This resource contains total of 73 logarithmic equations of various type and difficulty. Students will apply the properties of logarithms to solve logarithmic equations algebraically. The packet has 3 worksheets: ⟐ The first worksheet has the students solving 23 logarithmic equations using the two primary methods - converting to exponential form and using the one-to-one property (3 pages). ⟐ The second worksheet is solving logarithmic equations by using the Product , Quotient and Power Rules (total of 24 problems, 3 pages) ⟐ The third worksheet has students solving logarithmic equations by using the properties of logarithms and the primary methods in combination (total of 26 problems, 4 pages). It could be used as a review on Logarithmic Equations. Solutions are rational and irrational numbers. There are some problems where students are required to use a calculator to round the answer. Students will need to determine the domain of the logarithmic expressions to check for extraneous solutions and eliminate them. The worksheets can be used as an extra practice, an enrichment, an additional assessment or homework assignment. All answer keys are included.

In this fun Valentine’s themed activity, students will practice simplifying trig expressions using the fundamental Pythagorean, quotient and reciprocal identities. Activity Directions: Students are asked to simplify 12 trig expressions. The corrected equivalent expresssions (the answers) are recorded on twelve of 13 hearts on a given picture. Every time students arrive at a correct answer, they will “win the heart” having this answer written on it. Students are also asked to find the only one heart who can NOT be won. The product can possibly be used as a partner or a group activity(group of 3). Student recording sheets, answer keys and solutions are provided. I hope you and your students ENJOY!

In this lessson, students learn to apply the three most important Pythagorean identites and their variations. The lesson covers the following applications of Pythagorean identities: • Evaluating trigonometric functions • Simplifying trigonometric expressions • Verifying or proving other trigonometric identities It includes o 6 solved examples & 6 similar to them for students to try to solve them by their own o guidelines o 21 various and engaging practice problems o answer keys and full solutions The lesson can be divided into two or three parts if preferred.

This product is designed to be used for groups of 2, 3 and/or 4 members! It practices solving exponential equations with different bases using the properties of exponents and square roots without using logarithms. All the equations are of type “EXPONENTIAL FUNCTION = REAL NUMBER” and result in linear. There are included many examples where the base of the exponential function is a decimal, a fraction or an irrational number/square root. Activity Directions: Partners will each have their own set of 10 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 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 of my version LEVEL 1 of this product. It contains easier exponential equations where the base of the exponential function is a counting number. https://www.tes.com/teaching-resource/resource-12627174

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

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.

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 activity practices solving rational equations reducible to linear by cross multiplication method. The types of equations included are described in details in the preview file. All coefficients and almost all of the solutions of the equations are integers. Activity Directions: In task 1, partners are notified that each pair of their problems (A1, B1), (A2, B2) and the rest have solutions of opposite signs. Students reduce the rational equations to linear using the cross multiplication and solve for the variable. They compare answers with each other to check if they have solved the equations properly. In task 2, partners are given another set of rational equations. This time they must determine the root of which of the equations of one partner is opposite in sign to the root of randomly chosen equation of the other partner. Solving each of their equations ( by cross multiplying ) and comparing the solutions will help partners to find out which pairs of equations have solutions of opposite signs. There is else one extra question. Partners need to find out which of another rational equations given have no solution. Partners response sheet and student recording sheets are specially designed and provided for this activity. All answer keys are included as well.

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.

These tests can be used in Algebra 2 and Regular Pre-Calculus class. The product assesses students on properties of logarithms and solving logarithmic equations. There are included common and natural logarithms. All of the equations can be reduced to a linear or quadratic form. Extraneous solutions are possible so students will need to check answers or determine the domain of the respective logarithmic functions. The resource contains multiple choice questions. Included are two different versions along with FULL typed SOLUTIONS to both (14 problems). A recording sheet is provided as well. I have also included engaging homework with pretty answers (14 problems with answer keys).

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 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.

There are two problems (A and B questions) on each of the 8 cards. Question A is to evaluate a limit analytically and Question B is to prove a limit’s equality. Half of the cards are 8 questions asking students to find the limits of rational and involving radicals functions as x approaches infinity. The other half of the cards contains limits where x approaches a finite number. Students are to find the limits of rational functions, functions involving radicals and trigonometric functions (some of which use the “special Limits" ( sin x /x, (1 - cos x)/ x^2)) . The limits in this activity can all be found without L’Hopital’s rule. The cards can be used as a partner or a group activity or as a review. There is a student recording sheet included. Answer keys are provided.

This is a great activity that practices solving quadratic equations with rational roots. There are included quadratics in standard and vertex form, though more of the equations have terms on both sides. Students are asked to solve the equations by the most appropriate method. Activity Directions: Students solve 12 quadratic equations. They use a given table to find which character (letter, number or sign) corresponds to each of their answers and fill in another table to obtain a funny password. Students tell the password to the teacher. If it is correct, then they have solved all equations right. There are included 4 different versions ( 4 passwords) so this activity can be used as a group activity. Answer keys are included.

This activity practices solving complete quadratic equations by all methods. 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 three groups of six equations which must be solved by a specified method.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 three groups of six equations by a specified method. 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 or they can solve the problems on a separate sheet of notebook paper. All answer keys are provided. You can split this activity into two or three parts!

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.