In this fun Valentine’s themed activity, students will practice evaluating definite integrals using u- substitution. Activity Directions: Students are instructed to evaluate 12 definite integrals using u- substitution. The corrected values are recorded on twelve of 13 hearts on a given picture. Every time students arrive at a correct answer, they will “win the heart” having this answer written on it. Students are also asked to find the only one heart who can NOT be won. The product can possibly be used as a partner or a group activity (group of 2 and 3). Student recording sheets and answer keys are provided. I hope you and your students enjoy! ♡ Happy Valentine’s Day! ♡

This is an engaging practice that investigates infinite limits both graphically and algebraically. Students are asked to graph 8 functions and evaluate 24 limits (right and left-hand limits included) based on these graphs. Then students are asked to prove 11 equalities that is to check whether 11 infinite limits are evaluated correctly. Students are provided with rooms to show work and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem. All the graphs are presented in the answer keys. The resource can be used for class work, as an individual practice or homework assignment.

This product includes 24 integration problems to be solved by u-substitution. Your students can work alone, in pairs, or small groups to complete the problems placed on 12 cards ( there are 2 problems on each card – one indefinite and one definite integral to be evaluated as both integrals have the same integrand). Students recording sheets are provided and created as worksheets so the product can be used for cooperative learning, extra practice, homework assignment or even as an assessment. Typed solutions (appropriate for teachers!) are provided.

This is a complete rigorous lesson on Advanced Techniques of Integration for students enrolled in AP Calculus BC or Calculus 2. ( The resource contains 47 problems - 17 with full typed solutions and 30 with answer keys) Lesson Objective: Find indefinite integrals and evaluating definite integrals using integration by parts. It includes A. Detailed Guided Notes (5 pages) including derivation of Integration by Parts formula and 7 worked out examples with indefinite and definite integrals as 4 examples perform Integration by Parts once 3 examples including repeated Integration by Parts( twice and for third time). The students are guided through the process of picking u, du, v, and dv. B. 20 Classifies Practice Problems ( 10 come with full typed solutions and other 10 are similar to them for students to try their own. Students are given the answers. ) C. 12 Assignment Problems with answer keys ( 6 indefinite and 6 definite integrals ). D. 2 versions Multiple Choice Exit Tickets /Quizzes/ Assessments ( with answer keys)

This is a collaborative and challenging activity to practice evaluating indefinite integrals by using Integration by Parts. It aims to develop and consolidate student’s skills in integration by this special method. Partners work through 8 sections (or less if preferred). Each section contains one integral. Activity Directions: A partner start solving an integral while the other partner is waiting for the answer to integrate it. In the next section, partners take turns and it goes the same way. An alternative way ( I think it is better way) to use this activity: Partner A solves an integral of a section while Partner B solves an integral of the other (the next in line) section. Then they swap papers and each partner integrates the function that his partner has obtained previously. The problems are well thought so the obtained functions after the first integrating can be also integrated by parts! A HINT is provided in each section that gives the sum of the partners’ answers. Answer keys are included. I hope this activity will be stimulating and beneficial for your calculus students.

This product is designed for students to practice integration using the methods of partial fractions and long division. It includes 16 sections each consisting of three related problems. In each section, students are instructed (a) first to use long division to write an improper rational expression as a sum of a polynomial and a proper fraction or/and to express a proper fraction as a sum of partial fractions (b) then to find the indefinite integral whose integrand is the function given in (a) © and at last to evaluate a definite integral having the same integrand as the integrand of the integral given in (b). The first eight sections contain problems that require using of partial fraction decomposition only. The next four sections include problems that require using long division only and in the last four sections students need to use both methods of integration in combination. ◈ One of the examples require using a substitution to be integrated by partial fraction decomposition. The problems include linear factors, quadratics, repeated factors, cubics, and quartics. Full solutions are provided.

In this activity students will evaluate 16 definite integrals using their properties and the following techniques of integration: ► integration by substitutions (u-substitution & trig substitutions) ► integration by parts ► completing the square ► trigonometric integrals & using trig identities ► partial fractions decomposition and long division The resource contains multiple - choice questions - definite integrals to be calculated. Problems range in difficulty as the problems of the second part of the quiz are more complex. Students will need their correct answers to find out the configuration of a hidden constellation. Here’s how: Students are given a figure with shapes of a circle, called “stars”. Sixteen of them are labeled with the correct answers of students’ questions and form the configuration of the constellation Draco. Students connect the “stars” of the constellation with straight lines in a specified sequence. At last, they try to identify the constellation. A recording sheet is included for students to show how the answers are obtained. An answer key is included. The product can be used for class work, independent or grouped (groups of 2 or 4). It could be splitted into two parts. The quiz can be used as an assessment as well.

This is a collaborative activity to practice evaluating indefinite integrals by using their BASIC properties and the table of common integrals. Partners work through 20 sections each containing one integral. Activity Directions: A partner start solving an integral while the other partner is waiting for the answer to check it by differentiating. In the next section, partners take turns and it goes the same way. An alternative way to use this activity: Partner A solves an integral of a section while Partner B solves an integral of the other (the next in line) section. Then they swap papers and differentiate the obtained functions to check each other’s work. If extra practice is needed Partner A and Partner B can change places with each other and continue solving. Applying both integrating and differentiating help students gain a better understanding of integration. I hope it will be beneficial for your calculus students. Answer keys and full solutions (typed and handwritten clearly) are included.

In this fun Valentine’s themed activity, students will practice evaluating definite integrals using the properties of integrals and the table of basic integrals. Activity Directions: Students are instructed to evaluate 12 definite integrals using the table of basic integrals. The corrected values are recorded on twelve of 13 hearts on a given picture. Every time students arrive at a correct answer, they will “win the heart” having this answer written on it. Students are also asked to find the only one heart who can NOT be won. The product can possibly be used as a partner or a group activity (groups of 2 or 3). Student recording sheets and answer keys are provided. I hope you and your students enjoy! ♡ Happy Valentine’s Day! ♡

Students will practice condensing logarithms with this multiple-choice game. On each page there are two problems each in a table. In the table there are given a picture of a parrot, a logarithmic expression that students have to condense and four answer choices. Name of parrot species corresponds to each answer choice. If students solve the problem correctly they will find out what parrot species is this one on the picture. The problem are 12 and vary in difficulty. The distractors are well thought. Answer key is provided.

This resource contains 16 indefinite integrals with their detailed solutions (typed). Students will use Integration by Parts to find the integrals. The packet has 2 worksheets: The first worksheet has the students evaluating 8 indefinite integrals The second worksheet is finding also 8 indefinite integrals as some examples are a bit more challenging.

In this packet you will find 22 practice problems students can use to practice finding the area between curves. Students need to analyze the problems, find the points where the curves intersect (in 8 of the problems), sketch the graph, setup the integral necessary to find the area and to integrate to find the area. The integration involved is basic and using u- substitution. One example requires trig substitution and else one example requires finding a suitable substitution to be solved.There are five problems with trig functions.There is one problem where students will have to divide the problem into two integrals. All examples are with vertical strips. The product is useful for independent/extra practice and homework assignment. Detailed typed answer keys are included.

These are 6 practice/review tickets on indefinite integrals. Each ticket contains 9 various challenging problems. For each ticket there are included one problem or two on the following topics: basic integration integration using u – substitution integration by parts integration using suitable substitution integration by partial fractions decomposition There are included rational, radical, exponential, logarithmic, trigonometric and inverse trigonometric functions. The product can be possibly used as an independent practice/quizzes 6 different forms, as a group activity (groups of 2 to 6 members), homework assignment or assessment. Recording sheet is provided. Answer keys are included.

This is an engaging and collaborative partner activity for analyzing and sketching graphs of polynomial and rational functions using calculus. Students will use limits, first and second derivatives to provide information about function behavior and then sketch the graph of the function. Activity Directions: Students are given five sections to work through. In each section partners are given two functions of the same type to identify their features (intercepts, asymptotes, intervals of increase and decrease, local maximum and minimum points, intervals of concave up and concave down, inflection points). After finding all the important parameters students are asked to draw a graph of the function. ▸The functions of a section differ only by coefficients so partners obtain similar results and graphs with the same shape. Students are provided recording/response sheets with a number of steps of the general algorithm for investigation of functions, rooms to record their results and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem so sketching to become easier. This product can be also used as a group activity, for collaborative learning, for enrichment and extra practice, as independent practice and homework assignment. Detailed typed answer keys are included. All the graphs are drawn as well. BONUS: I have included 4 additional sections for extra practice or enrichment. (These are without answer keys.)

This is an engaging card sort activity for studying the intervals of concavity and inflection points of given functions. The functions (common and composite) include polynomials, radical, exponential, logarithmic, trigonometric and inverse trigonometric expressions. They are specially selected so that each function has not more than one inflection point. Activity Directions: Students determine the intervals of concave up/concave down and the inflection points of each of 12 given functions. They are also given 16 cards each with a statement written on it. The statements concern the concavity and inflection points of the given functions and are true or false. Partners are asked to use their studies on the functions to verify the statements and sort the cards into two groups - “TRUE” and “FALSE”. Thus students do comparative analysis of the functions. This product can be possibly used as an independent practice, as a partner or a group activity (groups of 3 and 4). Student recording sheet and all answer keys are provided.

This is an engaging and fascinating activity for studying the intervals of concavity of given functions. The functions included are polynomials, rational, radical, exponential, logarithmic and trigonometric. They are specially selected so that each function has more than one points of inflection. If students solve all the 16 problems correctly, they will find out 16 math calculus terms (each consisting of two words). Some of the terms might not be still popular and students will learn them. Activity Directions: Partners are instructed to identify the intervals where 8 functions given concave up and the intervals where another 8 functions concave down. They look for their answers in a given table and search for a math calculus term corresponding to each of their answers(there is a word corresponding to an interval). The problems are written on task cards. This product can be possibly used as an independent practice, as a partner or a group activity (groups of 4). Student recording sheet and answer keys are provided.

These are 6 Christmas themed task or station cards grouped with 10 to 15 similar problems per card. There are a total of 81 carefully chosen problems concerning the following applications of the derivatives: ❄finding critical points (Card A - 15 problems) ❄ determining intervals of increasing and decreasing (Card B - 15 problems) ❄ finding local extrema (Card C - 15 problems) ❄ finding absolute extrema on the specified intervals (Card D - 10 problems) ❄ finding inflection points (Card E - 14 problems) ❄ determining intervals of concavity (Card F - 12 problems) The functions included are rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions). The cards can be used individually or with groups. Student recording sheets are included. Detailed answer keys/solutions (handwritten clearly) are included.

This is a set of three mazes (three versions) to practice solving improper integrals. Students are given 24 integrals. They will need to determine whether some of these integrals are divergent or convergent. If some integral diverges it must be evaluated. Then students use their answers to navigate through the maze. Not all boxes are used in this maze to prevent students from just guessing the correct route. Recording sheets are provided for students to show all work. For extra practice, students can solve all the problems and find out how many of the improper integrals are divergent. (There are 30 different improper integrals in this activity total and 9 of them diverge). Answer keys are included.

In this activity students will practice solving improper integrals. There are two problems (A1 and A2 questions) on each of 8 aliens themed task cards. “An alien asks” two types of questions - question A1 is to evaluate an improper integral if it diverges and question A2 is to prove an improper integral equality. This activity can be used for class work, independent practice, as partner activity or group activity ( groups of 2 or 4). Answer keys and solutions ( handwritten clearly) to problems A1 – H1 are provided.