IB Math AI SL case studies
IB Math AI SL · Put your knowledge to work in context.
IB Mathematics: Applications and Interpretation SL (MAAI SL) is a Standard Level course in the IB Diploma Programme. It is designed for students who enjoy mathematics in real-world contexts and who plan to study subjects such as economics, psychology, business, or social sciences at university. The IB Math AI SL case studies are 5 cases and about 2,931 words.
1Reducing-balance depreciation and a sinking fund for a cargo e-bike
A courier co-operative in Porto buys a cargo e-bike for €4,200 and depreciates it at a reducing-balance rate of 18% per year, applied at the end of each year. In the same month it opens a maintenance fund, depositing €150 at the end of every month into an account paying a nominal annual rate of 2.4% compounded monthly; each deposit is made after that month's interest is credited.
571 words, about 3 min2Ticket pricing for a 240-seat cinema: revenue versus profit
A 240-seat independent cinema in Sheffield charges £9.00 per ticket and currently sells about 1,080 tickets a week. The owner's customer survey suggests that for every £0.50 rise in price, weekly attendance falls by 40, and that this linear relationship is reasonable up to a price of £15.00.
654 words, about 3 min3Skate ramp compliance and plywood order
A youth centre is building a skate ramp against the end wall of its hall. The design is a right-angled wedge: the platform is 1.35 m above the floor, the horizontal run from the floor to the foot of the platform is 4.5 m, and the ramp is 2.4 m wide.
567 words, about 3 min4Café wait-time model against a complaint log
A café owner has 300 timed orders from last month and models the wait between ordering and receiving a drink as normally distributed with mean 4.2 minutes and standard deviation 1.1 minutes. The owner wants to advertise that '90% of drinks are served within five minutes' and is also considering a five-minute guarantee that refunds the price of any drink that takes longer.
584 words, about 3 min5Can design with a filling-line height constraint
A drinks company is designing a closed cylindrical can to hold 330 ml, which it will fill on an existing line. Metal for the circular top and base costs 0.060 cents per cm², while metal for the curved side costs 0.035 cents per cm² because it is a different alloy.
555 words, about 3 min