CLEP College Algebra case studies
CLEP College Algebra · Put your knowledge to work in context.
The CLEP College Algebra exam is a standardized multiple-choice test that lets you earn college credit for material usually taught in a one-semester college algebra course. It is intended for anyone who already knows the algebraic vocabulary, symbols, and notation currently taught and wants to demonstrate that knowledge without sitting through the course. The CLEP College Algebra case studies are 5 cases and about 2,501 words.
1Canceling a Common Factor in a Rational Expression
During a peer-tutoring session, two students simplify the rational expression (x^2 − 9)/(x^2 + x − 12), which appears in a cost-per-unit model where x is the number of hundreds of units produced and x ≥ 0. Maya writes (x − 3)/(x + 4) and states that the domain is all real numbers except x = −4.
470 words, about 2 min2Solving a Rational Inequality Without Cross-Multiplying
During a fundraiser planning meeting, a student solves the inequality (x − 1)/(x + 3) ≤ 2, where x represents hundreds of tickets sold and x ≥ 0 in the actual context. The student cross-multiplies and writes x − 1 ≤ 2(x + 3), then x ≥ −7, so the solution is [−7, ∞).
424 words, about 2 min3Choosing the Correct Branch for an Inverse
An engineer is calibrating a sensor whose response is modeled by f(x) = x^2 − 4x + 7, but the sensor is only designed to accept inputs x ≥ 2. Two technicians propose inverse functions for converting a reading back to an input.
530 words, about 3 min4Dividing Complex Impedances and Checking a Radical Claim
An electronics lab is reducing two complex impedances. The equivalent impedance is Z = (3 + 4i)/(1 − 2i) ohms, where i^2 = −1.
462 words, about 2 min5Deciding When a Linear System Has No Unique Solution
During an algebra review, a student analyzes the linear system 2x + ky = 7 and 4x + 6y = 15. The student substitutes k = 3, notices that the x- and y-coefficients are proportional, and concludes that the system has infinitely many solutions because 'one equation is a multiple of the other.' The tutor points out that the right-hand sides are 7 and 15, not 7 and 14.
615 words, about 3 min