2016-2017+Classwork

= AP Calculus Classwork =

This page contains the notes and classwork for each day of class. __ **Thursday** ____ **, June 8** ____ **, 2017** __ Today, students finished the presentations of their final projects. The final group presented on the topic of Conic Sections. Students them completed a survey to reflect on the year.

__ **Wednesday** ____ **, June 7** ____ **, 2017** __ Today, students continued the presentations of their final projects. The next two groups presented on the topics of Polar Coordinates and Parametric Equations. The presentations will conclude tomorrow.

__ **Tuesday** ____ **, June 6** ____ **, 2017** __ Today, students continued the presentations of their final projects. The next two groups presented on the topics of parametric equations and conic sections. The presentations will continue tomorrow.

__ **Monday** ____ **, June 5** ____ **, 2017** __ Today, students continued the presentations of their final projects. The next group presented on the topic conic sections. The presentations will continue tomorrow.

__ **Friday** ____ **, June 2** ____ **, 2017** __ Today, students continued the presentations of their final projects. The next two groups presented on the topics of Polar Coordinates and Matrices. The presentations will continue on Monday.

__**Thursday, June 1, 2017**__ Today, students began the presentations of their final projects. The first two groups presented on the topics of Parametric Equations and Matrices. The presentations will continue tomorrow and throughout next week.

Today, students continued to work on their lesson project. The main component of the project - the lesson itself - will be due tomorrow at the beginning of class. Students will then begin to present their lessons to the class.
 * __ Wednesday, May 31, 2017 __ **

Today, students continued to work on the lesson component of the project. They will have the next two days to complete the lesson. Students will turn in their complete lesson and presentations will begin on Thursday.
 * __ Tuesday, May 30, 2017 __ **

Today, students completed and turned in the second component of their final project - the lesson outline. Then, they began to work on the main part of the project - the lesson itself. Students will continue to work on this lesson for the next few days, and turn it in at the beginning of class next Thursday.
 * __ Thursday, May 25, 2017 __ **

Today, students continued to work on their final project. They worked on the outline of their presentation (due tomorrow) and began to work on the actual presentation. They will continue working on the presentation until next Wednesday.
 * __ Wednesday, May 24, 2017 __ **

Today, students turned in the first part of their final project - the 4-5 example problems. They then continued to work on putting together the lesson to teach their topic. The next component of the project - the outline of the lesson - is due on Thursday.
 * __ Tuesday, May 23, 2017 __ **

Today, students continued to work on their final project. They completed their practice problems (Due at the beginning of class tomorrow) and worked on the outline of their presentation (Due Thursday). They will continue working on the presentation throughout the week.
 * __ Monday, May 22, 2017 __ **

Today, students continued to work on their final project. They explored different types of example problems that could be used in their lessons. They will continue to work on practice problems (Due Tuesday) and begin to outline (Due Thursday) and create their presentation throughout next week.
 * __ Friday, May 19, 2017 __ **

Today, students continued to work on their final project. They began to explore different types of example problems that could be used in their lessons. They will continue to work on practice problems and begin to outline and create their presentation tomorrow and next week.
 * __ Thursday, May 18, 2017 __ **

Today, students began to work on their final project. In this project, students will explore and learn about a topic that was not covered in the AP curriculum (conic sections, polar coordinates, matrices, or parametric equations) and then create a lesson that they could use to teach the class about this topic. We will continue to work on this project throughout the next few weeks.
 * __ Wednesday, May 17, 2017 __ **

Today we continued to review the solutions to the released 2017 free response problems. We looked at problems 5 and 6 from the non-calculator section. Tomorrow, we will finish the final problem and begin our final project of the year.
 * __ Monday, May 15, 2017 __ **

Today we began to review the solutions to the released 2017 free response problems. We looked at the two problems on the calculator section, and the beginning of the non-calculator section. We will continue to review more problems on Monday.
 * __ Friday, May 12, 2017 __ **

AP Exam Day!!
 * __ Tuesday, May 9, 2017 __ **

Today, we had our last review day for the AP exam. We talked about some strategies for reviewing for the test, key concepts, and some last minute tips for getting ready for tomorrow's exam. Students also worked on more practice multiple choice and free response problems of their choice.
 * __ Monday, May 8, 2017 __ **

Today, we worked on more practice free response problems. We looked at practice problems related to slope fields, differential equations, and tangent line approximations. Monday, we will have one final day of review before Tuesday's AP exam.
 * __ Friday, May 5, 2017 __ **

Today, we continued to work on more practice free response problems - in which a table of values is given for a function, and the table is used to estimate the derivative at a point, the average value of the function, or a definite integral for the function. We will continue with more practice free response on Friday.
 * __ Wednesday, May 3, 2017 __ **

Today, we took our final practice AP multiple choice section (with a calculator). Tomorrow, we will continue to review practice free response problems, and can review the solutions to the multiple choice sections during class and after school.
 * __ Tuesday, May 2, 2017 __ **

Today, we took another practice AP multiple choice section (non-calculator). We will take the second part of the practice multiple choice (calculator section) tomorrow and continue to work on practice free response problems for the rest of the week.
 * __ Monday, May 1, 2017 __ **

Today, we continued to work on more practice free response problems. We looked at two more problems related to tables of values, position, velocity, and acceleration. On Monday, we will take another practice multiple choice section (without a calculator).
 * __ Friday, April 28, 2017 __ **

Today, we continued to review the multiple choice problems - this time from the calculator practice section we took last week. We talked about more strategies for the multiple choice, and reviewed important topics and concepts that come up frequently on the multiple choice.
 * __ Thursday, April 27, 2017 __ **

Today, we continued to work on more practice free response problems. We looked at two more problems related to accumulation functions, position, velocity, and acceleration. Tomorrow, we will continue to review the multiple choice problems from last week.
 * __ Wednesday, April 26, 2017 __ **

Today, we began to review the multiple choice problems from the non-calculator practice section we took last week. We also talked about some different strategies for the multiple choice, and reviewed important topics and concepts that come up frequently on the multiple choice.
 * __ Tuesday, April 25, 2017 __ **

Today, we had another day of practice free response problems - related to applications of rates of change, Net Change Theorem, average value of functions, and other applications of integrals and derivatives. We will continue with more practice free response problems on Wednesday and Friday, and will review the answers to last week's multiple choice sections tomorrow and Thursday.
 * __ Monday, April 24, 2017 __ **

Today, we worked on practice free response problems. We looked at problems related to derivatives and integrals of functions, given the graph of a function or its derivative. We will continue with more practice free response problems and will review the practice multiple choice tests, next week.
 * __ Friday, April 21, 2017 __ **

Today, we took a second practice AP multiple choice section (with a calculator). We will continue to work on practice free response problems one Friday, and review the solutions to the multiple choice sections next week.
 * __ Wednesday, April 19, 2017 __ **

Today, we took a practice AP multiple choice section (non-calculator). We will take another practice multiple choice (with calculator) section tomorrow.
 * __ Tuesday, April 18, 2017 __ **

Today, we began to talk about preparing for the AP exam. We talked about the timing and the format of the exam, how it is scored, the types of problems covered, and some strategies for the exam. We then talked about the plan for preparing for the AP exam over the next few weeks, and then worked on a few practice multiple choice problems.
 * __ Monday, April 17, 2017 __ **

Today, we had a recitation day to work on problems related to area between curves and volumes of solids of revolution (disk or washer method). We will have a quiz on these topics (sections 7.1 and 7.2) tomorrow.
 * __ Thursday, April 6, 2017 __ **

Today, we worked on practice AP problems related to the area between functions and the volumes of solids of revolution. We also talked about how the calculator can be used to figured out parts of these types of problems. We will have a recitation day tomorrow to review these topics, and will then have a quiz on Friday.
 * __ Wednesday, April 5, 2017 __ **

Today, we continued to look at volumes of solids. We reviewed one more example of the disk and washer methods, then looked at how to find the volume of a solid with a different cross section. We talked about examples of solids with triangular and rectangular cross sections, and how to use integration to find their volume. We will work on AP problems related to these topics tomorrow and Thursday, then have a quiz on area and volume on Friday.
 * __ Tuesday, April 4, 2017 __ **

Today, we continued to work on examples of finding volumes of solids of revolution. We looked at examples of rotating regions about different axes, including vertical and horizontal axes. We also focused on the differences between the disk method and the washer method for finding volume. We will continue with more volume tomorrow.
 * __ Monday, April 3, 2017 __ **

Today, we continued to look at how to use integration to find the volume of a solid of revolution. We reviewed how the disk method can be used to find the volume of some solids. We then continued to look at the washer method, which can be used to find the volumes of solids with "holes". We will continue with more on volumes of solids of revolution on Monday.
 * __ Friday, March 31, 2017 __ **

Today, we began to look at how integration can be used to find the volume of a solid of revolution. We looked at how a region on the x-y plane can be rotated to create a three-dimensional solid, and how disks can be used to find the volume of this solid. We looked at a couple examples of how to use this disk method to find the volume of a solid of revolution. We will continue with more on area and volume tomorrow.
 * __ Thursday, March 30, 2017 __ **

Today, we continued to look at examples of how to find the area between the graphs of two functions. We looked specifically at functions that intersect at more than one point, including those that require multiple integrals to solve and those that are integrated with respect to y.
 * __ Wednesday, March 29, 2017 __ **

Today, we began a new unit on area between curves and volumes of solids of revolution. We started by talking about how to find the area between the graphs of two functions, given an interval. We also looked at how to find the area between two graphs that intersect. We will continue with more on areas between curves tomorrow.
 * __ Tuesday, March 28, 2017 __ **

Today, we continued to work on more AP practice free response problems related to differential equations, applications of derivatives, tangent lines, and other applications.
 * __ Monday, March 27, 2017 __ **

Today, we had a quiz on sections 6.1-6.3 - solutions to differential equations, slope fields, solving differential equations by separating variables, and applications of differential equations.
 * __ Friday, March 24, 2017 __ **

Today, we had a recitation day to review sections 6.1-6.3 - solutions to differential equations, slope fields, solving differential equations by separating variables, and applications of differential equations. We also looked at an example of an AP Free Response problem related to differential equations and slope fields. We will have a quiz on these topics tomorrow.
 * __ Thursday, March 23, 2017 __ **

Today, we reviewed how to solve differential equations using separation of variables. We then began to look into some applications of differential equations - including radioactive decay and population growth - and worked through a number of examples. We will have a recitation/review day tomorrow and then a quiz on differential equations and slope fields on Friday.
 * __ Wednesda __ **** __ y, March 22, 2017 __ **

Today, we continued to look at more with differential equations. We talked about how some differential equations can be solved by separating the variables and finding the indefinite integral. We looked at a few examples of these types of separable differential equations. We then briefly began to look at some of the applications of differential equations, which we will continue with tomorrow.
 * __ Tuesday, March 21, 2017 __ **

Today, we continued with more on differential equations. We reviewed how to verify whether or not a function is a solution to a differential equation. We also reviewed what a slope field is and how to match a slope field with the corresponding differential equation. We will continue with more on differential equations tomorrow.
 * __ Monday, March 20, 2017 __ **

Today, we began a new unit on differential equations. We talked about what a differential equation is and what a solution to a differential equation looks like. We also looked at how to verify solutions to differential equations. We will continue with more on differential equations and slope fields next week.
 * __ Friday, March 17, 2017 __ **

Today, we reviewed how to find the inverse of a function and how to confirm whether or not two functions are inverses. We then looked at the relationship between derivatives of functions and their inverses, as well as a formula for finding the inverse of a function. We worked on a couple of examples of finding derivatives of inverses.
 * __ Thursday, March 16, 2017 __ **

Today, we had a quiz on Chapter 5 - related to finding integrals and derivatives of exponential and logarithmic functions with different bases (sections 5.1, 5.2, 5.4, and 5.5).
 * __ Wednesday, March 15, 2017 __ **

Today, we had one more review day on problems from the last two weeks of homework - related to finding integrals and derivatives of exponential and logarithmic functions with different bases. We will have a quiz tomorrow on these topics (sections 5.1, 5.2, 5.4, and 5.5).
 * __ Monday, March 13, 2017 __ **

Today, we continued to work on review problems from the last two weeks of homework - related to finding integrals and derivatives of exponential and logarithmic functions with different bases. We will have a recitation day on Monday to work on more of these problems, and a quiz on Tuesday on these topics (sections 5.1, 5.2, 5.4, and 5.5).
 * __ Friday, March 10, 2017 __ **

Today, we worked in groups to review problems from the last two weeks of homework - related to finding integrals and derivatives of exponential and logarithmic functions with different bases. We will have a recitation day tomorrow to work on more of these problems, and a quiz on Monday on these topics (sections 5.1, 5.2, 5.4, and 5.5).
 * __ Thursday, March 9, 2017 __ **

Today, we looked at more exponential and logarithmic equations - this time with bases other than //e.// We looked at how to find the derivatives of these kinds of functions, as well as how to find integrals of exponential functions with different bases. We will have review days tomorrow and Friday to practice with exponential and logarithmic functions. We will then have a quiz on these topics on Monday.
 * __ Wednesday, March 8, 2017 __ **

Today, we looked at how to find derivatives and integrals of the natural exponential function ( //f// (//x//) = //e//^//x//). We looked at the definition of the natural exponential function, and how it is related to the natural log function. We then looked at examples of how to find derivatives and integrals of different natural exponential functions. We will continue with more on derivatives and integrals of exponential and logarithmic functions (with different bases) tomorrow.
 * __ Tuesday, March 7, 2017 __ **

Today, we had a recitation day in which students worked on practice problems for finding integrals and derivatives of natural logarithmic functions. We will look at exponential functions and functions with other bases this week.
 * __ Monday, March 6, 2017 __ **

Today, we reviewed how to find the derivatives of logarithmic functions. We then looked at how to find integrals related to logarithmic functions, which are usually found by using variable substitution. We also looked at how this can help us to find integrals of different trigonometric functions.
 * __ Friday, March 3, 2017 __ **

Today, we began to look at logarithmic functions. We talked about the definition of the natural log function (based on an integral) and also looked at some properties of log functions. We then looked at how to find the derivative of a logarithmic function, or a composition involving a logarithmic function. We will continue with more on logarithmic functions tomorrow.
 * __ Thursday, March 2, 2017 __ **

Today, we students worked on two more AP practice problems - related to applications of derivatives and integrals to net change, rate of change, and accumulation functions. Tomorrow, we will begin to look at the integrals and derivates related to exponential and logarithmic functions.
 * __ Wednesday, March 1, 2017 __ **

Today, we had a test on Chapter 4 - estimating area (left, right, midpoint, trapezoid), definite integrals, indefinite integrals and antiderivatives, the Fundamental Theorem of Calculus, average value of a function, and other applications of integrals.
 * __ Tuesday, February 28, 2017 __ **

Today, we had a review/recitation day on the topics we have learned in Chapter 4 - estimating area (left, right, midpoint, trapezoid), definite integrals, indefinite integrals and antiderivatives, the Fundamental Theorem of Calculus, average value of a function, and other applications of integrals. We will have a test on these topics tomorrow.
 * __ Monday, February 27, 2017 __ **

Today, we worked on one more AP practice problem related to graphs of functions, applications of derivatives, and area under curves. We will have a review day on Monday to work on indefinite and definite integrals, and will have a test on these topics on Tuesday.
 * __ Friday, February 24, 2017 __ **

Today, we continued with more AP practice problems to review the topics we have learned recently - including the Fundamental Theorem of Calculus, indefinite integrals, applications of integrals, and motion problems. We will then have review days tomorrow and Monday to work on indefinite and definite integrals, and will have a test on these topics on Tuesday.
 * __ Thursday, February 23, 2017 __ **

Today, we continued with more on integration by substitution. We looked at a couple more examples of how to use substitution to integrate complex functions. We also looked at how to use substitution to evaluate definite integrals, focusing on the changing of the limits of integration. We will look at more AP practice problems related to integrals tomorrow and Friday.
 * __ Wednesday, February 22, 2017 __ **

Today, we worked on one more AP practice problems to review the topics we have learned recently - including the Fundamental Theorem of Calculus, indefinite integrals, and applications of integral. We will look at more with integration by substitution tomorrow, and work on more AP problems Thursday and Friday. We will then have a review day Monday to work on indefinite and definite integrals, and will have a test on these topics next Tuesday.
 * __ Tuesday, February 21, 2017 __ **

Today, we had a recitation day to work on homework from this week - including the Fundamental Theorem of Calculus and other applications of integrals. Next week, we will look at AP practice problems related to these topics and more integration by substitution.
 * __ Friday, February 17, 2017 __ **

Today, we looked at more strategies for finding indefinite integrals of complex functions. We talked about how to use pattern matching to find the antiderivative of a composite function - matching the pattern of the Chain Rule. We will continue with more on integrals tomorrow and next week.
 * __ Thursday, February 16, 2017 __ **

Today, we worked on a few of practice AP problems related to the Fundamental Theorem of Calculus and its applications. We looked at two problems using graphs to find definite integrals and to connect the ideas of the integral and the derivative. We also looked at a problem using a table to find average values, estimate integrals, and estimate derivatives.
 * __ Wednesday, February 15, 2017 __ **

Today, we continued to look at the Fundamental Theorem of Calculus and its applications. We looked at the definite integral as a function, and discussed the Second Fundamental Theorem of Calculus. We also discussed the concept of the integral as an accumulation function and looked at the Net Change Theorem.
 * __ Tuesday, February 14, 2017 __ **

Today, we began to look at the Fundamental Theorem of Calculus (FTC), which provides the connection between antiderivatives (indefinite integrals) and definite integrals (area). We looked at a number of examples of how this can be used to evaluate definite integrals or find the area under the graphs of complex functions. We also looked at how to use the FTC to find the average value of a function over an interval. We will continue with more on the FTC and its applications tomorrow.
 * __ Monday, February 13, 2017 __ **

Today, we continued to look at indefinite integrals. We worked on a number of examples of finding different types of indefinite integrals. We also looked at how to solve differential equations, using indefinite integrals, when given an initial condition. We will continue with more on integration next week.
 * __ Friday, February 10, 2017 __ **

Today, we began to look at antiderivatives, or indefinite integrals. We talked about the definition of an antiderivative, as well as the different types of questions that require you to find an antiderivative. We also talked about the rules for indefinite integrals, which are related to the rules we have seen for derivatives. We will continue with more on indefinite integrals tomorrow.
 * __ Wednesday, February 8, 2017 __ **

Today, we had a quiz on estimating area (left, right, midpoint, trapezoids, etc.; using tables of values or graphs) and definite integrals (sections 4.2, 4.3. 4.6).
 * __ Tuesday, February 7, 2017 __ **

Today, students then had recitation day to practice problems related to estimating area and definite integrals. We will have a quiz tomorrow on estimating area (left, right, midpoint, trapezoids, etc.) and definite integrals (sections 4.2, 4.3. 4.6).
 * __ Monday, February 6, 2017 __ **

Today, we reviewed another example of using the trapezoid method to estimate the area under the graph of a function. Students then had recitation day to practice problems related to estimating area and definite integrals. We will have another recitation day on Monday and a quiz on Tuesday on estimating area (left, right, midpoint, trapezoids, etc.) and definite integrals (sections 4.2, 4.3. 4.6).
 * __ Friday, February 3, 2017 __ **

Today, we reviewed one more example of evaluating definite integrals based on graphs. We also looked at a few examples of AP free response problems on estimating area and definite integrals using tables of values. We will have recitation days tomorrow and Monday to practice problems related to estimating area and definite integrals. We will then have a quiz on Tuesday on estimating area (left, right, midpoint, trapezoids, etc.) and definite integrals (sections 4.2, 4.3. 4.6).
 * __ Thursday, February 2, 2017 __ **

Today, we looked at two more methods for approximating the area under a function - the Trapezoid Method and the Midpoint Sum. We looked at how these are used, and compared two examples of each method, as well as derived a formula for the Trapezoid Method. Tomorrow, we will look at more examples of approximating area, include AP style free-response problems.
 * __ Wednesday, February 1, 2017 __ **

Today, we continued to talk about the definite integral. We reviewed how to write a definite integral to represent the area under the graph of a function. We then looked at a number of different properties of definite integrals that will help us to evaluate them. We will continue with more on definite integrals and area tomorrow.
 * __ Tuesday, January 31, 2017 __ **

Today, we reviewed how to estimate the area under the graph of a function using Left and Right Sums. We then talked about the definition of a Riemann Sum and of a Definite Integral, which is the limit of a sum as the number of rectangles increases to infinity. We looked at a couple of examples of calculating simple definite integrals using geometric formulas, and examples of how it corresponds to the limit of a summation. We will continue with more on definite integrals tomorrow.
 * __ Monday, January 30, 2017 __ **

Today, we continued to look at examples of how to estimate the area under the graph of a function using left and right (or upper and lower) sums of rectangles. We also reviewed how the limit of the summation as the number of rectangles increases to infinity can give the exact area. We will continue with more on area approximations on Monday.
 * __ Friday, January 27, 2017 __ **

Today, we continued to look at examples of how to estimate the area under the graph of a function using left and right sums of rectangles. We also talked about summation notation, which can be used to represent the sums of different sequences of numbers or expressions. We also looked at one example of how a summation and limits can be used to find the exact area under a graph. We will continue with more on area and summation notation tomorrow.
 * __ Thursday, January 26, 2017 __ **

Today, we began a new unit to explore the second major problem in Calculus - finding the area under a curve. We talked about how to find the area of simple functions, and then began to look at how rectangles can be used to estimate the area under more complex functions. We also talked about the meaning of the area, and worked on a few examples of estimating the area using left and right sums of rectangles.
 * __ Wednesday, January 25, 2017 __ **

Today, we took the second part of the midterm (free response) covering the first three chapters - limits and continuity, derivatives, and applications of derivatives (increasing/decreasing, max/min, concavity, etc.).
 * __ Tuesday, January 24, 2017 __ **

Today, we took the first part of the midterm (multiple choice) covering the first three chapters - limits and continuity, derivatives, and applications of derivatives (increasing/decreasing, max/min, concavity, etc.). Tomorrow, we will take the second part of the midterm (free response).
 * __ Monday, January 23, 2017 __ **

Today, we talked about the topics from Chapter 3 (applications of derivatives - increasing/decreasing, max/min, concavity, etc.) that will be covered on the midterm. Students then began to work on practice problems for these topics. We will have the midterm on Monday and Tuesday.
 * __ Friday, January 20, 2017 __ **

Today, we talked about the topics from Chapter 2 (derivatives and rules of differentiation) that will be covered on the midterm. Students then began to work on practice problems for these topics. We will continue with more review and practice problems tomorrow and the midterm will be on Monday and Tuesday.
 * __ Thursday, January 19, 2017 __ **

Today, we began to review for next week's midterm. We talked about the topics from Chapter 1 that will be covered on the midterm. Students then began to work on practice problems for these topics. We will continue with more review and practice problems tomorrow and Friday.
 * __ Wednesday, January 18, 2017 __ **

Today, we continued with more practice AP free response problems, related to different topics we have learned throughout the year. We looked at a number of example problems that demonstrate the type of problems that can come up on the non-calculator section of the free response. Tomorrow, we will begin to review for the midterm.
 * __ Tuesday, January 17, 2017 __ **

Today, we continued to work on more practice AP problems - this time focusing on multiple-choice. We looked at a number of example problems that demonstrate the type of problems that can come up on the multiple-choice non-calculator section of the exam. We will look at more examples of free response questions on Tuesday.
 * __ Friday, January 13, 2017 __ **

Today, we worked on a couple of practice AP free response problems related to tangent line approximations. We also talked about the type of problems and topics that will show up on the midterm, and how we will review for it.
 * __ Thursday, January 12, 2017 __ **

Today, we continued to look at how to use the tangent line approximation at a point to estimate function values near a point. We looked at a couple more examples of how to find the tangent line and how to compare its values to the functions values. Tomorrow, we will look at AP practice problems related to this topic.
 * __ Wednesday, January 11, 2017 __ **

Today, we looked at how the tangent line to a function at a point can be used to approximate the value of the function at nearby points. We worked through a couple of examples of using this tangent line approximation for different types of functions. We will continue with more tangent line approximations tomorrow.
 * __ Tuesday, January 10, 2017 __ **

Today, we reviewed a number of the AP practice problems from the break work packet. We talked about the types of problems and concepts that come up often on the AP exam, particularly the free response section. We also looked at different strategies for approaching these types of problems.
 * __ Monday, January 9, 2017 __ **

Today, we continued with more optimization (or applied maximum/minimum) problems. Students worked in groups to finish the problems from yesterday and a few groups then presented the solutions to the class. On Monday, we will work on reviewing the AP practice problems from the break work packet.
 * __ Friday, January 6, 2017 __ **

Today, we continued with more optimization problems. We worked on one more example as a class, and then students worked on groups on more practice problems. Two or three groups will present the solutions to these problems to the class tomorrow.
 * __ Thursday, January 5, 2017 __ **

Today, we began to look at optimization problems, which are also known as applied maximum/minimum problems. These are applications of the use of the derivative to find maximum or minimum values of different quantities for a given set of constraints (for example, finding the minimum volume of a solid with a given surface area). We will continue with more of these problems tomorrow.
 * __ Wednesday, January 4, 2017 __ **

Today, students worked on AP practice problems - related to graphs of derivatives, relative extrema, increasing/decreasing, concavity and the second derivative test, velocity/acceleration, and other topics we have learned through the first few months of the year.
 * __ Friday, December 23, 2016 __ **

Today, we had a test on Chapter 3 - extrema on an interval, Rolle's theorem and the MVT, increasing/decreasing and the First Derivative Test, concavity and the second derivative, and graphs of functions and their derivatives.
 * __ Thursday, December 22, 2016 __ **

Today, we had a recitation day to work on homework and practice problems from Chapter 3 - related to L'Hopital's Rule, extrema on an interval, the Mean Value Theorem, increasing/decreasing and the First Derivative Test, concavity and the second derivative, and graphs of functions and their derivatives. We will have a test on Chapter 3 tomorrow.
 * __ Wednesday, December 21, 2016 __ **

Today, we looked at one more AP practice problem. We then had a recitation day to work on homework and practice problems from Chapter 3 - related to L'Hopital's Rule, extrema on an interval, the Mean Value Theorem, increasing/decreasing and the First Derivative Test, concavity and the second derivative, and graphs of functions and their derivatives. We will have another recitation day tomorrow and a test on Chapter 3 on Thursday.
 * __ Tuesday, December 20, 2016 __ **

Today, we worked on practice AP free response problems related to applications of derivatives and second derivatives, as well as position, velocity, and acceleration. We will finish these problems tomorrow and will have recitation days tomorrow and Wednesday to work on practice problems from Chapter 3 - related to L'Hopital's Rule, extrema on an interval, the Mean Value Theorem, increasing/decreasing and the First Derivative Test, concavity and the second derivative, and graphs of functions and their derivatives. We will have a test on Chapter 3 on Thursday.
 * __ Monday, December 19, 2016 __ **

Today, we continued with graphs of functions and their derivatives. We reviewed the key concepts of increasing/decreasing functions, extrema, concavity, and points of inflection - and the connections to the graph of a derivative. Students then worked in groups on an activity to match the graphs of functions with the graphs of their derivatives and second derivatives.
 * __ Friday, December 16, 2016 __ **

Today, we continued to look at the graphs of functions and their derivatives. We talked about how to find the domain, intercepts, and asymptotes of a function. We also looked at how to find the intervals of increasing/decreasing and relative extrema using the first derivative, as well as how to find the points of inflection and concavity from the second derivative. We will continue with more on graphs of functions tomorrow.
 * __ Thursday, December 15, 2016 __ **

Today, we reviewed how to use the second derivative of a function to find the points of inflection and describe concavity for the function. We then looked at another example of the second derivative test, in which the sign of the second derivative can be used to determine if a critical number is a relative maximum or a relative minimum. We will continue with more on applications of the first and second derivatives tomorrow.
 * __ Wednesday, December 14, 2016 __ **

Today, we began to look at the applications of the second derivative, and what it can tell you about a function. We looked at the definitions of concavity and points of inflection. We then looked at how the second derivative of a function can be used to find its points of inflection and describe its concavity, as well as how it can be used to determine extrema of a function. We will continue with more on the second derivative tomorrow.
 * __ Tuesday, December 13, 2016 __ **

Today, we had a quiz on L'Hopital's Rule and sections 3.1-3.3 - extrema on an interval, Rolle's Theorem, the Mean Value Theorem, increasing/decreasing functions, the First Derivative Test, and graphs of derivatives. We will continue with more applications of derivatives tomorrow.
 * __ Friday, December 9, 2016 __ **

Today, we reviewed how to find the relative extrema of a function. Students then had a recitation day to work on practice problems on L'Hopital's Rule and sections 3.1-3.3 - extrema on an interval, Rolle's Theorem, the Mean Value Theorem, increasing/decreasing functions, the First Derivative Test, and graphs of derivatives. We will have a quiz on these topics tomorrow.
 * __ Thursday, December 8, 2016 __ **

Today, we finished the AP practice problems that we had started on Monday. We also looked at a few review problems related to extrema and the Mean Value Theorem. We will have a recitation/review day tomorrow to work on homework and review problems and will have a quiz on 3.1-3.3 (and L'Hopital's Rule) on Friday.
 * __ Wednesday, December 7, 2016 __ **

Today, we worked on a couple of AP practice problems - related to graphs of derivatives, relative extrema, increasing/decreasing, and velocity/acceleration. On Wednesday, we will work on one more AP problem and some review problems, and then have recitation time on Thursday for the topics we have learned so far in Chapter 3. We will then have a quiz on these topics on Friday.
 * __ Monday, December 5, 2016 __ **

Today, we reviewed how to find the intervals on which a function is increasing or decreasing, and how to find its relative minima/maxima. We then talked about the relationship between the graph of a function and the graph of its derivative, and worked on a few problems with graphs. We will look at some practice AP problems on Monday.
 * __ Friday, December 1, 2016 __ **

Today, we reviewed how to find the critical numbers of a function. We then talked about how the derivative of a function can be used to find the intervals on which the function is increasing or decreasing and looked at the First Derivative Test, which can be used to find the relative maxima and minima for a function. We looked at a number of examples of how to use this test for different types of functions.
 * __ Thursday, December 1, 2016 __ **

Today, we looked at a couple more examples of Rolle's Theorem and The Mean Value Theorem. We also looked at an application of the Mean Value Theorem to a problem involving position and velocity. Tomorrow, we will look at how the derivative of a function can be used to find the intervals on which a function is increasing or decreasing, as well as to find relative maxima and minima of a function.
 * __ Wednesday, November 30, 2016 __ **

Today, we continued to look at theorems related to the derivative and its properties. We looked at the Mean Value Theorem and Rolle's Theorem, which relate the slope of the secant line between two end points of an interval to the slope of a tangent line at a point within the interval. We will continue with more on these theorems tomorrow.
 * __ Tuesday, November 29, 2016 __ **

Today, we started Chapter 3, in which we will explore applications of the derivative. We looked at the definitions of absolute and relative extrema and critical numbers. We then talked about how to find the extrema of a function on a closed interval, and looked at a few examples of this type of problem. We will continue with more on applications of derivatives next week.
 * __ Monday, November 28, 2016 __ **

Today, we looked at an application of continuity - the Intermediate Value Theorem. We talked about the wording of the theorem itself, and then looked at a few different examples of how it can be applied. We will continue with more applications of derivatives next week.
 * __ Wednesday, November 23, 2016 __ **

Today, we looked at a few more examples of how to apply L'Hopital's Rule. Tomorrow, we will look at the Intermediate Value Theorem, and will continue to look at different applications of derivatives next week.
 * __ Tuesday, November 22, 2016 __ **

Today, we began to look at our first application of derivatives - called L'Hopital's Rule. We looked at how this rule applies to limits that are in indeterminate form, and how the rule can be used to find these limits using derivatives. We will continue with more on L'Hopital's Rule tomorrow.
 * __ Monday, November 21, 2016 __ **

Today, students continued to work on their project on related rates, which will be due on Monday at the beginning of class.
 * __ Friday, November 18, 2016 __ **

Today, students continued to work on their project on related rates, which they will work on tomorrow and turn in on Monday.
 * __ Thursday, November 17, 2016 __ **

Today, we began to look at related rates problems - in which differentiation is used to relate the rate of change of one quantity to the rate of change of another. We looked at a few examples of related rates problems, and also talked about the steps for solving these problems. Students then began to work on their problem set on related rates, which they will continue for the next two days of class.
 * __ Wednesday, November 16, 2016 __ **

Today, we took a test on Chapter 2 - Differentiation - including the definition of the derivative, rules of differentiation, position/velocity/acceleration, rates of change, Product/Quotient/Chain rules, and implicit differentiation.
 * __ Tuesday, November 15, 2016 __ **

Today, we had another review day on Chapter 2 - Differentiation. We will have a test on this chapter tomorrow - including the definition of the derivative, rules of differentiation, position/velocity/acceleration, rates of change, Product/Quotient/Chain rules, and implicit differentiation.
 * __ Monday, November 14, 2016 __ **

Today, we had a review day on Chapter 2 - Differentiation. We will have another review day on Monday and a test on this chapter on Tuesday - including the definition of the derivative, rules of differentiation, position/velocity/acceleration, rates of change, Product/Quotient/Chain rules, and implicit differentiation.
 * __ Thursday, November 10, 2016 __ **

Today, we looked at a number of different types of Free Response questions related to derivatives that come up often on the AP exam. We worked on problems on position/velocity/acceleration, tangent line approximations, and implicit differentiation and talked about strategies for addressing these types of problems. Tomorrow, we will have a review/recitation day to prepare for Monday's test on Chapter 2.
 * __ Wednesday, November 9, 2016 __ **

Today, we continued to work on problems related to position/velocity/acceleration (and other rates of change) that are similar to those that students will see on the AP exam. We also briefly looked at strategies for simplifying complex algebraic expressions and started to look at AP practice problems. We will look at some AP practice Free Response problems on Wednesday.
 * __ Monday, November 7, 2016 __ **

Today, we looked at two more review problems for implicit differentiation. We also looked at more examples of position/velocity/acceleration problems and rate of change problems that are similar to those that students will see on the AP exam. We reviewed how derivatives can be used to solve these kinds of problems. Students then began to work in groups on a number of these types of problems. We will continue with these problems and more AP practice problems next week.
 * __ Friday, November 4, 2016 __ **

Today, we continued with more on implicit differentiation. We looked at how to find the slope or equation of the tangent line to a point on an implicitly defined function. We also looked at how to use implicit differentiation to find the second derivative of an implicitly defined function. We then briefly looked at how to solve projectile motion problems.
 * __ Thursday, November 3, 2016 __ **

Today, we began to look at implicit differentiation. We talked about the difference between explicitly defined and implicitly defined functions. We then looked at the steps for finding the derivative of a function that is defined implicitly, without having to solve for y first. We will continue with more implicit differentiation tomorrow.
 * __ Wednesday, November 2, 2016 __ **

Today, we continued with more examples of the Chain Rule. We also looked at examples in which the Chain Rule needs to be used in conjunction with the Product or Quotient Rule, and other examples in which the Chain Rule must be used multiple times in a problem.
 * __ Monday, October 31, 2016 __ **

Today, we began to look at the derivatives of more complex functions. We talked about the Chain Rule, which can be used to find the derivatives of compound functions (functions "inside" of other functions). We looked at examples of how to use the Chain Rule, and how to recognize the "inside" function and the "outside" function in a compound function. We will continue with more on the Chain Rule on Wednesday.
 * __ Friday, October 28, 2016 __ **

Today, we took a quiz on sections 2.1-2.3 - the definition of the derivative, the basic rules of derivatives, the Product and Quotient rules, and position/velocity/acceleration problems.
 * __ Thursday, October 27, 2016 __ **

Today, we worked on one review problem related to the Quotient rule. Then, students worked on homework problems to prepare for tomorrow's quiz - which will cover the definition of the derivative, the basic rules of derivatives, the Product and Quotient rules, and position/velocity/acceleration problems.
 * __ Wednesday, October 26, 2016 __ **

Today, we continued to look at examples of the Product and Quotient rules, as well as examples of how to simplify functions before differentiating. We also talked about how the derivative represents a rate of change of a function, and how this can be applied to problems involving position, velocity, and acceleration.
 * __ Tuesday, October 25, 2016 __ **

Today, we looked at more rules for finding derivatives. We talked about how to find derivatives using the Product and Quotient Rules. We also talked about the different kinds of questions related to tangent lines that can be solved using derivatives. We will continue with more on these rules and applications tomorrow.
 * __ Monday, October 24, 2016 __ **

Today, we reviewed how to find the derivative of a function, and how the derivative can then be used to find the slope of the tangent line to the function at any point. Students then had a recitation day to work on practice problems related to derivatives and tangent lines.
 * __ Friday, October 21, 2016 __ **

Today, we continued to talk about finding the derivative of a function. We reviewed the limit definition of the derivative and worked through a few examples of using the limit definition. We then began to look at a number of rules for finding derivatives - including the constant rule, the power rule, the constant multiple rule, the sum and difference rules, and the sine and cosine rules.
 * __ Thursday, October 20, 2016 __ **

Today, we talked more about the graphs of derivatives of functions. We talked about what the graphs of derivatives of basic functions look like, as well as how to sketch the graph of the derivative of a function. We looked at how the intervals where a function is increasing or decreasing, and the points where it has a local max or min, affect the graph of its derivative.
 * __ Tuesday, October 18, 2016 __ **

Today, we continued to look at the derivative of a function. We reviewed the definition of the derivative, and talked about how the graph of a function and the graph of its derivative are related. Students then worked on an activity to match the graphs of functions to the graphs of their derivatives. We will continue with more on graphs of functions tomorrow.
 * __ Monday, October 17, 2016 __ **

Today, we talked about how to find the slope of the secant line to a function through two points, and how limits can be used to find the slope of a tangent line to a function at a single point. We then looked at examples of how to find the slope of the tangent line to a given function at a given point. We also talked about the derivative of a function, which is another function that gives the slope of the tangent line at any point. We will continue with more on derivatives, and graphs of derivatives, on Monday.
 * __ Friday, October 14, 2016 __ **

Today, we began a new chapter on the derivative and rates of change. We talked about rate of change in the context of the average velocity and instantaneous velocity of an object. We looked at a formula for finding the average velocity of an object, using the position function. Students then worked on an activity to explore the difference between average and instantaneous velocity, which involves limits. We will continue with more rates of change and limits tomorrow.
 * __ Thursday, October 13, 2016 __ **

Today, we had a test on Chapter 1 - covering limits, continuity, and asymptotes.
 * __ Tuesday, October 11, 2016 __ **

Today, we had one more review/recitation day to work on practice problems from Chapter 1 - covering limits, continuity, and asymptotes. We will have a test on these topics tomorrow.
 * __ Monday, October 10, 2016 __ **

Today, we had a review/recitation day to work on practice problems from Chapter 1 - covering limits, continuity, and asymptotes. We will have another review day on Monday and a test on Tuesday on these topics.
 * __ Friday, October 7, 2016 __ **

Today, we reviewed how to find limits at infinity, and how these are related to the rules for horizontal asymptotes. Students then worked in pairs on AP style practice problems related to the topics from Chapter 1 - limits. We will have recitation/review days tomorrow and Monday and will have a test on Chapter 1 on Tuesday.
 * __ Thursday, October 6, 2016 __ **

Today, we reviewed how to determine the continuity of a piecewise function and how to find values to make a function continuous. We then began to look at how to find vertical and horizontal asymptotes of functions. We also talked about how vertical asymptotes are related to infinite limits and horizontal asymptotes are related to limits at infinity.
 * __ Wednesday, October 5, 2016 __ **

Today, we continued to look at continuity of functions. We talked about more one-sided limits of functions and how these can be used to talk about the continuity of more complicated functions or piecewise functions. We also looked at how to prove that a piecewise function is continuous (or not) algebraically, and how to find a constant to make a piecewise function continuous.
 * __ Thursday, September 29, 2016 __ **

Today, we began to look at continuity of functions. We talked about what continuity means informally, and what types of behavior can cause a function to fail to be continuous at a point. We then looked at the formal definition of continuity and discussed the difference between a removable and a non-removable discontinuity.
 * __ Wednesday, September 28, 2016 __ **

Today, we had a quiz on sections 1.1-1.3 - the basic problems of Calculus, estimating limits graphically and numerically, and finding limits analytically.
 * __ Tuesday, September 27, 2016 __ **

Today, we reviewed how to find limits of functions using different approaches. Students then worked on review problems to prepare for tomorrow's quiz on sections 1.1-1.3 - the basic problems of Calculus, estimating limits graphically and numerically, and finding limits analytically.
 * __ Monday, September 26, 2016 __ **

Today, we continued to look at different approaches for finding limits. We talked about how to find the limit of basic functions analytically by plugging in values. We then also looked at how to find the limits of more complex functions using the dividing out, rationalizing, or other techniques.
 * __ Friday, September 23, 2016 __ **

Today, we began to talk about limits. We looked at the notation for limits and how limits can be found using tables of values (numerically). We looked at an example of how the table of values can be used to show the difference between a vertical asymptote and a hole in the graph of a function. We also talked about how to find limits graphically and the different types of behavior where a limit would not exist.
 * __ Thursday, September 22, 2016 __ **

Today, we began to look at what types of problems can be solved in Calculus. We talked about the difference between problems that can be solved with and without Calculus. We then began to look at the two main problems we will study in Calculus - the Tangent Line problem and the Area Problem.
 * __ Wednesday, September 21, 2016 __ **

Today, we reviewed what the graphs of different types of functions look like. Students then worked on a couple of activities to practice identifying the types of graphs and matching them with the corresponding equations, and to practice sketching graphs of different functions by hand.
 * __ Tuesday, September 20, 2016 __ **

Today, we took a quiz on properties of functions - domain and range, transformations, composition of functions, and inverses. We will continue to review important types of functions and begin to look at limits the rest of this week.
 * __ Monday, September 19, 2016 __ **

Today, we had recitation day to work on homework and review problems related to domain and range, transformations, composition of functions, and inverses. We will have a quiz on these topics on Monday.
 * __ Friday, September 16, 2016 __ **

Today, we looked at another example of finding an inverse function, finding its domain and range, and confirming that two functions are inverses. We then reviewed some important information students need to know related to trigonometric, exponential, and logarithmic functions. We will have a recitation day tomorrow and will have a quiz on Monday on domain and range, transformations, composition of functions, and inverses.
 * __ Thursday, September 15, 2016 __ **

Today, we looked at inverse functions. We talked about what an inverse function is, how to verify whether two functions are inverses (analytically as well as graphically), and how to find an inverse function (as well as its domain and range).
 * __ Wednesday, September 14, 2016 __ **

Today, we reviewed how to find the composition of two functions. We then reviewed any problems from the summer assignment that students had questions about. We will continue with more on functions this week.
 * __ Tuesday, September 13, 2016 __ **

Today, we reviewed how to evaluate, graph, and find the domain and range for piecewise functions. We then looked at transformations of functions, including how to describe transformations based on the equation and how to graph transformations of functions. We also reviewed composition of functions - how to evaluate them and how to find the domain and range.
 * __ Monday, September 12, 2016 __ **

Today, we reviewed how to find the domain and range of different functions. We then looked at piecewise functions, and talked about how to evaluate them, as well as how to graph them and how to find their domain and range. We will continue with more properties of functions tomorrow.
 * __ Friday, September 9, 2016 __ **

Today, we reviewed the notation and definition of functions. We also reviewed how to evaluate a function for a given input and how to find the domain and rage of different types of functions. We will continue with more review of functions and their properties tomorrow.
 * __ Thursday, September 8, 2016 __ **

Today, we reviewed the syllabus for the course - including grading, rules, expectations, and procedures. We then had a discussion about students' expectations for the course, as well as things that they were or were not looking forward to.
 * __ Wednesday, September 7, 2016 __ **