Unit 8 Test (Lessons 8.18.5)
Unit 8  Day 16
Unit 8
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
Day 15
Day 16
All Units
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
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
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.
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!