STPM Mathematics 954 case studies
STPM Mathematics 954 · Put your knowledge to work in context.
STPM Mathematics 954 is the mathematics paper in Sijil Tinggi Persekolahan Malaysia, the pre-university qualification taken after SPM and widely used for university admission in Malaysia and abroad. It suits candidates who need a rigorous, proof-aware mathematics background for science, engineering, computing, economics or actuarial pathways. The syllabus balances pure mathematics, with algebra and functions, calculus, and vectors and geometry, against statistics, probability and distributions, and hypothesis testing and inference. Expect to write mathematics rather than pick answers: structured questions reward clear method, correct notation and justified conclusions, and later parts often build on earlier results. The STPM Mathematics 954 case studies are 5 cases and about 2,415 words.
1Pollutant concentration and the valid inverse model
A water-treatment tank is monitored for 12 hours after a filter is switched on. The pollutant concentration, C mg/L, is modelled by C(t) = (3t + 20)/(t + 4), where t is the time in hours, 0 ≤ t ≤ 12.
525 words, about 3 min2Minimising the cost of a cylindrical vat under a height limit
A dairy cooperative needs a closed cylindrical vat with capacity 8.00 m³. The curved side is made from stainless sheet costing 45 per m², while each flat circular end costs 70 per m² because of extra stiffening.
401 words, about 2 min3Drone path, restricted plane, and tower clearance
An inspection drone follows the straight-line path r(λ)=(1+2λ)i+(2−λ)j+(1+3λ)k, λ≥0, distances in km. A sensitive installation is protected by the plane 2x+y−z=4; the restricted side is 2x+y−z 4.
530 words, about 3 min4Underfill inspection and a normal approximation
A pharmaceutical filling line produces vials of sterile solution. Historically 2.0% of vials are underfilled.
416 words, about 2 min5Wait-time claim, p-value interpretation, and sample size
A coffee chain advertises that the mean wait at a city branch is no more than 4.5 minutes. A consumer group records waiting times for a random sample of 36 customers at a busy period.
543 words, about 3 min