WACE Maths Methods case studies
WACE Maths Methods · Put your knowledge to work in context.
WACE Mathematics Methods is the Australian Tertiary Admission Rank (ATAR) mathematics course offered in Western Australian senior secondary schools and examined by the School Curriculum and Standards Authority (SCA). It suits students who intend to study mathematics, engineering, physical sciences, economics or health sciences at university, and who are comfortable with algebra and graphical reasoning. The WACE Maths Methods case studies are 5 cases and about 3,278 words.
1Diluted Dose with a Hidden Domain Restriction
A pharmacist models the concentration of a drug in a patient's bloodstream using C(t) = (12t)/(t^2 + 4) for t ≥ 0, where C is measured in mg/L and t in hours after administration. A colleague proposes a simplified model C2(t) = 3t/(t + 1) after arguing that for large t the two formulas behave similarly.
586 words, about 3 min2Tide Model with a Phase Shift and Restricted Window
A harbour's water depth is modelled by D(t) = 4 + 3 sin(πt/6 + π/4) metres, where t is hours after midnight and 0 ≤ t ≤ 24. A ferry requires a depth of at least 5.5 m to dock safely.
940 words, about 5 min3Optimising a Folded Cardboard Tray with a Material Constraint
A student cuts squares of side x cm from each corner of a rectangular sheet measuring 24 cm by 18 cm and folds up the sides to form an open tray of volume V(x) = x(24 - 2x)(18 - 2x). The student claims the maximum volume occurs at x = 4 because that is halfway between the endpoints 0 and 9.
625 words, about 3 min4Radioactive Decay Model with a Measurement Discrepancy
A sample of a radioisotope has activity A(t) = A0 e^(-kt), with A in becquerels and t in days. Two measurements are recorded: A(0) = 800 Bq and A(10) = 500 Bq.
530 words, about 3 min5Normal Approximation to a Binomial Quality-Control Problem
A factory produces components with a 4% defect rate, independently. A batch of 500 components is inspected.
597 words, about 3 min