These are 7 monster themed task cards as there are 2 problems per card/slide/page - the one problem is multiplying two rational expressions and the other problem is dividing rational expressions. Students multiply or divide as they factor the numerators and denominators and then cancel the common factors. Students will need to use factoring out a GCF and the polynomial identity for difference of squares to simplify each expression given. This product can be used as independent and extra practice, partner activity (in the first page/slide partner A will perform multiplication and partner B will perform division, on the next page/slide partner A will divide and partner B will multiply rational fractions and etc), homework assignment and even as an assessment. The answer key is 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 a fun and engaging activity on simplifying complex fractions. On each page/slide students are given a complex fraction to simplify and a picture of an animal holding a blank sign on which is written an answer. There are also two buttons labeled “Right” and “Wrong”. Students have to determine whether the animal “saying” the answer is right or wrong and then to strike through one of the buttons. The pages/slides are 12 as the problems increase in difficulty with each next page/slide. The answer key is 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 collaborative group activity on infinite geometric series. It contains a total of 60 problems and consists of 7 sections. In each section each member of a group has his own problem(s) to solve as the problems of the partners are similar. In the 1st section partners have to write given series in summation notation. In the 2th section each partner has given three series (two of them are in summation notation) and is asked to find the sum of each. 3th section: Students have to find the common ration of the infinite geometric series with the given sum and first term. 4th section: Students have to find the first term of the infinite geometric series with the given sum and common ratio. 5th section: Each member of a group is given four series (in summation notation) and has to determine which of them converge and to give the value of each convergent series. 6th section: Students have to convert repeating decimals to fractional form. 7th section: Students are given geometry problems to solve by use of a geometric series. This activity may turn into competition between groups. The product can be also used as four different forms of independent practice, extra practice, enrichment and homework assignment. Student recording sheet and answer keys are included.

This is a fun and engaging multiple - choice game on converting quadratic functions from standard to vertex form. Students are given 12 slides/pages - 12 problems to solve. On each slide/page there is given a quadratic function and a realistic illustration of a dinosaur, 4 optional answers as each corresponds to a name of a dinosaur. Students enjoy converting the functions as they want to find out which are these dinosaurs. Answer keys 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 three slides on a page for easy and more economic printing!

This is an engaging activity on exploring quadratic functions. On each slide/page students are given a quadratic function in standard form and six statements concerning its characteristics (vertex, axis of symmetry, x-and y-intercepts, range, intervals of increase or decrease, value of the minimum or maximum). Each statement is written in a cell of a table where there are also given two options/buttons “True” and “False”. Students are asked to determine which of the statements are true and which are false and then to strike through the incorrect buttons or choose/mark the correct buttons/options. The slides/pages with problems are 8 (8 quadratic functions to be explored). This activity can be used as an independent practice, extra practice, homework assignment. Answer key is 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 and three slides on a page for easy and more economic printing!

This is a collaborative and challenging activity to practice finding first and second derivatives of simple and composite functions. The functions in this activity include polynomials, rational fractions, radicals, trig and inverse trig expressions, exponential expressions and natural logarithmic functions. Students work through 14 sections/problems(or less if preferred). Each section contains one function to be differentiated by the partners. One partner starts solving first to find the first derivative of the function, then the other partner differentiates the function that his partner has obtained to find the second derivative. In the next section, partners take turns and it goes the same way. Alternative way to use this activity: Partners can work over finding the first derivatives of the functions of two randomly chosen different sections and then to swap papers to find the second derivative of the same functions. A hint is provided in each section that gives the sum of the partners’ answers. Typed and detailed answer keys are included. I hope this activity will be stimulating and beneficial for your calculus students.

This is an engaging three levels practice on adding and subtracting rational expressions. Students are given three pages/slides as there are 8 problems per page/slide. Students have to add or subtract and then simplify their results if possible. The problems are well thought so after adding or subtracting students will obtain rational fractions that can be simplified. On the first page/slide (problems level 1) students add and subtract rational expressions having the same denominators or the one fraction has a denominator a-b and the other fraction has a denominator b-a. On the second page/slide (level 2) students add and subtract rational fractions having different denominators. Students will need to factor the denominators factoring out a GCF and using the difference of squares formula. On the third page/slide (problems level 3) students add and subtract three rational fractions with different denominators. It is not needed for students to solve all of the problems as classwork, however they can have some of the problems as homework. The product can be used as a group activity as well (groups of 4 as each student will solve 2 problems from each page/slide). 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 practice on multiplying matrices with carefully chosen problems some with nice answers. There are included nine challening tasks. Here is a description of the tasks: Task 1. Given a matrix A (2x2). Students have to determine f(A) which is a quadratic function of A (two problems here) Task 2 is proving that two matrices (2x2) are commuting (two problems included) Task 3 is finding AB and BA given A^t (3X2) and B (3x2). Task 4 is proving that A^2=A , A is 3x3 Task 5. Given a matrix A (3x3). Students have to determine f(A) which is a quadratic function of A. Taks 6 is finding AB as A is 3x3 and B is 3x3. The answer is really nice. Task 7 is finding AB-BA (two problems here) Task 8 is performing indicated operations AB+CD Task 9. Given matrices A,B and C. Students have to prove that A(BC)=(AB)C Students have enough room to show work on the practice sheets. This resource can be used as independent and extra practice, enrichment and homework. Answer key is included.

This is an engaging practice on calculating the determinant of a matrix (2x2 and 3x3). It consists of two parts. Part 1 are problems on matrices 2x2 and part 2 are problems on matrices 3x3. There are included a total of 5 tasks. Task 1 (part 1) is calculating the determinants of six matrices 2x2. Task 2 (part 2) - students have to express the determinant of each of eight matrices 2x2 in the terms of the variables in them. Task 1 (part 2) is computing the determinant of each of six matrices 3x3. Task 2 (part 2) -students have to express the determinants of each of 5 matrices 3x3 in the terms of the variables in them. Task 3 (part 2) is solving four equations of type detA=detB as A is a 3x3 matrix and B is 2x2 matrix, detA=Number as A is a 3x3 matrix. Tasks 2 and 3 of part 2 contain challenging problems. Worksheets have enough room for students to show work. This resource can be used as independent/extra practice, enrichment and homework. Answer keys are included.

This is an engaging activity on multiplying polynomials. Students are given 2 pages/slides with 16 problems - 4 levels as there are 4 problems for each level. Each problem correctly solved gives points (problem of level 1 gives 1 point, level 2 problem - 1.5 points, level 3 problem - 2 points and level 4 problem - 3 points). So students try to get as many points as they can. There are 4 pages/slides included where students can build the answer of each problem using monomials given. This activity can be completed individually (maximum efforts) or students can work in groups of 2 or 4. If students work in pairs there will be two problems of each level for each partner to solve (optimum pressure). If students work in groups of four there will be only one problem of each level for each member of the group (minimum pressure). This activity can also be turned to competition between groups (which group will finish first or will get maximum points). 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 practice/homework on multiplying matrices contaning 10 tasks (19 problems). Here is a description of the tasks included: Task 1. Students have to find the sum of indicated elements for the product AB given the matrices A and B. (5 related problems) Task 2 is finding the product A^t B where A^t is the transpose of the matrix A. Task 3. Given matrices A and B. Students have to calculate f(A) and f(B) which are quadratic functions of A and respectively of B. A is 2x2 and B is 3x3 (2 problems) Task 4. Given three matrices A, B and C. Students have to check whether AB=AC Tasks 5,6,7 is proving that two matrices are commuting. In taks 5 the matrices are 2x2, in task 6 - 3x3 and in task 7 the matrices are 4x4. Task 8 is computing the difference AB-BA given the matrices A and B (two problems) Task 9 is finding the product AB where A and B are 4x4. The answer will be suprisingly nice. Task 10. Given four matrices. Students have to compute the products ABC,CAB,BAD and DBA. (four problems) Students will need to use separate sheets of papers to show work. This resource can be used as homework, as class/extra/independent practice too however it should be taken into account that it will take more time as the problems are many and some are challenging. Answer key is included.

This resource contains total of 86 well thought out practice problems on rational functions. Students will determine the characteristics of the rational functions – domain, range, holes, x – and y- intercepts, vertical, horizontal and slant asymptotes. There are eight practice worksheets from A to H where the problems are grouped/classified by topic. ◈ WS A - finding the domain ( 12 problems) ◈ WS B – finding the range ( 10 problems) ◈ WS C - finding the x – intercepts (12 problems) ◈ WS D – finding the y- intercepts ( 12 problems) ◈WS E – finding the vertical asymptotes ( 10 problems) ◈ WS F – finding the horizontal asymptote (12 problems) ◈ WS G – finding the slant (oblique) asymptote (8 problems) ◈ WS H – determining the holes (10 problems) This product can be used as in-class practice, an independent practice or group activity. It can be also used as an assessment or homework. Typed answer keys are included.

This product is designed for practice after teaching a lesson on introduction to complex numbers. It contains a total of 51 challenging examples as the problems are grouped by the following topics: identifying the real and imaginary parts of a complex numbers (9 examples) identifying the conjugate (9 examples) simplifying expressions involving i^n where n is a whole number (15 examples) simplifying expressions involving radicals with negative radicands (6 examples) factoring quadratic binomials ax^2 + b, where a and b are whole numbers (6 examples) solving quadratic equations ax^2 + b= 0, where a and b are whole numbers (6 examples) I have also included a homework assignment containing 18 examples. The product can be used as a classwork, independent practice, and for practice after teaching a lesson on introduction to complex numbers, homework assignment and assessment. Practice sheets give room for students to show work. All answer keys are included.

Students will practice factoring the sum and difference of cubes with this forest dwarf themed four levels activity. The first page/slide contains 13 problems of level 1, the second page/slide -10 problems of level 2, the third page/slide - 9 problems of level 3 and the fourth page/slide contains 9 problems of level 4. As the problems are challenging and many students can work in groups of two or three to complete this activity. The teacher can decide which of the problems each member of the group will solve (the problems are labeled with large Latin letters). Students are provided with 4 tables (for each level one table) where they can record their answers. Four answer key pages/slides are included 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!

These are five Christmas themed review tickets each containing three types of problems - 4 problems on multiplying binomials (FOIL method) to obtain a quadratic trinomial, 4 problems on factoring trinomials (two with the leading coefficient equal to 1 and two with the leading coefficient different from 1) and 4 problems on solving quadratic equations by factoring. Students are provided with empty boxes on each ticket where to record their answers. (Students can show work on separate sheet of paper). Students can work independently or in groups to complete this activity. 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 activity practices solving quadratic equations with complex solutions. There are included quadratics in standard and vertex form, though most of the equations have terms on both sides. Students will need to simplify polynomial expressions. They are asked to solve the equations by the most appropriate method ( by completing the square or using the quadratic formula ). 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 3 different versions so the product can be used as a partner activity or for groups of 3. The resource also works well as independent practice. Answer keys are included.

These are 12 Thanksgiving task cards for partners – a total of 48 problems in which students will practice solving exponential and logarithmic equations. There are one exponential (equation A) and one logarithmic equation(equation B) on each card. The equations involve a parameter. Students are asked to solve each of the equations A and B for two given different values of the parameter. Thus, students have four problems per card – problems Aa, Ab, Ba and Bb. Students can work in pairs (partner activity) or in groups of three and four (group activity). The equations require the use of logarithms and exponentials as inverses. Exponential equations include problems that can be solved using a common base along with problems that require logarithms (a^x=b and a^(cx +d) = b, where a=b or/and a≠b). Common base problems require combining exponents using laws of exponents. Logarithmic equations include basic logarithmic equations ( log (base a) x = b and log (base a) (cx+d)=b ) and some problems in which students must apply the properties of logarithms (adding and subtracting logarithms). The cards can be used individually as well. The teacher or student can choose which problems to be solved – like problems 1Aa, 2Ba, 3Ab, 4Bb, etc. Student recording sheets and full solutions (handwritten clearly) are included.

This is an engaging and fun multiple-choice game on trigonometric identities. It consists of 12 problem pages/slides. On each page/slide there is given a trigonometric expression, four answer choices (trig expressions A,B,C and D) as to which correspond the name of breed of rabbit, it is also given a picture of a rabbit. If students determine correctly to which of the fourth expressions in A, B, C and D is equal the given trig expression they will find out what breed is the rabbit on the picture. Students can circle the right answer or record their answers on a separate sheet of paper, they can also show their work on separate sheets of paper. Students need to know Pythagorean identities Quotient identities Co-function identities Reciprocal identities and how to use them in simplifying trig expressions to complete this activity. 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 three slides on a page for easy and more economic printing!

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.