Students will have to solve the real world problem of locker smell …
Students will have to solve the real world problem of locker smell leakage by building an air filter that will cover the vents on the top of a locker. This project goes well with a curriculum on the particle nature of gases and phase changes.
This is a simple task touching on two key points of functions. …
This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.
This task looks at zeroes and factorization of a general polynomial. It …
This task looks at zeroes and factorization of a general polynomial. It is related to a very deep theorem in mathematics, the Fundamental Theorem of Algebra, which says that a polynomial of degree d always has exactly d roots, provided complex numbers are allowed as roots and provided roots are counted with the proper "multiplicity.''
The intention of this task is to provide extra depth to the …
The intention of this task is to provide extra depth to the standard A-APR.2 it is principally designed for instructional purposes only. The students may use graphing technology: the focus, however, should be on what happens to the function g when x=0 and the calculator may or may not be of help here (depending on how sophisticated it is!).
For a polynomial function p, a real number r is a root …
For a polynomial function p, a real number r is a root of p if and only if p(x) is evenly divisible by x_r. This fact leads to one of the important properties of polynomial functions: a polynomial of degree d can have at most d roots. This is the first of a sequence of problems aiming at showing this fact.
This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The …
This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The argument here generalizes, as shown in ``Zeroes and factorization of a general polynomial'' to show that a polynomial of degree d can have at most d roots. This task is intended for instructional purposes to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions.
Test the pH of things like coffee, spit, and soap to determine …
Test the pH of things like coffee, spit, and soap to determine whether each is acidic, basic, or neutral. Visualize the relative number of hydroxide ions and hydronium ions in solution. Switch between logarithmic and linear scales. Investigate whether changing the volume or diluting with water affects the pH. Or you can design your own liquid!
Test the pH of things like coffee, spit, and soap to determine …
Test the pH of things like coffee, spit, and soap to determine whether each is acidic, basic, or neutral. Visualize the relative number of hydroxide ions and hydronium ions in solution. Switch between logarithmic and linear scales. Investigate whether changing the volume or diluting with water affects the pH. Or you can design your own liquid!
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