This is a collaborative and challenging activity to practice evaluating indefinite integrals by using Integration by Parts. It aims to develop and consolidate student’s skills in integration by this special method. Partners work through 8 sections (or less if preferred). Each section contains one integral. Activity Directions: A partner start solving an integral while the other partner is waiting for the answer to integrate it. In the next section, partners take turns and it goes the same way. An alternative way ( I think it is better way) to use this activity: Partner A solves an integral of a section while Partner B solves an integral of the other (the next in line) section. Then they swap papers and each partner integrates the function that his partner has obtained previously. The problems are well thought so the obtained functions after the first integrating can be also integrated by parts! A HINT is provided in each section that gives the sum of the partners’ answers. Answer keys are included. I hope this activity will be stimulating and beneficial for your calculus students.

This resource contains 16 indefinite integrals with their detailed solutions (typed). Students will use Integration by Parts to find the integrals. The packet has 2 worksheets: The first worksheet has the students evaluating 8 indefinite integrals The second worksheet is finding also 8 indefinite integrals as some examples are a bit more challenging.

This is an engaging and challenging practice aiming to improve students skills on integration by substitution. There are given total of 13 integrals. The integrands are functions involving radicals, rational and exponential functions. For the first 8 problems students are asked to use a given substitution to find an integral. For the next 5 problems students will need to show more flexible thinking as this time they are required to find a suitable substitution to evaluate an integral. The problems require the use of u-substitution, integration by parts and integration by partial fractions and long division. Make sure these problems are appropriate for your students - download the preview and look at the thumbnails to see problem examples. The practice worksheets have enough room for students to show their work. Full solutions (handwritten clearly) are included.

This is an engaging and challenging practice aiming to improve students skills on integration by substitution. There are given total of 12 definite integrals. The integrands are functions involving radicals, rational and exponential functions. For the first 8 problems students are asked to use a given substitution to find an integral. For the next 4 problems students will need to show more flexible thinking as this time they are required to find a suitable substitution to evaluate an integral. The problems require the use of u-substitution, integration by parts and integration by partial fractions and long division. The practice worksheets have room for students to show their work. Answer keys are included.

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 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 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 is a fun multiple-choice activity on applying exponent laws (only positive exponents included). On each slide/page there are two similar problems (expressions with two or three variables). Students have to simplify each expression and choose the correct answer between four optional answers. The problem is “labeled” with a large Latin letter written on a picture of a hen. The answer choices are “labeled” with small Latin letters written on pictures of chicks. Students write the letter of the chosen chick to the hen so to match the problem to its answer. The problem pages/slides are 10 (so students are provided with 20 problems). The problems increase in difficulty. This activity can be completed individually or in pairs. The 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 four slides on a page for easy and more economic printing!

This is a fun multiple-choice game on simplifying nth root expressions with variables. On each page/slide students are given an expression to simplify, four answer choices, a picture of a prehistoric animal and there is a name of a prehistoric animal corresponding to each answer choice. Students solve the problem and use their answer to find out what is the name of the prehistoric animal on the picture. The pages/slides are 10 as there are included problems with 3th, 4th, 5th, 6th, 7th, 8th, 9th and 10th root. Students have to use absolute value when necessary. 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 an engaging activity on the chain rule. On each page/slide students are given the solution of one problem and another similar problem to the first one to try to solve it by their own. Each problem consists of two sub problems - a) problem which is finding the first derivative and b) problem - computing the first derivative at a point (for a given value of the variable x). There are given the solutions of 8 problems and 8 similar to them problems for independent work. Functions included are composition of polynomial, rational, radical,exponential, logarithmic, trigonometric and inverse trigonometric functions. The last three problems are more challenging - students have to find the first derivative of a function of the type f(g(h(x))) using first the power rule for the function f. The product can be used after teaching a lesson on the chain rule, as an independent/extra practice and homework assignment. 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 that investigates infinite limits both graphically and algebraically. Students are asked to graph 8 functions and evaluate 24 limits (right and left-hand limits included) based on these graphs. Then students are asked to prove 11 equalities that is to check whether 11 infinite limits are evaluated correctly. Students are provided with rooms to show work and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem. All the graphs are presented in the answer keys. The resource can be used for class work, as an individual practice or homework assignment.

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 is an engaging and challenging practice on adding, subtracting and scalar multiplication of matrices. It consists of 8 practice tickets as each ticket contains three related tasks. The answer of the first task is needed for the answer of the second task to be found. The answer of the second task is needed for the third task to be completed. In each task students perform indicated operations to find a matrix. When students have completed the tasks on a ticket they would have found three related matrices A, B and C. If the answer for the obtained matrix C is correct then the obtained answers for the matrices A and B are correct as well. The matrices included are 4x1, 2x2, 2x3, 3x2, 3x3 and 4x3. You will need to print, cut and laminate (for durability) the tickets. Student recording sheets and answers keys are provided.

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 is a collaborative activity to practice solving complete quadratic equations in standard form by all methods. Students work through sections. In each section, each partner has one equation to solve by a specified method. Equations of the partners in each section are DEPENDENT. The problems are 28 WELL THOUGHT OUT that all have integer coefficients and solutions. Activity Directions: In Section One, Partner A starts solving the equation given and finding its roots while Partner B waits to receive the values of these roots from Partner A. Once the solution set is found Partner A “provides” Partner B with its numbers . Then Partner B places the numbers into the empty squares of his own equation given with two missing coefficients and solves the equation. There is an important instruction - the number which has its absolute value less to be put in place of the first missing coefficient. In Section Two partners repeat the same actions, however this time Partner B starts first. In Section Three, Partner A starts solving first again and it goes still the same way. Recording sheets are included for students to show work . All answer keys are included as well. NOTE: The pages are designed in a way that each partner can solve ten equations or even only six.

Students will use the basic integration formulas solving definite integrals with this fun password search activity. Activity Directions: Students solve 12 definite integrals using basic integration techniques, the properties of definite integrals (integral of sum of functions and moving the constant across the integral sign) and the fundamental theorem of calculus. Students 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 integrals right. Students can work independently or in pairs. Answer key is included.

This is a collaborative activity to practice evaluating indefinite and definite integrals by using advanced techniques of integration(** integration by parts and using u-, trigonometric and other types substitutions**). There are given 15 problems some with differentiated instructions. Problems list can be used as 15 mini task cards. Students can work through the problems cooperatively or in groups of 3 or 5. Student recording sheets and answer keys are included. Typed solutions to problems are provided.

These are 10 owl themed task cards each containing 3 similar problems on trigonometric functions, expressions and identities. The first and second cards are finding the value of trig function given the value of another trigonometric function and to which quadrant belongs the angle (from I to IV quadrant), the third card is evaluating trig expressions given the value of the angle(s), the fourth card is evaluating a trig expression given the value of trig function, 5th card is evaluating numerical trig expressions, 6th card is evaluating trig function given the value of another trig function as here co-function identities are involved, 7th card is determining which of given six expressions are positive and which are negative, 8th card is expressing trig expressions in terms of tan(teta), 9th card is simplifying trig expressions and 10th card is proving trig identities. Students need to know Pythagorean, reciprocal, co-function and quotient identities to handle the problems. The resource can be used as a review, group activity (groups of 2 or 3), independent extra practice, homework and even as an assessment (the teacher can chose how many problems and which of the problems the student to solve to check his knowledge and skills). There is included a page where students can record their answers in a table. Answer key is included.

These are 50 practice problems on complex numbers in polar form. The problems are grouped by topic ❆ finding the polar form of a complex number (practice sheet A, 15 problems) ❆ converting complex numbers from polar to rectangular form (practice sheet B, 10 problems) ❆ finding the product of two complex numbers in polar form ( practice sheet C, 5 problems) ❆ finding the quotient of two complex numbers in polar form (practice sheet D, 5 problems) ❆ finding powers of complex numbers in polar form using DeMoivre’s Theorem (practice sheet E, 5 problems) ❆ finding roots of complex numbers in polar form (practice sheet F, 10 problems) I hope the practice sheets give enough room for students to show work. This resource can be used as an independent/extra practice, enrichment, review, homework assignment or even as an assessment. Answer keys are included.

This is an engaging famous inventors themed 6 levels practice on dividing polynomials using long division. The problem pages/slides are 6 as the problems included on 1st page/slide are level 1 problems, the problems included on 2nd page/slide are level 2 problems and etc. Each page/slide contains 5 similar problems. Students can record their answers in the empty boxes on the pages/slides. This resource can be used as individual practice, as partner or even group 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!