NZ Scholarship Calculus case studies
NZ Scholarship Calculus · Put your knowledge to work in context.
NZ Scholarship Calculus is a challenging assessment for top secondary school students in New Zealand. It is part of the New Zealand Scholarship awards, which recognise students who show deep understanding of a subject, high-level critical thinking and the ability to apply ideas to complex situations. The NZ Scholarship Calculus case studies are 5 cases and about 2,073 words.
1Brewery Filtration Window with a Parameterised Rate Model
A small brewery models its filtration rate by R(t)=(t^2+at+8)/(t+b) litres per hour, where t is hours after start, 0≤t≤12, and a,b are positive constants. During commissioning, the rate is 6 L/h at t=2 and 7 L/h at t=5.
359 words, about 2 min2Coastal Cable Route with Endpoint and Cost Sensitivity Checks
A coastal council must connect an offshore monitoring platform A to a treatment plant C on a straight shoreline. The point B on the shore nearest A is 8 km from A, and C is 15 km along the shore from B.
439 words, about 2 min3Vase Volume from a Rotated Profile and the Mean-Radius Trap
A potter is designing a cylindrical-symmetry vase by rotating the curve r(x)=a+1/(x+1) centimetres about the x-axis, for 0≤x≤4, where x is height in cm and r is radius. The parameter a 0 is chosen so the interior volume is exactly 500 cm^3.
435 words, about 2 min4Series RLC Filter: Phase Requirement versus Impedance Magnitude
A technician is tuning a series RLC filter connected to a 50 Hz AC supply. The resistance is R=20 Ω and the inductance is L=0.15 H.
418 words, about 2 min5Drone Path Warning Intervals and Closest Approach
A drone follows the parabolic path y=12−x^2/8, with x measured in kilometres east of a radar station and y in kilometres altitude; the usable path is −8≤x≤8. The radar dish is at (0,4).
422 words, about 2 min