MATSEC IM Pure Mathematics case studies
MATSEC IM Pure Mathematics · Put your knowledge to work in context.
MATSEC Intermediate Matriculation (IM) Pure Mathematics is a Maltese sixth-form qualification examined by the MATSEC Examinations Board at the University of Malta. It is an Intermediate-level subject, meaning it is lighter and narrower than Advanced level, and candidates usually take it alongside two or three A-levels to complete a matriculation profile for entry to the University of Malta, MCAST and other institutions. It also suits mature and private candidates who need documented evidence of quantitative ability for science, engineering, computing or economics pathways. The syllabus builds technique rather than long proofs: manipulation of algebraic expressions and polynomials, function behaviour and graph sketching, exponentials and logarithms, sequences and series, trigonometric identities and equations, coordinate geometry, vectors, complex numbers, and differentiation and integration with applications. The MATSEC IM Pure Mathematics case studies are 5 cases and about 2,401 words.
1Cubic with a Factor and a Remainder: Recovering Coefficients
During a revision session, a candidate is given the cubic p(x)=x³+ax²+bx+6, where a and b are real constants. The examiner states that (x−2) is a factor of p(x), and that when p(x) is divided by (x−1) the remainder is 4.
423 words, about 2 min2Comparing Quarterly and Continuous Compounding
A student has €2,500 from a summer job and is comparing two savings products before starting university. Account A pays a nominal annual rate of 4.8% compounded quarterly.
445 words, about 2 min3The Ambiguous Sine Rule in a Triangular Plot
A surveyor is measuring a triangular plot ABC for a client. She records AB = 7.0 m, BC = 5.0 m and angle BAC = 35°.
607 words, about 3 min4Open-Top Box: Domain Restrictions and Integer Cuts
A packaging technician is designing an open-top box from a single rectangular sheet of card measuring 40 cm by 30 cm. Identical squares of side x cm are cut from each corner, and the remaining card is folded up to form the sides.
445 words, about 2 min5Velocity Sign Changes: Displacement Versus Distance
A particle moves along a straight line. Its velocity, in metres per second, is modelled by v(t)=3t²−12t+9 for 0≤t≤4, where t is in seconds.
481 words, about 2 min