Pancyprian Advanced Math case studies
Pancyprian Advanced Math · Put your knowledge to work in context.
The Pancyprian Advanced Mathematics Examination (Παγκύπριες Εξετάσεις Προχωρημένων Μαθηματικών) is a written, constructed-response examination used in Cyprus for advanced mathematics placement or certification, typically taken by upper-secondary graduates preparing for university entry or by candidates seeking formal recognition of mathematical competence. It is intended for students who have completed a rigorous mathematics curriculum and can sustain multi-step reasoning without a calculator on symbolic problems. The Pancyprian Advanced Math case studies are 5 cases and about 2,242 words.
1Infusion Model: Constants, Plateau and Inverse
A pharmacology team models the plasma concentration of a drug during a controlled infusion by C(t)=At/(t+B), where t is hours from the start, C is in mg/L, and A and B are positive constants. Two measurements are treated as reliable: at t=2 h the concentration is 8 mg/L, and at t=6 h it is 12 mg/L.
454 words, about 2 min2Road-to-Bridge Transition: Matching Value and Slope
A civil engineer is joining a straight approach road to a curved bridge deck. For 0≤x≤1, measured in tens of metres from the junction, the approach profile is f(x)=x²+3x+2.
458 words, about 2 min3Arch Service Deck: Integrals and Design Constraints
A concrete arch is modelled by the region under y=9−x² and above the ground y=0, for −3≤x≤3, with x and y in metres. A horizontal service deck is to be placed at height y=k, where 0<k<9, across the arch.
473 words, about 2 min4Eight-Year Membership: Geometric Series and Binomial Bound
A sports club advertises two payment plans for an eight-year membership. Plan A charges €600 in the first year, and each later year's fee is 5% higher than the previous year's fee.
419 words, about 2 min5Parallel AC Circuit: Impedance, Current and Power Factor
An electrical technician is checking a parallel AC circuit before it is connected to a 20 V rms supply. The two branches have impedances Z₁=6+8i Ω and Z₂=12−5i Ω, where i²=−1 and the supply voltage is taken as 20+0i V rms.
438 words, about 2 min