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.

This activity provides students practice with graphing quadratic inequalities. On each slide/page, students are given five quadratic inequalities and one graph. Students have to choose the inequality which represents the given graph (to match the graph with the correct inequality). There are 5 graphs of quadratic functions with the leading coefficient a>0 and 5 graphs of quadratic functions with the leading coefficient a<0. The quadratic inequalities are of all types - including equal to and not equal to inequalities. All functions are given in standard form. There are included two slides/pages with empty text boxes provided where students can record and justify their answers. Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here.

This is an engaging and collaborative partner activity on writing linear equations in slope- intercept form. There are 12 sections as in section 1 Partner A is given two points and Partner B is given a point and slope. In section 2 Partner A is given a point and slope and Partner B is given two points. In section 3 Partner A again is given two points and Partner B is given a point and slope. In section 4 Partner A is given a point and slope and Partner B is given two points… In each section the answer of Partner’s A problem is the same as the answer of Partner’s B problem. Students are instructed to compare their answers and check whether their results match. If their answers don’t match, they work together to figure out what went wrong. I hope the practice sheets give enough room for students to show work. Answer keys are included.

These product can be used to introduce laws of exponents or for engaging practice after teaching a lesson on exponent rules. There are 121 laws of exponents problems in all divided into 17 sections(from A to Q). In each section each “rule” is written and includes 1 to 4 worked out examples and 3 to 8 similar to them problems for students to try to solve them by their own. Students will apply A) product rule with same base B) product rule with same exponents C) quotient rule with same base D) quotient rule with same exponents E) power rule F) power rule with radicals G) negative exponents rules Students will also multiply and divide negative and fractional exponents, exponents with different bases and different power indicators, exponents with variables and in the last section students will perform adding and subtracting exponents. The practice sheets give room for students to show work. Answer keys are included.

This resource contains total of 20 problems. Students will practice solving linear inequalities in one variable. Problems of various difficulty are classified into 3 different types: ⟐ The first worksheet has the students solving 8 one-step inequalities. They are asked to solve each inequality, graph its solutions and express the graph using interval notation. ⟐ The second worksheet is finding the solution sets of each of 6 two-step inequalities. Students are asked to solve each inequality, graph its solutions and express the graph as an inequality involving x. They are also asked to express the graph using interval notation. ⟐ The third worksheet has the students solving 6 multi-step inequalities. They solve each inequality, graph its solutions and express the graph as an inequality involving x. Students also express the graph using interval notation. Students are provided a drawn number line for each inequality. The product can be used in class for cooperative learning , as a partner or a group activity ( groups of 3), independent practice, an assessment or homework assignment. Answer keys are provided.

This is a fish species themed maze on square root and cube root. Each problem is evaluating the sum or difference of square root and cube root (√a±∛b). 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 to display their answer path. They can also show their calculations writing in a table provided. Answer key is included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here.

In this fun ghosts themed activity, students will practice finding a derivative at a point. The problems covers all the basic derivative rules, including power rule, product and quotient rules, chain rule, polynomial, rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic functions. Activity Directions: Student work through 12 problems (functions given). They choose a function to find the value of its first derivative at the given value of x. The solutions of all problems are written on twelve of 13 ghosts on a given picture. Every time students arrive at a correct answer, they will “cast out the ghost” having this answer written on it. Students are also asked to find the only one ghost who can NOT be cast out. The product can possibly be used as a partner or a group activity(group of 3). Student recording sheets are provided and an answer key.

This fun Thanksgiving themed activity will help students review such topics as ♦ first, second and higher order derivatives ♦ intervals of increasing and decreasing ♦ critical points and local extrema The functions included are polynomial, rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions). The problems covers all the basic derivative rules, including power rule, product and quotient rules and chain rule. Activity Directions: Students work through 15 problems. All the answers are written on 15 of 18 turkeys on a given picture. Every time students arrive at a correct answer, they will “get the turkey” having this answer written on it. Students are asked to find three happy turkeys who can NOT be caught. The product can be possibly used as a partner or a group activity (group of 3). Student recording sheets and the answer key are provided. I wish you very happy and blessed Thanksgiving!

This activity is created for your students to practice their skills with more complicated trig integrals. It contains problems on indefinite integrals of product and ratio of sine and cosine involving powers of sine and cosine. In general, the integrals are of (sin(x))^n(cos(x))^m, where m and n are integers. Students will need to use trigonometric identities (Pythagorean, Power Reduction Identities, Double-Angle Identities), integration by u-substitution, integration by parts along with algebra skills to manipulate the integrands. There are 16 problems for them to complete with room to show work. Students аrе given the answer to each problem with missing coefficients they have to find and insert/fill in. This resource can be used for class work, independent or grouped, HW, enrichment, or an assessment. Answer keys are included.

This is a complete rigorous lesson on Advanced Techniques of Integration for students enrolled in AP Calculus BC or Calculus 2. ( The resource contains 47 problems - 17 with full typed solutions and 30 with answer keys) Lesson Objective: Find indefinite integrals and evaluating definite integrals using integration by parts. It includes A. Detailed Guided Notes (5 pages) including derivation of Integration by Parts formula and 7 worked out examples with indefinite and definite integrals as 4 examples perform Integration by Parts once 3 examples including repeated Integration by Parts( twice and for third time). The students are guided through the process of picking u, du, v, and dv. B. 20 Classifies Practice Problems ( 10 come with full typed solutions and other 10 are similar to them for students to try their own. Students are given the answers. ) C. 12 Assignment Problems with answer keys ( 6 indefinite and 6 definite integrals ). D. 2 versions Multiple Choice Exit Tickets /Quizzes/ Assessments ( with answer keys)

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 product is designed for students to practice integration using the methods of partial fractions and long division. It includes 16 sections each consisting of three related problems. In each section, students are instructed (a) first to use long division to write an improper rational expression as a sum of a polynomial and a proper fraction or/and to express a proper fraction as a sum of partial fractions (b) then to find the indefinite integral whose integrand is the function given in (a) © and at last to evaluate a definite integral having the same integrand as the integrand of the integral given in (b). The first eight sections contain problems that require using of partial fraction decomposition only. The next four sections include problems that require using long division only and in the last four sections students need to use both methods of integration in combination. ◈ One of the examples require using a substitution to be integrated by partial fraction decomposition. The problems include linear factors, quadratics, repeated factors, cubics, and quartics. Full solutions are provided.

In this packet you will find 22 practice problems students can use to practice finding the area between curves. Students need to analyze the problems, find the points where the curves intersect (in 8 of the problems), sketch the graph, setup the integral necessary to find the area and to integrate to find the area. The integration involved is basic and using u- substitution. One example requires trig substitution and else one example requires finding a suitable substitution to be solved.There are five problems with trig functions.There is one problem where students will have to divide the problem into two integrals. All examples are with vertical strips. The product is useful for independent/extra practice and homework assignment. Detailed typed answer keys are included.

This resource contains a total of 24 problems. Students will practice taking the derivatives of some complicated functions by logarithmic differentiation. The packet has 2 worksheets: ⟐ The first worksheet has the students finding the first derivatives of 12 complicated functions using natural logarithms. ⟐ The second worksheet also contains 12 problems of finding the derivatives by logarithmic differentiation as some of the examples are more complex. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner or group activity – like that: ⟡ Partner A will solve WS #1 (page 1) while Partner B solves WS # 1 (page 2), then they swap papers and Partner A will solve WS #1 (page 2) while Partner B solves WS #1 (page 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. Partners continue working through WS # 2 in the same manner with pages 2 and 3 or pages 1 and 2… ⟡ Worksheet # 2 can be used as a group activity ( for groups of 3 as its pages are three and each page contains 4 problems). Full solutions (handwritten clearly) are provided.

This is a mushrooms themed maze on solving rational equations using cross multiplication. 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. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here.

This is an engaging teacher themed practice on natural logarithms. There are four problem pages/slides each containing two main tasks A and B. Task A is condensing logarithms - students have to simplify three or four expressions (without and with variables) using the properties of natural logarithms; task B is solving three or four logarithmic equations with natural logarithms and/or exponential equations using natural logarithms (a total of 30 various problems). Students are provided with an empty box below each problem where they can record their answers. Please view the preview to see all the problems included. Students can work independently or in pairs. Answer keys are included (four answer key slides 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 slides on a page for easy and more economic printing!

There are two problems (A and B questions) on each of the 8 cards. Question A is to evaluate a limit analytically and Question B is to prove a limit’s equality. Half of the cards are 8 questions asking students to find the limits of rational and involving radicals functions as x approaches infinity. The other half of the cards contains limits where x approaches a finite number. Students are to find the limits of rational functions, functions involving radicals and trigonometric functions (some of which use the “special Limits" ( sin x /x, (1 - cos x)/ x^2)) . The limits in this activity can all be found without L’Hopital’s rule. The cards can be used as a partner or a group activity or as a review. There is a student recording sheet included. Answer keys are provided.

This activity is designed to be used for groups of 4, 3 and/or 2 members. It practices: • solving radical equations with one and two square roots • solving linear and quadratic equations • checking for extraneous solutions The radical equations contain: a monomial and/or a binomial under a radical symbol a radical expression on one side of the equation and a monomial or a binomial on the other side radical expressions on one side and respectively on the both sides of the equations (“radical equals radical”) Most of the equations require rearranging and isolating the radical and the rest are set up to square both sides. All the equations require squaring once. Activity Directions: Partners will each have their own set of eight problems of various difficulty. They reduce them to linear or quadratics and continue solving by any method they choose. Students write down the solutions of the problems on the recording sheet provided. They are instructed to check for extraneous solutions. Partners record their answers in tables on a group response sheet designed in such a way that students can analyze and compare their results easily. They must verify that all equations actually have the same solution except only one which has two distinct roots. I called this special equation “black sheep equation” and it is the equation B8. It can not be simply found without checking for extraneous solutions. All answer keys are provided. I hope your students enjoy searching for the “black sheep” and have fun with this activity.

In this fun Valentine’s themed activity, students will practice simplifying trig expressions using the fundamental Pythagorean, quotient and reciprocal identities. Activity Directions: Students are asked to simplify 12 trig expressions. The corrected equivalent expresssions (the answers) are recorded on twelve of 13 hearts on a given picture. Every time students arrive at a correct answer, they will “win the heart” having this answer written on it. Students are also asked to find the only one heart who can NOT be won. The product can possibly be used as a partner or a group activity(group of 3). Student recording sheets, answer keys and solutions are provided. I hope you and your students ENJOY!