Mathematics Advanced calculus practice questions
Original calculus drills focused on method, interpretation and common errors.
Calculus success routine
Identify function, domain, derivative/integral need, units and interpretation. Show working even when using technology.
Question 1
A function has derivative f′(x)=3x²−12x+9. Find the stationary points of f and determine their nature.
Check: solve f′(x)=0, use second derivative or sign test, state x-values and nature.
Question 2
The velocity of a particle is v(t)=6t²−18t+12. Determine when the particle is stationary and describe the motion before and after those times.
Question 3
Explain why a correct derivative can still lead to an incorrect maximum/minimum answer.
Error audit
Track algebra errors, sign errors, interpretation errors and incomplete nature tests separately.