FY12CE Mathematics case studies
FY12CE Mathematics · Put your knowledge to work in context.
FY12CE Mathematics is a final-year secondary mathematics examination-style credential covering seven weighted domains: Calculus (35%), Linear Algebra and Vector Geometry (15%), Probability and Statistics (15%), Differential Equations (10%), Discrete Mathematics and Logic (10%), Numerical Methods and Computation (10%), and Mathematical Modeling and Applications (5%). It suits candidates finishing a Year 12 programme who need a broad, proof-aware mathematical foundation before university study in engineering, economics, computer science, or the physical sciences, and mature candidates refreshing their skills. The FY12CE Mathematics case studies are 5 cases and about 3,384 words.
1Open-Top Cylindrical Bin: Cost Minimization with a Height Cap
A fabricator is quoting a batch of 500 open-top cylindrical steel bins. Each bin must hold 2.0 L (2000 cm^3).
784 words, about 4 min2Strain-Gauge Calibration: Least Squares After a Suspect Reading
A calibration technician records a strain gauge's output y (mV) at five known loads x (kN): (1, 2.10), (2, 3.95), (3, 6.10), (4, 7.85), (5, 10.20). The intended model is y = a + bx.
621 words, about 3 min3Mixing Tank Alarm: Salt Concentration During Filling and After Outlet Adjustment
A 500 L mixing tank initially contains 250 L of solution with 100 kg of dissolved salt. Brine containing 0.20 kg/L of salt enters at 8.0 L/min.
643 words, about 3 min4Screening Test: PPV, Repeat Testing, and a Limited Confirmation Budget
A regional clinic screens 10,000 adults, of whom 2,000 are in a high-risk subgroup with family history. The general-population prevalence is 0.80%; in the high-risk subgroup it is 6.0%.
661 words, about 3 min5Valve Controller Root-Finding: Ten-Iteration Error Guarantee
A process engineer must solve f(x) = x^3 - 2x - 5 = 0 for a valve setting x in [2,3]. The controller has a fixed budget of 10 iterations per cycle and must guarantee an absolute error below 10^{-6} before the next control action.
675 words, about 3 min