AP Precalculus case studies
AP Precalculus · Put your knowledge to work in context.
AP Precalculus is a College Board Advanced Placement course and exam intended for students who want college-level credit or placement in precalculus-level mathematics before moving on to calculus. The exam measures understanding of the mathematical content in units 1–3 and the ability to apply skills such as algebraically manipulating functions, equations, and expressions; translating mathematical information between representations; and communicating with precise language and rationales. Questions draw on general functions, polynomial and rational functions, exponential and logarithmic functions, and trigonometric and polar functions, presented graphically, numerically, analytically, and verbally, with real-world modeling contexts. The exam is hybrid digital: multiple-choice questions and free-response questions appear in the Bluebook app, while free-response answers are handwritten in paper booklets. The AP Precalculus case studies are 4 cases and about 1,619 words.
1The Vending Machine's Glitchy Pricing
A campus vending machine charges 1.75 per snack. During a software glitch, the machine rounds the total cost to the nearest dollar (rounding halves up) before charging.
457 words, about 2 min2Fencing a Garden Against a Wall
A homeowner has 40 meters of fencing to enclose a rectangular garden along the back wall of a house; the wall forms one full side, so fencing is needed for only three sides. She wants the garden's area to be at least 150 square meters.
501 words, about 3 min3Cooling Coffee and a Doubling Culture
A lab technician monitors two processes. Process A: a cup of coffee at 90°C cools in a 20°C room; after 10 minutes it is 65°C.
305 words, about 2 min4Ferris Wheel and a Polar Sensor
A Ferris wheel has radius 12 m and center 14 m above the ground. A rider boards at the lowest point and the wheel turns counterclockwise at a constant rate, completing one revolution every 40 seconds.
356 words, about 2 min