QCE Maths Methods case studies
QCE Maths Methods · Put your knowledge to work in context.
QCE Mathematical Methods is a Queensland senior secondary subject that contributes to the Queensland Certificate of Education and is commonly used as a prerequisite or assumed-knowledge subject for tertiary courses in engineering, health sciences, economics, business and the physical sciences. It suits students who are comfortable with algebraic manipulation and who want a mathematically rigorous pathway rather than a purely applied one. The QCE Maths Methods case studies are 5 cases and about 1,716 words.
1Fitting a Parabola to a Cable Sag
A suspension bridge has a main cable that, between two identical towers, is modelled by a parabola. The towers are 120 m apart and each is 30 m tall above the deck.
421 words, about 2 min2Average Rate versus Instantaneous Rate in a Cooling Tank
A tank of water cools so that its temperature T (°C) after t minutes is modelled by T(t) = 20 + 60e^(−0.05t) for 0 ≤ t ≤ 90. A technician measures the temperature at t = 0 and t = 40, computes an average rate of change, and reports that the water is cooling at that constant rate.
331 words, about 2 min3Normal Distribution Cut-off for a Scholarship
Scores on a selection test are approximately normally distributed with mean 62 and standard deviation 11. A scholarship is awarded to the top 8% of candidates.
310 words, about 2 min4Solving a Trigonometric Equation on a Restricted Domain
The height of a point on a Ferris wheel above the ground is h(t) = 12 + 10 sin(πt/15), where t is in seconds and 0 ≤ t ≤ 60. A maintenance gate can only be opened when the point is at least 17 m above the ground, and the gate must stay open for a continuous interval.
343 words, about 2 min5Logarithmic Model and Doubling Time
A bacterial culture grows so that population P after t hours is P(t) = 400e^(0.35t) for t ≥ 0. A lab protocol says the culture must be subcultured before the population reaches 5000.
311 words, about 2 min