Prerequisite knowledge for calculus

This post describes foundational reasoning abilities and mathematical knowledge students need to develop before beginning a course in calculus. 1. Covariational reasoning This type of reasoning involves recognition of two quantities that are changing together. A student who considers how two quantities in a dynamic situation change together is said to be engaging in covariational…

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Application of the Discriminant

The discriminant of a quadratic equation, ax2 + bx + c = 0 is D = b2 – 4ac. If D>0, the quadratic equation has two distinct roots; if D<0, then the equation has no real roots; and, if D=0, the we have two equal roots. Let’s apply it in the following problem. What is…

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