CLEP Calculus case studies
CLEP Calculus · Put your knowledge to work in context.
The CLEP Calculus exam is a College Board credit-by-examination test that assesses an intuitive understanding of calculus at the level of a one-semester college course. It is aimed at students who already know algebra, geometry, trigonometry, and analytic geometry and who want to demonstrate that knowledge rather than sit through the course. The CLEP Calculus case studies are 5 cases and about 2,060 words.
1The Piecewise Repair Bill
A small fabrication shop models the cost of a rush job with a piecewise function. For a job requiring x hours of machine time (0 ≤ x ≤ 10), the quoted price in dollars is f(x) = (x² − 4x + 7) for 0 ≤ x < 3, f(x) = (A·x + B) for 3 ≤ x ≤ 10.
519 words, about 3 min2The Shadow Revenue Limit
A campus coffee cart models daily revenue from a new drink as R(t) = 120·(1 − e^(−0.4t))/t dollars, where t is the number of weeks since launch (t 0). At launch week t = 0 the formula is undefined, producing a 0/0 form, but the owner needs a sensible "launch-day revenue rate" to justify the investment.
355 words, about 2 min3Optimizing the Fenced Pen
A biology student has 60 meters of fencing to enclose a rectangular pen against a long, straight barn wall. The barn side needs no fence, so fencing covers only three sides: two widths (perpendicular to the barn) and one length (parallel to the barn).
425 words, about 2 min4The Leaking Tank Accumulation
A water tank drains through a valve. The flow rate at time t (minutes) is measured to be r(t) = 6 − 0.5t liters per minute for 0 ≤ t ≤ 12, after which the valve is closed and flow is zero.
374 words, about 2 min5The Average Value Audit
A quality engineer samples the temperature (in °C) of a cooling component over an 8-minute window and models it as T(t) = 20 + 16e^(−0.5t) for 0 ≤ t ≤ 8. She must report two numbers to her manager: (1) the average temperature over the window, defined as the mean value of T over [0, 8], and (2) the temperature at the midpoint in time , T(4).
387 words, about 2 min