MATSEC AM Pure Mathematics case studies
MATSEC AM Pure Mathematics · Put your knowledge to work in context.
MATSEC Advanced Level Pure Mathematics is a matriculation-level mathematics qualification offered within Malta's MATSEC system, typically taken by students in their final two years of secondary schooling who intend to progress to university courses in mathematics, engineering, the sciences, economics or computing. It is a written examination built around structured, multi-part questions in which the reasoning and working matter as much as the final answer, so candidates are assessed on whether they can construct a mathematical argument rather than recognise a correct option. The MATSEC AM Pure Mathematics case studies are 5 cases and about 2,170 words.
1The Fence That Doubled Back
A farmer has 60 m of fencing and wants to enclose a rectangular pen against an existing straight wall, using the wall as one side so only three sides need fencing. She sketches a pen of width x metres perpendicular to the wall and length y metres parallel to it, and writes 2x + y = 60.
424 words, about 2 min2When Newton Slips Past the Root
A student is finding the root of f(x) = x³ − 2x + 2, which has a single real root near x = −1.8. She starts Newton–Raphson from x₀ = 0 and is puzzled: the iterates jump to 1, then to 0, then back to 1, and never settle.
454 words, about 2 min3Two Ships and a Bearing
Ship A leaves port O at noon travelling due east at 12 km/h. Ship B leaves the same port at 13:00 travelling on a bearing of 060° at 16 km/h.
474 words, about 2 min4The Integral That Will Not Close
A student must evaluate the definite integral of 1/(x² − 1) from 0.5 to 2. He tries a direct antiderivative and gets a nonsensical negative area.
425 words, about 2 min5The Modulus Argument That Split in Two
A student must solve z² = −5 + 12i for complex z and mark both solutions on an Argand diagram. He converts −5 + 12i to modulus–argument form, finds the modulus is 13, and computes the argument as arctan(12/(−5)) ≈ −67.4°, which he writes as a negative angle.
393 words, about 2 min