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 is designed to be used for groups of 4, 3 and/or 2 members. It practices: • solving radical equations with one and two square roots • solving linear and quadratic equations • checking for extraneous solutions The radical equations contain: a monomial and/or a binomial under a radical symbol a radical expression on one side of the equation and a monomial or a binomial on the other side radical expressions on one side and respectively on the both sides of the equations (“radical equals radical”) Most of the equations require rearranging and isolating the radical and the rest are set up to square both sides. All the equations require squaring once. Activity Directions: Partners will each have their own set of eight problems of various difficulty. They reduce them to linear or quadratics and continue solving by any method they choose. Students write down the solutions of the problems on the recording sheet provided. They are instructed to check for extraneous solutions. Partners record their answers in tables on a group response sheet designed in such a way that students can analyze and compare their results easily. They must verify that all equations actually have the same solution except only one which has two distinct roots. I called this special equation “black sheep equation” and it is the equation B8. It can not be simply found without checking for extraneous solutions. All answer keys are provided. I hope your students enjoy searching for the “black sheep” and have fun with this activity.

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 is designed to be used for groups of 4 members! It includes four different multiple - choice quizzes each of eight radical equations and a brief biographical text of NASA research mathematician Katherine Johnson (to be completed). Students will practice solving radical equations reducible to linear and quadratics. Extraneous solutions are included. The radical equations contain: a monomial and/or a binomial under a radical symbol a radical expression 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”) Most of the equations require rearranging and isolating the radical and the rest are set up to square both sides. All the equations require squaring once. Activity Directions: Students solve all the equations. The answers they get will give them pieces of a brief biographic story about the American scientist Katherine Johnson. It can stimulate student interest in Math and provide a role model for all students. Recording sheets are provided for students to show all work. Answer keys are included.

This activity practices solving exponential equations with same base and with different bases without using logarithms. It requires knowledge of the properties of exponents. All exponential equations given are reducible to quadratic equations with two distinct rational roots. Partners have their own set of two groups of equations. The FIRST GROUP contains equations which have exponential expressions with same bases and the SECOND GROUP of equations is more challenging as having exponential expressions with different bases. The amusing part of this activity is creating compound words corresponding to each solution set of the exponential equations given. All answer keys are included. I hope you and your students enjoy this activity.

This activity practices solving incomplete quadratic equations by taking square roots. The equations are in VERTEX FORM. Solutions are rational (integers and fractions) and irrational numbers. The amusing 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 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.

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 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 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) them. The words written on these balloons will be eliminated too. Partners continue solving still that way and at last they will have some balloons “survived” inseparably with the words on them. They can arrange all these words remained to make a proverb. All answer keys are included. I hope your students enjoy “eliminating balloons” and searching for wisdom sayings.

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 product contains 40 trigonometric expressions with their detailed SOLUTIONS. The problems are separated into five groups/quizzes. EACH GROUP OF PROBLEMS REQUIRES APPLYING OF SPECIFIED IDENTITIES TO BE SOLVED as follows: • Double - Angle Identities • Half - Angle Identities • Angle – Sum and - Difference Identities • Sum Identities • Product Identities The problems have varying degrees of difficulty. The product can be divided into parts and used in a variety of ways to aid learners in reasoning and increase their ability to simplify trigonometric expressions: 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.

This is a set of two trigonometry mazes to practice proving and disproving trigonometric identities using the fundamental trigonometric identities ( Pythagorean, reciprocal, quotient identities). Students are given 24 statements. They will need to determine whether some of these statements are true or false, prove or disprove them and 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. Answer keys and FULL SOLUTIONS to the problems are included. This maze could be used as: a way to check for understanding, a review, cooperative learning, homework, individual practice, partner activity, before a quiz on the topic, and more.

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.

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 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.

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.

Students will practice solving trigonometric equations by the square root method with this activity. This includes 12 cards and 12 problems that require students to be skillful at solving basic trigonometric equations. The focus is on finding the primary solutions of a trigonometric equation on the interval (0, 2π]. Activity Directions: Partners work cooperatively to match each equation with its private solutions written on a card. They are instructed to record the equation in the middle of a card presenting its solutions. Then pupils should find cards with equivalent equations. They use the cards to determine three fours of equations having the same private solutions on the interval given and sort the cards into groups. A recording sheet is provided for students to give accountability to the teacher. All answer keys are included.

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.