2023 Paper 1
- Q1a Linear dependence and independence 10 marks
- Q1b Rank and nullity; rank-nullity theorem 10 marks
- Q1c Taylor's theorem with remainders 10 marks
- Q1d Improper integrals (unbounded interval/integrand) 10 marks
- Q1e Plane 10 marks
- Q2a Matrix of a linear transformation 15 marks
- Q2b Triple Integrals; Cylindrical and Spherical Coordinates 15 marks
- Q2c-i Paraboloid (elliptic and hyperbolic) 10 marks
- Q2c-ii Cone 10 marks
- Q3a Cayley-Hamilton theorem 20 marks
- Q3b Maxima and Minima of Multi-Variable Functions (Unconstrained) 15 marks
- Q3c Sphere 15 marks
- Q4a Rank of a matrix 15 marks
- Q4b Curve tracing (cartesian and polar) 20 marks
- Q4c Straight lines in 3D 15 marks
- Q5a Linear first-order 10 marks
- Q5b Properties of Laplace transform (linearity, shift, derivative, convolution) 10 marks
- Q5c Equilibrium of Forces in Three Dimensions 10 marks
- Q5d Simple harmonic motion (free, damped, forced) 10 marks
- Q5e Differentiation of a vector function of a scalar variable 10 marks
- Q6a Linear ODE with constant coefficients 15 marks
- Q6b Projectile motion 15 marks
- Q6c Gauss divergence theorem 20 marks
- Q7a-i Exact equations 10 marks
- Q7a-ii Clairaut's equation 10 marks
- Q7b Principle of virtual work 15 marks
- Q7c Serret-Frenet formulae 15 marks
- Q8a Laplace transform applied to IVP for second-order linear ODE with constant coefficients 15 marks
- Q8b Central force motion and Kepler's laws 20 marks
- Q8c Vector identities (curl of grad, div of curl, product rules) 15 marks