These are 50 practice problems on complex numbers in polar form. The problems are grouped by topic ❆ finding the polar form of a complex number (practice sheet A, 15 problems) ❆ converting complex numbers from polar to rectangular form (practice sheet B, 10 problems) ❆ finding the product of two complex numbers in polar form ( practice sheet C, 5 problems) ❆ finding the quotient of two complex numbers in polar form (practice sheet D, 5 problems) ❆ finding powers of complex numbers in polar form using DeMoivre’s Theorem (practice sheet E, 5 problems) ❆ finding roots of complex numbers in polar form (practice sheet F, 10 problems) I hope the practice sheets give enough room for students to show work. This resource can be used as an independent/extra practice, enrichment, review, homework assignment or even as an assessment. Answer keys are included.

In this activity students will practice solving quadratic equations in standard form by the quadratic formula and by completing the square. All equations have complex solutions. Students will also practice plotting points on a coordinate plane, representing the values of the complex roots of the quadratic equations. An amusing part is the drawing activity where partners will draw easy drawing symbols around the plotted points and will produce a nice picture together. Activity Directions: Each partner is supposed to solve individually eight quadratic equations. The equations are marked with different symbols. Student solves the equations given like this: one equation - by the quadratic formula and the other - by completing the square and it goes still that way. Students show detailed solutions on the recording sheets provided. Then partners plot all the points, representing the values of the complex solutions they have already found on a coordinate plane given. They consider the symbol of each equation to be the symbol of its roots as well. At last students draw the symbol of each equation around the plotted points, corresponding to its complex solutions. All answer keys and FULL SOLUTIONS of the problems are included.

This is a collaborative activity to practice solving complete quadratic equations in standard form by all methods. Students work through sections. In each section, each partner has one equation to solve by a specified method. Equations of the partners in each section are DEPENDENT. The problems are 28 WELL THOUGHT OUT that all have integer coefficients and solutions. Activity Directions: In Section One, Partner A starts solving the equation given and finding its roots while Partner B waits to receive the values of these roots from Partner A. Once the solution set is found Partner A “provides” Partner B with its numbers . Then Partner B places the numbers into the empty squares of his own equation given with two missing coefficients and solves the equation. There is an important instruction - the number which has its absolute value less to be put in place of the first missing coefficient. In Section Two partners repeat the same actions, however this time Partner B starts first. In Section Three, Partner A starts solving first again and it goes still the same way. Recording sheets are included for students to show work . All answer keys are included as well. NOTE: The pages are designed in a way that each partner can solve ten equations or even only six.

Students will use the basic integration formulas solving definite integrals with this fun password search activity. Activity Directions: Students solve 12 definite integrals using basic integration techniques, the properties of definite integrals (integral of sum of functions and moving the constant across the integral sign) and the fundamental theorem of calculus. Students 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 integrals right. Students can work independently or in pairs. Answer key is included.

This is a collaborative activity to practice evaluating indefinite and definite integrals by using advanced techniques of integration(** integration by parts and using u-, trigonometric and other types substitutions**). There are given 15 problems some with differentiated instructions. Problems list can be used as 15 mini task cards. Students can work through the problems cooperatively or in groups of 3 or 5. Student recording sheets and answer keys are included. Typed solutions to problems are provided.

These are 10 owl themed task cards each containing 3 similar problems on trigonometric functions, expressions and identities. The first and second cards are finding the value of trig function given the value of another trigonometric function and to which quadrant belongs the angle (from I to IV quadrant), the third card is evaluating trig expressions given the value of the angle(s), the fourth card is evaluating a trig expression given the value of trig function, 5th card is evaluating numerical trig expressions, 6th card is evaluating trig function given the value of another trig function as here co-function identities are involved, 7th card is determining which of given six expressions are positive and which are negative, 8th card is expressing trig expressions in terms of tan(teta), 9th card is simplifying trig expressions and 10th card is proving trig identities. Students need to know Pythagorean, reciprocal, co-function and quotient identities to handle the problems. The resource can be used as a review, group activity (groups of 2 or 3), independent extra practice, homework and even as an assessment (the teacher can chose how many problems and which of the problems the student to solve to check his knowledge and skills). There is included a page where students can record their answers in a table. Answer key is included.

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!

These are two engaging practice - the one is 6 levels practice and the other is mixed practice, both containing a total of 40 problems. The 6th levels practice consists of 6 departments each having 4 similar problems as the problems become more challenging with each level. Students have to find all the products and then classify the obtained polynomials. All the problems are of one variable x. This one can be used as class practice. The mixed practice consists of two tasks each having 8 problems. The first task is finding the eight products and classifying the obtained polynomials (the expressions are of one variable x). The second task is finding 8 products as this time the expressions include from two to four variables, students have to find the sum of coefficients of each of the obtained polynomials. Empty boxes where students can record their answers are provided. This one can be used as extra practice or homework. Answer keys are included.

This resource contains a total of 48 practice problems on Pythagorean theorem. The problems are classified into 4 categories as follows: A. Problems on finding the hypotenuse ( 8 problems with given figures and 6 text problems) B. Problems on finding the missing leg (7 problems with given figures and 6 text problems) C. Problems on finding the missing side (it could be the hypotenuse or a leg of the triangle) ( 6 problems with given figures) D. Problems using the Inverse of Pythagorean theorem – determining whether given dimensions belong to a right triangle (given 12 triples of numbers and 3 problems with given figures/triangles) The practice sheets give room for students to show work. Answer keys are included.

This is a rainy kids themed practice or partner activity on operations with complex numbers. The problem pages/slides are five, as on each page/slide there are given nine complex numbers from z1 to z9. On page/slide 1 students have to find 10 wanted sums which are like z1+z5; z4+z9; z1+z2+z3;…, on page/slide 2 students calculate wanted differences which are like z8-z3; z2-z3-z6;…on page/slide 3 students are asked to compute 10 products, on page/slide 4 students have to find 10 quotients. On page/slide 5 students perform the indicated operations which are mixed operations like z8+z1/z2; z4z8-z7;…etc. There is provided a table with empty boxes on each page/slide where students can type their answers. As the problems are many (50) this practice can be used as partner activity (even group activity) or like independent practice along with homework (students can solve some of the problems in class and the rest problems can be done as homework). 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 14 Algebra 2/Pre Calculus warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework. Each of them is a half-sheet in size and contains from 2 to 9 problems. Topics included: Evaluating Logarithms Evaluating Logarithmic Expressions (Inverse Properties of Logarithms) Adding and Subtracting Logarithms Multiplication of Logarithms Change of Base Formula Condensing Logarithms Expanding Logarithms Comparing Logarithms Domain of a Logarithmic Function Graph and Key Features of a Logarithmic Function Logarithmic Equations of type log(base a)f(x)=b Logarithmic Equations of Type log(base a)(f(x)=log(base a)(g(x) Logarithmic Equations of Type log(base a)f(x)±log(base a)g(x)=b Logarithmic Inequalities Answer keys are included.

These are 15 Algebra 2/Pre Calculus warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework on quadratic functions, quadratic inequalities, system of quadratic inequalities and nonlinear systems. Each of them is a half-sheet in size and contains from 4 to 6 problems. Topics included: Axis and Vertex of a Quadratic Function Vertex Form of a Quadratic Function Domain and Range of a Quadratic Function X- and Y- Intercepts of a Quadratic Function Monotonicity Intervals of a Quadratic Function Maximum and Minimum Values of Quadratic Functions Nonlinear Systems (Linear-Quadratic) Nonlinear Systems (Quadratic-Quadratic) Solving Nonlinear Systems Graphically Graphing Quadratic Inequalities in Two Variables (two warm-ups) Solving Quadratic Inequalities in One Variable Algebraically Graphing Systems of Quadratic Inequalities in Two Variables (two warm-ups) Solving Systems of Quadratic Inequalities in One Variable Algebraically Answer keys are included.

These are 15 Algebra 2/Pre Calculus warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework. Each of them is a half-sheet in size and contains from 3 to 9 problems. Topics included: Absolute Value of a Complex Number Adding and Subtracting Complex Numbers Multiplying Complex Numbers Dividing Complex Numbers Operations with Complex Numbers (Mixed) Quadratic Equations with Complex Roots (Square Root Method) Quadratic Equations with Complex Roots in Vertex Form Quadratic Equations with Complex Roots (Quadratic Formula) Determinant of a Matrix Adding and Subtracting Matrices, Multiplying a Matrix by a Number Multiplying Matrices Operations with Matrices (Mixed) Inverse Matrices Matrix Equations Systems of Linear Equations with 3 Variables Answer keys are included.

These are 15 Algebra 2/Pre Calculus warm-ups, do-nows, bell-ringers, entrance/exit tickets or mini-quizzes/mini homework. Each of them is a half-sheet in size and contains from 3 to 12 problems. Topics included: Evaluating Trigonometric Expressions with a Variable Evaluating Trig Expressions (No Variables) Exact Values of Trig Functions of an Acute Angle Simplifying Trig Expressions Verifying Trig Identities Simplifying and Evaluating Trig Expressions Using the Exact Value of a Trig Function Converting Between Radians and Degrees Equation of a Circle Operations with Functions Composition on Functions Graphs of Piecewise Functions Evaluating Piecewise Functions Pascal’s Triangle and the Binomial Theorem Graphs of Exponential Functions of type f(x)=a.b^x Inverse Functions Answer keys are included.

These are three practice worksheets on Parametric Equations and Parametric Curves. Students will work on ✦ eliminating the parameter, writing the parametric equation as a rectangular equation and identifying the graph of the parametric curve ( WS # 1, 14 problems) ✦ finding parametric equations (writing two new sets of parametric equations for given rectangular equations) ( WS # 2, 8 problems) ✦ graphing parametric curves (sketching the parametric curve for given pair of parametric equations and giving the orientation of the curve) (WS # 3, 12 problems) Functions involved are polynomial, absolute value, rational, radical, exponential, logarithmic and trigonometric. 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, homework assignment and even as an assessment. Detailed answer keys ( handwritten clearly) are included.

Students will practice the chain rule with this fun multiple-choice game. On each page/slide there are given a picture of a horse, a function that students have to differentiate and four answer choices. Name of horse breed corresponds to each answer choice. Students solve the problem and choosing an answer they find out what horse breed is this one on the picture. The problem pages/slides are 12. The functions included are polynomial, rational, radical, exponential, logarithmic, trigonometric and inverse trigonometric. 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 three slides on a page for easy and more economic printing!

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 is a fun and engaging multiple-choice game on multiplying radicals. There are 10 pages/slides with problems as each page/slide contains two similar problems. Each problem is labeled with a large alphabet letter written on a picture of a mother penguin. Students are given four answer choices labeled with the small letters a,b,c and d each written on the picture of a baby penguin. Students solve a problem, choose an answer and write the letter of the baby penguin to its mother matching the problem with its answer. The problems increase in difficulty with each next page/slide. On the first four pages/slides students multiply two radicals, in page/slide 5 they multiply three terms, in pages/slides 6, 7 and 8 students will need to use the distributive property and FOIL and in pages/slides 9 and 10 students multiply radicals with variables in the radicands. This activity can be used as an independent practice and partner activity. If students work in pairs student A will solve the first problem of a page/slide and student B will solve the second problem of the same page/slide and because they have similar problems students can help each other with methods. The 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 or three slides on a page for easy and more economic printing!

This product contains 50 trigonometric expressions with their detailed typed solutions. The problems are separated into five groups/quizzes. EACH GROUP of expressions REQUIRES APPLYING OF SPECIFIED IDENTITIES to be simplified as follows: • The fundamental Pythagorean identity • Quotient identities • Reciprocal identities • Pythagorean identities • Co-function identities The problems have varying degrees of difficulty. The product can be divided into parts and used in a variety of ways: in class practice (teacher can show the solutions to some of the examples to assist students in completing the rest successfully) as partner activity or group activity (students can assist one another throughout simplifying the expressions) an assessment or homework Student recording sheets are provided and full solutions to the problems as well.

This is a resource on arithmetic sequences having 14 practice pages and containing a total of 70 problems arranged by topic/type and difficulty level. Students will use the explicit formula and the formula for the sum of the first n terms. ➤ Using the explicit formula students will have to find the nth term (problems Level 1) the first term (problems Level 1) the common difference (Level 1) the number of terms (Level 1) the first term and the common difference solving systems of two equations (Level 2) ➤ Using the formula for the sum of the first nth terms students will have to find the sum of the first nth terms (problems Level 1) the nth term and Sn (Level 1) the first term and Sn (Level 1) the number of terms and Sn (Level 1) ➣ When given Sn ( problems level 2) students will have to calculate n and d - the nth term and d n and nth term the first term and d the first and nth terms n and first term The practice sheets can be used for independent and extra practice, enrichment, as a group activity (groups of 2, 3 and/or 4), homework and even as an assessment.