Students will apply L’Hospital’s Rule to evaluate limits. The resource contains practice problems classified into 4 categories according to the indeterminate forms – 0/0, infinity / infinity, zero ⨯ infinity and infinity minus infinity. There are 10 problems for each category and else 10 extra review problems(total of 50 limits). The functions included are rational, exponential, logarithmic, trig and inverse trig functions. The product can be used in class for cooperative learning , as a partner or a group activity, independent (extra) practice, enrichment or homework assignment. Full solutions (handwritten clearly) are provided.

Students will review the most of the concepts of Calculus with this funny themed practice. There are 3 problem pages/slides as the first contains 12 problems on Differential Calculus (finding the first derivative the product and chain rule, implicit differentiation, relative extrema, inflection points, finding limits using L’Hospital’s Rule), the second page/slide contains 12 problems on Integral Calculus (finding indefinite integrals -basic integration,u-substitution, integration by parts, evaluating definite integrals, improper integrals, differential equations) and the third page/slide has 11 problems on both Differential and Integral Calculus (finding limits of radical and trigonometric functions, limits at infinity, absolute extrema of functions on given intervals, evaluating integrals, finding the volume of a region bounded by given functions and revolved about x and y axes). Students can work independently which is better if time permits or in groups of 2 or 3. Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here.

In this lessson, students learn to apply the three most important Pythagorean identites and their variations. The lesson covers the following applications of Pythagorean identities: • Evaluating trigonometric functions • Simplifying trigonometric expressions • Verifying or proving other trigonometric identities It includes o 6 solved examples & 6 similar to them for students to try to solve them by their own o guidelines o 21 various and engaging practice problems o answer keys and full solutions The lesson can be divided into two or three parts if preferred.

This is a collaborative and challenging activity for classifying critical points of a function using the first and second derivative tests. The functions in this activity include polynomials, rational fractions, radicals, exponential and natural logarithmic expressions, trig and inverse trig expressions. Partners work through 12 sections/problems (functions given). Partner A will use the First Derivative Test to find the local extrema for the given function while Partner B uses the Second Derivative Test to find the local extrema for the same function. Then partners compare their results. In the next section, Partner A will use the Second Derivative Test and Partner B will use the First Test to locate all the relative extrema. Partners compare their answers again. Detailed typed answer keys are provided.

This is a self-checking practice created for students to find the first and second derivatives of common and composite functions. The functions include polynomials, rational fractions, radicals, trig and inverse trig expressions, exponential expressions and natural logarithmic functions. In each section, students have to differentiate once or twice a function given and then to prove that this function satisfies a given differential equation. Thus, students check whether they have computed the derivatives correctly. (There are sections 12 in total - 12 functions and 12 differential equations). The resource can be used for class work, independent practice or partner activity, for enrichment and homework assignment. Typed solutions to the problems are provided.

With this fun and engaging answer pass activity, students will practice adding, subtracting, multiplying and dividing complex numbers (includes rationalizing the denominator by multiplying by the conjugate). Students use each previous answer to find the next answer when working on the problems in a practice sheet. There are five practice sheets each containing 10 challenging problems. Practice sheet A is adding complex numbers, Practice sheet B is subtracting, Practice sheet C is multiplying, Practice sheet D is dividing complex numbers and Practice sheet E is performing operations with complex numbers and simplifying complex number expressions. The activity can be used individually or in groups. Answer keys are included.

This 4 pages practice sheet has 30 specially chosen questions on Rolle’s Theorem and the Mean Value Theorem . The topics covered include: verifying Rolle’s Theorem and applying Rolle’s Theorem (16 problems) verifying the Mean Value Theorem and applying of the Mean Value Theorem (14 problems) The functions included are polynomial, rational, radical, exponential, logarithmic, trigonometric and inverse trigonometric. The product can be used as independent/extra/practice, enrichment, group work, homework assignment or as an assessment. Detailed typed answer keys are included.

These are 6 practice/review tickets on indefinite integrals. Each ticket contains 9 various challenging problems. For each ticket there are included one problem or two on the following topics: basic integration integration using u – substitution integration by parts integration using suitable substitution integration by partial fractions decomposition There are included rational, radical, exponential, logarithmic, trigonometric and inverse trigonometric functions. The product can be possibly used as an independent practice/quizzes 6 different forms, as a group activity (groups of 2 to 6 members), homework assignment or assessment. Recording sheet is provided. Answer keys are included.

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 is an engaging and collaborative partner activity for analyzing and sketching graphs of polynomial and rational functions using calculus. Students will use limits, first and second derivatives to provide information about function behavior and then sketch the graph of the function. Activity Directions: Students are given five sections to work through. In each section partners are given two functions of the same type to identify their features (intercepts, asymptotes, intervals of increase and decrease, local maximum and minimum points, intervals of concave up and concave down, inflection points). After finding all the important parameters students are asked to draw a graph of the function. ▸The functions of a section differ only by coefficients so partners obtain similar results and graphs with the same shape. Students are provided recording/response sheets with a number of steps of the general algorithm for investigation of functions, rooms to record their results and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem so sketching to become easier. This product can be also used as a group activity, for collaborative learning, for enrichment and extra practice, as independent practice and homework assignment. Detailed typed answer keys are included. All the graphs are drawn as well. BONUS: I have included 4 additional sections for extra practice or enrichment. (These are without answer keys.)

These are 6 Christmas themed task or station cards grouped with 10 to 15 similar problems per card. There are a total of 81 carefully chosen problems concerning the following applications of the derivatives: ❄finding critical points (Card A - 15 problems) ❄ determining intervals of increasing and decreasing (Card B - 15 problems) ❄ finding local extrema (Card C - 15 problems) ❄ finding absolute extrema on the specified intervals (Card D - 10 problems) ❄ finding inflection points (Card E - 14 problems) ❄ determining intervals of concavity (Card F - 12 problems) The functions included are rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions). The cards can be used individually or with groups. Student recording sheets are included. Detailed answer keys/solutions (handwritten clearly) 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)