This activity practices proving and disproving trigonometric identities using • double - anlge formula • half – angle formula • angle - sum and - difference formulas • sum - to - product formulas • product - to - sum formulas The activity aims to stimulate students interest in history of math and physics as well. Students are given a set of 16 cards each with two statements written on it – one statement concerns a fact about famous mathematicians and physicists, and the other is a trigonometric identity. The statements are both true or they are both false. Thus, students are challenged to find one and the same answer to two different type questions. If they already know the answer to the text statement on a card, then they have a hint – to prove or disprove the relevant to it trigonometric identity. In case students don’t know whether the stated as a fact on the card is true, verifying the identity will help them in searching the right answer. After students prove or disprove the trigonometric identities, they sort the cards into two groups - “TRUE” and “FALSE”. Recording sheets are provided for students to show all work. Answer keys and FULL TYPED SOLUTIONS (proofs) to the problems are included. The cards could be used in class practice as a way to check for understanding, a review, cooperative learning, individual practice, partner or group activity, before a quiz on the topic, and more.

In this resource, students will practice solving rational equations reducible to quadratics using three types methods for solving:  Cross Multiplying  Multiplying by the LCD  Factoring to find the LCD This activity includes monomial, binomial, and trinomial denominators. The problems have a varying degree of difficulty. This product was not intended to include extraneous solutions. All the equations have two distinct real solutions (rational and irrational). The amusing part is creating compound words corresponding to each solution set of the rational equations given. Activity Directions: There are 18 problems total, separated into two sets. Partners start solving their own set of three groups of three equations by a specified method and check for extraneous solutions. Once students has found the solution set of each equation, they are given two tables to use. There is a word corresponding to each number written in table 1 . Using this table, students find which two words correspond to each solution set of their equations and make compound words. They record the solution set of each rational equation and the compound word corresponding to it in table 2 . Student recording sheets are specially designed and provided for this activity. Answer keys are included.

This is a challenging practice on solving rational inequalities. On each slide/page there are two inequalities as there are given two questions concerning each inequality. Students solve an inequality and answer the questions related to the inequality typing their answers in empty boxes provided. Questions are like these: “Which are the whole numbers that satisfy the inequality?”,“What is the smallest whole number that satisfies the inequality?”,“How many negative integers satisfy the inequality?” and similar. Students will be able to answer these two questions correctly only if they have solved the respective inequality correctly. The product can be used as independent and extra practice, enrichment and homework assignment. Students can also work in pairs with the slides (student A will solve the one inequality and answer the questions to it and student B will solve the other inequality and answer the other two questions). 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!

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.

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.

Students will practice solving rational equations with these zoo animals themed task cards. On each card/slide/page students are given two equations as they are notified that the one will result in linear equation and the other will result in quadratic equation. Answer keys are included. The product can be used as independent practice, extra practice, partner activity (partner A will solve problems 1A, 2B, 3A, 4B…etc and partner B will solve problems 1B, 2A, 3B, 4A,…etc), homework assignment. *There are not included equations with extraneous solutions. 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!

These are 4 digital aliens themed task cards/slides/pages on rational exponents. There are 8 problems per card/slide/page (a total of 32 challenging problems). The first four problems are writing 4 expressions in exponential form and the last four problems are writing 4 expressions in simplified radical form. The product can be used as an independent practice with 4 different forms or as a group activity (groups of 2 or 4). 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 slides on a page for easy and more economic printing!

This is a Christmas activity for groups of maximum three members on exponent rules (positive and negative powers). There are 8 slides/cards/pages with problems. On each slide/card partners are given three similar problems. Each partner solves one of the problems given on this slide/card. The problems are labeled with large Christmas gingerbread letters. Partners have the opportunity to collaborate and compare results of similar problems with this activity. The problems included require students to use their knowledge of the following exponent rules: *Product of Powers *Power of a Product *Power of a Power *Quotient of Powers *Negative Exponent Rule The problems are challenging and require the knowledge of using more than one exponent rule at once. This activity may turn into a competition between groups to become more fun. The product can be also used in class as independent practice and extra practice. 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 four slides on a page for easy and more economic printing!

This is an engaging and collaborative bunny themed group activity (groups of 2, 3 and/or 4) on solving radical equations. On each page/slide partners are given 4 similar equations to solve. This gives them the opportunity to work together and help each other with methods. There are included equations that result in quadratics and there are equations with extraneous solutions. The problems increase in difficulty with each next slide. Here are the type of the equations included: 1 and 2 slides/pages) Radical = Number (the radicand is linear function) 3 and 4 slides/pages) Radical = Number (the radicand is quadratic function) 5 slide/page) Radical = Radical ( the one radicand is linear and the other radicand is quadratic function) 6 slide/page) Radical = Linear Function (the radicand is quadratic function) 7 and 8 slides/pages) Radical + or - Radical = Number (the radicands are linear functions) This product can be also used for independent practice having 4 different forms, extra practice and homework. 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 practice on solving logarithmic equations. On each slide/page students are given 4 problems as problem A is level 1 problem of type log(base a) f(x)=b, problem B is level 2 problem of type log(base a)f(x)=log(base a)g(x), problem C is level 3 problem - students will need here to add or subtract logarithms with the same bases and use the property alogx=log(x^a), problem D is level 4 problem of type mlog^2(base a)+nlog(base a) +p=0 (logarithmic equation of quadratic type). the pages/slides with problems are 6 and there is else one page/slide with the answer keys. The product can be used as independent practice, group activity, extra practice, enrichment, homework assignment. 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 and self-checking teachers themed practice on exponential and logarithmic equations. The problem pages/slides are eight. On each slide/page students are given one exponential equation to solve for x and one logarithmic equation to solve for y, students are also given a hint - a system with two variables as it is known that the roots of the equations satisfy this system. Students can solve the system or just substitute the values of x and y they have obtained in it to check whether their work is correct. (Each equation and system are thought to have only solution! Some logarithmic equations have extraneous solutions. Systems are linear, nonlinear, consisting of exponential and logarithmic equations and containing radical equations ). There is also a table provided where students can record their answers. Students can work individually or in pairs to complete this activity. Answer key is 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!

These are 6 digital thanksgiving themed task cards on exponential equations. There are 4 problems per card/slide (A, B, C and D problem) as the problems increase in difficulty level. The last problem is an exponential equation of quadratic type ( by the substitution a^x=y it results in quadratic equation). The last two cards/slides contains the most challenging equations. Students can work independently with the cards or in small 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 three slides/cards on a page for easy and more economic printing!

This is an engaging and fun group activity (maximum of 5 members) on multiplying polynomials. The first page/slide is a table as the first column of it are given polynomials from A to G, the first row are given polynomials from H to L (the cell 11 is empty). There is a picture of an animal in each of the other cells. Students have to find the polynomial of each animal finding each of the products AH, BH,…AJ, BJ…,etc. Each member of the group have to find the polynomials of 7 animals (the teacher can chose which to be the animals). I have included one page/slide sample and another page where the teacher to chose the tasks of each member of the group. There is else one page/slide with questions to the group like how many animals have polynomials of third degree and which of the animals have sixth degree polynomials. There are provided empty boxes where students to record their answers. This activity can be also used as independent practice along with homework (the students can find the polynomials of some of the animals and the rest of the problems can be done as homework). 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 matching activity on radical operations with higher indexes (3th, 4th, 5th, 6th, 7th, 8th, 10th and 12th root). The problems are 26 grouped in 3 pages/slides and labeled with celebrate alphabet letters. On the first page/slide students are given 9 problems, students have to find the sum or difference of two radical terms having the same indexes. On the next page/slide (another 9 problems) students have to find the product or quotient of two radical terms with different indexes. And on the last third page/slide students have to simplify 8 radical expressions. Students have to perform more than one operations with the radicals (using distributive property, formulas for square of a sum and square of a difference, product of a sum and difference of the same radical terms). After solving the problems students search for their answers in a table given. They record the letter of each problem in the empty box where is the answer of the problem (matching each problem with its answer). This activity can be completed individually or students can work in groups of 2 or 3. 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 three slides on a page for easy and more economic printing!

This is a fun multiple-choice activity on rationalizing the denominator involving the Greek mythology. There are 10 problem pages/slides as each page/slide contains one problem. Students rationalize the denominator and use their answer to find out which Greek God is on the given picture of the slide. The answer choices are four as a name of a Greek God or Hero corresponds to each answer choice. Answer keys include short information for the Greek Gods which are corresponding to the correct answers. 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 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 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 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 and fun activity on solving trigonometric equations called “Who Did Say This?”. Students are given 12 trigonometric equations to solve. Each problem is “accompanied” by an aphorism. Students can find the answers of the problems on the next page/slide. Each answer of a problem is “accompanied” by the name of the author of the aphorism to the problem. If students solved all the equations correctly they will find who had said each of the twelve aphorisms. Students can draw a numbered oval in the field of the answer they have chosen as correct. Answer key is included. NOTE: This product is created as a Google Slides product. **I have converted it to PDF item here. **

This is a fun matching activity on complex fractions called “What kind of butterfly is this?”. Students are provided with 10 challenging problems as there is one problem given on each page/slide. The number of the problem is the number of a butterfly/moth given on a picture. Students solve the problem and search for its answer in a table. The answer reveals the name of the butterfly numbered with the same number as the problem. Students are instructed to record in the table the number of the problem/butterfly in the row where is its answer and beside the name of the butterfly (to match the problem with its answer). There is also an interesting fact given for each butterfly on each page/slide. This product stimulates student interests in both algebra and zoology. The 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!