This resource contains 56 questions. It focuses on solving polynomial equations in standard form by using factoring (GCF, grouping, factoring difference of squares, sum and difference of cubes, perfect square trinomials, quadratic trinomials) and synthetic division. The problems are classified into categories according to the problem solving technique and the types of roots of polynomial equations (only real or real, imaginary and complex). There are also included quartic equations in quadratic form. ⟐ The first and second worksheets(two different variants/forms) have the students solving by factoring polynomial equations only with real solutions. These two worksheets can be used as a partner activity. (total of 16 problems) ⟐ The third and forth worksheets (two different variants/forms) are finding the real, imaginary and complex solutions of polynomial equations by factoring. These two worksheets can be used as a partner activity. (total of 16 problems) ⟐ The fifth and sixth worksheets have the students solving by factoring quartic equations only with real solutions with real and imaginary roots (total of 12 problems) ⟐ The seventh and eighth worksheets have the student solving by synthetic division polynomial equations only with real roots having real, imaginary and complex solutions (total of 12 problems) Typed answer keys are included.

These are 14 practice pages on geometric sequences. Students will use the explicit formula and the formula for the sum of the first n terms. ➤ Using the explicit formula students will have to find the nth term (problems Level 1) the first term (problems Level 1) the common ratio (Level 1) the number of terms (Level 1) the first term and the common ratio solving systems of two equations (Level 2) ➤ Using the formula for the sum of the first nth terms students will have to find the sum of the first nth terms (problems Level 1) the first term and Sn (Level 1) the common ratio and Sn (Level 1) the number of terms and Sn (Level 1) ➣ When given Sn (problems level 2) students will have to calculate n and r the nth term and r n and nth term the first term and r the first and nth terms n and first term The practice sheets can be used for independent and extra practice, enrichment, as a group activity( groups of 2, 3 and/or 4), homework and even as an assessment. Answer keys are included.

These are 14 kids with numbers themed task cards on reviewing factoring techniques. Each card contains 4 problems of one type. Cards 1 and 2 are on factoring out the greatest common factor (problems group 1); Cards 3 and 4 are factoring using the difference of squares formula (problems group 2); Cards 5 and 6 are factoring perfect square trinomials (problems group 3); Cards 7 and 8 are factoring using the sum and difference of cubes formulas (problems group 4); Cards 9 and 10 are factoring by grouping (problems group 5); Cards 11 and 12 are on factoring quadratic trinomials (problems group 6); Cards 13 and 14 are on factoring using combined methods (problems group 7) Two pages/slides with tables are provided where students can record their answers. These cards can be used individually or students can work in groups of 2,3 and/or 4. Answer keys are included. NOTE: This product is created as a Google Slides product.** I have converted it to PDF item here. **

These are 10 Algebra 2/Pre Calculus warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework on polynomial equations and inequalities. Each of them is a half-sheet in size and contains to 6 problems (excluded is only one containing 4). Topics included: Polynomial Equations with Real Roots Dividing Polynomials with Long Division Evaluating Polynomials Using Horner’s Rule Factoring Polynomials (Using Horner’s Rule and Finding the Zeros) Forming Polynomials Given the Roots Polynomial Equations with Complex Roots Polynomial Equations in Factored Form Polynomial Inequalities in Factored Form Polynomial Inequalities in Standard Form Partial Fraction Decomposition Answer keys are included.

Engage your students with various problems on product to sum and sum to product trigonometric identities with these 9 task cards (3 to 5 similar problems per card) containing a total of 30 problems. Students will express sums and differences as products and products as sums, simplify expressions and verify identities. They can work independently on cards or in groups of 2 and 3. Full typed solutions are provided.

This is an engaging multiple-choice practice on solving trigonometric equations(basic, multiple angles, of quadratic type, such that can be solved by factoring). There are 5 pages, containing a total of 20 problems each having five optional answers. The first 8 problems are finding all the solutions of each equation given, the next 12 problems are determining the sum of the solutions of an equation on a closed interval. Students have an empty field below each problem where to write down their solution. Detailed typed solutions are provided.

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 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 a collaborative activity to practice evaluating indefinite integrals by using Integration by Parts. It aims to develop and consolidate student’s skills in both integration and differentiation as well. Partners work through 16 sections (or less if preferred) each containing one integral. Activity Directions: A partner start solving an integral while the other partner is waiting for the answer to check it by differentiating. In the next section, partners take turns and it goes the same way. An alternative (saving time) 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 differentiate the obtained functions to check each other’s answers. A purpose of this activity is to aid learners gain a better understanding of integration. I hope it will be helpful for your calculus students. Typed answer keys are included

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 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 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.