ hits every value between f(a),f(b)
EVT
f cts on [a,b] โ†’ has abs max AND min
lim sin(x)/x as xโ†’0
= 1

Differentiation Rules

Limit Definition
f'(a) = lim[hโ†’0] (f(a+h)โˆ’f(a))/h
Power Rule
d/dx[xโฟ] = nxโฟโปยน
Product Rule
d/dx[fg] = f'g + fg'
Quotient Rule
d/dx[f/g] = (f'g โˆ’ fg') / gยฒ
Chain Rule
d/dx[f(g(x))] = f'(g(x))ยทg'(x)
d/dx[eหฃ]
= eหฃ
d/dx[ln x]
= 1/x
d/dx[aหฃ]
= aหฃยทln a
Inverse Function
(fโปยน)'(a) = 1/f'(fโปยน(a))

Applications of Differentiation

MVT
f'(c) = [f(b)โˆ’f(a)]/(bโˆ’a)
Linearization
L(x) = f(a) + f'(a)(xโˆ’a)
Critical Points
where f'(x)=0 or f'(x) DNE

Integration

FTC Part 1
d/dx[โˆซโ‚หฃ f(t)dt] = f(x)
FTC Part 2
โˆซโ‚แต‡ f'(x)dx = f(b)โˆ’f(a)
โˆซxโฟ dx
= xโฟโบยน/(n+1) + C
โˆซeหฃ dx
= eหฃ + C
โˆซ(1/x) dx
= ln|x| + C
โˆซsin x dx
= โˆ’cos x + C
โˆซcos x dx
= sin x + C
โˆซsecยฒx dx
= tan x + C

Differential Equations & Applications

Exponential Model
dy/dt=ky โ†’ y=Ceแตแต—
Logistic Model
dP/dt=kP(1โˆ’P/M), carrying cap=M
Area Between Curves
โˆซโ‚แต‡ (topโˆ’bottom) dx
Disk Method
V=ฯ€โˆซโ‚แต‡ [R(x)]ยฒ dx
Washer Method
V=ฯ€โˆซโ‚แต‡ [Rยฒโˆ’rยฒ] dx
Average Value
f_avg=(1/(bโˆ’a))โˆซโ‚แต‡ f(x)dx

Standard Trig Values

Degrees Radians sin ฮธ cos ฮธ tan ฮธ

๐ŸŽฏ Key Identities for AP

  • sinยฒx + cosยฒx = 1
  • 1 + tanยฒx = secยฒx
  • 1 + cotยฒx = cscยฒx
  • sin(2x) = 2 sin x cos x
  • cos(2x) = cosยฒx โˆ’ sinยฒx = 1 โˆ’ 2sinยฒx