2015-2016+Classwork

= Pre-Calculus 2015-2016 Classwork =

This page contains the notes and classwork for each day of class for the Pre-Calculus 1st period section.

Today, we had the second part of our final exam - covering sum and difference identities, solving trig equations, graphs of basic functions, limits, and continuity.
 * __ Thursday, June 9, 2016 __ **

Today, we had the first part of our final exam - covering exponential and logarithmic functions, graphs of sine and cosine, and trigonometric identities. We will take the second part of the final tomorrow.
 * __ Wednesday, June 8, 2016 __ **

Today, we had our final day of review for the final exam. Students worked on a number of example problems for the topics that will be covered on the two parts of the final exam - which will be given tomorrow and Thursday.
 * __ Tuesday, June 7, 2016 __ **

Today, we continued to review for the final exam. We looked at two more topics that will be covered on the final - graphs of functions and limits. We reviewed how to sketch graphs of functions and how to match functions with their graph, as well as different ways to find or estimate limits of functions. We will have one more review day tomorrow and will have our final exam on Wednesday and Thursday.
 * __ Monday, June 6, 2016 __ **

Today, we continued to review for the final exam. We looked at the next topic that will be covered on the final - sum and difference and double angle trig identities. We looked at examples of how these can be used to evaluate trig functions of different angles and to solve equations involving trig functions. We will continue with more review on Monday.
 * __ Friday, June 3, 2016 __ **

Today, we continued to review for the final, which will be next week (June 8th and 9th). We looked at the next major topic that will be covered on the final - trig identities - and worked on practice problems for proving new trig identities and simplifying expressions using trig identities. We will continue with more review related to trig tomorrow.
 * __ Thursday, June 2, 2016 __ **

Today, students continued to work on review problems for the final exam - focusing on exponential and logarithmic functions and graphs of sine and cosine. We will continue with more review tomorrow.
 * __ Wednesday, June 1, 2016 __ **

Today, we began to review for the final, which will be next week (June 8th and 9th). We talked about the topics that will be covered on the final, as well as strategies students can use to review for the final. We then reviewed about how to solve exponential/logarithmic equations and how to sketch graphs of sine and cosine. Students then worked on practice problems for these two topics. We will continue with more review tomorrow.
 * __ Tuesday, May 31, 2016 __ **

Today, we reviewed how to determine whether or not a piecewise function is continuous. We also looked at a few problems in which we had to find values of constants to make a function continuous. Next week, we will begin to review for the final exam, which will be given in two parts on June 8th and 9th.
 * __ Friday, May 27, 2016 __ **

Today, we continued to look at the continuity of functions. We reviewed how to find the intervals on which a function is continuous and how to identify discontinuities. We then worked on a number of examples of determining whether or not a piecewise function is continuous. We will have one more day of continuity tomorrow.
 * __ Thursday, May 26, 2016 __ **

Today, we began to look at the continuity of a function. We talked about the definition of continuity at a point, as well as the different situations in which a function would fail to be continuous at a point. We also talked about the idea of one-sided limits, which are important for continuity of piecewise functions. We will continue with more continuity and limits tomorrow.
 * __ Wednesday, May 25, 2016 __ **

Today, we had a quiz on estimating or finding limits graphically, numerically, and analytically - including dividing out, rationalizing, and other techniques. We will continue with more on limits and continuity later this week.
 * __ Tuesday, May 24, 2016 __ **

Today, we had one more day of review on estimating or finding limits graphically, numerically, and analytically - including dividing out, rationalizing, and other techniques. We will have a quiz on limits tomorrow.
 * __ Monday, May 23, 2016 __ **

Today, we had a review day on estimating or finding limits graphically, numerically, and analytically - including dividing out, rationalizing, and other techniques. We will have another review day on Monday and will have a quiz on limits on Tuesday.
 * __ Friday, May 20, 2016 __ **

Today, we reviewed how to find limits using the dividing out a rationalizing techniques. We then looked briefly at a few other techniques for finding more complex limits. We will have review days for limits tomorrow and Monday and will have a quiz on limits on Tuesday.
 * __ Thursday, May 19, 2016 __ **

Today, we reviewed how to find limits using the dividing out technique. We then looked at another technique for finding limits analytically - called rationalizing. We will look at other techniques for complex limits tomorrow.
 * __ Wednesday, May 18, 2016 __ **

Today, we continued with more on finding limits analytically. Students worked on a number of practice problems for different strategies, including dividing out. We will look at other strategies - including rationalizing - tomorrow.
 * __ Tuesday, May 17, 2016 __ **

Today, we continued to look at methods for finding limits of function analytically. We looked at one of the methods that can be used when functions are undefined at a certain point - the dividing out technique. We will continue to work on methods for finding limits tomorrow.
 * __ Monday, May 16, 2016 __ **

Today, we had a quiz on finding and explaining //x//-intercepts, vertical asymptotes, and holes of rational functions. We then began to look at how to find limits of simple functions algebraically. We will continue with more on limits next week.
 * __ Friday, May 13, 2016 __ **

Today, we continued to review //x//-intercepts, vertical asymptotes, and holes of rational functions, and their connections to limits. We will have a short quiz tomorrow and will continue with more on limits after the quiz.
 * __ Thursday, May 12, 2016 __ **

Today, we reviewed how to find the //x-//intercepts, vertical asymptotes, and holes of a rational function. We looked at how this can be done with factoring the numerator and denominator, and talked about its connection to limits. We will have another day of reviewing rational functions tomorrow and will have a short quiz on Friday.
 * __ Wednesday, May 11, 2016 __ **

Today, we continued to talk about finding limits of functions as they approach a given point. We looked at a second method for estimating limits - using a table of values. We looked at a couple examples of how to use a table to estimate a limit.
 * __ Tuesday, May 10, 2016 __ **

Today, we began to talk about the concept of the limit of a function as it approaches a point. We talked about the distinction between a function value at a point and the limit as the function approaches that point. We then looked at the first of three methods for approximating limits - using graphs of functions - and talked about when a limit fails to exist. We will continue with more on limits and estimating limits tomorrow.
 * __ Monday, May 9, 2016 __ **

Today, we continued to look at an overview of Calculus and the types of problems that can be solved using it. We talked about the difference between terms in Pre-Calc and Calc - tangent line vs. secant line, average vs. instantaneous velocity, and function value vs. limit. We then looked at the difference between the types of problems that can be solved with Pre-Calc and those that require Calculus.
 * __ Friday, May 6, 2016 __ **

Today, we began to look at an overview of Calculus and the types of problems that can be solved using it. We looked at how to find the average velocity of an object over a time interval. We then talked about the difference between average and instantaneous velocity, as well as other differences between Pre-Calc and Calc. Students then worked on an activity in which they explored the difference between average velocity and instantaneous velocity.
 * __ Thursday, May 5, 2016 __ **

Today, we began to look at simplifying rational expressions. We reviewed different strategies for factoring, and then looked at how factoring can be used to simplify the product or quotient of two rational expressions. We also looked at how common denominators and factoring can be used to simplify the sum or difference of rational expressions. We will look at the basic problems in Calculus tomorrow and Friday, and will continue with more related to rational expressions/functions next week.
 * __ Wednesday, May 4, 2016 __ **

Today, we continued with more properties of exponents. We also looked at how to simplify expressions involving exponents, including negative exponents and fractional exponents. We will look at simplifying rational expressions tomorrow.
 * __ Tuesday, May 3, 2016 __ **

Today, we reviewed some of the important properties of exponents that students need to know for Calculus. We looked at how to deal with roots of numbers or expressions, how to convert between exponential and root form, and how to simplify expressions involving exponents or roots. We will continue with more on roots and exponents tomorrow.
 * __ Monday, May 2, 2016 __ **

Today, we continued with more on analyzing graphs of velocity functions. Students worked in groups to analyze two different velocity graphs - finding function values, intervals of positive/negative/zero values, and intervals of increasing/decreasing/constant values. Students also looked at what these different values mean in the context of the problem. Next week, we will review some properties of exponents and rational expressions that are important in Calculus.
 * __ Friday, April 29, 2016 __ **

Today, we continued with analyzing graphs of functions and their applications. We looked at a graph of velocity versus time and analyzed it - including when the function is positive or negative or when the function is increasing and decreasing, and the meanings of these intervals. We will continue with more on analyzing graphs tomorrow.
 * __ Thursday, April 28, 2016 __ **

Today, we looked at analyzing graphs of functions and their applications. We looked at graphs of distance versus time and velocity versus time and analyzed their meanings - including when the functions are positive or negative and the meanings of these intervals. We will continue with more on analyzing graphs tomorrow and Friday.
 * __ Wednesday, April 27, 2016 __ **

Today, we had a quiz on graphing functions and matching functions - including linear, quadratic, cubic, absolute value, square root, sine, and cosine functions - along with piecewise functions.
 * __ Monday, April 25, 2016 __ **

Today, we reviewed how to graph important functions and how to match functions with graphs - including linear, quadratic, cubic, absolute value, square root, sine, and cosine functions. We will have a quiz on these graphs, along with piecewise functions, on Monday.
 * __ Friday, April 22, 2016 __ **

Today, we continued to work on graphing and evaluating piecewise functions. We looked at a couple of different strategies for graphing piecewise functions. We also reviewed any questions that students had about the graphs of functions we looked at last week. We will continue with review of graphing functions tomorrow and will have a quiz on graphs on Monday.
 * __ Thursday, April 21, 2016 __ **

Today, we began to look at piecewise functions, which are important in higher-level math. We looked at how to evaluate a piecewise function, as well as how to sketch a graph of a piecewise function. We worked on a few examples and talked about different strategies for graphing. We will continue with piecewise functions tomorrow.
 * __ Wednesday, April 20, 2016 __ **

Today, we had one more day of review on the graphs of important types of functions. We looked at graphing four more types of functions (square root, absolute value, sine, and cosine) and talked about the information and steps needed to graph each type. We then worked on a few examples of graphing these functions. Tomorrow, we will begin to look at piecewise functions, which are also important in higher-level math.
 * __ Tuesday, April 19, 2016 __ **

Today, we continued with more on graphs of functions. We reviewed the steps for graphing different types of polynomials (linear, quadratic, cubic/quartic) and worked on examples of graphing each. We will continue with graphing more types of functions tomorrow (square root, absolute value, sine/cosine).
 * __ Monday, April 18, 2016 __ **

Today, we continued to look at graphs of important types of functions. We looked at how to identify the type of a function and its equation based on its graph. Then, students worked in groups on an activity to match graphs with their corresponding equations, based on the type of graph and other characteristics. We will look at more with graphs next week.
 * __ Friday, April 15, 2016 __ **

Today, we continued to work on sketching graphs of different types of functions that are important for Calculus. We reviewed a couple of the basic types, and students continued to work on sketching graphs of different functions. Tomorrow, we will work on matching graphs to equations for these types of functions.
 * __ Thursday, April 14, 2016 __ **

Today, we began a new mini-unit on graphs of functions. We talked about the important families of functions that students need to be comfortable with in higher level math, and also talked about the information needed to sketch graphs of some of these functions. Students then worked in groups on sketching graphs of different functions by hand. We will continue with more graphs of functions tomorrow.
 * __ Wednesday, April 13, 2016 __ **

Today, we had a quiz on the sum and difference and double-angle identities (sections 5.3 and 5.4) - evaluating trig functions of different angles, simplifying expressions involving trig functions, solving trig equations, and proving new identities.
 * __ Tuesday, April 12, 2016 __ **

Today, we had one last review day on sum and difference and double-angle identities (sections 5.3 and 5.4). We will have a quiz tomorrow on evaluating trig functions of different angles, simplifying expressions involving trig functions, solving trig equations, and proving new identities.
 * __ Monday, April 11, 2016 __ **

Today, we continued with more on the double-angle identities. We reviewed how these identities can be used to solve equations involving sine and cosine of double angles. We then looked at how these identities can be used to prove other identities. We will review the sum and difference and double-angle identities on Monday and have a quiz on these on Tuesday.
 * __ Friday, April 8, 2016 __ **

Today, we reviewed how to solve trig equations and prove new identities using the double angle formulas. Students then worked on review problems for applying the sum, difference, and double angle identities to simplify expressions, solve equations, or prove new identities. We will continue with more of these identities tomorrow.
 * __ Thursday, April 7, 2016 __ **

Today, we reviewed how to solve trig equations and began to look at the double-angle identities for sine and cosine. These identities can be derived from the sum identities for sine and cosine. We then looked at how these identities can be used to solve more complex trig equations. We will continue with more on the double-angle identities tomorrow.
 * __ Wednesday, April 6, 2016 __ **

Today, we reviewed how to solve trig equations and how to use the sum and difference identities. We also briefly looked at the double-angle identities for sine and cosine. We then worked on a group activity in Kahoot to review evaluating trig functions, trig graphs, and trig identities. We will continue with more on the double-angle identities tomorrow.
 * __ Tuesday, April 5, 2016 __ **

Today, we continued with more on the sum and difference formulas. We first reviewed how to use them to find values of sine and cosine for different angles. We then looked at how these same identities can be used to condense expressions involving sine and cosine or to prove new identities. We will begin to look at the double-angle identities tomorrow.
 * __ Monday, April 4, 2016 __ **

Today, we continued to look at more trigonometric identities. We looked at the sum and difference identities for sine and cosine. We then worked on a number of examples of how this can be used to find the values of sine and cosine for different angles. We will continue with more on sum and difference identities on Monday.
 * __ Friday, April 1, 2016 __ **

Today, we took a quiz on sections 5.1 and 5.2 - solving trigonometric equations, simplifying trigonometric expressions, and proving trigonometric identities.
 * __ Thursday, March 31, 2016 __ **

Today, we had one last day of review on solving trigonometric equations, simplifying trigonometric expressions, and proving trigonometric identities. We will have a quiz on these topics tomorrow.
 * __ Wednesday, March 30, 2016 __ **

Today, we continued with more practice on proving trigonometric identities. Students completed the problems they began in groups yesterday, then each group presented one problem solution to the rest of the class. We will review solving trigonometric equations and simplifying trigonometric expressions tomorrow, then have a quiz on these topics on Thursday.
 * __ Tuesday, March 29, 2016 __ **

Today, we had another day of practice on proving trigonometric identities. We reviewed the strategies we had used last week and looked at a few more examples. Students then worked in groups on more practice problems, which they will present to the class tomorrow.
 * __ Monday, March 28, 2016 __ **

Today, we continued to work on proving trigonometric identities. We reviewed some of the strategies we looked at on Friday, and worked on a couple more examples as a class. Students then worked in groups on more examples of proving trig identities.
 * __ Monday, March 21, 2016 __ **

Today, we continued to work with trigonometric identities - this time using them to prove new trigonometric identities. We talked about a number of different strategies for proving identities, including some of the same strategies we used when simplifying. We then talked about a number of examples of proving identities. We will continue with more proofs on Monday.
 * __ Friday, March 18, 2016 __ **

Today, we continued to work on simplifying trigonometric expressions using the trig identities we talked about yesterday. We looked at a number of strategies for simplifying (including factoring, FOILing, and common denominators) as well as different ways of using identities.
 * __ Thursday, March 17, 2016 __ **

Today, we began to look at trigonometric identities. We talked about what an identity is and looked at a few different kinds of trig identities (including Reciprocal Identities and Pythagorean Identities). We then began to look at how these identities can be used to simplify more complex trigonometric expressions. We will continue with more trigonometric identities tomorrow.
 * __ Wednesday, March 16, 2016 __ **

Today, we reviewed how to solve different types of trigonometric equations. We talked about the steps for solving trig equations - including factoring, GCF, and using special right triangles/unit circle. Students then worked in groups on more practice problems, which were presented to the class. We will begin to look at trigonometric identities tomorrow.
 * __ Tuesday, March 15, 2016 __ **

Today, we began a new unit on solving trigonometric equations, trigonometric identities, and simplifying expressions using trigonometric identities. We review how to solve basic quadratic equations, as well as how to find angles that have a given value of sine or cosine. We then looked at how factoring, along with a knowledge of the unit circle, can be used to solve equations involving sin x and/or cos x. We will continue with more on trigonometric equations tomorrow.
 * __ Monday, March 14, 2016 __ **

Today, students completed their lessons on logarithmic and exponential applications. We then began a new unit on solving trigonometric equations, trigonometric identities, and simplifying expressions using trigonometric identities. We looked at how to solve basic quadratic equations, as well as how to find angles that have a given value of sine or cosine. We then looked at how factoring, along with a knowledge of the unit circle, can be used to solve equations involving sin x and/or cos x. We will continue with more on trigonometric equations next week.
 * __ Friday, March 11, 2016 __ **

Today, students continued to present their lessons on logarithmic and exponential applications. Each group presented to one or two other groups.
 * __ Thursday, March 10, 2016 __ **

Today, students began to present their lessons on logarithmic and exponential applications. Each group presented to one or two other groups. We will continue with more of these presentations tomorrow.
 * __ Wednesday, March 9, 2016 __ **

Today, students completed their work on the applications of logarithmic and exponential equations project. Groups worked on finishing their final lesson to be presented to their classmates. The complete lesson will be due at the beginning of class tomorrow, and we will begin the presentations at that time.
 * __ Tuesday, March 8, 2016 __ **

Today, students continued to work on the project for exploring applications of logarithmic and exponential equations. Groups completed and submitted the outline portion of the project and then began to work on the actual lesson and PowerPoint. The complete lesson will be due at the beginning of class on Wednesday.
 * __ Monday, March 7, 2016 __ **

Today, students began to work on the project for exploring applications of logarithmic and exponential equations. They began by exploring and researching their topics, and started to put together the outline for the lesson they will create. The outline portion of the project will be due at the end of class on Monday.
 * __ Friday, March 4, 2016 __ **

Today, we began to look at an application of exponential growth functions - calculating values of investments using compound interest. We looked at a few examples of the types of problems that can be solved related to investments. We also began to look at the project that students will start tomorrow and work on next week - in which they will explore another application of exponential and log functions and create a lesson to teach their classmates.
 * __ Thursday, March 3, 2016 __ **

Today, we reviewed how to solve exponential and logarithmic equations. We then looked at a few more complicated examples of exponential and logarithmic equations and talked about strategies to solve these. Finally, we briefly looked at some applications of exponential and logarithmic functions, which we will explore in more depth tomorrow and with a project beginning on Friday.
 * __ Wednesday, March 2, 2016 __ **

Today, we looked at how to evaluate logarithms on the calculator using the Change of Base formula. We also looked at a number of different ways to solve exponential and logarithmic equations, and worked on practice problems for these approaches. This week, we will look at more solving equations and will begin to work on a project in which we will explore applications of exponential and logarithmic functions.
 * __ Tuesday, March 1, 2016 __ **

Today, we had a quiz on exponential growth and decay functions, population growth and decay, basic logarithms, properties of logarithms, and solving equations involving logarithms. We will look into applications of exponential and logarithmic functions starting tomorrow.
 * __ Monday, February 29, 2016 __ **

Today, we continued to work on review problems on exponential growth and decay functions, population growth and decay, basic logarithms, properties of logarithms, and solving equations involving logarithms. We will have a quiz on these topics on Monday.
 * __ Thursday, February 25, 2016 __ **

Today, we worked on review problems on exponential growth and decay functions, population growth and decay, and evaluating logarithms. We will have one more review day tomorrow and a quiz on these topics on Monday.
 * __ Wednesday, February 24, 2016 __ **

Today, we reviewed how to condense multiple logarithms into a single logarithm using the Product, Quotient, and Power rules. We then worked on an activity to review how to evaluate logarithms. We will have review days tomorrow and Thursday on exponential growth and decay functions, population growth and decay, basic logarithms, properties of logarithms, and solving equations involving logarithms. We will have a quiz on these topics on Monday.
 * __ Tuesday, February 23, 2016 __ **

Today, we continued to work with the Product, Quotient, and Power rules for logarithms. We reviewed how to expand a single logarithm into multiple logarithms using these rules, and then looked at examples of how to condense multiple logarithms into a single logarithm using the rules. We also briefly talked about different applications of logs. We will continue with more on logs tomorrow.
 * __ Monday, February 22, 2016 __ **

Today, we reviewed how to solve equations involving logarithms. We then began to look at the Power, Quotient, and Product Rules for logarithms. We looked at a few examples of how these work with basic logarithms, then looked at how these rules can be used to expand more complex logarithms into combinations of simpler logs. We will continue with more on these rules next week.
 * __ Friday, February 19, 2016 __ **

Today, we continued to work on evaluating logarithms. We reviewed how to evaluate logarithms without a calculator, and then began to look at how to solve equations by converting between exponential and logarithmic form. We also began to look at properties of logarithms for expanding or condensing expressions involving logarithms. We will continue with more properties of logarithms tomorrow.
 * __ Thursday, February 18, 2016 __ **

Today, we began to look at logarithms. We talked about the definition of logarithms, and how they are related to exponential expressions. We then worked on a number of examples of evaluating logarithms with different bases - including common logs (base 10) and natural logs (base e). We will continue with more on logs tomorrow.
 * __ Wednesday, February 17, 2016 __ **

Today, we continued to look at some applications of exponential growth and decay functions. We looked at a few more examples of population growth and decay, including examples of how to write an equation given the population and growth rate. We also looked at examples of other applications. We will begin to look at logarithmic functions tomorrow.
 * __ Tuesday, February 16, 2016 __ **

Today, we continued to look at exponential growth and decay functions. We reviewed the difference between growth and decay, and looked at how the end behavior of growth and decay functions can be represented using limits. We also looked at a few applications of exponential functions to model population growth and decrease. We will continue with more on exponential and logarithmic functions next week.
 * __ Friday, February 12, 2016 __ **

Today, we began a new unit on exponential and logarithmic functions. We talked about the definition of an exponential function, as well as the distinction between an exponential growth and an exponential decay function. We also looked at the graphs and tables of exponential growth and decay functions. We will continue with more on exponential functions tomorrow.
 * __ Thursday, February 11, 2016 __ **

Today, we had a quiz on the Law of Sines, the Law of Cosines, and word problems related to these laws (sections 5.5 and 5.6). Tomorrow, we will begin to explore exponential and logarithmic functions.
 * __ Wednesday, February 10, 2016 __ **

Today, we had a review day to work on practice problems for the Law of Sines, the Law of Cosines, and word problems related to these laws. We will have a quiz on these topics tomorrow.
 * __ Tuesday, February 9, 2016 __ **

Today, we reviewed how to solve problems using the Law of Cosines. We then began to talk about some examples of word problems that can be solve using the Law of Sines and/or the Law of Cosines. We worked on a few examples as a class, and then students worked in groups on others. We will have a review day for these laws tomorrow, and will then have a quiz on Wednesday.
 * __ Monday, February 8, 2016 __ **

Today, we continued to work on examples of solving triangles with the Law of Sines or Law of Cosines. We talked about the types of triangles that can be solved with the Law of Sines (AAS and SSA) and those that require the Law of Cosines (SAS and SSS). We worked on examples of each, and will continue with more examples, including word problems, on Monday.
 * __ Friday, February 5, 2016 __ **

Today, we looked at a couple more examples of the Law of Sines, and then began to look at the Law of Cosines. This law can be used to solve triangles when given SAS or SSS information. We first worked on an activity to derive the Law of Cosines, and then looked at an example of how it can be used. We will continue with more on the Law of Cosines tomorrow.
 * __ Thursday, February 4, 2016 __ **

Today, we continued to look at how to solve triangles using the Law of Sines. We looked at an example of solving when given two angles and a corresponding side. We also looked at two examples of solving when given two sides and one angle, including the "ambiguous" case in which two triangles are possible with the given information. We will continue with more solving triangles, and will look at the Law of Cosines, tomorrow.
 * __ Wednesday, February 3, 2016 __ **

Today, we began to look at how to use trig functions to solve problems involving triangles that are not right triangles. We looked at the first method for doing this - called the Law of Sines - which students derived through a group activity. We also looked at an example of how this law is used. We will continue with more examples tomorrow.
 * __ Tuesday, February 2, 2016 __ **

Today, we took the second part of the midterm - covering properties of rational functions, solving rational equations, special right triangles, circular angles, inverse trig functions, and graphs of trig functions.
 * __ Monday, February 1, 2016 __ **

Today, we took the first part of the midterm - covering domain and range, composition of functions, inverses of functions, transformations, and graphs of polynomials. On Monday, we will have the second part of the midterm - covering properties of rational functions, solving rational equations, special right triangles, circular angles, inverse trig functions, and graphs of trig functions.
 * __ Friday, January 29, 2016 __ **

Today, we had one last day of review for the midterm. We worked on practice problems for topics related to trigonometry - special right triangles, circular angles, inverse trig functions, and graphs of trig functions. We will have the midterm tomorrow and Monday.
 * __ Thursday, January 28, 2016 __ **

Today, we continued to review for next week's midterm. Students worked on practice problems from chapter 2 - graphing polynomial functions, properties of rational functions, and solving rational equations. We will have one more day of review tomorrow and will then have the midterm on Friday and Monday.
 * __ Wednesday, January 27, 2016 __ **

Today, we continued to review for the midterm. Students worked on more practice problems from chapter 1 - domain and range, composition of functions, inverses of functions, and transformations. We will continue to review on Monday and Tuesday and will then have the midterm on Wednesday and Thursday.
 * __ Friday, January 22, 2016 __ **

Today, we began to review for the upcoming midterm. We talked about the topics that will be covered on the midterm, and students worked on practice problems from chapter 1 - domain and range, composition of functions, inverses of functions, and transformations. We will continue to review tomorrow, Monday, and Tuesday and will then have the midterm on Wednesday and Thursday.
 * __ Thursday, January 21, 2016 __ **

Today, we worked on more word problems that can be solved using trigonometry. We worked on one problem as a class for warm-up, and students also worked on a number of problems in groups to practice different strategies for solving these problems. We also briefly looked at the topics on the Midterm, which we will begin reviewing for tomorrow.
 * __ Wednesday, January 20, 2016 __ **

Today, we began to look at how to solve problems using trigonometric functions. We looked at a number of examples of solving word problems using sine, cosine, and tangent functions, and talked about strategies for approaching these problems. We will continue with more solving problems with trig tomorrow.
 * __ Tuesday, January 19, 2016 __ **

Today, we had a quiz on sections 4.4 and 4.7 - inverse trig functions, compositions of trig functions, and sketching graphs of sine and cosine (amplitude, period, frequency).
 * __ Friday, January 15, 2016 __ **

Today, we had one more review day on sections 4.4 and 4.7 - inverse trig functions, compositions of trig functions, and graphs of sine and cosine. We will have a quiz on these topics tomorrow.
 * __ Thursday, January 14, 2016 __ **

Today, we reviewed how to sketch graphs of sine and cosine. We then began to review topics from sections 4.4 and 4.7 - inverse trig functions, compositions of trig functions, and graphs of sine and cosine. We will have another day of review tomorrow and will have a quiz on these topics on Friday.
 * __ Wednesday, January 13, 2016 __ **

Today, we reviewed how to find the amplitude, period, and frequency of a sinusoid function and how to sketch the graph of one cycle of the function. We then worked on practice problems for these graphs. For the next two classes, we will review inverse trig functions and graphs of sine and cosine. We will have a quiz on these topics on Friday.
 * __ Tuesday, January 12, 2016 __ **

Today, we continued to look at graphs of sine and cosine. We reviewed how to find the amplitude, period, and frequency. We then talked about how to sketch the graph of one period of this function. We will continue with more on graphs of sine and cosine, including applications, tomorrow.
 * __ Monday, January 11, 2016 __ **

Today, we continued to look at graphs of sine and cosine. We reviewed how to find the amplitude, max, and min values of the function. We then looked at how to find the period and frequency of a sine or cosine graph. We will continue with more on graphs of sine and cosine, including sketching the graphs, on Monday.
 * __ Friday, January 8, 2016 __ **

Today, we looked at two more examples of how to evaluate the composition of trig functions and inverse trig functions. We then began to talk about the graphs of sine and cosine, and how they are related to the unit circle. We talked about the fact that sine and cosine are periodic functions, which means that they repeat the same pattern of values. We then began to talk about the properties of these functions - including amplitude, wavelength, and frequency - which we will continue tomorrow.
 * __ Thursday, January 7 __ **** __, 2016 __ **

Today, we continued to work on inverse trig functions and compositions of trig functions. We worked on a number of practice problems, and looked at the properties of compositions of trig functions and inverse trig functions, as well as the compositions done in the opposite order. Students then worked in pairs on more review problems.
 * __ Wednesday, January 6, 2016 __ **

Today, we continued to work on inverse trig functions. We reviewed how to evaluate inverse trig functions for different input values, using special right triangles or the unit circle. We also looked at a few examples of how to evaluate the compositions of inverse trig functions and trig functions. We will continue with more of these compositions tomorrow.
 * __ Tuesday, January 5, 2016 __ **

Today, we began to look at inverse trig functions. We talked about the definitions of inverse trig functions - finding the angle (in radians) that corresponds to a given value for sine, cosine, or tangent. Then, we looked at the rules for finding inverse sine, cosine, and tangent for different inputs - both negative and positive - and worked on a number of examples. We will continue with more on inverse trig functions tomorrow.
 * __ Monday, January 4, 2016 __ **

Today, we worked on review problems on radians and degrees, trig functions from triangles, special right triangles, and trig functions of circular angles. We looked at a few problems together, and then students worked in groups on a number of other review problems.
 * __ Wednesday, December 23, 2015 __ **

Today, we had a quiz on converting between radians and degrees, trig functions from triangles, special right triangles, and trig functions of circular angles. We will continue with more on trigonometry tomorrow.
 * __ Tuesday, December 22, 2015 __ **

Today, we had one more review day on converting between radians and degrees, trig functions from triangles, special right triangles, and trig functions of circular angles. We will have a quiz on these topics (sections 4.1-4.3) tomorrow.
 * __ Monday, December 21, 2015 __ **

Today, we had a review day to practice with converting between radians and degrees, trig functions from triangles, special right triangles, and trig functions of circular angles. We will have one more review day on Monday and will have a quiz on these topics (sections 4.1-4.3) on Tuesday.
 * __ Friday, December 18, 2015 __ **

Today, we reviewed how to find the values of trig functions for circular angles, using reference angles, the values from the 30-60-90 and 45-45-90 triangles, and the signs of the quadrants. Students then worked on filling out the Unit Circle, which is a compact way of representing the values of sine and cosine for all of the the important angles, including 0, 90, 180, and 270 degrees. Tomorrow and Monday, we will review the topics related to Trigonometry that we have learned so far. We will then have a quiz on these topics on Tuesday.
 * __ Thursday, December 17, 2015 __ **

Today, we reviewed how to find the values of trig functions using 30-60-90 and 45-45-90 triangles. We then began to look at circular angles, which are used to represent angles larger than 90 degrees and negative angles. We talked about how to find the values of trig functions for these angles, using the values from 30-60-90 and 45-45-90 along with the signs of the quadrants.
 * __ Wednesday, December 16, 2015 __ **

Today, we continued to look at trig functions of right triangles. We also began to look at trig functions of two special right triangles - the 30-60-90 and 45-45-90 triangles - as well as exploring some of the values of the different trig functions of these angles (given in radians or degrees). We will continue with more on trig functions - including applying them to circular angles - tomorrow.
 * __ Tuesday, December 15, 2015 __ **

Today, we began a new unit on Trigonometry. We talked about the definition of Trigonometry and what students already knew about it. We then looked at the two ways used to measure angles - radians and degrees - and how to convert between them. We also looked at the definitions of the six basic trig functions and how to find their values from a given triangle. We will continue with more on Trigonometry tomorrow.
 * __ Monday, December 14, 2015 __ **

Today, we had a test on Chapter 2 - properties and graphs of polynomials, properties of rational functions, and solving rational equations.
 * __ Friday, December 11, 2015 __ **

Today, we had a review day on the topics we have learned in Chapter 2 - including properties and graphs of polynomials, properties of rational functions, and solving rational equations. We will have a test on these topics tomorrow.
 * __ Thursday, December 10, 2015 __ **

Today, we reviewed a few more examples of solving rational equations. Students then began to work on a review worksheet to practice the topics we have learned in Chapter 2 - including properties and graphs of polynomials, properties of rational functions, and solving rational equations. We will have a review day tomorrow and will have a test on these topics on Friday.
 * __ Wednesday, December 9, 2015 __ **

Today, we began to look at solving rational equations. We talked about the steps for solving these types of equations, by first multiplying by the LCD of each fraction in the problem. We also talked about the importance of checking solutions to these problems, and looked at a few examples. We will continue with solving more rational equations tomorrow.
 * __ Tuesday, December 8, 2015 __ **

Today, we took a quiz on the properties of rational functions - including domain, x-intercepts, vertical asymptotes, holes, horizontal asymptotes, and y-intercepts - and on writing rational functions from given properties. We will begin to look at solving rational equations next week.
 * __ Friday, December 4, 2015 __ **

Today, we had one more review day on rational functions - finding x-intercepts, vertical asymptotes, holes, horizontal asymptotes, and y-intercepts and using given information to write an equation of a rational function. We will have a quiz on these topics tomorrow.
 * __ Thursday, December 3, 2015 __ **

Today, we had a review day on rational functions - finding x-intercepts, vertical asymptotes, holes, horizontal asymptotes, and y-intercepts and using given information to write an equation of a rational function. We will have another review day tomorrow and will have a quiz on these topics on Friday.
 * __ Wednesday, December 2, 2015 __ **

Today, we continued to review the properties of rational functions - x-intercepts, vertical asymptotes, holes, horizontal asymptotes, and y-intercepts - and how to use given information about properties of rational functions to write an equation of a rational function. We will review rational functions tomorrow and Thursday and will have a quiz on these topics on Friday.
 * __ Tuesday, December 1, 2015 __ **

Today, we reviewed how to find different properties of rational functions - x-intercepts, vertical asymptotes, holes, horizontal asymptotes, and y-intercepts. We then looked at how to use given information about properties of rational functions to write an equation of a rational function. We will continue with more writing rational functions tomorrow.
 * __ Monday, November 30, 2015 __ **

Today, we reviewed how to find horizontal asymptotes and y-intercepts for rational functions. We then briefly looked at how to use given information about properties of rational functions to write an equation of a rational function. We will continue with more on rational functions next week.
 * __ Wednesday, November 25, 2015 __ **

Today, we reviewed how to find x-intercepts, vertical asymptotes, and holes of a rational function. We then looked at how to use the degrees of the numerator and the denominator to find the horizontal asymptote (if any) of a rational function, and how to find the y-intercept of a rational function. We will continue with more on rational functions and limits tomorrow.
 * __ Tuesday, November 24, 2015 __ **

Today, we began to look at rational functions. We talked about the definition of a rational function and looked at examples of graphs of rational functions. We talked about the important properties of these graphs - including x-intercepts, y-intercepts, vertical asymptotes, holes, and horizontal asymptotes - and began to look at how the zeroes of the numerator and denominator can tell us some of these properties. We will continue with more on rational functions tomorrow.
 * __ Monday, November 23, 2015 __ **

Today, we took a quiz on graphing polynomials - finding degree and leading coefficient, end behavior, zeroes, and multiplicity. Next week, we will start to look at rational functions.
 * __ Friday, November 20, 2015 __ **

Today, we had one more day of review on graphing polynomials - finding degree and leading coefficient, end behavior, zeroes, and multiplicity. We will have a quiz on graphing polynomials tomorrow.
 * __ Thursday, November 19, 2015 __ **

Today, we continued to review the steps for graphing polynomials - including finding degree and leading coefficient, end behavior, zeroes, and multiplicity. We will have one more day of review tomorrow and will have a quiz on graphing polynomials on Friday.
 * __ Wednesday, November 18, 2015 __ **

Today, we reviewed how to find the end behavior of a polynomial and how to find the zeroes and multiplicity using factoring. We then looked at the steps for graphing polynomials, and worked on a number of different examples. We will continue with more graphing polynomials tomorrow.
 * __ Tuesday, November 17, 2015 __ **

Today, we continued to look at graphs of polynomial functions. We reviewed how to find the degree, leading coefficient, and end behavior. We then looked at how to factor third and fourth degree polynomials to find the zeroes, and how to sketch the graph of the polynomial once we have the factored form. We will continue with more graphing tomorrow.
 * __ Monday, November 16, 2015 __ **

Today, we continued to look at polynomial functions. We reviewed how to find the degree and leading coefficient, and also talked about how to describe the end behavior using limit notation. We also began to talk about how to factor a cubic polynomial to find the zeroes. We will continue with more factoring and zeroes on Monday.
 * __ Friday, November 13, 2015 __ **

Today, we began to look at polynomial functions. We talked about a number of vocabulary terms used for polynomials. We also looked at the number of zeroes and extrema that a polynomial will have, based on its degree. Finally, we looked at how to describe the end behavior of a polynomial, based on its degree and leading coefficient.
 * __ Thursday, November 12, 2015 __ **

Today, we had a quiz on transformations of functions and quadratic functions - finding the vertex and zeroes of a quadratic function and graphing, as well as applications of quadratic functions to Physics and Geometry. Tomorrow, we will begin to look at polynomial functions.
 * __ Tuesday, November 10, 2015 __ **

Today, we worked on review problems for topics related to transformations of functions and quadratic functions - finding the vertex and zeroes of a quadratic function and graphing, as well as applications of quadratic functions to Physics and Geometry. We will have a quiz on these topics tomorrow.
 * __ Monday, November 9, 2015 __ **

Today, students continued to work on applications of quadratic functions - including solving projectile motion problems and area problems. We then reviewed a few of these examples as a class. We will have a review of transformations of graphs, graphing quadratic functions and their applications on Monday, and will have a quiz on Tuesday.
 * __ Friday, November 6, 2015 __ **

Today, we continued to work with quadratic functions. We reviewed how to graph quadratic functions, and then began to look at different applications of quadratic functions. We looked at examples of how quadratic functions can be used to solve projectile motion problems, like those that come up in Physics. We will continue with more applications of quadratic functions tomorrow.
 * __ Thursday, November 5, 2015 __ **

Today, we continued to review graphing quadratic functions. We worked on review problems for how to find the zeroes (using factoring, illegal move, square roots, or quadratic formula) and how to find the vertex, and then how to use these to sketch a graph of the quadratic function. We will continue with more on quadratic functions tomorrow.
 * __ Wednesday, November 4, 2015 __ **

Today, we continued to look at graphing quadratic functions. We talked about different methods for finding the zeroes and vertex of a quadratic function, and then how to use these to sketch the graph of the function. We looked at a number of examples of how to use these different strategies (factoring, illegal move, square roots, quadratic formula).
 * __ Monday, November 2, 2015 __ **

Today, we began a new unit on quadratic and polynomial functions. We reviewed how to factor quadratic expressions, and then talked about what the graph of a quadratic function would look like, and how you would graph it by hand. We will look at the detailed steps for graphing quadratic functions by hand on Monday.
 * __ Friday, October 30, 2015 __ **

Today, we reviewed how to identify the transformations of a function from a basic function and then sketch its graph - working on examples with quadratic functions. We then worked on writing the equation of a function based on its graph and transformations from the basic function. We also began to look at how to graph more general forms of quadratic functions. We will continue with more graphs of quadratic functions tomorrow.
 * __ Thursday, October 29, 2015 __ **

Today, we continued to work on transformations of functions. We reviewed how to identify the transformations of a function from a basic function and then sketch its graph - working on examples with square root and absolute value. We then worked on writing the equation of a function based on its graph and transformations from the basic function.
 * __ Wednesday, October 28, 2015 __ **

Today, we began to look at transformations of functions - including vertical and horizontal shifts and reflections. We started by looking at how changes to the square root function change the graph. We then talked about what kinds of changes to a function (in general) result in transformations, and what this does to the graph of the function. We also worked on using the transformations to graph the functions by hand.
 * __ Tuesday, October 27, 2015 __ **

Today, we had a quiz on combining functions algebraically, composition of functions and domain, inverses of functions, and confirming inverses with composition. Students then briefly worked on an activity to preview transformations, which we will look at tomorrow.
 * __ Monday, October 26, 2015 __ **

Today, we had another day of review on compositions and inverses. We looked at examples of how to find the inverse of a function and its domain, as well as an example of finding compositions of functions and their domains. We also reviewed the solutions to our classwork problems from yesterday. We will have a quiz on compositions of functions, inverses, and domains on Monday.
 * __ Friday, October 23, 2015 __ **

Today, we reviewed how to check if two functions are inverses using composition. Students then worked on review problems for finding algebraic combinations or compositions of functions, finding domains, finding inverses of functions, and verifying inverses using composition. We will have another review day tomorrow and will have a quiz on these topics on Monday.
 * __ Thursday, October 22, 2015 __ **

Today, we reviewed how to find the inverse of a function algebraically. We also talked about how to find the domain and range of an inverse function, and how these are related to the domain and range of the original function. Finally, we looked at how composition can be used to verify whether or not two functions are inverses. We will continue with more on inverse functions tomorrow.
 * __ Wednesday, October 21, 2015 __ **

Today, we completed one more review problem on compositions of functions. We then began to look at inverse functions. We talked about two different ways to find the inverse of a function, and what the inverse means, as well as how to find the domain and range of the inverse. We will continue with more on inverses tomorrow.
 * __ Tuesday, October 20, 2015 __ **

Today, we had one more day of review on the composition of two functions, how to evaluate the composition, and how to find the domain of the composition. We worked on the warm-up and a few more examples together as a class. Students then worked in groups on more review problems to further practice this concept.
 * __ Monday, October 19, 2015 __ **

Today, we continued to work on composition of functions. We looked at more examples of how to find the composition and its domain and one example of how to decompose a composition of two functions. Students then worked in groups on review problems to practice the different ways of combining functions. We will continue with more on functions next week.
 * __ Friday, October 16, 2015 __ **

Today, we reviewed how to create a new function from two different functions by dividing them, and how to then find the domain of this new function. We then talked about another way to create a new function from two other functions - composition. We looked at examples of finding the composition of two functions and then finding the domain of this new function. We also looked at examples of finding the composition evaluated at different values. We will continue with more composition tomorrow.
 * __ Thursday, October 15, 2015 __ **

Today, we continued to look at more operations with functions. We talked about how functions can be combined together to form new functions - using addition, subtraction, multiplication, or division - and how to find the domain of these new functions.
 * __ Tuesday, October 13, 2015 __ **

Today, we took a quiz on sections 1.2 and 1.3 - domain and range, increasing/decreasing functions, local max/min, symmetry, and the 12 basic functions. We will continue with more on functions next week.
 * __ Friday, October 9, 2015 __ **

Today, we reviewed a number of the properties of the 12 basic functions. Students then worked on review problems to prepare for tomorrow's quiz - on domain and range, increasing/decreasing functions, local max/min, symmetry, and the 12 basic functions.
 * __ Thursday, October 8, 2015 __ **

Today, we reviewed how to determine if a function is even, odd, or neither. Students then finished creating their "flash cards" for the 12 Basic Functions and then worked in groups to answer a number of questions about the properties of these functions. We will continue to review the functions and the basic properties of functions tomorrow, and will have a quiz on these topics on Friday.
 * __ Wednesday, October 7, 2015 __ **

Today, we reviewed how to find the domain and range of a polynomial, and how to use the graph of a function on a calculator to find the local maxima and minima, as well the intervals on which a function is increasing or decreasing. We then looked at one more important property of functions - symmetry. We then began to create "flash cards" for the 12 Basic Functions we will study throughout the year, which we will continue tomorrow.
 * __ Tuesday, October 6, 2015 __ **

Today, we continued to look at different properties of functions. Students graphed functions on the calculator and we focused on the key properties - including continuity, intervals of increasing and decreasing, and local maxima and minima. We will continue with more properties of functions tomorrow.
 * __ Monday, October 5, 2015 __ **

Today, we reviewed how to find the domain and range of different functions. We then looked at how to use a table of values for a function to sketch the graph, and then how to use the graph to find the range of a function. Students worked on an activity in groups to practice finding the range this way. We will continue with more properties of functions next week.
 * __ Friday, October 2, 2015 __ **

Today, we reviewed how to find the domain of a function and how to evaluate a function for a given value. We then began to look at the range of a function, and talked about two different ways to find the range - using the domain and using a graph. We worked on a number of examples of different types of functions. We will continue with more on domain and range next week.
 * __ Thursday, October 1, 2015 __ **

Today, we began a new unit (chapter 1 in the textbook) in which we will explore different properties of functions. We talked about the definition of a function, how to evaluate a function, and what the "domain" of a function means. We then looked at examples of different functions and how to find their domains.
 * __ Wednesday, September 30, 2015 __ **

Today, we took a quiz on the first unit - including interval and inequality notation, properties of exponents, solving linear equations, solving linear inequalities, and slope-intercept form equations. Tomorrow, we will begin to look at functions and their properties.
 * __ Tuesday, September 29, 2015 __ **

Today, we reviewed how to find the slope-intercept form equation of a line given a line parallel or perpendicular to it. Then, students worked on review problems to prepare for next Tuesday's quiz - which will cover interval and inequality notation, properties of exponents, solving linear equations, solving linear inequalities, and slope-intercept form equations.
 * __ Tuesday, September 22, 2015 __ **

Today, we reviewed how to find the slope-intercept form equation of a line given different information. We also talked about parallel and perpendicular lines, and talked about how to find the slope-intercept form equations of a line, given a line that is parallel or perpendicular to it. We will have a review day tomorrow for all of the topics we have learned so far, and will have a quiz next Monday.
 * __ Monday, September 21, 2015 __ **

Today, we reviewed one more example of solving an equation involving fractions. We then began to look at how to find the slope-intercept form equation of a line and graph it. We looked at examples of how to do this when given different information. We will continue with more on graphing linear equations next week.
 * __ Friday, September 18, 2015 __ **

Today, we reviewed how to solve linear equations, linear inequalities, and compound inequalities. We worked on a number of examples of solving these types of multistep equations and inequalities, including those involving fractions. We will look at graphing linear equations tomorrow and Monday.
 * __ Thursday, September 17, 2015 __ **

Today, we continued to work on practice problems related to properties of exponents. We reviewed how to convert between exponential and radical form, as well as how to simplify expressions involving exponents. We also looked at more complex examples that combined multiple rules in one problem.
 * __ Wednesday, September 16, 2015 __ **

Today, we reviewed how to simplify expressions using the properties of exponents. We then talked about the meaning of fractional exponents, and how these are related to roots. We looked at how to convert between exponential form and radical from when dealing with fractional exponents, and worked on a number of examples of this.
 * __ Friday, September 11, 2015 __ **

Today, we reviewed how to convert between interval and inequality notation, as well as how to describe and graph intervals of real numbers. We then looked at some different properties of exponents, and worked on practice problems for simplifying expressions using the properties of exponents.
 * __ Thursday, September 10, 2015 __ **

Today, we began to look at different ways to represent intervals of real numbers. We reviewed how to graph linear inequalities on a number line. We then introduced interval notation, and talked about how to convert between inequality and interval notation, as well as how to graph and describe intervals from either notation.
 * __ Wednesday, September 9, 2015 __ **

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.
 * __ Tuesday, September 8, 2015 __ **