Abitur Mathematics case studies
Abitur Mathematics · Put your knowledge to work in context.
The Abitur is the German university entrance qualification, awarded after passing the final examinations of the gymnasiale Oberstufe. Mathematics is one of the two mandatory advanced-level subjects (Leistungsfächer) in most states, so the written Abitur examination in mathematics carries particular weight. The Abitur Mathematics case studies are 5 cases and about 2,540 words.
1Antibiotic concentration after a single dose
A veterinary clinic treats a sheep with a single intravenous dose of an antibiotic. A simplified two-compartment model predicts plasma concentration C(t)=a t e^(-kt) mg/L, where t is hours after injection and a,k 0.
439 words, about 2 min2Beginner ski slope and drainage pipe
A snow park is shaping a beginner slope whose centreline height above the base station is modelled by h(x)=x^3/8 - 3x^2/4 +4 for 0≤x≤6, where x is horizontal distance in metres and h is height in metres. The designers require the slope to descend from the start, pass through a local minimum, and then rise gently to the exit so that skiers can reach the lift without pushing.
504 words, about 3 min3Robot rail and laser safety curtain
A warehouse robot travels along a straight overhead rail modelled by r(s)=(4,1,2)+s(1,2,0), where distances are in metres and s is a real parameter. A laser safety curtain lies in the plane E: 2x - y + 2z = 6.
442 words, about 2 min4Late-delivery rate and hypothesis test
An online retailer promises next-day delivery on at least 95% of orders. In a random sample of 200 orders, 16 arrived late.
602 words, about 3 min5Bakery production plan with a labour offer
A cooperative bakery makes country loaves (x per day) and rye loaves (y per day). Each country loaf uses 0.5 oven-hour and 0.25 labour-hour; each rye loaf uses 0.75 oven-hour and 0.25 labour-hour.
553 words, about 3 min