HKDSE Maths M1 case studies
HKDSE Maths M1 · Put your knowledge to work in context.
This independent study page provides practice for HKDSE Maths M1. Its editorial learning areas include Calculus; Probability Statistics; Algebra Functions; Sequences Series. The questions develop subject knowledge and application through worked reasoning, distinctions between competing answers, and practical scenarios. Study the relevant guide before attempting a mixed set, then explain the evidence or calculation that supports each answer. Topics on this exam: Calculus, Probability Statistics, Algebra Functions, and Sequences Series. The HKDSE Maths M1 case studies are 4 cases and about 1,985 words.
1Screening Test: PPV, Repeat Testing, and a Limited Confirmation Budget
A regional clinic screens 10,000 adults, of whom 2,000 are in a high-risk subgroup with family history. The general-population prevalence is 0.80%; in the high-risk subgroup it is 6.0%. The screening test has sensitivity 92% and specificity 96%. The clinic can run a second, independent confirmatory test that costs 60 currency units per patient; treatment started on a false positive causes 250 units of avoidable harm, while a true case missed because treatment is delayed costs 400 units.
661 words, about 3 min2Auditing a Raffle's Expected Payout and Fairness Claim
A student council runs a raffle to fund a trip. Each ticket costs 5. There are 400 tickets sold. The prizes are: one grand prize of 300, two second prizes of 100 each, and ten third prizes of 20 each.
448 words, about 2 min3Interpreting a Confidence Interval from a Small Sample
Assume independent packet masses from an approximately normal population. A student measures the mass of 9 randomly selected packets of seeds from a production line and obtains a mean of 50.2 g with a sample standard deviation of 1.5 g. The student constructs a 95% confidence interval for the population mean using the normal critical value 1.96 and reports 50.2 ± 0.98, i.e., (49.22, 51.18). A classmate says the interval is wrong because the sample is small and the population standard deviation is unknown.
466 words, about 2 min4Coste por tramos en una pastelería: continuidad, mínimo y pedido adicional
La pastelería Ca'n Joan, en Inca, modela el coste diario C(x), en euros, de producir x kg de ensaimadas. Para 0 ≤ x ≤ 200, C(x) = 0,01x² + 4x + 300. La dirección ha observado que, a partir de 200 kg, el coste marginal se dispara por el segundo turno, y quiere sustituir ese tramo por una recta C(x) = ax + b para x 200. Para que la función sea creíble, C debe ser continua y derivable en x = 200; además, se busca el nivel de producción que minimiza el coste medio por kg, C(x)/x, y compararlo con producir 200 kg.
410 words, about 2 min