QCAA Specialist Mathematics case studies
QCAA Specialist Mathematics · Put your knowledge to work in context.
QCAA Specialist Mathematics is a Queensland senior secondary subject in the Australian curriculum, assessed through school-based internal assessment and external written examinations set by the Queensland Curriculum and Assessment Authority. It suits students who enjoy rigorous abstraction and intend to pursue mathematics, engineering, physical sciences, computer science or economics at university, and it is generally taken alongside Mathematical Methods rather than instead of it. The QCAA Specialist Mathematics case studies are 5 cases and about 1,656 words.
1The Misleading Average of a Piecewise Rate
A tank holds 240 L of water and drains through a valve whose flow rate is modelled by r(t) = 12 − 3t L/min for 0 ≤ t ≤ 4, but the valve is physically unable to run in reverse, so for t 4 the effective outflow is capped at 0 L/min. A student computes total outflow as the integral of r(t) from 0 to 8, obtaining 96 − 96 = 0 L, and concludes the tank is unchanged after 8 minutes.
356 words, about 2 min2Roots of Unity and a Suspect Symmetry
A student is asked to find all complex z satisfying z⁴ = −16. They write z = 2cis(θ) and solve 4θ = π, giving θ = π/4, so z = 2cis(π/4) only.
326 words, about 2 min3When the Discriminant Lies About a Real-World Model
A projectile is launched from ground level with speed 20 m/s at angle θ to the horizontal. A wall of height 8 m stands 15 m away.
338 words, about 2 min4A Hypothesis Test With a One-Sided Story
A manufacturer claims batteries last at least 500 minutes on average. A sample of 40 batteries gives mean 492 minutes with sample standard deviation 18 minutes.
330 words, about 2 min5Matrix Model of a Closed Economy That Will Not Balance
A simple two-sector economy has input-output matrix A = [[0.2, 0.4],[0.5, 0.1]], where aᵢⱼ is the input from sector i needed per unit output of sector j. Final demand is d = [30, 20]ᵀ.
306 words, about 2 min