CEMC case studies
CEMC · Put your knowledge to work in context.
CEMC refers to the mathematics contests and assessments written by the Centre for Education in Mathematics and Computing at the University of Waterloo. Students in elementary through high school take them to measure their problem-solving ability against a widely used Canadian standard, and strong results are often cited in scholarship and enrichment applications. The CEMC case studies are 5 cases and about 1,619 words.
1Scaling a Recursive Exhibition Layout
A gallery builds a fractal display on a square floor of side 1. Stage 1 places a square of side 1/2 at the corner (0,0).
387 words, about 2 min2Triangulating an Inaccessible Tower
A surveyor must find the height of a tower whose base is on the far bank of a river. From point A on the near bank, the angle of elevation to the top T is 32°.
350 words, about 2 min3Modular Scheduling of Repeating Events
Two maintenance alarms run on cycles. Alarm X sounds every 18 minutes starting at minute 0; alarm Y every 30 minutes starting at minute 0.
282 words, about 1 min4A Converging Approximation Under Debate
A student proposes approximating a quantity with the partial sums S n = sum {k=1}^{n} (−1)^{k+1}/k, the alternating harmonic series. A classmate argues that because the terms 1/k shrink to zero, the series must converge - and moreover that reordering the terms cannot change the total, since 'addition is commutative.' The teacher notes the series converges to ln 2 ≈ 0.6931 but that the reordering claim deserves scrutiny.
308 words, about 2 min5Fairness in a Sealed-Bid Allocation
A club of 10 members must choose 3 to sit on a committee. A randomization scheme is proposed: each member independently flips a fair coin, and if exactly 3 heads appear those 3 form the committee; otherwise the process restarts.
292 words, about 1 min