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04-BS-1: Undated paper

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 General Solutions of Three First–/Second–Order ODEs
  2. Question 2 Critically-Damped Forced Oscillator (Initial Value Problem)
  3. Question 3 Initial Value Problem with Real Distinct Roots and Linear Forcing
  4. Question 4 Tangent Line to the Intersection of Two Quadric Surfaces
  5. Question 5 Volume Inside a Sphere and Above a Cone (Spherical Coordinates)
  6. Question 6 Line Integral Along the Equatorial Circle of a Hemisphere
  7. Question 7 Steady-State Response of a Damped Mass-Spring System to a Periodic Square Wave

Start with Question 1 →

National Exams — 04-BS-1 Mathematics. Three-hour, closed-book exam. Format: seven questions offered; Question 1 is split (a) 7, (b) 7, (c) 6 marks, Questions 2–7 are 20 marks each; any five questions constitute a complete paper and only the first five appearing in the answer book are marked. All seven are solved below for completeness.

Reference texts: Kreyszig, Advanced Engineering Mathematics (10th ed., Wiley) — ODEs, Laplace transforms and Fourier series for periodic forcing, tangent lines to surface intersections, line/surface integrals; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — spherical coordinates and volumes, vector line integrals.