This is an engaging and collaborative group activity on finding the absolute extrema of a function (extrema on an interval). The functions included are polynomial, rational, involving radicals, exponential, logarithmic and trigonometric. There are 10 sections - 10 functions. Students work in groups of two, three or/and four. In each section, each member of a group is asked to find the absolute extrema of the given function on a specified closed interval . Thus one and the same function will be examined for absolute extrema at most in four different particular intervals. The collaborative part of this activity is in the initial stage of solving where partners find the first derivative of the given function and determine all the critical values. Students compare their results, find and fix any errors to continue solving in the right direction. They evaluate the function at the critical points found and the end points again having the opportunity to compare their calculations. As a consequence their final (different) answers must be all correct. Student recording sheets with steps that lead to solution and answer keys are included. The product can be also used as an independent/extra practice with 4 different forms and assignment or homework.

In this 16 questions - partner activity, students apply L’Hospital’s Rule to evaluate limits. There are included the following indeterminate forms - 0/0, infinity / infinity, infinity minus infinity, zero ⨯ infinity, zero^zero, infinity^zero and 1^infinity. The functions included are polynomial, exponential, logarithmic, trig and inverse trig functions. Each partner has his own set of 8 problems. Partners will use L’Hospital’s Rule to evaluate their first two limits directly. They will need to manipulate to make zero/zero or infinity/infinity and then to apply L’Hospital’s Rule to evaluate the next six limits. ► THE FORM of the limit and THE ANSWER of each of Partner’s A problems are THE SAME as the form of the limit and the answer of each Partner’s B corresponding problem. (Problems A1 and B1 are corresponding, so as problems A2 and B2 and so on). Students are instructed to show all work and check whether their results match. Full solutions are provided.

This engaging and fun activity has the student find the equation to a tangent line at a given value of the variable x. The functions included are polynomial, rational, involving radicals, exponential, logarithmic and inverse trigonometric. Students work independently or in groups of two or three to solve 13 problems. They use a table to find out the syllables corresponding to each of their answers. Then students record the syllables in another table and read the resulting sentence. It is a motivational quotation by the Professor Steven Strogatz about calculus. Student recording sheet and answer keys are included.

Students will practice finding vertical, horizontal and slant asymptotes using limits in this activity. There are included rational, involving radicals, exponential and natural logarithm functions. Students will work through 7 sections (or less if preferred). There is a function given in each section and differentiated instructions to each of the partners. In each section they share their work like this – Partner A finds all the vertical asymptotes of the given function while Partner B finds the slant asymptote of the same function. In the next section Partner B finds the vertical asymptotes of another function while Partner A finds the slant. There are sections where one of the partners is asked to find the horizontal asymptotes and the other partner – the vertical. The last section asks Partner A to find the left horizontal asymptote and Partner B – the right horizontal asymptote of a function. Students recording sheets are specially designed for this activity with HINTS and rooms to show work. Partners have to record all their answers in a table on a partners’ response sheet provided. Answer key is included.

This resource contains total of 16 limits. Students will apply the properties of limits and evaluate the limits algebraically by factoring and substitution methods. They will also need to use basic trig limits and identities to solve the limits of trig functions. The limits in this activity can all be found without L’Hopital’s rule. 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 trigonometric functions. The worksheets can be used as extra practice, for enrichment, an assessment or homework. It can be also used as a partner activity – like that: 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. All answer keys are included.

In this 24 questions- activity, students apply L’Hospital’s Rule to evaluate limits. There are included the following indeterminate forms - 0/0, infinity / infinity, infinite minus infinity and the product of zero and infinity. All functions are included from polynomial to square root, from exponential to log, from trig to inverse trig functions. There are two similar versions of this practice each consisting of two sections. Each section contains three groups of two limits. The problems IN EACH SECTION have THE SAME ANSWER! In section1, two problems have the form 0/0; the next two have the form infinity/infinity and the last two problems have the form infinity minus infinity. In section 2, two problems have the form 0/0; the next two have the form infinity/infinity and the last two problems have the form the product of zero and infinity. ( Not all of the questions require L’Hospital’s Rule (i.e. another valid method could be used) however students are instructed to use only L’Hospital’s Rule to find the limits.) This activity can be used for class work, independent or grouped (groups of 2 or 4). It can be used as an assessment and homework as well. Answer keys are included.

This is a collaborative and challenging activity to practice finding derivatives by implicit differentiation. All of the equations are selected to be solved for y to get the form y= f(x). Functions included are polynomial, rational, including radicals, exponential, logarithmic, trigonometric and inverse trigonometric. Activity Directions: Partners work through 8 sections (or less if preferred). Each section contains one equation in two variables x and y. Partner A solve it for y and then differentiate the function y=f(x) directly to find the derivative of y(x). Partner B deals with the same equation using implicit differentiation to find the derivative of y. When partners are ready, they check that their derivatives are the same. In the next section, Partner A will use implicit differentiation while Partner B applies differentiation directly. Once the work is completed, partners compare their derivatives again. Partners are supposed to get the same answers in each section. This activity can be used once more like that - next time partners can practice the same examples exchanging their roles – Partner A takes the position of Partner B and Partner B takes the position of Partner A. In such a way each partner will solve each of the problems using two solution techniques.

This is a collaborative and fun robots themed group activity on polynomial inequalities. On each slide/card students are given 4 similar problems as the problems increase in difficulty with each next slide/card. There are included inequalities with polynomials factored at the left side, inequalities where polynomials are not factored completely and inequalities where polynomials are in their standard form. Students must be able to factor quadratic and biquadratic trinomials, using the difference of squares formula, and factoring by grouping. Students work in groups of 2, 3 and/or 4 or this activity can be also completed individually as half of the problems can be solved as classwork and the other half - as homework. 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 partner activity takes the student through solving rational inequalities of varying difficulty with all terms on the left side. The problems require answers on a number line and in interval notation. Some problems do require factoring. Activity Directions: Partners solve two inequalities in each section ( there are 12 sections). Then they are asked to find the intersection of the two solution sets. Students can determine the intersection and draw the overlap on their response sheet OR they can use a given list of figures presenting the overlap of the solutions to the inequalities for each section. They cut the figures and paste them in their corresponding fields on the response sheets provided or match each problem to its answer ( each figure is labeled with a letter ). Partners are also required to answer a well thought question concerning the intersection of the two solution sets in each section like what is the largest whole number that satisfies both inequalities. Students can also work in 4 groups of 2 – each group solve three sections, then groups swap papers and solve another three sections. I have included adapted response sheets if it is preferred this activity to be completed individually. All answer keys are included.

This resource contains total of 36 problems. Students will practice solving quadratic inequalities with one variable algebraically. They are asked to write the solution sets using interval notation. Problems of various difficulty are classified into 3 different categories according to whether discriminant is positive, zero or negative. There is also included review problems (mixed inequalities where discriminant is positive, zero or negative). ⟐ The first worksheet has the students solving 8 quadratic inequalities. It’s given that D > 0. ⟐ The second worksheet is finding the solution sets of each of 10 quadratic inequalities. It is indicated that D = 0. ⟐ The third worksheet has the students solving 10 quadratic inequalities. Given that D < 0. ⟐ The fourth worksheet contains 8 review problems - mixed quadratic inequalities. Students have to determine whether discriminant is positive, zero or negative and solve the problems. The product can be used in class for cooperative learning , as a group activity or an independent practice, review, an assessment or homework assignment. Answer keys are included.

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 resource contains total of 24 problems. Students will practice solving biquadratic inequalities algebraically. They are asked to write the solution sets using interval notation. Problems are classified into types according to the form of polynomials (factored or standard). ⟐ The first worksheet has the students solving a total of 8 inequalities in factored form. ⟐ The second worksheet is finding the solution sets of 8 inequalities in standard form. ⟐ The third worksheet contains 8 inequalities where there are polynomials in expanded and factored forms on both sides (problems level 2) Answer keys are NOT included.

In this activity students will practice solving quadratic equations in standard form by the quadratic formula and by completing the square. All equations have complex solutions. Students will also practice plotting points on a coordinate plane, representing the values of the complex roots of the quadratic equations. An amusing part is the drawing activity where partners will draw easy drawing symbols around the plotted points and will produce a nice picture together. Activity Directions: Each partner is supposed to solve individually eight quadratic equations. The equations are marked with different symbols. Student solves the equations given like this: one equation - by the quadratic formula and the other - by completing the square and it goes still that way. Students show detailed solutions on the recording sheets provided. Then partners plot all the points, representing the values of the complex solutions they have already found on a coordinate plane given. They consider the symbol of each equation to be the symbol of its roots as well. At last students draw the symbol of each equation around the plotted points, corresponding to its complex solutions. All answer keys and FULL SOLUTIONS of the problems are included.

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.

This is a matryoshka dolls themed digital maze on solving quadratic equations with complex solutions. Students start solving and use each answer to navigate through the maze. Students will need to solve 13 problems properly to complete the maze. Students can draw a line/curve to display their answer path. Answer key is included.

Students will solve problems involving the area of plane figures (triangles, rectangles, parallelograms, rhombi, squares, trapezoids and regular hexagons) with this collaborative activity. The problems require students to use trigonometry, Pythagorean Theorem and Heron’s formula! There are 6 task cards grouped with 3 problems per card so that students can work in groups of 3 (or 2). Problems include: Finding the area Finding a dimension given the area Card 1 have problems involving area of triangles, card 2 – area of rectangles, card 3 – area of parallelograms and a rhombus, card 4 – area of squares, card 5 – area of regular hexagons and card 6 – area of trapezoids. Student recording sheets and full solutions (handwritten clearly) are provided.

This resource includes an engaging practice on quadratic equations with complex solutions containing 32 problems and homework assignment with 16 problems. Students will solve quadratic equations by the square root method, by completing the square and by the quadratic formula. The practice problems are classified/arranged by type: A. quadratic equations having b=0 and ac>0 (8 problems) B. the real and imaginary parts of the complex roots of a quadratic equation are both rational numbers ( √D= ai , a - a whole number) (8 problems, level 1) C. the real and/or imaginary part(s) of the complex roots of a quadratic equation is/are irrational number(s) ( √D= √a i , a - a whole number) (8 problems, level 2) D. finding a quadratic equations with given the pair of roots (8 problems) The practice sheets give room for students to show work. The product can be used as a classwork, independent practice, for practice after teaching a lesson on quadratic equations with complex solutions/roots, homework assignment and assessment. Answer keys are included.

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!