WHY Calculus with Precalculus?

Problems Precalculus followed by Calculus I		Solutions Calculus with Precalculus I
Only a small percentage of precalculus students successfully complete calculus I. Nationally, only about 30 to 40% of students who start Precalculus complete Calculus I.		More students succeed in completing calculus with precalculus. At several colleges and universities, public and private, 57 to 91% of students who began calculus with precalculus completed both terms the same year.
Students don't see the relevance of many precalculus ideas. In precalculus, simplifying f(x + h) – f(x) is only an exercise in manipulating symbols.		Precalculus techniques are motivated by their immediate uses in calculus. Students calculate slopes of secant and tangent lines as they review how to manipulate the symbols f(x + h) – f(x).
Students are unable to use their precalculus skills in a calculus setting.  In precalculus, students can solve linear equations, yet they have difficulty solving for dy/dx in implicit differentiation problems.		Precalculus skills are reviewed as needed in calculus.   Students review algebraic techniques to solve equations when finding extrema of functions.
Precalculus is often a “rerun” for students. Students are discouraged by repeating a course they had in high school.		Students learn new material from the start in calculus with precalculus.   Calculus ideas are introduced as precalculus topics are reviewed.