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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 coloring activity provides students with 12 problems. Students will solve logarithmic equations (extraneous solutions included). After solving a problem, the students find their answer in a table. This tells them what color to use in the coloring page. Students are asked to show work on a recording sheet provided. Answer key is included.

This coloring activity provides students with 12 problems. Students will solve quadratic equations by factoring. Six of the equations have the leading coefficient equal to 1 and the other half have the leading coefficient >1. After solving a problem, the students find their answer in a table. This tells them what color to use in the coloring page. Students are asked to show work on a recording sheet provided. Answer key is included.

This coloring activity provides students with 12 problems. Students will write linear equations in slope-intercept form given the slope and a point. After solving a problem, the students find their answer in a table. This tells them what color to use in the coloring page. Students are asked to show work on a recording sheet provided. Answer key is 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 an astronauts and aliens themed maze on simplifying cube roots with variables. Students start solving and use each answer to navigate through the maze. Students will need to solve 13 problem properly to complete the maze. Students can draw a line 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.

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 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 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.

This is an engaging and fascinating activity for studying the intervals of concavity of given functions. The functions included are polynomials, rational, radical, exponential, logarithmic and trigonometric. They are specially selected so that each function has more than one points of inflection. If students solve all the 16 problems correctly, they will find out 16 math calculus terms (each consisting of two words). Some of the terms might not be still popular and students will learn them. Activity Directions: Partners are instructed to identify the intervals where 8 functions given concave up and the intervals where another 8 functions concave down. They look for their answers in a given table and search for a math calculus term corresponding to each of their answers(there is a word corresponding to an interval). The problems are written on task cards. This product can be possibly used as an independent practice, as a partner or a group activity (groups of 4). Student recording sheet and answer keys are provided.

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 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 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!

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!

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!