Estimating is a common skill in all math classes. Linear approximations are the primary type of estimation calculus students learn. Students will gain a solid understanding of this skill which is the basis for future advanced calculus concepts such as Newton’s Method.

Concepts included in this lesson are:

· Review of tangent lines.

· Linear approximations.

· Determining if the approximation is an overestimation or an underestimation.

· Optional linear approximation for trigonometric functions.

The no prep lesson and worksheet are easy for students to follow and complete. You can print this lesson and use it as an in-class activity or download the digital learning choice for distance learning students. Even if you have a hybrid class, both types of students can access this lesson. This can also be used for students who were absent when the instructor taught this lesson. Since many of the questions are like previous AP exam questions, this makes a great review.

AP Standards:

CHA-3.F.1 The tangent line is the graph of a locally linear approximation of the function near the point of tangency.

CHA-3.F.2 For a tangent line approximation, the function’s behavior near the point of tangency may determine whether a tangent line value is an underestimate or an overestimate of the corresponding function value.

This lesson includes an optional part on linear approximations for trigonometric functions with guided practice and worksheet question.

An alternative way to use this lesson is as a review for the AP Exam. Students complete the worksheet, but if they have difficulty, they may refer to the lesson at that point.

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