NCEA Level 3 Calculus case studies
NCEA Level 3 Calculus · Put your knowledge to work in context.
NCEA Level 3 Calculus is the highest of the three NCEA senior mathematics subjects in New Zealand's national qualification framework, taken in Year 13 and typically used as a prerequisite pathway into engineering, physical sciences, mathematics, and economics at tertiary level. It is designed for students who are comfortable with algebraic manipulation and who intend to study a mathematically demanding degree. The NCEA Level 3 Calculus case studies are 5 cases and about 3,798 words.
1Hot-water cylinder: constrained surface-area minimisation
A manufacturer produces stainless-steel hot-water cylinders. Each is a right circular cylinder of radius r metres and height h metres with a flat base and a hemispherical dome on top, so the overall height is h + r .
729 words, about 4 min2Parabolic arch bridge: clearance, focus and model checking
A road passes under a masonry arch that springs from ground level on both sides. The clear span is 12.0\ m and the crown is 5.0\ m above the road at the centre of the span.
824 words, about 4 min3Harbour tide models: harmonics, general solutions and timetable risk
The harbour master at a small port models the water depth over the bar as d 1(t) = 3.2 + 2.4 \! ( t{6} ) metres, where t is hours after midnight and the tide repeats every 12 hours.
757 words, about 4 min4Feedback loop stability: conjugate roots and a complex locus
An engineering student is checking the stability of a feedback loop. The characteristic equation, with real coefficients, is p(z) = z^3 - 5z^2 + 11z - 15 = 0 , and the system is stable only if every root has negative real part.
788 words, about 4 min5Draining irrigation tank: separable DE, validity limit and scaling
A vertical cylindrical irrigation tank has internal cross-section 2.0\ m^2 and depth 4.0\ m , with a small valve at the base. The tank is full and there is no inflow when the caretaker opens the valve at t = 0 .
700 words, about 4 min