FY13CE Pure Mathematics case studies
FY13CE Pure Mathematics · Put your knowledge to work in context.
FY13CE Pure Mathematics is a written, constructed-response examination in pure mathematics at the standard associated with the FY13CE designation. It is aimed at candidates who need a secure, proof-based command of single-variable calculus, algebra, trigonometry, vectors and complex numbers rather than routine procedural fluency alone. Because solutions are marked on method as well as answer, the paper rewards clear structure: state the result you are proving, justify each step, and finish with a definite conclusion. The syllabus spans twelve areas, from proof and logic through algebra, sequences, coordinate geometry, trigonometry, exponentials and logarithms, differentiation and integration with their applications, vectors in three dimensions, complex numbers, matrices and linear transformations, and numerical methods. The FY13CE Pure Mathematics case studies are 5 cases and about 1,941 words.
1Parity proof with a converse slip
In a revision session on proof, a candidate is asked to prove: for every integer n, if n^2 is even then n is even. The candidate writes: 'Assume n is even.
431 words, about 2 min2Drug dose recurrence and the limit shortcut
A patient is given 8.0 mg of a drug at the same time each day. Immediately after the nth dose, the amount in the bloodstream is A n mg.
371 words, about 2 min3Sine-rule survey with two possible triangles
During a land survey, triangle ABC represents three boundary posts. The measured sides are AB=8.4 m and AC=6.1 m, and the measured angle at B is angle ABC=32.0 degrees.
415 words, about 2 min4Open-box optimisation with an inadmissible root
A manufacturer cuts squares of side x cm from each corner of a rectangular sheet measuring 24 cm by 18 cm, then folds the flaps to make an open box. The volume is V(x)=x(24-2x)(18-2x).
388 words, about 2 min5Skew drone paths and the unchecked coordinate
Two drone flight paths are modelled by straight lines in a three-dimensional coordinate system measured in kilometres. Path L1 has equation r=(1,2,3)+lambda(2,-1,1); path L2 has equation r=(4,0,5)+mu(1,1,2).
336 words, about 2 min