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 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 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 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 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 exponential equations using natural logarithms. Activity Directions: Students have to solve 12 equations. All correct answers (expressions with natural logarithms) and also incorrect are labeled with big Latin letters and typed in table 1. Students are asked to use this table and table 2 with mathematicians’ names so to find the mathematician’s name corresponding to each of their answers. If students solve all the equations correctly, they will learn 12 mathematicians involved in history of logarithms. This activity can be used as a group activity. Students could compete to see who can get all or most names first. It can be also used as a partner activity as well (each partner will solve 6 problems). Answer keys are provided.

These are three practice worksheets on Parametric Equations and Parametric Curves. Students will work on ✦ eliminating the parameter, writing the parametric equation as a rectangular equation and identifying the graph of the parametric curve ( WS # 1, 14 problems) ✦ finding parametric equations (writing two new sets of parametric equations for given rectangular equations) ( WS # 2, 8 problems) ✦ graphing parametric curves (sketching the parametric curve for given pair of parametric equations and giving the orientation of the curve) (WS # 3, 12 problems) Functions involved are polynomial, absolute value, rational, radical, exponential, logarithmic and trigonometric. I hope that the practice worksheets give your students enough room to show their work. This resource can be possibly used as an independent /extra practice, as an enrichment, homework assignment and even as an assessment. Detailed answer keys ( handwritten clearly) are included.

This fun matching activity allows students to practice applying the exponent rules to 12 challenging expression. The properties of exponents included are: multiplying with same base dividing with same base negative exponents power to a power zero exponents There are given twelve “tickets/cards” each with the face of a cartoon hero – a boy or a girl. The hero „says“ his/her name and „ask“ the student to simplify a given expression, then to use the answer to find what breed is his/her (the hero’s ) favorite dog or cat. Students have one sheet with the pictures of twelve different breeds of dogs and another sheet with the pictures of twelve different breeds of cats. There is an expression corresponding to each picture. 12 of these corresponding to the pictures expressions are the answers. Thus students using the pictures and their answers can find what breed is the favorite dog or cat to each of the twelve cartoon heroes. Students can work in groups of 2 or/and 3. Student recording sheet and answer keys are included. Note: You will need paper size A4 to print this document.

These are three versions (three levels) independent practice on factoring polynomials by determining the greatest common factor. Versions A and B contain 15 problems each and version C has 10 more challenging examples. The product can be used as an extra practice, enrichment or homework assignment. It can be also used as a group activity - competition between groups of 2 or 3 as the members of the group will chose who which version to solve. The practice sheets give enough room for students to show work. Answer keys are included.

These product can be used to introduce laws of exponents or for engaging practice after teaching a lesson on exponent rules. There are 121 laws of exponents problems in all divided into 17 sections(from A to Q). In each section each “rule” is written and includes 1 to 4 worked out examples and 3 to 8 similar to them problems for students to try to solve them by their own. Students will apply A) product rule with same base B) product rule with same exponents C) quotient rule with same base D) quotient rule with same exponents E) power rule F) power rule with radicals G) negative exponents rules Students will also multiply and divide negative and fractional exponents, exponents with different bases and different power indicators, exponents with variables and in the last section students will perform adding and subtracting exponents. The practice sheets give room for students to show work. Answer keys are included.

These are 8 Christmas practice tickets on factoring trinomials and simplifying rational expressions. On each page/slide students are given first to factor four quadratic trinomials - two with a=1 and two with a>1, and second to simplify two rational expressions consisted of the given quadratic trinomials. Students may struggle in the first task however they will enjoy when canceling the common factors in the second task. These tickets can be used for independent and group work (groups of 2 or 4 members). 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 complex zeros of polynomials. There are 12 sections. In each section each partner is given a polynomial (partner A is given polynomial A, and partner B is given the polynomial B). Partners have to find all the zeros of polynomials and to determine the common zeros between polynomials A and B. There are included polynomials of 3th, 4th and 5th degrees. This activity can be used as an independent practice as well. Students will search for the common roots between each two given polynomials which I think is more fun than just finding the complex zeros of a series of “random” polynomials. Answer keys are included. NOTE: This product is created as a Google Slides product. **I have converted it to PDF item here. **

This is a fun and engaging activity on finding zeros of polynomials (real and complex). There are two problem pages/slides. On the first page/slide students are given 12 problems as each problem is “accompanied” by a riddle. On the second page/slide there are given the answers of the problems as each answer of a problem is “accompanied” by the answer of the riddle. 12 “false” answers are included to mislead the students if they try to guess the riddles without finding the zeros of polynomials. Students can draw numbered ovals (from 1 to 12) which to write on the answers they have chosen to be correct. Polynomials included are of 3th, 4th, 5th and 6th degree. I recommend students to show work! Answer key is included. NOTE: This product is created as a Google Slides product. **I have converted it to PDF item here. **

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.