AP Calculus AB free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper AP Calculus AB set, then download the 4-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
The gradient of the curve y = (4x + 3)⁴ at x = 1 is
A 10976
B 1372
C -5488
D 5488
Correct answer: D — 5488
- Differentiate with the chain rule: dy/dx = 16(4x + 3)³.
- Substitute x = 1: 5488.
- Why the other options are wrong:
- A (10976): This is the correct answer (5488) doubled: a scaling factor was applied (or a factor missed) that the working above does not use.
- B (1372): This forgets the chain-rule factor (the derivative of the inside).
- C (-5488): Check the sign of the derivative.
Chain rule: multiply the outer derivative by the derivative of the inside function.
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Questions about this sample
What is in the AP Calculus AB 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 AB papers are there?
20 original papers for students preparing for the AP Calculus AB 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.