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CalculusABCs

FRQ Intelligence

Position-by-position breakdown of the AP® Calculus BC free-response section.

174 questions analyzed · 2003–2025 · 20 years of data (excludes 2012, 2017, 2020)

90%
Q6 Predictability
Taylor Series
26 of 29 BC Q6s
66%
Q2 Content
Parametric/Polar
BC-exclusive topics
50%
No Calculator
Q4–Q6 Always
Q3 mixed by year
41%
BC-Exclusive
∼2.5 Questions
Per exam on average

Question Breakdown

QCalc?Most LikelyFreqKey Skills
1
Calc
Area/Volume35%Definite integral, washer/disk, accumulation
2
CalcBC
Parametric Motion35%Speed, arc length, ½∫r²dθ
3
Mixed
Function Analysis24%FTC, extrema, Riemann sums
4
No Calc
Graph of f′48%FTC 1&2, inflection points
5
No Calc
Differential Eq35%Euler's, separation, improper
6
No CalcBC
Taylor Series90%Ratio test, error bounds, IOC

Position Predictability

Q1Variable
35%
Q2BC Focus
66%
Q3Variable
24%
Q4Moderate
48%
Q5Variable
35%
Q6Guaranteed
90%

Problem Frequency by Archetype

Taylor Series29 · 16.7%
Function Analysis29 · 16.7%
Particle Motion25 · 14.4%
Area/Volume23 · 13.2%
Table Analysis18 · 10.3%
Differential Eq18 · 10.3%
Rate In/Out17 · 9.8%
Polar Area11 · 6.3%

Unit Coverage

Unit 649%
Unit 436%
Unit 833%
Unit 1021%
Unit 918%

Top 10 Skills

1Definite Integral Setup
50%
2FTC Applications
25%
3Taylor Polynomial
17%
4Parametric Speed
15%
5Euler's Method
7%
6Polar Area ½∫r²dθ
6%
7Alt. Series Error
4%
8Ratio Test / IOC
4%
9Washer/Disk
4%
10Riemann Sums
4%

Common Mistakes

#1
Missing units
Always include context + units
#2
Sign chart without words
f has max because f′ changes + to −
#3
Distance vs displacement
∫|v|dt ≠ ∫v dt
#4
Calculator in degree mode
Check RADIAN before starting
#5
Local vs global max
Candidates test: check endpoints

The Stakes

If you can't do Taylor Series
lose Q6, 15% of FRQ score
If you skip parametric/polar
lose Q2, another 15%
That's 30% you can't even attempt
Before you pick up your pencil

Scoring Quick Reference

Easy Points
Integral setup (even without dt)
Include units in context
How You Lose Points
Degree mode: first earned point
No constant in DE: max 2–3 pts

Time Strategy

Per Question15 min
90 min ÷ 6
Part (a)3–4 min
Setup + solve
Parts (b)–(d)3–4 min each
Build on prior
Review5 min
Check units & signs

The pattern is structural. In 22 years, Q6 has been Taylor Series 90% of the time. Q2 has been parametric or polar 66% of the time. These aren’t trends, they’re features of the exam. Master these positions and you’ve locked in 30% before you see the questions.