AP Calculus BC Exam Questions and
Answers
Euler's Method - Correct Answers -(x,y) | dx | dy/dx | dx(dy/dx)=dy | (x+dx, y+dy)
Integration by Parts ∫udv= - Correct Answers -uv-∫vdu
∫lnxdx - Correct Answers -xlnx-x+C
Taylor Series - Correct Answers -(fⁿ(a))/n!)(x-a)ⁿ
Maclaurin Series - Correct Answers -A Taylor series about x=0
Maclaurin Series e^x= - Correct Answers -1+x+(x²/2!)+(x³/3!)+...
Maclaurin Series cosx= - Correct Answers -1-(x²/2!)+(x⁴/4!)-...
Maclaurin Series sinx= - Correct Answers -x-(x³/3!)+(x⁵/5!)-...
Maclaurin Series 1/(1-x)= - Correct Answers -1+x+x²+x³+...
Maclaurin Series ln(x+1)= - Correct Answers -x-(x²/2)+(x³/3)-(x⁴/4)+...
Slope of a Parametric Equation dy/dx= - Correct Answers -(dy/dt)/(dx/dt)
Area of a Polar Curve - Correct Answers -∫1/2[r(θ)]²dθ from θ₁to θ₂
Derivitive of a Polar Curve dy/dx= - Correct Answers -(dy/dθ)/(dx/dθ)
Conversion from Polar to x= - Correct Answers -rcosθ
Conversion from Polar to y= - Correct Answers -rsinθ
Geometric Series - Correct Answers -a+ar+ar²+ar³+...arⁿ⁻¹+...=∑arⁿ⁻¹ from n=1 to ∞
diverges if |r|≥1; converges to a/(1-r) if |r|<1.
sin2x= - Correct Answers -2sinxcosx
sin²x+cos²x= - Correct Answers -1
1+tan²x= - Correct Answers -sec²x
Answers
Euler's Method - Correct Answers -(x,y) | dx | dy/dx | dx(dy/dx)=dy | (x+dx, y+dy)
Integration by Parts ∫udv= - Correct Answers -uv-∫vdu
∫lnxdx - Correct Answers -xlnx-x+C
Taylor Series - Correct Answers -(fⁿ(a))/n!)(x-a)ⁿ
Maclaurin Series - Correct Answers -A Taylor series about x=0
Maclaurin Series e^x= - Correct Answers -1+x+(x²/2!)+(x³/3!)+...
Maclaurin Series cosx= - Correct Answers -1-(x²/2!)+(x⁴/4!)-...
Maclaurin Series sinx= - Correct Answers -x-(x³/3!)+(x⁵/5!)-...
Maclaurin Series 1/(1-x)= - Correct Answers -1+x+x²+x³+...
Maclaurin Series ln(x+1)= - Correct Answers -x-(x²/2)+(x³/3)-(x⁴/4)+...
Slope of a Parametric Equation dy/dx= - Correct Answers -(dy/dt)/(dx/dt)
Area of a Polar Curve - Correct Answers -∫1/2[r(θ)]²dθ from θ₁to θ₂
Derivitive of a Polar Curve dy/dx= - Correct Answers -(dy/dθ)/(dx/dθ)
Conversion from Polar to x= - Correct Answers -rcosθ
Conversion from Polar to y= - Correct Answers -rsinθ
Geometric Series - Correct Answers -a+ar+ar²+ar³+...arⁿ⁻¹+...=∑arⁿ⁻¹ from n=1 to ∞
diverges if |r|≥1; converges to a/(1-r) if |r|<1.
sin2x= - Correct Answers -2sinxcosx
sin²x+cos²x= - Correct Answers -1
1+tan²x= - Correct Answers -sec²x
