{"id":194,"date":"2024-07-01T14:17:44","date_gmt":"2024-07-01T14:17:44","guid":{"rendered":"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/?post_type=content&p=194"},"modified":"2024-08-07T10:40:23","modified_gmt":"2024-08-07T10:40:23","slug":"chapter-14-pre-calculus-and-calculus","status":"publish","type":"content","link":"https:\/\/routledgelearning.com\/teachingsecondarymathematics\/content\/resources\/chapter-14-pre-calculus-and-calculus\/","title":{"rendered":"Chapter 14 – Pre-Calculus and Calculus"},"content":{"rendered":"\n
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\n\tHome<\/a>\n<\/span>\/<\/span>\n\tResources<\/a>\n<\/span>\/<\/span>\n\tChapter 14 \u2013 Pre-Calculus and Calculus\n<\/span><\/div><\/div><\/div>\n\n\n\n
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Chapter 14 – Pre-Calculus and Calculus<\/h1>\n\n\n

Beginning with a conference at Tulane University in January 1986, there developed in the mathematics community a sense that calculus was not being taught in a way befitting a subject that was at once the culmination of the secondary mathematics curriculum and the gateway to collegiate science and mathematics.<\/p>\n\n\n\n

Pre-calculus can be considered an extension of Algebra II and trigonometry. It fills in the gaps and reviews students in preparation for calculus. It can be approached from a function and\/or graphic perspective. Due to the advances in technology, a combined approach is a more feasible option when you consider the dynamics of the tools available to teachers and students. When it comes to calculus, the sad truth is that calculus is not a realization of secondary school preparation and an exciting beginning to future mathematical study. Instead, calculus continues to serve as an exit from the study of mathematics and related subject areas for many students<\/p>\n<\/div>\n\n\n\n

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Exercises<\/h2>\n\n\n\n
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Exercise 14.1<\/h3>\n\n\n\n
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  1. It is said that you learn something best when you teach it. That is true{em}but does that give you license to use a class as guinea pigs? How much should you know about a topic before embarking on the study of it with a class?<\/li>\n\n\n\n
  2. You undoubtedly have had some logic as a part of your undergraduate program. Out of that information, what could be inserted into a precalculus course and why? If you have not had logic beyond basic truth tables, research the subject to determine what should be included in the precalculus class. As a part of your research, you should include a description of how much time it will take you to learn the material well enough to teach it.<\/li>\n\n\n\n
  3. Part 2 of this exercise mentions learning material prior to teaching it. Does this imply you will be lecturing? Is lecturing more acceptable in an advanced course, because these are more capable students and there is so much information to cover? Why or why not?<\/li>\n<\/ol>\n<\/div>\n\n\n\n
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    Exercise 14.2<\/h3>\n\n\n\n

    Using a graphing calculator or software, do the following:<\/p>\n\n\n\n

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    1. Graph one of each type of the functions:<\/li>\n<\/ol>\n\n\n\n

                  f<\/em>(x<\/em>) = Constant<\/p>\n\n\n\n

                  f<\/em>(x<\/em>) = Linear<\/p>\n\n\n\n

                  f<\/em>(x<\/em>) = Quadratic<\/p>\n\n\n\n

                  f<\/em>(x<\/em>) = Polynomial<\/p>\n\n\n\n

                  f<\/em>(x<\/em>) = Rational<\/p>\n\n\n\n

                  f<\/em>(x<\/em>) = Exponential<\/p>\n\n\n\n

                  f<\/em>(x<\/em>) = Logarithmic<\/p>\n\n\n\n

      Select any three of these functions and describe their similarities and differences. List the main points you would bring out to students if you were comparing and contrasting the selected three in a precalculus class.<\/p>\n\n\n\n