AP Calculus BC free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper AP Calculus BC set, then download the 4-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
Which of the following series converges?
A Σ (n = 1 to ∞)
B Σ (n = 0 to ∞) (
C Σ (n = 2 to ∞)
D Σ (n = 1 to ∞) 1/n^(
Correct answer: D — Σ (n = 1 to ∞) 1/n^( • Test each series: p-series Σ 1/n^p converges only when p > 1; geometric series Σ r^n converges only when |r| < 1.
- Only Σ (n = 1 to ∞) 1/n^( • Σ (n = 0 to ∞) ( • Σ (n = 2 to ∞)
- Σ (n = 1 to ∞)
- Why the other options are wrong:
- A (Σ (n = 1 to ∞)
- B (Σ (n = 0 to ∞) ( • C (Σ (n = 2 to ∞) p-series converge for p > 1 and geometric series for |r| < 1; the nth-term test kills any series whose terms do not tend to 0.
3
2 )
3
Your sample is downloading. Liked it? AP Calculus BC Paper 1 is the full paper: 45 multiple-choice questions and 6 free-response questions (54 marks), 3 hours 15 minutes, 99 marks in all, with a worked solution for every question.
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Questions about this sample
What is in the AP Calculus BC free sample?
The first 3 questions from paper 1 of the set, in the real exam layout, followed by the step-by-step worked answers. It is a 4-page PDF; this page shows question 1 with its answer.
How many full AP Calculus BC papers are there?
20 original papers for students preparing for the AP Calculus BC exam. Each is 45 multiple-choice questions and 6 free-response questions (54 marks), 3 hours 15 minutes, 99 marks in all, with a worked solution for every question. Papers start at A$11.99 and download instantly as a PDF.
Are these official past papers?
No. The sample is taken from our own original practice paper and is not an official past paper or affiliated with any exam authority.