This document contains 8 questions related to optimal control theory for an exam. The questions cover various topics: 1) Bellman's principle of optimality and applying it to find optimal trajectories. 2) Deriving recurrence relations for dynamic programming and explaining its characteristics. 3) Finding the optimal control law using the Hamilton-Jacobi-Bellman equation to minimize a performance measure. 4) Explaining the fundamental theorem of calculus of variations and determining an extremal for a given functional. 5) Deriving costate equations, determining the control to minimize the Hamiltonian, and boundary conditions for optimal transfer between states. 6) Explaining how two-point boundary value problems can be solved using variation of extrem