This resource contains 24 challenging problems on condensing logarithms. There are given 3 expressions on each task card/slide. The expressions are labeled with Native American boy/Thanksgiving themed large alphabetic letters. The problems increase in difficulty. The last 5 problems are the most difficult and require using the properties log(base 1/a) (b)= - log(base a) (b) and log (base a^n)(b)=1/n log(base a)(b) to be solved. The product can be used as an engaging (thanksgiving) classwork or group activity (groups of 2 and 3). Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has four slides on a page for easy and more economic printing!

This is an engaging teacher themed practice on natural logarithms. There are four problem pages/slides each containing two main tasks A and B. Task A is condensing logarithms - students have to simplify three or four expressions (without and with variables) using the properties of natural logarithms; task B is solving three or four logarithmic equations with natural logarithms and/or exponential equations using natural logarithms (a total of 30 various problems). Students are provided with an empty box below each problem where they can record their answers. Please view the preview to see all the problems included. Students can work independently or in pairs. Answer keys are included (four answer key slides at the end of this document). NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has two slides on a page for easy and more economic printing!

This is an elephant themed maze on solving polynomial equations (3th and 4th degree equations with real and imaginary roots). Students start solving and use each answer to navigate through the maze. Students will need to solve 13 equations properly to complete the maze. Students can draw a line to display their answer path. Students can show their work writing in the table on the second page/slide. Detailed answer keys are included.

These are 10 owl themed task cards each containing 3 similar problems on trigonometric functions, expressions and identities. The first and second cards are finding the value of trig function given the value of another trigonometric function and to which quadrant belongs the angle (from I to IV quadrant), the third card is evaluating trig expressions given the value of the angle(s), the fourth card is evaluating a trig expression given the value of trig function, 5th card is evaluating numerical trig expressions, 6th card is evaluating trig function given the value of another trig function as here co-function identities are involved, 7th card is determining which of given six expressions are positive and which are negative, 8th card is expressing trig expressions in terms of tan(teta), 9th card is simplifying trig expressions and 10th card is proving trig identities. Students need to know Pythagorean, reciprocal, co-function and quotient identities to handle the problems. The resource can be used as a review, group activity (groups of 2 or 3), independent extra practice, homework and even as an assessment (the teacher can chose how many problems and which of the problems the student to solve to check his knowledge and skills). There is included a page where students can record their answers in a table. Answer key is included.

This is an engaging and fun multiple-choice game on trigonometric identities. It consists of 12 problem pages/slides. On each page/slide there is given a trigonometric expression, four answer choices (trig expressions A,B,C and D) as to which correspond the name of breed of rabbit, it is also given a picture of a rabbit. If students determine correctly to which of the fourth expressions in A, B, C and D is equal the given trig expression they will find out what breed is the rabbit on the picture. Students can circle the right answer or record their answers on a separate sheet of paper, they can also show their work on separate sheets of paper. Students need to know Pythagorean identities Quotient identities Co-function identities Reciprocal identities and how to use them in simplifying trig expressions to complete this activity. Answer key is included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has three slides on a page for easy and more economic printing!

This is an engaging thinking kids themed activity on multi-step equations and inequalities having no solutions, all real numbers as solutions and having the same solution. The problem pages/slides are six as each contains five problems. On each page/slide there is a picture of a boy or a girl “saying” that the given equations/inequalities all have no solution or having all real x as solutions or having the same solution. The boy/girl “askes”:“Am I right?” So the students have to solve all the equations/inequalities to check the statement and determine if the boy/girl is right or wrong. There are provided empty boxes where students can record their findings. This activity can be completed independently or in groups of 2. Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has three slides on a page for easy and more economic printing!

This is an engaging sorting activity on limits at infinity. Problem pages/slides are two. On the first page/slide students have 8 limits at infinity of rational functions and a sorting mat with three departments - one is limits at infinity equal to 0, the second is limits at infinity equal to plus/minus infinity and the third department is limits equal to a constant different from zero. Students find the limits and then sort them recording the letters of the limits into their correct place in the sorting mat. On the second page/slide there are given 9 limits at infinity of radical functions and the same sorting mat. A page with a table where students can record their exact answers is also included. Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has two and three slides on a page for easy and more economic printing!

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.

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.

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.

This is an engaging and challenging practice aiming to improve students skills on integration by substitution. There are given total of 12 definite integrals. The integrands are functions involving radicals, rational and exponential functions. For the first 8 problems students are asked to use a given substitution to find an integral. For the next 4 problems students will need to show more flexible thinking as this time they are required to find a suitable substitution to evaluate an integral. The problems require the use of u-substitution, integration by parts and integration by partial fractions and long division. The practice worksheets have room for students to show their work. Answer keys are included.

This is an engaging and challenging practice aiming to improve students skills on integration by substitution. There are given total of 13 integrals. The integrands are functions involving radicals, rational and exponential functions. For the first 8 problems students are asked to use a given substitution to find an integral. For the next 5 problems students will need to show more flexible thinking as this time they are required to find a suitable substitution to evaluate an integral. The problems require the use of u-substitution, integration by parts and integration by partial fractions and long division. Make sure these problems are appropriate for your students - download the preview and look at the thumbnails to see problem examples. The practice worksheets have enough room for students to show their work. Full solutions (handwritten clearly) 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.

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 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 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.

This activity is created for your students to practice their skills with more complicated trig integrals. It contains problems on indefinite integrals of product and ratio of sine and cosine involving powers of sine and cosine. In general, the integrals are of (sin(x))^n(cos(x))^m, where m and n are integers. Students will need to use trigonometric identities (Pythagorean, Power Reduction Identities, Double-Angle Identities), integration by u-substitution, integration by parts along with algebra skills to manipulate the integrands. There are 16 problems for them to complete with room to show work. Students аrе given the answer to each problem with missing coefficients they have to find and insert/fill in. This resource can be used for class work, independent or grouped, HW, enrichment, or an assessment. Answer keys are included.

In this engaging and self-checking activity students will practice integration of trig functions using the following trig substitutions: ▸ t = tan(x/2) ▸ t = sinx or t = cosx ▸ t = tanx There are 12 task cards – recording sheets with space provided for students to show their work. Students have 4 indefinite integrals for each type trig substitution. They are instructed which one trig substitution(s) to apply so to solve the problems easily. After finding the integral, students must fill in the missing function f(x) in a corresponding empty rectangle for the answer given coded at the bottom of the worksheet card. The product can be used as an independent practice or for class work to organize students in cooperative learning groups. It is also great for extra integration practice or enrichment. Answer keys are included. Typed solutions to problems A, D, E and H are provided to be possibly used as a guide. NOTE: There are also included worksheet cards with only the problems given (without answers) so the cards can be used as worksheets, homework assignment and even as an assessment.

This is a collaborative activity to practice evaluating indefinite integrals by using Integration by Parts. It aims to develop and consolidate student’s skills in both integration and differentiation as well. Partners work through 16 sections (or less if preferred) 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 (saving time) 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 answers. A purpose of this activity is to aid learners gain a better understanding of integration. I hope it will be helpful for your calculus students. Typed answer keys are included