2019 Paper 1
- Q1a Continuity of real functions 10 marks
- Q1b Functions of two/three variables: limits, continuity 10 marks
- Q1c Matrix of a linear transformation 10 marks
- Q1d Solution of system of linear equations 10 marks
- Q1e Straight lines in 3D 10 marks
- Q2a Differentiability 15 marks
- Q2b Orthogonal and unitary matrices 15 marks
- Q2c-i Sphere 10 marks
- Q2c-ii Cone 10 marks
- Q3a Maxima and minima of single-variable functions 15 marks
- Q3b Paraboloid (elliptic and hyperbolic) 15 marks
- Q3c-i Rank of a matrix 15 marks
- Q3c-ii Rank and nullity; rank-nullity theorem 5 marks
- Q4a Cayley-Hamilton theorem 15 marks
- Q4b Ellipsoid 15 marks
- Q4c-i Partial derivatives 12 marks
- Q4c-ii Jacobian 8 marks
- Q5a Exact equations 10 marks
- Q5b Particular integral via operator method 10 marks
- Q5c Friction (limiting friction) 10 marks
- Q5d Work-energy theorem 10 marks
- Q5e Gradient: definition, geometric meaning, computation 10 marks
- Q6a Stability of equilibrium (energy criterion) 15 marks
- Q6b Line integrals 15 marks
- Q6c-i Reduction of order with one solution known 10 marks
- Q6c-ii Laplace transform 10 marks
- Q7a Method of variation of parameters 15 marks
- Q7b Curvature and torsion 15 marks
- Q7c Simple harmonic motion (free, damped, forced) 20 marks
- Q8a Clairaut's equation 15 marks
- Q8b Orbits under inverse-square central force 15 marks
- Q8c-i Gauss divergence theorem 15 marks
- Q8c-ii Stokes' theorem 5 marks