Helping math teachers bring calculus to life
AP Exam Review
Week 1 - Friday (Day 5)
Focus Areas
-
Interpretations of tabular data
-
Limit techniques
Review Activity 1: FRQ Friday
Materials: 2010 AB2
Teaching Tips
To finish their first week of review, students will complete 2010 AB2 in class. After a brief review of our FRQ procedures (pencil, blue or black ink, calculator active, read carefully, write legibly), they begin independent work for 10 minutes. Today, the final 5 minutes may be spent working with a partner. This empowers frustrated students to continue working and we find that solutions are often more rigorous and complete. Furthermore, by grading the “composite” responses, focus is shifted from adding up points to identifying general trends in student responses (strengths, weaknesses, misconceptions, etc.) in order to better inform future instruction.
Review the scoring guidelines before you sit down to evaluate student work. It’s OK to be stingy when awarding points!! A much-respected expert, Lin McMullin, encourages rigorous grading: “You should be more stringent. Why show your students the minimum they can get away with? That does not help them! Do your students a favor: score the review problems more stringently than the readers. If their answer is not quite right, take off some credit and help them learn how to do better. It will help them in the long run.”
Calculus students are expected to apply concepts and interpret their results using multiple representations: graphical, numerical, analytical, and verbal. When function behavior is given in numerical (tabular) form, we can reasonably anticipate certain questions will be asked.
-
Using the average rate of change over an interval to estimate the value of a derivative is a common first question. Providing evidence of a difference quotient and including correct units on the solution are key!
-
Tabular data provides an excellent platform for approximating definite integrals with Riemann sums (left, right, and mid), often with unequal intervals. Again, students must be able to attach correct units and interpret their approximation in context.
-
Applications of the IVT, MVT, and the FTC (when finding an average value) are common --- along with a request to justify their use! Students must be prepared to discuss continuity and differentiability, as well as interpret solutions in context.
-
ENCOURAGE students to show all the expressions leading to their final answer and to label solutions carefully.
-
DISCOURAGE students from assuming function behavior or values not explicitly given in the problem or attempting to create regression equations.
Review Activity 2: Limit Technique Card Sort
Materials
Answer Key
Teaching Tips
In Unit 1, students spent time studying various strategies for evaluating limits. Throughout the course they added to their repertoire (such as recognizing the definition of the derivative in Unit 2 or L’hospital’s rule in Unit 4). What’s most important on the AP Exam is that students be able to look at any limit question and choose an appropriate evaluation method. To practice this skill we are re-visiting the Limit Technique Card Sort from Unit 1 Day 5. Students first categorize the limit questions by strategy, and then evaluate them using analytical methods. Some students may notice they now have new tools to evaluate these limits and might add L’hospital’s rule as one of the methods. For further tips on facilitating this activity and some insights into common student errors, check out our original post.