Posted in Calculus

Variables, Constants and Parameters

Whether a mathematical notation is a variable,  parameter, or constant depends on what you mean by it.

  • If you intend to represent the value of a quantity whose measure varies within a situation, then you are using that notation as a variable.
  • If you intend to represent the value of a quantity whose measure is the same within all situations (e.g., pi), then you are using that notation as a constant.
  • If you intend to represent the value of a quantity that is constant in a particular situation, but which can vary from one situation to another, then you are using that notation as a parameter.

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Posted in Algebra, Calculus

Teaching the derivative function

Most Grade 10 syllabus do not yet include the concept and calculation of derivative. At this level, the study of function which started in Year 7 and Year 8 on linear function is simply extended to investigating other function classes such as polynomial function to which linear and quadratics belong, the exponential function and its inverse, rational function etc. There is no mention of derivative. This should not prevent teachers from deriving functions based on the properties of the function students already know. Continue reading “Teaching the derivative function”

Posted in Calculus

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

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Posted in Algebra, Calculus

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. Continue reading “Application of the Discriminant”