Writing a Precalculus Assessment

• Include questions in multiple representations (graphical, analytical, tabular, verbal)

• Write questions that reflect learning targets and require conceptual understanding

• Include multiple choice and short answer or free response questions

• Determine scoring rubric before administering the assessment (see below)

• Offer opportunities to practice with and without calculators throughout the year

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Questions to Include

• Evaluating limits from graphs

• Evaluating limits from tables

• Evaluating limits from equations (rational functions, memorized graphs, difference quotients)

• Justifying continuity at a point

• Classifying types of discontinuity from an equation and graph

• Justifying a conclusion with the Intermediate Value Theorem

• Writing equations of functions that have particular horizontal and vertical asymptotes and holes (expressed as limit statements)

• Evaluating limits at infinity

• Interpreting limit statements

• Finding values that would remove a discontinuity

• Selecting a graph that satisfies given limit statements

• Error analysis in a continuity justification

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Grading Tips

Look for more than just correct answers. Give students feedback on their justifications, communication, and mathematical thinking. We recommend that you prepare a rubric for the free response and short answer items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn  points.

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Reflections

Students that felt comfortable with the ideas in this unit finished this assessment fairly quickly. We tried to balance more straightforward limit questions with those that required solving for a parameter or thinking about what is and is not guaranteed in a particular situation. As expected, students did better on the former and worse on the latter. Of all the ideas in this unit, students tended to struggle with limits at infinity (Lesson 8.5) the most. The idea of comparing growth rates will show up many more times in AP Calculus!