HKDSE Maths M2 case studies
HKDSE Maths M2 · Put your knowledge to work in context.
The Hong Kong Diploma of Secondary Education (HKDSE) is the public examination taken by senior secondary school candidates in Hong Kong. Mathematics is one of the four Category A core subjects, alongside Chinese Language, English Language and Citizenship and Social Development. Mathematics has a Compulsory Part plus two Extended Parts; Extended Part Module 2 (Algebra and Calculus) is the strand this page supports, aimed at candidates who need stronger algebraic manipulation and calculus for university study in mathematics, engineering, the physical sciences or economics. The HKEAA publishes the assessment framework for each Senior Secondary subject, so candidates should confirm the Module 2 syllabus, paper structure and any school-based assessment arrangements there rather than relying on memory. The HKDSE Maths M2 case studies are 5 cases and about 1,850 words.
1Brine-loop balancing with a singular valve setting
A small desalination pilot plant circulates brine through three tanks. Let x, y and z be the adjustment flows in L/min added to tanks A, B and C.
573 words, about 3 min2Capsule tank material cost
A food-grade mixing capsule is made from a right circular cylinder of radius r cm and height h cm with two hemispherical end caps. Its total volume must be exactly 500 cm³.
341 words, about 2 min3Draining conical filter
An inverted conical filter has height 30 cm and top radius 10 cm. Water drains through a valve at a constant 4 cm³/s.
325 words, about 2 min4Binomial calibration of a sensor
A calibration correction for a pressure sensor is modelled by (1 + kx)^n for small normalized error x, with k and n positive constants and n an integer. Bench tests give the coefficient of x as 10 and the coefficient of x² as 40.
302 words, about 2 min5Rotated diffuser profile
A lighting diffuser has a cross-section bounded by y = x e^(-x/2), the x-axis, x = 0 and x = 4, with x and y in centimetres. The profile is rotated about the x-axis to form a solid diffuser.
309 words, about 2 min