AP Calculus BC Study Guide Exam with
complete solutions 2024/2025
sin² θ + cos² θ = - ANSWER-1
1 + tan² θ = - ANSWER-sec² θ
1 + cot² θ = - ANSWER-csc² θ
sin(-θ) = - ANSWER--sin θ
cos(-θ) = - ANSWER-cos θ
tan(-θ) = - ANSWER--tan θ
sin(A + B) = - ANSWER-sinAcosB + sinBcosA
sin(A - B) = - ANSWER-sinAcosB - sinBcosA
cos(A + B) = - ANSWER-cosAcosB - sinAsinB
cos(A - B) = - ANSWER-cosAcosB + sinAsinB
sin 2θ = - ANSWER-2sinθcosθ
cos 2θ = - ANSWER-cos² θ - sin² θ
= 2cos² θ - 1
= 1 - 2sin² θ
tan θ = - ANSWER-sin θ / cos θ
= 1 / cot θ
cot θ = - ANSWER-cos θ / sin θ
, = 1 / tan θ
sec θ = - ANSWER-1 / cos θ
csc θ = - ANSWER-1 / sin θ
cos² θ = - ANSWER-()(1 + cos 2θ)
sin² θ = - ANSWER-()(1 - cos 2θ)
d/dx (x^n) = - ANSWER-nx^(n - 1)
d/dx (fg) = - ANSWER-fg' + gf'
d/dx (f / g) = - ANSWER-(gf' - fg') / g^2
d/dx f(g(x)) = - ANSWER-f'(g(x))g'(x)
d/dx (sin x) = - ANSWER-cos x
d/dx (cos x) = - ANSWER--sin x
d/dx (tan x) = - ANSWER-sec² x
d/dx (cot x) = - ANSWER--csc² x
d/dx (sec x) = - ANSWER-secxtanx
d/dx (csc x) = - ANSWER--cscxcotx
d/dx (e^x) = - ANSWER-e^x
d/dx (a^x) = - ANSWER-a^x * ln a
d/dx (ln x) = - ANSWER-1 / x
d/dx (Arcsin x) = - ANSWER-1 / √(1 - x²)
d/dx (Arctan x) = - ANSWER-1 / (1 + x²)
complete solutions 2024/2025
sin² θ + cos² θ = - ANSWER-1
1 + tan² θ = - ANSWER-sec² θ
1 + cot² θ = - ANSWER-csc² θ
sin(-θ) = - ANSWER--sin θ
cos(-θ) = - ANSWER-cos θ
tan(-θ) = - ANSWER--tan θ
sin(A + B) = - ANSWER-sinAcosB + sinBcosA
sin(A - B) = - ANSWER-sinAcosB - sinBcosA
cos(A + B) = - ANSWER-cosAcosB - sinAsinB
cos(A - B) = - ANSWER-cosAcosB + sinAsinB
sin 2θ = - ANSWER-2sinθcosθ
cos 2θ = - ANSWER-cos² θ - sin² θ
= 2cos² θ - 1
= 1 - 2sin² θ
tan θ = - ANSWER-sin θ / cos θ
= 1 / cot θ
cot θ = - ANSWER-cos θ / sin θ
, = 1 / tan θ
sec θ = - ANSWER-1 / cos θ
csc θ = - ANSWER-1 / sin θ
cos² θ = - ANSWER-()(1 + cos 2θ)
sin² θ = - ANSWER-()(1 - cos 2θ)
d/dx (x^n) = - ANSWER-nx^(n - 1)
d/dx (fg) = - ANSWER-fg' + gf'
d/dx (f / g) = - ANSWER-(gf' - fg') / g^2
d/dx f(g(x)) = - ANSWER-f'(g(x))g'(x)
d/dx (sin x) = - ANSWER-cos x
d/dx (cos x) = - ANSWER--sin x
d/dx (tan x) = - ANSWER-sec² x
d/dx (cot x) = - ANSWER--csc² x
d/dx (sec x) = - ANSWER-secxtanx
d/dx (csc x) = - ANSWER--cscxcotx
d/dx (e^x) = - ANSWER-e^x
d/dx (a^x) = - ANSWER-a^x * ln a
d/dx (ln x) = - ANSWER-1 / x
d/dx (Arcsin x) = - ANSWER-1 / √(1 - x²)
d/dx (Arctan x) = - ANSWER-1 / (1 + x²)
