GCE A/L Combined Mathematics case studies
GCE A/L Combined Mathematics · Put your knowledge to work in context.
The GCE Advanced Level Combined Mathematics examination is a Sri Lankan school-leaving and university-selection paper that combines pure mathematics with mechanics and statistics in a single subject. It is taken by students who intend to read engineering, physical science, mathematics, statistics, or computing at university, and by candidates who need a strong quantitative subject for their A/L aggregate. The GCE A/L Combined Mathematics case studies are 5 cases and about 2,559 words.
1Phase-Shifting Network with a Real Dial
An electronics laboratory is tuning a phase-shifting network whose normalized impedance is z = (k + 3i)/(1 − ki), where k is a real-number setting on a dial and i² = −1. A technician claims that z must be constant because the k-dependent terms in the numerator and denominator cancel.
615 words, about 3 min2Robot Arm Alignment with a Squared Equation
A robotic arm is being calibrated on a vertical board. Its end effector is programmed to move on the unit circle, so its position after a rotation through angle θ is P(cos θ, sin θ), with 0 ≤ θ < 2π.
465 words, about 2 min3Open-Top Can with Two Material Costs
A metal fabricator has an order for 500 open-top cylindrical cans, each with volume 500 cm³. The side wall is cut from one sheet and costs c per cm².
450 words, about 2 min4Ladder Equilibrium with a Climbing Painter
A uniform ladder of length 5 m and mass 20 kg rests against a smooth vertical wall and on rough horizontal ground, with its foot 3 m from the wall. A painter of mass 60 kg climbs the ladder.
552 words, about 3 min5Defective Items from Two Production Lines
A factory runs two production lines, A and B. Line A makes 60% of the daily output and has a defect rate of 2%.
477 words, about 2 min