CAPE Pure Maths Unit 1 case studies
CAPE Pure Maths Unit 1 · Put your knowledge to work in context.
CAPE Pure Mathematics Unit 1 is the first of two units in the Caribbean Advanced Proficiency Examination suite, administered by the Caribbean Examinations Council (CXC). It is taken mainly by sixth-form and post-secondary students in the Caribbean who need a rigorous pre-university mathematics qualification for university entrance, for further study in engineering, physical sciences, economics or mathematics itself, or for professional routes that demand strong quantitative skills. The CAPE Pure Maths Unit 1 case studies are 5 cases and about 4,048 words.
1Strain Correction Series for a Composite Rod
A materials laboratory calibrates a strain gauge bonded to a carbon-fibre test rod. The gauge responds nonlinearly, and the manufacturer's correction factor is C(x) = (1 + 3x)^(1/2), where x is the strain recorded by the logger, a small dimensionless number normally kept below 0.1.
758 words, about 4 min2Calibrating a Voltage Sensor with a Modulus Response
A pressure-rig technician is validating a sensor whose output voltage v, in volts, rises with test time t, in minutes, according to v(t) = 3t/(t + 1) for t ≥ 0. The display does not show voltage directly; it shows a processed bar reading R(v) = v − 2 + 1, a modulus function chosen so that the display never shows less than 1 bar.
874 words, about 4 min3Setting Out a Circular Pond and Its Tangent Path
A landscape architect is setting out a circular pond on a surveyed grid measured in metres. Three fixed items must sit exactly on the rim: a fountain base at A(0, 5), a bench at B(3, 6) and a lamp post at C(7, 4).
786 words, about 4 min4Maximising an Open Tray Under a Tooling Limit
A packaging firm stamps open trays from rectangular card blanks measuring 24 cm by 18 cm. A square of side x centimetres is cut from each corner and the remaining cross is folded up to form an open box; the volume is to be maximised.
818 words, about 4 min5Area, Volume and a Polygonal Approximation for a Stamped Plate
A metal badge is stamped from sheet 0.8 mm thick. On the design drawing the face of the badge is the plane region enclosed between the parabola y = x² and the line y = 2x + 3, with x and y in centimetres, and the region is later rotated about the x-axis to model the polymer coating applied to the domed face.
812 words, about 4 min