This is an engaging practice for a set of 30 problems on equation of a circle. It consists of four parts (four pages) Part 1/Page A contains 10 problems on finding the center and radius of a circle where in the first 6 problems the equations are given in standard form and in the last 4 problems the equations are given in general form. Students will need to complete the square to complete the last 4 tasks. Part 2/Page B have 8 text problems on writing equations for circles. Students are given the center and the radius the endpoints of the diameter the center and one point that the circle goes through it the center and an endpoint of the radius the center and the diameter the center and the circumference of the circle the center and the area of the circle Part 3/Page C is interpreting the graphs of 6 circles. Students will have to write the equation of each circle in both standard and general forms. Part 4/Page D is graphing the circle given its equation in standard form (6 problems). Grids are provided. The practice sheets give room for students to show work. 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 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 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!

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!

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.

These are 15 open-ended carefully chosen questions concerning the following: ❄ determining intervals of increasing and decreasing (2nd , 3th and 9th problems) ❄ finding local and absolute extrema (1st , 7th and 12th problems) ❄ finding inflection points (10th and 15th problems) ❄ determining intervals of concavity (9th problem) ❄ finding the slope and the equation of the tangent and the normal lines at a point ( 5th , 8th ,11th , 13th and 14th problems) ❄ computing second and higher order derivatives at a point (4th and 6th problems) The functions included are rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions). I hope that the practice sheets give your students enough room to show their work. This product is useful for independent and group practice, homework assignment or as an assessment. Detailed answer keys/solutions (handwritten clearly) are included.

This is a fun self-checking circuit activity on solving trigonometric equations of quadratic type. There is provided space for students to show work on the pages. Activity directions: Students begin with the problem #1, solve the problem, find the answer somewhere else on the pages ( which are three) and write “2” in the blank. Then student solve that problem (#2), search for the answer again and when find it write “3” in the next blank. Students continue in this manner until they return to the problem #1. They should solve all the problems before returning to the start point. Detailed typed answer keys are included.

This is a fun self-checking circuit challenging activity on perpendicular bisector containing 11 problems. Each problem is a word problem goind along with a diagram. There is provided enough space for students to show work on the pages. Activity directions: Students begin with the problem #1, solve the problem, find the answer somewhere else on the pages ( which are three) and write “2” in the blank. Then student solve that problem (#2), search for the answer again and when find it write “3” in the next blank. Students continue in this manner until they return to the problem #1. They should solve all the problems before returning to the start point. Full typed solutions are included.

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.

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 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!

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!

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!