JC Mathematics case studies
JC Mathematics · Put your knowledge to work in context.
JC Mathematics (often called Junior College Mathematics or JC Math) is a pre-university level mathematics credential taken by students completing the junior college stage of schooling, typically as preparation for university admission in quantitative fields. It is intended for candidates who have already mastered secondary-school algebra and who are ready to work with rigour: formal proof, multi-step modelling, and problems that combine several topics in a single item. The JC Mathematics case studies are 5 cases and about 3,164 words.
1Smooth Skatepark Ramp Profile
A skatepark designer is modelling the cross-section of a new ramp. The profile is described by f(x) = 1.2x for 0 ≤ x ≤ 2, and f(x) = a(x − 8)^2 + k for 2 < x ≤ 8, where x is horizontal distance in metres from the start and f(x) is height in metres.
703 words, about 4 min2Drone Inspection Paths and Safety Envelope
Two inspection drones move in a warehouse. Their positions in metres at time parameters t and s seconds are modelled by r A(t) = (1, 2, 3) + t(2, −1, 1) and r B(s) = (4, 0, 5) + s(−1, 2, 2), with 0 ≤ t ≤ 10 and 0 ≤ s ≤ 8.
683 words, about 3 min3Ammonia Pulse in a Recirculating Fish Tank
A fish farm uses a 500 m³ holding tank. Fresh water enters at 20 m³/h and well-mixed water leaves at the same rate, so the volume stays constant.
527 words, about 3 min4Sequential Screening With Two Diagnostic Kits
A clinic screens for a disease that affects 3% of its patients. Two kits are available.
596 words, about 3 min5Input-Output Model for Three Farm Cooperatives
Three cooperatives-grain, dairy and equipment-trade inputs with one another. Let x = (x₁, x₂, x₃)ᵀ be their total outputs in suitable units, and let A be the input matrix where aᵢⱼ is the amount of sector i needed to produce one unit of sector j.
655 words, about 3 min