Mathematics Methods Level 4 case studies
Mathematics Methods Level 4 · Put your knowledge to work in context.
Mathematics Methods Level 4 is a standalone, independent study resource for learners who have finished a senior secondary mathematical methods course and want to test whether their skills hold up under exam conditions. It suits students preparing for university entrance in mathematics, engineering, economics or the physical sciences, and adults returning to quantitative study who need a structured way to rebuild fluency. The Mathematics Methods Level 4 case studies are 5 cases and about 2,330 words.
1The Ferris Wheel Ticket Window
A small fairground runs a Ferris wheel whose passenger cabin height above the ground, in metres, is modelled by h(t) = 12 + 10·sin(πt/15), where t is in seconds after boarding at the platform. The platform is at the lowest point of the ride.
645 words, about 3 min2The Leaking Storage Tank
A cylindrical storage tank of radius 2 m and height 5 m is being drained. The volume of water remaining, in cubic metres, is modelled by V(t) = 20π − 0.4πt for 0 ≤ t ≤ 50 minutes, where t is time after draining begins.
495 words, about 2 min3Cooling Coffee and the Half-Life Trap
A forensic analyst models the temperature of a cup of coffee left in a 20 °C room using Newton's law of cooling: T(t) = 20 + 75·e^(−kt), where T is in °C and t in minutes. A thermometer reading at t = 0 gives 95 °C, and at t = 10 min gives 66 °C.
414 words, about 2 min4The Ramp Angle Dispute
A wheelchair ramp is being designed for a community centre entrance. The horizontal run is 6.0 m and the rise is 0.9 m, giving an incline angle θ with tan θ = 0.15.
383 words, about 2 min5The Quality-Control Sampling Decision
A factory produces circuit boards with a historical defect rate of 4%. A new production line is installed, and an inspector samples 150 boards, finding 12 defective.
393 words, about 2 min