AP Calculus BC follows the curriculum set forth by the College Board. It is worth the equivalent of two semesters of college credit upon successful completion of the AP examination in May. Students enrolled in this course are required to take this test. Topics covered include library of functions, limits, the derivative, applications of the derivative, definite and indefinite integrals, applications of integration, techniques of integration, infinite series and sequences, etc.
notes / updates
May 14, 2025 | BC FRQ 2025 The answer key below was typed fast and is not formatted properly, which means it likely has mistakes. Additionally, I have left out units and full reasoning/explanations.
The questions are on the collegeboard website.
Q1.
a. 2.778
b. 1.282
c. The limit is 0.
d. Absolute maximum @ t = 11.442. The maximum is 7.317.
Q2.
a. 1.031
b. 2.067
c. x(0.95532) = 0.770 (Use CIM to justify.)
d. 15.465
Q3.
a. 5 words per minute per minute
b. Yes, by IVT, R (c) = 155 at least once on [8, 10] since 155 is between R (8) = 150 and R (10) = 162. The function R is continuous because it is given as differentiable.
c. 1252
d. 1300
Q4.
a. g'(x) = f(x) by FTC, so g'(8) = f(8) = 1
b. g''(x) = f'(x), which changes sign at x = -3, 3, 6.
These are the inflection points on the graph of g.
c. g(12) = 9
g(0) = -9pi/2
d. Consider critical numbers and endpoints:
g(-6) = g(6) = 0
g(0) = -9pi/2
g(12) = 9
By the Closed Interval Method, the global minimum occurs at x=0.
Q5.
a. f''(1) = -9
b. T(x) = -1 + 2 (x - 1) - (9/2) (x - 1)^2
c. LEB = | 60 * 0.1^3/(3!)| = 1/100. The error cannot exceed the bound.
d. f(1.4) is approximately equal to -0.470.
Q6.
a. [1, 7) with work and reasoning
b. f' (x) = (1/3) (x - 4) + (1/3^2) (x - 4)^2 + (1/3^3) (x - 4)^3 + ... + (1/3^n) (x - 4)^n + ...
c.
a = r = (x-4)/3, so the series converges to a/(1 - r) = (x - 4) / (3 - x + 4) = (x - 4) /(7 - x)
d.
x=8 is not in the interval of convergence of the original function f(x), so f'(x) will not converge at x=8 either.