2024 Paper 1
- Q1a Bases and dimension; coordinates in a basis 10 marks
- Q1b Rank and nullity; rank-nullity theorem 10 marks
- Q1c Continuity of real functions 10 marks
- Q1d Taylor's theorem with remainders 10 marks
- Q1e Cylinder 10 marks
- Q2a Inverse of a matrix (adjoint and row reduction) 15 marks
- Q2b Jacobian 15 marks
- Q2c Plane 20 marks
- Q3a Matrix of a linear transformation 15 marks
- Q3b Maxima and minima of single-variable functions 20 marks
- Q3c Cone 15 marks
- Q4a Eigenvalues and eigenvectors 20 marks
- Q4b Double integrals 15 marks
- Q4c Sphere 15 marks
- Q5a Orthogonal trajectories (cartesian and polar) 10 marks
- Q5b Laplace transform applied to IVP for second-order linear ODE with constant coefficients 10 marks
- Q5c Differentiation of a vector function of a scalar variable 10 marks
- Q5d Stability of equilibrium (energy criterion) 10 marks
- Q5e-i Curvature and torsion 5 marks
- Q5e-ii Serret-Frenet formulae 5 marks
- Q6a Principle of virtual work 15 marks
- Q6b Simple harmonic motion (free, damped, forced) 15 marks
- Q6c-i Reduction of order with one solution known 10 marks
- Q6c-ii Method of variation of parameters 10 marks
- Q7a Picard's Existence/Uniqueness Theorem; Lipschitz Condition 15 marks
- Q7b Constrained motion 15 marks
- Q7c Stokes' theorem 20 marks
- Q8a Laplace transform applied to IVP for second-order linear ODE with constant coefficients 15 marks
- Q8b Gauss divergence theorem 15 marks
- Q8c Central force motion and Kepler's laws 20 marks