This is an engaging practice on rational expressions containing 41 problems that vary in difficulty. On page/slide 1 students have to evaluate three rational expressions for the given value of the variable and then to determine the domain of six rational expressions/functions. On page/slide 2 students are given 8 rational expressions to simplify them. On page/slide 3 students add or subtract rational expressions (8 problems), on page/slide 4 students multiply or divide rational expressions ( 8 problems) . On page/slide 5 students simplify more complicated rational expressions performing the indicated operations (4 problems) and at the end students have to prove four statements ( rational equalities). Students are provided empty spaces/boxes where to record their answers. 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 partner activity on graphing quadratic functions. Students will work through six sections as in each section partners have to graph two quadratic functions f(x) and g(x) on the same coordinate plane. Partner A will graph f(x) and partner B will graph the other function g(x). Students are also asked to solve the equation f(x)=g(x). Included are three cases: The graphs don’t have points in common and respectively the equation f(x)=g(x) doesn’t have real solutions (section 1 and section 4) The graphs share one common point and respectively the equation f(x)=g(x) has one real solution (sections 2 and 5) The graphs have two common points and respectively the equation f(x)=g(x) has two real solutions (sections 3 and 6) This activity can be used as independent practice as well. The practice sheets give enough room for students to show work. Grids are provided. Detailed answer keys are included. (The graphs are drawn by CorelDraw.)

This engaging practice allows students to explore and graph square and cube root radical functions. It contains 40 various and challenging problems. Students will have to ✤ identify the domain of given radical functions (4 problems) ✤ determine the range of functions (4 problems) ✤ find x- and y- intercepts of given function (4 problems) ✤ determine which of given points are on the graph of a given function (1 problem) ✤ find zeros of radical functions (4 problems) ✤ evaluate radical functions for given values of the variable (2 problems) ✤ find the point of intersection between two radical functions (4 problems) ✤ determine the value of a parameter given a radical function involving the parameter and passing through a given point (1 problem) ✤ find the inverse of 5 radical and 3 polynomial functions (8 problems) ✤ sketch the graph of given radical functions ( 8 problems) I hope the practice sheets give enough room for student to show work. Grids are provided. The product is useful for independent/extra practice, enrichment, review, homework assignment and assessment. Answer keys are included. (The graphs are drawn with CorelDraw!)

This is a classwork or practice on operations with complex numbers containing a total of 46 challenging examples. The problems are grouped by the following topics: adding complex numbers (12 examples) subtracting complex numbers (12 examples) multiplying complex numbers (12 examples) dividing complex numbers (10 problems) I have also included an engaging homework assignment containing 18 problems. The product can be used as a classwork, independent practice, practice after teaching a lesson on operations with complex numbers, homework assignment and an assessment. Practice sheets give room for students to show work. All answer keys are included.

This is an engaging and fun multiple-choice game on operations with complex numbers (adding, subtracting, multiplying, dividing, raising i to a power). On each page/slide students are given two similar problems. The problems are labeled with large Latin letters written on the pictures of teddy bears. There are four optional answers for each problem labeled with the small Latin letters a,b,c and d written on the pictures of heart shaped balloons. Students solve a problem, select an answer choice and draw the balloon with the chosen answer to the teddy bear (match each problem with its answer). This activity can be completed individually or students can work in pairs (partner activity). It can be used as St. Valentine’s Day activity as well. 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 two slides on a page for easy and more economic printing!

This product includes 24 integration problems to be solved by u-substitution. Your students can work alone, in pairs, or small groups to complete the problems placed on 12 cards ( there are 2 problems on each card – one indefinite and one definite integral to be evaluated as both integrals have the same integrand). Students recording sheets are provided and created as worksheets so the product can be used for cooperative learning, extra practice, homework assignment or even as an assessment. Typed solutions (appropriate for teachers!) are provided.

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 a collaborative activity to practice evaluating indefinite integrals by using their BASIC properties and the table of common integrals. Partners work through 20 sections 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 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 work. If extra practice is needed Partner A and Partner B can change places with each other and continue solving. Applying both integrating and differentiating help students gain a better understanding of integration. I hope it will be beneficial for your calculus students. Answer keys and full solutions (typed and handwritten clearly) are included.

This is a set of three mazes (three versions) to practice solving improper integrals. Students are given 24 integrals. They will need to determine whether some of these integrals are divergent or convergent. If some integral diverges it must be evaluated. Then students use their answers to navigate through the maze. Not all boxes are used in this maze to prevent students from just guessing the correct route. Recording sheets are provided for students to show all work. For extra practice, students can solve all the problems and find out how many of the improper integrals are divergent. (There are 30 different improper integrals in this activity total and 9 of them diverge). Answer keys are included.

These are 50 practice problems of various difficulty on converting polar and rectangular equations. Problems A1- A25 require students convert rectangular equations to polar equations (Practice A). Problems B1-B25 require students convert polar equations to rectangular equations (Practice B). I hope that the practice worksheets give your students enough room to show their work. This resource can be possibly used as an independent /extra practice, as an enrichment and homework assignment. Typed detailed answer keys/solutions are provided.

This resource contains 20 practice problems (20 functions given) for classifying critical points of a function. Functions included are polynomials, rational, including radicals (square and higher-index roots), exponential, logarithmic, trigonometric and inverse trigonometric. To solve each problem students will need to find critical numbers determine the intervals on which the function increases and decreases apply the First Derivative Test to classify the critical points as relative maximums, relative minimums or neither (locate relative extrema of a function). The product can be used as in class practice, an independent practice, partner activity, for group work, as enrichment. Detailed and typed answer keys are provided.

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.

These are 11 Algebra 1 warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework on exponent laws and radicals and scientific notation and operations. Each of them is a half-sheet in size and contains from 6 to 14 problems. Topics Included: Exponent Laws (Product and Power Rules) Exponent Laws (Quotient Rule) Exponent Laws (Zero and Negative Exponents) Scientific Notation and Operations with Scientific Notation Simplifying Radicals (No Variables) Simplifying Radicals with Variables Adding and Subtracting Radicals Multiplying Radicals Dividing Radicals Rationalizing the Denominator Operations with Radicals Answer key is included.

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 16 Algebra 1 warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework on slope of a line, equation of a line and linear function. Each of them is a half-sheet in size and contains from 2 to 8 problems. Topics included: Slope of a Line from 2 Points Slope of a Line from a Graph Slope of a Line from a Table 4.Slope of a Line from an Equation Graphing Lines in Slope-Intercept and Standard Forms Writing Equations of Lines from Graphs Writing Equations of Lines from 2 Points Writing Equation of a Line Given the Slope and a Point Writing Equation of a Line from a Table of Values Equations of Parallel and Perpendicular Lines X- and Y- Intercepts Linear Function Applications Inverse Linear Equations Piecewise Linear Functions Graphing Absolute Value Functions Equations of Proportional and Non-Proportional Relationships Answer keys are included.