2015 Paper 1
- Q1a Linear dependence and independence 10 marks
- Q1b Rank of a matrix 10 marks
- Q1c Indeterminate forms 10 marks
- Q1d Indefinite integrals 10 marks
- Q1e Sphere 10 marks
- Q2a Algebra of matrices 12 marks
- Q2b Lagrange's method of multipliers (constrained extrema) 13 marks
- Q2c Eigenvalues and eigenvectors 12 marks
- Q2d Cone 13 marks
- Q3a Matrix of a linear transformation 12 marks
- Q3b Sphere 13 marks
- Q3c-i Plane 6 marks
- Q3c-ii Straight lines in 3D 7 marks
- Q3d Double integrals 12 marks
- Q4a Double integrals 13 marks
- Q4b Bases and dimension; coordinates in a basis 12 marks
- Q4c Paraboloid (elliptic and hyperbolic) 13 marks
- Q4d Functions of two/three variables: limits, continuity 12 marks
- Q5a Linear first-order 10 marks
- Q5b Exact equations 10 marks
- Q5c Simple harmonic motion (free, damped, forced) 10 marks
- Q5d Principle of virtual work 10 marks
- Q5e Gradient: definition, geometric meaning, computation 10 marks
- Q6a Exact equations 12 marks
- Q6b Friction (limiting friction) 13 marks
- Q6c Gradient: definition, geometric meaning, computation 12 marks
- Q6d Rectilinear motion under variable force 13 marks
- Q7a-i Inverse Laplace transform 6 marks
- Q7a-ii Laplace transform applied to IVP for second-order linear ODE with constant coefficients 6 marks
- Q7b Projectile motion 13 marks
- Q7c Curl: definition, physical meaning, computation 12 marks
- Q7d First-order higher-degree ODEs 13 marks
- Q8a Common catenary 12 marks
- Q8b Central force motion and Kepler's laws 13 marks
- Q8c Line integrals 12 marks
- Q8d Euler-Cauchy equation 13 marks