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.

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.

These are 6 bee themed task cards/slides to help your students practice finding the sum or difference of radical expressions (square roots only). There are 4 problems per card/slide. The first problem includes two terms, the second problem - two or three terms, the third problem - three or four terms and the fourth problem is a sum or a difference of two or three terms with variable(s). The first and second cards are adding and subtracting radicals having the same radicands (level 1). The third, fourth, fifth and sixth cards include terms with different radicands (level 2). Students have to simplify each term to obtain a radical whose radicand is a prime number or a product of different prime numbers. After students have simplified the radical expressions they start combining the terms having the same radicands. The 6th card contains the most challenging problems. Students can work independently or in pairs. For instance, if students will work in pairs - student A solves the cards 1 and 3, student B solves the cards 2 and 4 as students A and B work together on the rest two cards - 5 and 6) 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!

This is an engaging practice on rational expressions containing 41 problems that vary in difficulty. On page/slide 1 students have to evaluate three rational expressions for the given value of the variable and then to determine the domain of six rational expressions/functions. On page/slide 2 students are given 8 rational expressions to simplify them. On page/slide 3 students add or subtract rational expressions (8 problems), on page/slide 4 students multiply or divide rational expressions ( 8 problems) . On page/slide 5 students simplify more complicated rational expressions performing the indicated operations (4 problems) and at the end students have to prove four statements ( rational equalities). Students are provided empty spaces/boxes where to record their answers. 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 or three slides on a page for easy and more economic printing!

This is an engaging partner activity on adding and subtracting polynomials called “Get the Same Answer”. There are 6 problem pages/slides as each contains two sections/tables. In each section are given 4 polynomials labeled with A,B, C and D. One of the partners has to find A+C for example and the other has to find B+D. Partners will compare their answers to see whether they have obtained one and the same answer. There is provided a box in each section where students can type their answer. The first six sections require sums to be found (like A+D, B+C) and the next six -differences (like A-D,C-B). Thus each partner will work on 6 questions on adding polynomials and 6 questions on subtracting polynomials. The problems in last 2 sections are more challenging as they include polynomials of 5 and 6th degrees. 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 two or three slides on a page for easy and more economic printing!

This is an engaging matching activity on dividing polynomials (no remainders!). On each page/slide students are given 6 problems and 6 answer choices. Students can record the question numbers in the empty squares provided next to the answers to match each problem with its answer. There are a total of 12 problems. Dividends are 3th, 4th and 5th degree polynomials and divisors are 1st, 2nd and 3th degree binomials and trinomials. 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 or three slides on a page for easy and more economic printing!

This is an engaging group activity (for groups of three members) on adding and subtracting polynomials. On each page/slide partners are given three similar examples. The problems are labeled with large animals themed alphabetic letters. On the first page/slide partner A may solve problem A, partner B may solve problem B and partner C - problem C. On the next page/slide partner A will solve problem D, partner B - problem E and partner C will solve problem F, and etc…Partners have the opportunity to collaborate and compare solutions to similar problems. This group activity may turn to competition to become more fun. There are 2 pages/slides on adding polynomials and the next 2 pages/slides are on subtracting polynomials. The last 4 slides contain more challenging problems where students have to perform both operations - adding and subtracting polynomials to simplify the given expression. The activity can be used as classwork and independent practice as well. 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 or three slides on a page for easy and more economic printing!

This is an American birds themed maze on dividing polynomials (no remainders). Students start solving and use each answer to navigate through the maze. Students will need to solve 12 problems properly to complete the maze. Students can draw a (colored) line to display their answer path. It would be nice if students show work on this activity. Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here.

This is an engaging African animals themed activity on classifying polynomials. The pages/slides with problems are five. On each page/slide students are given five polynomials to classify based on degree and number of terms. Students are provided with empty boxes where to record their answers. There are included polynomials from zero to tenth degree with one to five terms. This activity can be completed individually as independent practice, but it is also possible to be used as group activity. The answer keys are contained 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 or three slides on a page for easy and more economic printing!

This is an engaging practice on multiplying binomials. There are 4 pages/slides/4 levels each containing 3 problems. Students have to find the indicated products. Students are provided with empty text boxes where they can record their solutions and answers. There is given a hint for each problem - it is the sum of the coefficients of the polynomial that students have obtained. 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 or three slides on a page for easy and more economic printing!

This is a review activity on operations with polynomials - adding, subtracting, multiplying, dividing and mixed operations. On each page/slide there are given 6 polynomials (on the last slide are given eight) and 8 problems to be solved. (The given polynomials are labeled with large Latin letters). Page/Slide 1 is on adding polynomials, page/slide 2 - on subtracting, page/slide 3 - on multiplying polynomials, page/slide 4 - on dividing and page/slide 5 is on mixed operations with polynomials. Pages with tables where students can record their answers are provided. This activity contains a total of 40 problems and can be used not only as independent practice, but also as a group activity. Two or four members of a group can work on each page/slide as there are four or two problems for each partner to be solved. Answer keys are provided. 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 or three slides on a page for easy and more economic printing!

In this fun multiple- choice activity students will practice solving exponential equations using natural logarithms. There are 13 pages/slides each containing one problem with four optional answers. A picture of a lizard is given on each slide and the name of lizard species corresponds to each optional answer. Students solve the problem on the slide and use the obtained answer to find out what species is the lizard on the picture. 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 two or three slides on a page for easy and more economic printing!

This is an engaging sitting animals themed partner activity on evaluating piecewise functions called “Find My Numbers”. On each page/slide there are given three cards as an “animal sit” on each of them. There are two similar problems on each card, the one problem is for partner A and the other problem is for partner B. Each partner have to find the sum f(a)+f(b) for the cards on pages/slides 1 and 2 and the sum f(a)+f(b)+f© for the cards on page/slide 3. For each card partners will find two numbers which are the numbers of the animal sited on the card. The problem pages/slides are three providing 9 problems for each partner. On pages/slides 1 and 2 the piecewise functions consists of two functions and on page/slide 3 the piecewise functions consists of three functions. The functions included in this activity are only linear and quadratic. On page/slide 4 there is given a table where students can record their findings. 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 or three slides on a page for easy and more economic printing!

In this 24 questions – collaborative partner activity, students are to find the limits of various functions (polynomial, rational, radical, exponential, logarithmic) as x approaches infinity. To determine the limits, students will need to use a combination of techniques. The limits in this activity can all be found without L’Hopital’s rule. Each partner has his own set of 12 problems. Corresponding partners’ problems are thought carefully so that the answer of each of Partner’s A problems is the same as the answer of its corresponding problem of Partner’s B. almost all of them to be similar examples - limits of functions which are of the same type Students are instructed to show all work and check whether their results match. Answer keys are included.

These are 12 challenging practice problems on limits at infinity. Functions included are only exponential, natural logarithms and inverse tangents. The product can be used as independent practice, extra practice, enrichment and homework assignment. The practice sheets have enough room for students to show work. Answer keys are included.

This resource contains total of 20 problems. Students will practice differentiation of common and composite trig functions. The packet has 2 worksheets: ⟐ The first worksheet has the students finding the first derivatives of 10 trig functions using differentiation formulas, the product and quotient rules and the derivatives of the three main trig functions. ⟐ The second worksheet is finding the first derivatives of 10 composite trig functions using the chain rule. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner activity like: ⟡ Partner A will solve WS # 1 while Partner B solves WS # 2, then they swap papers and Partner A will solve WS # 2 while Partner B solves WS # 1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Typed solutions are provided.

This practice worksheet consists of 3 pages and contains 20 problems. Students will practice differentiation of trigonometric functions using the basic properties of derivatives, derivatives of the functions sinx, cox, tanx and cotx, the power, product, quotient and chain rules. There are examples with composite functions where trigonometric function is substituted into exponential and logarithmic functions and examples where exponential function is substituted into trigonometric function. There is one example where the trig function is radicand. Pages 1, 2 and 3 require students to find the first derivative of 17 functions. Page 3 has another 3 problems on finding the equation of the tangent line to a trig function at a given point. Useful for independent /extra practice, enrichment or homework assignment. Typed answer keys are included.

This resource contains a total of 24 problems. Students will practice taking the derivatives of some complicated functions by logarithmic differentiation. The packet has 2 worksheets: ⟐ The first worksheet has the students finding the first derivatives of 12 complicated functions using natural logarithms. ⟐ The second worksheet also contains 12 problems of finding the derivatives by logarithmic differentiation as some of the examples are more complex. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner or group activity – like that: ⟡ Partner A will solve WS #1 (page 1) while Partner B solves WS # 1 (page 2), then they swap papers and Partner A will solve WS #1 (page 2) while Partner B solves WS #1 (page 1). Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Partners continue working through WS # 2 in the same manner with pages 2 and 3 or pages 1 and 2… ⟡ Worksheet # 2 can be used as a group activity ( for groups of 3 as its pages are three and each page contains 4 problems). Full solutions (handwritten clearly) are provided.

This is the second part of my worksheets on Computing Limits. The resource contains total of 16 finite limits. Students will apply the properties of limits and evaluate limits algebraically by substitution, factoring and conjugate methods. The packet has 2 worksheets: ⟐ The first worksheet is solving 8 limits of functions involving radicals (square, cube and fourth roots). ⟐ The second worksheet is solving 8 limits involving functions containing both polynomials and trig expressions or radicals and trig expressions. These problems are more complicated and require using a combination of methods. The worksheets can be used as extra practice, for enrichment, an assessment or homework. It can be also used as a partner activity – like that ⟡ Partner A will solve WS #1 while Partner B solves WS # 2, then they swap papers and Partner A will solve WS #2 while Partner B solves WS #1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. ⟡ Partner A will solve the first four problems of WS # 1 while Partner B solves the rest four problems of the same WS. Then they swap papers and Partner A will compute the last four limits of WS # 1, while Partner B solves the first four problems of WS # 1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Partners continue working in the same way with WS # 2… All answer keys are included.

This resource contains a total of 16 problems. Students will practice taking the first derivatives of y(x) for each of given implicit functions by implicit differentiation. The packet has 2 worksheets each containing 8 various examples including polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions. The worksheets can be used as a class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner activity – like that: ⟡ Partner A will solve WS # 1 while Partner B solves WS # 2 , then they swap papers and Partner A will solve WS # 2 while Partner B solves WS # 1 . Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Typed solutions to all of the problems are provided.