This product contains 50 trigonometric expressions with their detailed typed solutions. The problems are separated into five groups/quizzes. EACH GROUP of expressions REQUIRES APPLYING OF SPECIFIED IDENTITIES to be simplified as follows: • The fundamental Pythagorean identity • Quotient identities • Reciprocal identities • Pythagorean identities • Co-function identities The problems have varying degrees of difficulty. The product can be divided into parts and used in a variety of ways: in class practice (teacher can show the solutions to some of the examples to assist students in completing the rest successfully) as partner activity or group activity (students can assist one another throughout simplifying the expressions) an assessment or homework Student recording sheets are provided and full solutions to the problems as well.

In this activity, students will practice solving rational equations resulting in linear and 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 equations have only rational roots. The problems have a varying degree of difficulty. Activity Directions: There are 20 problems total, separated into two sets. Partners start solving their own set of ten equations by the most appropriate method and check for extraneous solutions. They must determine the common root between each two partners’ corresponding equations. ( For instance, the equations (1a) and (1b) are corresponding and have one common root, similarly the equations (2a) and (2b)… ). Partners record their answers and mark the common roots in a table given OR they record each common root in the area of each pair of intersecting ellipses on a figure given. Student recording sheets are provided for partners to show all work. An answer key is included.

This activity is designed to be used for groups of 4 members! It practices solving quadratic equations by factoring. The most of the equations have one or two terms on the right side and need to be reduced in their standard form. The leading coefficient is 1. Solutions are only integers. Activity Directions: Partners will each have their own set of 8 quadratic equations. They start solving and write down the solutions of the problems on the recording sheet provided. Then students look for the answers they have found on the “skittles board” – set of “pairs of skittles” given with numbers on them. They will find that all their solution sets are written on these pairs. Each player must cross out or mark the pairs of skittles which represent the solution sets of his equations. The group which has solved all the equations correctly and has “knocked down all the skittles” first, wins. Answer keys are included.

This activity practices solving incomplete quadratic equations by taking square roots. Almost all of the equations are in standard form. Solutions are rational (integers and fractions) and irrational numbers. The fun part is finding an idiom corresponding to each solution sets of the partners’ quadratic equations labeled with one and the same small alphabetic letter. Activity Directions: Students start solving their own set of twelve equations by the square root method. They are given tables to use. Using table 2, each partner finds which two words correspond to each solution set of his equations. At last partners together rearrange the words corresponding to their equations labeled with one and the same small alphabetic letter and find out an idiom. They find out 12 different idioms and write them in table 3. Answer keys are included.

This activity practices solving quadratic equations. The half of the equations are in standard form and set to zero and the other half have one term on the right side of the equation. There are also included incomplete quadratic equations. Solutions are only rational numbers. Activity Directions: Partners will each have their own set of 8 quadratic equations. They solve the first four of them by factoring and the rest – by the most appropriate method they choose. Then they search for the numbers they have found on the “balloons board” - a set of balloons given with numbers and words on them. When students find their answers written on some of the balloons, they “burst”(strike-through) it. The word written on this balloon is eliminated too. Partners continue solving still that way and at last they will have some balloons “survived” inseparably with the words written on them. They arrange all these words to make a proverb. I have designed THREE DIFFERENT VARIANTS of “balloon boards” so the groups playing different versions to find out other proverbs.(The problems are the same.) All answer keys are included. I hope your students enjoy “eliminating balloons” and searching for wisdom sayings.

This resource contains total of 16 limits at infinity. Students will apply the properties of limits to evaluate the limits algebraically. The packet has 2 worksheets: ⟐ The first worksheet has the students solving 8 limits of rational functions. ⟐ The second worksheet is solving 8 limits of functions involving radicals. The worksheets can be used as an extra practice / enrichment, an assessment or homework assignment. It can be also used as a partner activity – for instance 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.

This activity is designed to be used for groups of 4 or 2 members. It practices solving radical equations, resulting in quadratics. The radical equations contain: quadratic function under a radical symbol a radical expression on one side of the equation and a number or/and linear function on the other side radical expressions on the both sides of the equations (“radical equals radical”) All the equations are set up to square both sides and require squaring once. Extraneous solutions are possible. This group activity focuses on matching cards to their matching mini – cards. Activity Directions: Partners are given two sets of different types radical equations (16 cards total). Each card contains two radical equations. Each member of a group chooses two or four cards of each set. The partners of a group look for their answers on 32 mini- cards given. They match each card to its two matching mini- cards. Students record their findings in tables on a group response sheet and show work on student recording sheets provided (solutions to the problems and verifying the solutions). This activity could be turned into competition between the groups. The first team that successfully completes all wins. Answer keys are included.

This activity practices computing FINITE limits (a total of 12 various examples) involving rational functions, radicals and trigonometric functions. Students will apply the properties of limits and evaluate the limits algebraically by factoring, conjugate and substitution methods. They will also need to use some basic trig limits. The limits in this activity can all be found without L’Hopital’s rule. Activity Directions: Students have to compute 12 limits. They are asked to use a table given to find the mathematician’s name corresponding to each of their answers. If students find all the limits correctly, they will learn the names of mathematicians involved in calculus. All answer keys are included.

In this activity students will practice solving radical equations with one and two radical terms resulting in quadratics. The radical equations contain: a monomial, a binomial and a trinomial under a radical symbol one and/or two radical expressions on one side of the equation and a monomial or a binomial on the other side radical expressions on the both sides of the equations (“radical equals radical”) Half of the equations require squaring once and the other half – squaring twice. Extraneous solutions are purposely NOT included, however partners will need to check their answers. The enjoyable part of this product is creating compound words corresponding to each solution set of the quadratic equations given. Activity Directions: Partners start solving their own set of twelve equations. (They have similar type of problems so they will meet similar difficulties). 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 quadratic equation and write down the compound word corresponding to it in table 2 . Students show down detailed solutions on student recording sheets specially designed for this activity. Answer keys are provided.

This activity practices solving logarithmic equations (24 problems) using the properties of logarithms: • Zero- Exponent Rule • Product Rule • Quotient Rule • Power Rule • One - To - One Property Some of the equations need to be transformed from the logarithmic to exponential form. All of the equations result in quadratics. Extraneous solutions are NOT included, however students must check answers or determine the domain of the respective logarithmic functions. Common logarithms are included. The amusing part of this product is creating compound words corresponding to each solution set of the quadratic equations given. Activity Directions: Partners start solving their own set of twelve equations. (They have similar type of problems so to meet similar difficulties). 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 quadratic equation and write down the compound word corresponding to it in table 2 . Students show down detailed solutions on student recording sheets specially designed for this activity. Answer keys are provided.

This is a challenging activity to promote students thought, creativity and discovery. The product can be used for groups of 4 members or as an individual practice (4 different versions included). Students will practice solving quadratic equations with rational and irrational coefficients having only irrational solutions. Some of the equations are in standard form and the other have one term on the right side of the equation. Each quadratic equation must be solved by a specified method - completing the square or the quadratic formula. There are problems included, where students need to • rationalize denominators containing radicals • find the square of a sum or a difference between rational and irrational numbers • find the common root between two equations Hints are included to help students check if their ”pretty” answers are correct. If this resource is used for group work, there is a group response sheet specially provided. There partners are instructed to calculate the sum or/and product of all their answers to corresponding problems. They record their findings, surprised to discover that their collective answers are “pretty” numbers too. A recording worksheet is included for students to show work. All answer keys are included.

This quiz game is designed to be used for groups of 4, 3 or 2 members. Students will practice solving rational equations ALL HAVING EXTRANEOUS SOLUTIONS using the most appropriate method for solving . The activity includes monomial, binomial, and trinomial denominators. The problems are well thought out so the partners have similar type of problems. This aims to encourage collaborative team-work. Activity Directions: There are 32 problems total, separated into four sets. Partners start solving their own set of equations and check for extraneous solutions. They “throw” the extraneous solution of each of the equations into its corresponding recycle bin on the “recycle bins board” given by writing the value of the extraneous root on the “falling” into the bin sheet of paper. The group which has thrown away all the extraneous solutions first and solved all the equations properly win. Student show detailed solutions on student recording sheets provided for this activity. All answer keys are provided as well.

This activity practices solving complete quadratic equations with complex solutions by completing the square and by the quadratic formula. All the equations have terms on both sides. Partners have similar type of problems so as to meet similar difficulties. They will each have their own set of twelve equations which must be solved by a specified method. The amusing part of this product is creating compound words corresponding to the solution sets of the quadratic equations given. Activity Directions: Partners are instructed to solve half of their problems by completing the square and the other half – by the quadratic formula. Using a table given, they find which two words correspond to the solution set of each of their equations and make compound words. They record their findings in another table provided. Students show detailed solutions on student recording sheets specially designed for this activity or they can solve the problems on a separate sheet of notebook paper. Answer keys are included. I hope your students enjoy this activity.

This activity is a perfect way to challenge your advanced learners on topic quadratic equations. It contains more complex problems, much more engaging than the ordinary one. Students will practice solving quadratic equations with rational coefficients having only rational solutions. Each quadratic equation must be solved by a specified method. There are problems included, where students need to compute • the sum and product of the roots of two equations • the absolute value of the sum and difference of the roots of an equation • the sum of the squares and cubes of the roots of a quadratic equation Hints ( formulae) are provided to help students check their ”pretty” answers.

This group activity practices solving quadratic equations by factoring. The half of the quadratic equations are in standard form and the other half of them have terms on both sides. The accent is put on finding a common root between two and more equations. The fun part is finding out the configurations of two hidden constellations. Activity Directions: Students will each have their own set of two groups of seven equations. The first group of equations are labeled with big Latin letters and the second group – with small Latin letters. All the equations with one and the same letter have a common root. Partners solve, compare their answers and determine the common root for each group of equations. They record their answers in a table provided on a group response sheet and mark the common root between equations A, then – between equations B and etc. Students are also given a figure with circled numbers called “stars”. Some of these “stars” form configurations of two constellations. The “stars” of the first constellation are numbered with the values of common roots of the equations, labeled with big Latin letters. Respectively, the “stars” of the second constellation are numbered with the values of the common roots of the equations, labeled with small Latin letters. Once students have determined the common roots, they look for their values on the figure and connect the stars with straight lines in a given order so they can find the configurations of the two hidden constellations. At last partners try to identify which are the constellations (Ursa Major and Ursa Minor). Recording worksheets are provided for students to show work. All answer keys are included as well. THIS ACTIVITY CAN BE DIVIDED INTO TWO PARTS!

This product is designed to be used for groups of 2, 3 and/or 4 members. The activity practices solving simple exponential equations with different bases without using square roots and logarithms. All the equations are of type “Exponential function = Counting Number ” and the base of the exponential function is a counting number too. All the equations result in linear. Activity Directions: Partners will each have their own set of 12 exponential equations. They start solving and write down the solutions of the problems on the recording sheet provided or on a separate sheet of paper. Then students look for the numbers they have found on the “keyholes board” - a set of keyholes given with numbers on them. They find some of their answers written on the keyholes, so that way they get the correct keys to “unlock” them. Partners mark the “unlocked keyholes” on the board. They record which are the “unlocked keyholes” and count them. Partners show the teacher their results. The group which is ready first and who has worked correctly wins. All answer keys are included. Here is the link for Level 2 of this activity: https://www.tes.com/teaching-resource/resource-12627193

Students will practice solving rational equations reducible to linear by cross multiplication with this activity. (The types of the problems are described in details in the preview file. All coefficients and almost all of the solutions are integers). Activity Directions: Students work in groups of 4. There are a total of 32 problems. Each member of a group will work through 8 rational equations, where half of them are marked with a flower drawing and the other half are marked with a ball drawing. The flowers and the balls of each partner of a group are colored in one and the same color. Students solve all the problems. They find their answers on a picture of a meadow given and draw a flower or a ball on this picture around their answers. Then they colorize them with the respective color. For instance, if a number on the picture is the solution of an equation marked with a red ball, the student will draw a ball around this number and will colorize it in red. The sum of the answers of each partner is zero. Students recording sheets are specially designed and provided for this activity. All answer keys are included. This activity is engaging and at the same time relaxing. I hope your students enjoy it. NOTE: You will need a** colored printer** to use this activity!

This resource includes multiple-angle trigonometric equations for your students to solve on the interval [0, 2π). There are four sections, each containing three different equations. The equations included in each section involve respectively double, triple, half and quadruple angle. No identities are required other than the reciprocals of the six basic trigonometric functions. Students will only need to use algebraic manipulations to isolate the trigonometric function on one side of the equation. Activity Directions: There are given three equations and a set of radians in each section. Students start solving the equations on the specified interval. Then they must determine which one of the equations has the given set as its own private solutions. The possible answers are – one, two or not even one of the equations has the given set as its own private solutions. This activity can be used as individual practice or in a small group. It can be used as an assessment as well. An answer key is included.

The activity contains more challenging problems on different types of trigonometric equations. Students will practice solving trigonometric equations by factoring, the quadratic formula and the square root method. The equations require the use of fundamental trigonometric identities double - and half- angle, angle - sum and - difference, sum - to- product and product - to -sum identities There are four sections, each containing four different equations. Students find the general solutions to each of the equations in a section. Then they must determine which of the equations have a given general solution as their own solution. Thus students find groups of trigonometric equations having a common general solution. This quiz can be used in class practice or as a group activity (groups of 4). It can be used for enrichment/extra practice, review, as an assessment or homework as well. All answer keys are included.

In this activity, students will practice simplifying 24 trigonometric expressions using fundamental identities such as reciprocal identities, quotient identities, Pythagorean identities and cofunction identities. The problems are carefully thought out so that 23 of them have one and the same exact value and ONE HAS NOT THE SAME VALUE AS THE OTHERS. Students simplify and evaluate each of the expressions given. They must find out the different expression. (The problems have varying degrees of difficulty.) The product is designed to be used in class practice, as partner activity, group activity, an assessment or homework. Student recording sheets are provided. SOLUTIONS TO ALL THE PROBLEMS are included.