This is a self-checking circuit activity on finding indefinite integrals using integration by parts. Activity directions: Students begin with the problem #1, solve the problem, find the answer somewhere else on the pages ( which are three) and write “2” in the blank. Then student solve that problem (#2), search for the answer again and when find it write “3” in the next blank. Students continue in this manner until they return to the problem #1. They should solve all the 11 problems before returning to the start point. There is provided space for students to show short solutions on the pages. They can record their detailed solutions on separate sheets of paper and attach them to the worksheets of this circuit. Answer keys are included. Full solutions handwritten clearly are provided.

This is an engaging and self-checking derivatives practice - 8 (black kitten and pumpkin- themed) task cards each containing 4 tasks/problems. On each card is given a function. CARDS 1- 4, 7, 8 Students are asked to find the first derivative (1 task) find the second derivative (2 task) compute first and second derivatives at given points and then substitute the values in a given equality to verify it (3 task) prove that the given function satisfy a given first or second - order differential equations (4 task) Students do NOT need to solve the differential equations! They only substitute in them. CARDS 5 and 6 require finding the first, second, third and forth derivatives. Students calculate derivatives at given points and show that a given equality is true. Then they prove that the given functions satisfy third and fourth – order differential equations. Students can use the cards working in groups of 2 and/or 4. The cards can be also used as an independent practice. The teacher or the student can choose which problems of each card to be solved like 1a, 2b, 3a, 4c, 5d…etc. Student recording sheets and detailed answer keys/solutions (handwriten clearly) are included.

This is a fun self-checking circuit activity on evaluating limits algebraically (rational, radical and trigonometric functions included). There is provided enough space for students to show work on the pages. Activity directions: Students begin with the problem #1, solve the problem, find the answer somewhere else on the pages ( which are three) and write “2” in the blank. Then student solve that problem (#2), search for the answer again and when find it write “3” in the next blank. Students continue in this manner until they return to the problem #1. They should solve all the problems before returning to the start point. Full typed solutions are included.

This is a fun mermaids themed matching activity on inverse functions. The problem slides/pages are four as there are four problems per each slide/page; on each slide/page students are also given the answers of the fourth problems. Students are asked to find the inverse function of each function given and then use the tool of curvilinear coupling to match each problem with its answer. On the first slide/page the given functions are linear, on the second slide/page the functions are polynomial (quadratic, qubic, quartic), on the third slide/page the given functions are radical (square root, cube root, 4th root) and on the fourth slide/page the functions are rational. There are 5 answer key slides. 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 and four slides on a page for easy and more economic printing!

This activity is designed to be used for groups of 4 members! It includes four different multiple - choice quizzes each of eight radical equations and a brief biographical text of NASA research mathematician Katherine Johnson (to be completed). Students will practice solving radical equations reducible to linear and quadratics. Extraneous solutions are included. 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 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: Students solve all the equations. The answers they get will give them pieces of a brief biographic story about the American scientist Katherine Johnson. It can stimulate student interest in Math and provide a role model for all students. Recording sheets are provided for students to show all work. Answer keys are included.

This is a collaborative group activity (for groups of 2, 3 and/or 4 members) on inverse functions. It consists of 12 sections as in each section there are 4 similar problems – one problem for each of the partners. The functions included are linear (in section 1);quadratic functon in standard form (section 2) ;quadratic functions in vertex form (section 3);cubic functions in the form (x+a)^3 + b (section 4);polynomial functions in the form a(x+b)^n+c (section 5); square root functions in the form a + b√(x+c) (section 6);cube root functions c + ∛(ax+b) (section 7);n-root functions (section 8);rational functions of the type (ax+b)/(cx+d) (section 9);exponential functions of the type e^(ax+b) + c (section 10); logarithmic functions ln(ax+b) (section 11); trigonometric functions of the type asin(x+b), acos(x+b), atan(x+b) and acot(x+b) (section 12) This activity may be turned into a competition between groups. In each section, it is given the certain number of points that each problem solved correctly gives. The number of points are directly proportional to the difficulty level of the problems. Students recording sheets are provided. Answer keys are included.

These are two forms of engaging practice on arc length and area of a sector. The forms are similar and each form contains 7 problems graduated in difficulty. The first problem is finding the arc length and sector area of four pictured sectors as the measure of the central angle and the radius are given. The second problem is calculating the area of a pictured segment. The next five problems are text problems. For problem 3, students have to find the length of an arc given its angle measure and the diameter of the circle. Problem 4 is finding the diameter of a circle given an arc length and its central angle. For problem 5 given are the radius and an arc length, students have to find the sector area. Problem 6: given the radius and the sector area, student will find the central angle and the exact and approximate values of the arc length. And problem 7: given the arc length and sector area, students have to evaluate the diameter and circumference of the circle. The product can be used except as independent practice in class as an assessment and homework assignment. Answer keys are included.

These are 4 forms practice on double and half angle identities. Each form contains 5 challenging problems. The first problem is finding the exact value of trigonometric function using half angle identities. The second problem is evaluating a trig function of double angle 2α given the value of trig function of angle α and in which quadrant lies the angle alpha. The third problem is finding the values of three trig functions of angle alpha, half alpha or double alpha given the value of one trig function and in which quadrant lies the angle alpha. The fourth problem is simplifying two expressions and the fifth problem is proving an identity. The product can be used as independent practice, extra practice, group activity (groups of 2,3 and/or 4), enrichment, homework, and as an assessment. 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 slides **on a page for easy and more economic printing!

This activity practices finding derivatives using the chain rule. The composite functions include rational, radical, trigonometric and inverse trigonometric, exponential and logarithmic functions. The most of the problems are challenging for students to improve their skills on differentiation using the chain rule. There are 12 black kitten - themed task cards each containing 2 tasks. On each card is given a function. Students are asked to find the first derivative (1 task) compute the first derivative at a given point (2 task) Students can use the cards working individually or in groups of 2, 3 and/or 4. Student recording sheets and typed answer keys are included.

This resource contains total of 50 problems. Students will practice differentiation using the basic properties of derivatives and the power rule only. The packet has 6 worksheets: ⟐ The first and second worksheets WS # 1A and WS # 1B are similar. Students will have to find the first derivatives of 10 various functions ( polynomial, rational and radical). These are designed to be possibly used as a partner activity. ⟐ The third worksheet is finding the first derivatives of 10 functions as some of the examples are a bit more complicated and challenging than WS # 1A and WS #1B problems. ⟐ The fourth worksheet is finding the second derivatives of 8 various functions ( polynomial, rational and radical). ⟐ The fifth worksheet has the students finding the equation of the tangent line for 6 given functions at indicated points. ⟐ The sixth worksheet asks the students to determine the intervals on which 6 given functions are increasing and decreasing. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be used as a partner activity – for instance: ⟡ Partner A will solve WS # 1A while Partner B solves WS # 1B, then they swap papers and Partner A will solve WS # 1B while Partner B solves WS # 1A. 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. Answer keys are NOT included!

This is an engaging card sort activity for studying the intervals of concavity and inflection points of given functions. The functions (common and composite) include polynomials, radical, exponential, logarithmic, trigonometric and inverse trigonometric expressions. They are specially selected so that each function has not more than one inflection point. Activity Directions: Students determine the intervals of concave up/concave down and the inflection points of each of 12 given functions. They are also given 16 cards each with a statement written on it. The statements concern the concavity and inflection points of the given functions and are true or false. Partners are asked to use their studies on the functions to verify the statements and sort the cards into two groups - “TRUE” and “FALSE”. Thus students do comparative analysis of the functions. This product can be possibly used as an independent practice, as a partner or a group activity (groups of 3 and 4). Student recording sheet and all answer keys are provided.

In this activity students will practice solving improper integrals. There are two problems (A1 and A2 questions) on each of 8 aliens themed task cards. “An alien asks” two types of questions - question A1 is to evaluate an improper integral if it diverges and question A2 is to prove an improper integral equality. This activity can be used for class work, independent practice, as partner activity or group activity ( groups of 2 or 4). Answer keys and solutions ( handwritten clearly) to problems A1 – H1 are provided.

This is a collaborative and fun robots themed group activity on polynomial inequalities. On each slide/card students are given 4 similar problems as the problems increase in difficulty with each next slide/card. There are included inequalities with polynomials factored at the left side, inequalities where polynomials are not factored completely and inequalities where polynomials are in their standard form. Students must be able to factor quadratic and biquadratic trinomials, using the difference of squares formula, and factoring by grouping. Students work in groups of 2, 3 and/or 4 or this activity can be also completed individually as half of the problems can be solved as classwork and the other half - as homework. Answer keys are contained 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 or three slides on a page for easy and more economic printing!

This is an engaging activity on solving radical equations with higher indexes. There are 4 pages/slides with problems. There are included 2nd, 3th, 4th, 5th, 6th, 7th, 8th, 9th and 10th roots. On each page/slide students solve four given equations for the variables x, y , z and t. Students first find the variable x from the first equation, then they substitute the value of x in the second equation to find the value of the variable y. Then students use the value of y to find the value of z from the third equation and at the end students use the value of z to find the value of the variable t from the fourth equation. Students record their answers in the empty boxes provided. On each page/slide students are given a relation between the fourth variables x,y,z and t so to check if they have obtained the correct answers. Students can work independently or in groups (of 2 or 4) to complete this activity. Answer key is contained 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 a fun multiple-choice game called “What Species of Turtle am I?” on inverse functions. On each slide/page students are given one function and are asked to find its inverse function. There is also a picture of a turtle, four answer choices and four names of turtle species corresponding to each optional answer. Students solve the problem and chose an answer, the answer will reveal to them what species is the turtle. The slides/pages with problems are seven. The functions included are quadratic, cubic, rational, radical (square and cube roots), exponential and trigonometric. 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 and three slides on a page for easy and more economic printing!

These are 9 practice tickets on real zeros of polynomials. There are 3 problems per ticket - given are third degree polynomial, a fourth degree and a fifth degree polynomial as each problem is worth respectively 3, 4 and 5 points. The product can be used as independent practice of 9 forms, group activity (students can work in groups of 2,3,4 and more members) that can turn into a competition. The group gathered maximum points wins. The tickets can be also used as homework assignment or even as an assessment. 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!

These are 12 turkey/Thanksgiving themed task cards. The cards are grouped with three similar problems per card. Students will review and demonstrate their knowledge of the following topics: domain and range of rational, radical and logarithmic functions - cards 1 and 2 horizontal and vertical asymptotes of rational, radical and logarithmic functions - cards 3 and 4 real zeros of rational, radical and logarithmic functions – card 5 intervals of monotonicity of rational, radical and logarithmic functions – card 6 real and imaginary zeros of polynomials (factoring polynomials, finding x- and y- intercepts, solving polynomial equations), solving polynomial inequalities in standard and factored form, solving rational inequalities – cards 7, 8, 10, 11 and 12 division of polynomials – card 9 Students can use the cards working in groups of 2, 3 and/or 4. The cards can be also used as an independent practice. The teacher or the student can choose which problems of each card to be solved like 1a, 2b, 3a, 4c…etc. Student recording sheets are provided. Typed answer keys are included. Have a Blessed Thanksgiving!

This is an engaging practice on exploring quadratic functions. Students are given 66 quadratic functions in standard and vertex forms. They have to identify/find the axis of symmetry (9 problems) the vertex (10 problems) the minimum or maximum (8 problems) the range (6 problems) the intervals of increasing and decreasing (10 problems) the y- intercept (9 problems) the x- intercepts (14 problems) This practice can help learners strengthen their understanding on characteristics of quadratic functions and then deal with the process for graphing quadratics easily. The practice worksheets have enough room for students to show their work. Answer keys are included.

This is an engaging practice for a set of 30 problems on equation of a circle. It consists of four parts (four pages) Part 1/Page A contains 10 problems on finding the center and radius of a circle where in the first 6 problems the equations are given in standard form and in the last 4 problems the equations are given in general form. Students will need to complete the square to complete the last 4 tasks. Part 2/Page B have 8 text problems on writing equations for circles. Students are given the center and the radius the endpoints of the diameter the center and one point that the circle goes through it the center and an endpoint of the radius the center and the diameter the center and the circumference of the circle the center and the area of the circle Part 3/Page C is interpreting the graphs of 6 circles. Students will have to write the equation of each circle in both standard and general forms. Part 4/Page D is graphing the circle given its equation in standard form (6 problems). Grids are provided. The practice sheets give room for students to show work. Answer keys are included.

These are two products in one - two password search activities. The resource includes a total of 24 examples in which students will convert between radians and degrees. Product 1: Students solve 12 problems to convert given radian measures into degrees. Then 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 problems right. Product 2: Students solve 12 problems to convert given degree measures into radians. Then 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 problems right. The practice sheets give enough room for students to show work. Answer keys are included.