2017 Paper 1
- Q1a Diagonalization via Eigenvectors 10 marks
- Q1b Congruence and similarity of matrices 10 marks
- Q1c Double integrals 10 marks
- Q1d Paraboloid (elliptic and hyperbolic) 10 marks
- Q1e Shortest distance between two skew lines 10 marks
- Q2a Areas, surface areas, volumes via integration 15 marks
- Q2b Sphere 15 marks
- Q2c Sphere 10 marks
- Q2d Subspaces 10 marks
- Q3a Rank and nullity; rank-nullity theorem 15 marks
- Q3b Eigenvalues and eigenvectors 10 marks
- Q3c Partial derivatives 15 marks
- Q3d Second-degree equations in three variables 10 marks
- Q4a Reduction of Second-Degree Equation to Canonical Form 15 marks
- Q4b Solution of system of linear equations 15 marks
- Q4c Improper integrals (unbounded interval/integrand) 10 marks
- Q4d Double integrals 10 marks
- Q5a Formulation of differential equations 10 marks
- Q5b Orthogonal trajectories (cartesian and polar) 10 marks
- Q5c Work-energy theorem 10 marks
- Q5d Curl: definition, physical meaning, computation 10 marks
- Q5e Differentiation of a vector function of a scalar variable 10 marks
- Q6a-i Particular integral via operator method 8 marks
- Q6a-ii Variables separable 8 marks
- Q6b-i Clairaut's equation 10 marks
- Q6b-ii Linear ODE with constant coefficients 7 marks
- Q6c Stability of equilibrium (energy criterion) 17 marks
- Q7a Curvature and torsion 16 marks
- Q7b-i Particular integral via operator method 9 marks
- Q7b-ii Method of variation of parameters 8 marks
- Q7c Constrained motion 17 marks
- Q8a Work and Potential Energy; Conservation 16 marks
- Q8b Laplace transform applied to IVP for second-order linear ODE with constant coefficients 17 marks
- Q8c-i Gauss divergence theorem 9 marks
- Q8c-ii Line integrals 8 marks