Idempotent

This activity teaches calculus AB or BC students to use integrals as the dot product operation on functions, treating functions as vectors and performing orthogonal projection on them. The result is a method for approximating functions with polynomials which is different from Taylor series. BC calculus students will also do a quick exploration of Fourier series. Pre-planning: 1 period for AB version ; 2 periods for BC version decide whether activity will be group based or individual minimum on

AP Calculus teachers need something to teach after the AP test in May. If your students are serious about learning and you are serious about teaching, why not get them started learning quantum mechanics? Seriously. This resource includes three activities, each with three parts which explore wavefunctions and the Schrodinger equation. Students will solve differential equations, find quantized energy levels, approximate solutions with power series, and generally be amazed at the power of calcu

Geometric mean is a topic in geometry that is only used to calculate a pointless length in right triangles. It is a throwaway topic, right? If your students are tired of having their time wasted memorizing calculations they will never use again, they will be demanding to know why they should learn about the geometric mean. Included are three mini-lessons -- one each for geometry honors, precalculus honors, BC calculus. You are saying, "But I only teach, geometry. Why would I bother paying f

Included are two versions of a semester 1 final exam for a standard AB Calculus curriculum. The first version consists of the simple versions of standard questions; the second version consists of challenging versions of standard questions. They can be used as tests or practice tests. The tests can be finished without a calculator. The questions assume the student is familiar with the derivatives of all elementary functions. A brief introduction to anti-derivatives is optional and those ques

Self-executing lessons are ideal for sub-plans, as supplemental material for "flipped" classrooms, or for any teacher wanting to leverage their limited instructional time. The learning of basic notation and rules is accomplished via pattern recognition. This self-executing lesson will get precalculus students started learning calculus over the summer so that next year begins smoothly. It would be particularly useful for calculus teachers needing to accelerate the pacing of their curriculum. DA

Series convergence is a difficult topic because there are so many possible tests and multiple intermediate steps for each test and sometimes multiple tests that all have to be executed in the correct order. Biologists use a tool called a dichotomous key to classify organisms that look similar. This is a dichotomous key for classifying a series as absolutely convergent, conditionally convergent, or divergent. On each page is a question and, depending on the answer, instructions to go to another

This is a short guide for calculus students (and teachers) for the topic of series convergence tests. It explains in simple language how the three possible classifications of a series -- absolutely convergent, conditionally convergent, divergent -- are related to the three main tests -- Integral Test, Alternating Series Test, Series Divergence Test. All other tests are shortcuts based on these three to be used with specific types of series. Instructors and curious students will be pleased to g

Honestly, I'm just tired of hearing the wrong definition for continuity from teachers and textbooks alike. It is time for us as a species to move on from pretending that continuity is about "drawing a graph without picking up your pencil." Technically, that property is 'path connectedness.'

Some schools allow students to take AB Calculus one year and BC Calculus the next year. Such schools are rare and so this review is in low demand. There's no point in my putting a price tag on it. It is designed to review the most important topics from Precalc that are actually used in calculus and then immediately follow them with an application learned in AB Calc. All questions are intended to be very simple; this a warm-up for their brains to begin the school year ready to learn.

College Board has changed the format of the AP Calculus test this year. We are all scrambling to prepare our students for it. Here are two mock tests that I slapped together for my AB students. I was pressed for time so the formatting is sloppy and there may be typos. Please point out any errors which need to be fixed. I aimed to include all "mandatory" topics. Topics included: limits/continuity derivative rules (power, chain, product) implicit diff related rates optimization/graphing equati

Most calculus teachers prepare their students for the AP Calculus test incorrectly. The key skill for success on the AP Calculus test is annotation. The skill of annotation is often taught in ways that are counter-productive. The most common way to misteach annotation is to have students highlight the numbers and functions so as not to be distracted by the scary words in a word problem. The second most common way that annotation is mistaught is to have students translate "into their own words"

Most AP Calculus preparation incorrectly focuses on reviewing calculus which is not enough for students to succeed on the AP Calculus AB/BC test. This resource provides test-specific knowledge that is not taught in an AP calculus course. The AP test consists of 30-40% questions on simple derivative and integral calculations. The rest of the test is standard questions asked in standard ways with standard solutions. A common mistake is to think that the AP test requires creativity: it does not. Su