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 8 practice tickets designed for Trigonometry and PreCalculus Classes on finding the exact value of inverse trigonometric functions and evaluating trig function of an inverse trig function. There are 3 problems per ticket. The first problem is proving an equality of the type: trig function of an inverse trig function is equal to a real number. The second problem is finding the value of an expression of the type: trig function of the sum or difference of inverse trig functions. The arguments of the arcsin and arccos are +1 and – 1, 0.5 and -0.5, √3/2 and -√3/2, √2/2 and - √2/2 and the arguments of arctan and arccot are +1 and -1, √3 and - √3, √3/3 and - √3/3. The third problem is to evaluate an expression of the type trig function of an inverse function as this time the arguments of the inverse trig functions are fractions like -1/3, -2/5, -3/2 and students will need to use the Pythagorean identities to evaluate the given expressions. The product can be used as independent/extra practice, group activity, homework and even as an assessment. Student recording sheet and answer keys are included.

In this engaging and collaborative group activity (for groups of four), students will practice operations on functions (adding, subtracting, multiplying and dividing). There are 7 sections as each section has four subsections A, B, C and D (a total of 112 problems). In each subsection are given different pairs of functions as each partner has to perform adding, subtracting, multiplying or dividing. The subsections are four so each partner to go through the fourth different operations on functions. In section 1 the given functions f(x) and g(x) are both linear. In section 2 f(x) is a quadratic binomial and g(x) is a linear function. Section 3: f(x) and g(x) are both quadratic binomials. Section 4: f(x) or g(x) is a cubic binomial and g(x) or f(x) is a quadratic trinomial. Section 5: f(x) and g(x) are both radical functions. Section 6: f and g are rational functions. Section 7: in subsections A and B f and g are both exponential functions and in subsections C and D f and g are both trigonometric functions. The teacher can choose on which sections the students to work on. This group activity may turn into competition between groups. ☞The resource can be also used as four different forms of independent practice. Answer keys are included.

In this partner activity, students will practice composition of two functions. The composite functions are notated two different ways: f(g(x)) and (f o g)(x). There are included linear, quadratic, rational, radical, absolute value, trigonometric and exponential functions. There are 10 sections as in each section partners are given two functions. In section 1, Partner A has to find f(g(x)) and Partner B has to find g(f(x)). In section 2 Partner A has to find g(f(x)) and Partner B – f(g(x)). In section 3, Partner A again has to find f(g(x)) and Partner B – g(f(x)) and so on. Students find out that in each section they get quite different results and understand that it is important to be careful which function comes first. The practice sheet give room for students to show work. Answer keys are included.

This is a collaborative partner activity on dividing polynomials using long division. Dividends are polynomials of third, forth, fifth and sixth degree and divisors are binomials and trinomials of first, second and third degree. This activity takes each partner through 12 problems (12 sections). Partners corresponding problems are similar (problem 1A is similar to problem 1B, problems 2A is similar to problem 2B and etc). Students must get the same quotient and different remainders. They record their answers on partners’ response sheet. A recording sheet is also provided. Answer keys are included.

This is a collaborative partner activity on partial fractions decomposition. It takes each partner through 8 problems of the following types – rational fraction with denominator (ax+b)(cx+d) ax^2 +bx +c where the quadratic trinomial can be factored (ax+b)^2 (ax^2 +b)(cx+d) (ax+b)(cx+d)^2 (x+a)(x+b)(x+c) x(ax^2 +bx +c) as the quadratic trinomial can not be factored (ax^2 +c)^2 Partners corresponding problems are similar (problem 1A is similar to problem 1B, problems 2A is similar to problem 2B and etc). This activity can also be used as a review in AP Calculus BC or College Calculus 2 before the Techniques of Integration section on Partial Fraction. 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.

These are 12 cards for partners – a total of 48 trigonometric equations. Students will practice solving basic trig equations, equations with multiple angles and equations of quadratic type. They will need to use factoring method and the quadratic formula, the fundamental and double-angle identities. There is one trig equation involving a parameter on each card. Students are asked to solve the equation for four given different values of the parameter. Thus, students have four problems per card – problems 1A, 1B, 1C and 1D. Students can work in pairs (partner activity) or in groups of three and four (group activity). This is a wonderful way to get students working on different, but similar problems helping each other with methods. The cards can be used for independent work as well. The teacher or student can chose which problems to solve – like problems 1A, 2C, 3B, 4A, 5D, etc. Student recording sheet and 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.

This resource contains total of 32 problems. Students will practice solving polynomial inequalities algebraically. They are asked to write the solution sets using interval notation. Problems are classified into 2 categories according to the form of polynomials ( factored or standard) of 2 levels of difficulty for each category of polynomial inequalities. Examples include second, third and fourth - degree polynomials. ⟐ The first and second worksheets have the students solving a total of 16 inequalities in factored form ( level 1 & level 2). ⟐ The third worksheet is finding the solution sets of 8 inequalities in standard form ( level 1) ⟐ The fourth worksheet contains 8 inequalities where there are polynomials in expanded form on both sides (problems level 2) The product can be used in a variety of ways – in class for cooperative learning, as a partner or a group activity, independent practice or homework assignment. Answer keys are provided.

In this fun bats themed activity, students will practice finding zeros of polynomial functions. There are included third, fourth and fifth degree polynomials. The zeros are real (rational and irrational) and complex numbers. Activity Directions: Students are instructed to find the zeros of each of 12 polynomials. The roots of all polynomials are recorded on twelve of 13 bats on a given picture. Every time students arrive at a correct answer, they will “chase away the bat” having this answer written on it. Students are also asked to find the only one bat who can NOT be chased away. The product can possibly be used as a partner or a group activity(group of 3). Student recording sheets and answer keys are provided.

This is an engaging and challenging practice on simplifying exponential expressions (the variable x is in the power indicator). The problems require good skills in using the rules of exponents (forward and backward). There are 4 different versions/forms as forms A and B have similar examples, so have the forms C and D. On each form students are given eight expressions. Students are asked to simplify them into the form a^f(x) or b. a^f(x) . This practice is much helpful for the next step - solving exponential equations. The product can be used as an independent practice or partner activity. I hope the practice worksheets give enough room for students to show their work. Answer keys are included.

This is an engaging practice or quiz on radical equations. It consists of 14 equations of varying difficulty levels, ranging from simple to complex. Problem types include: · Radical function equals to a constant · Radical function equals to monomial · Radical function equals to radical function · Radical function equals to binomial · Sum and difference of two radical functions equals to a constant Students must check all solutions by plugging them into the original equation to ensure they are selecting the correct answer. The product is useful for independent /extra practice, review, homework or assessment/quiz. Answer keys are included.

This is an engaging and challenging practice on finding and using the values of special angles from the unit circle to evaluate 10 trigonometric expressions. The expressions include two or three trig functions combined using algebraic operations like A = 2sin(pi/4) - tan(4pi/3). All values of angles are given in radians. Students can use their unit circle. The practice worksheets give enough room for students to show their work. The product is useful for classwork as extra/ advanced practice, enrichment or homework. Full solutions are included.

This is a collaborative and fun partner activity on finding the vertex of a quadratic function. Students will work in pairs through 12 sections (or less ). In each section, a partner is given a quadratic function in standard form to determine its vertex. Partners compare their results to see whether in each section they have obtained one and the same answer. The practice worksheets give room for students to show their work. Answer keys are included.

In this 16 questions - partner activity, students will solve systems of linear equations with two variables by the most appropriate method (substitution and/or elimination methods). The answer of each of Partner’s A problems is the same as 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 check whether their results match. If their answers don’t match, they work together to figure out what went wrong. Student recording sheet and answer keys are provided.

This is a collaborative group activity (for groups of 2,3 and/or 4 members) on factoring difference of squares. It consists of 12 sections as in each section there are 4 similar problems - one problem for each of the partners. Problems gradually increase in difficulty with each subsequent section. Problem types include: difference of squares of monomials ( Level 1) difference of square of monomial and square of binomial (Level 2) difference of square of binomial and square of monomial (Level 2) difference of square of binomials (Level 3) 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 offers. The number of points are directly proportional to the difficulty level of the problem. I hope the practice sheets provide enough room for students to show work. Answer keys are included.

Students will factor polynomials with four terms using the factor by grouping method in this collaborative partner activity. It consists of 12 sections as in each section students are given one and the same problem. Partner A is instructed to group the first two terms together and then to group the last two terms together, while Partner B is instructed to group the first and third terms together and then to group the second and forth terms together. Thus partners see that factoring by grouping problems can be approached at least in two different ways. In the next section students are given the next problem as this time Partner A is instructed to group the first and third terms together and then to group the second and forth terms together and Partner B is instructed to group the first two terms together and then to group the last two terms together. Then, in the same manner as in section 1, Partner A groups the first two terms together and …etc. I hope your students will love this activity and find it enjoyable and helpful. The practice sheets provide room for students to show work. Full solutions are included.

These are three versions (three levels) independent practice on factoring polynomials by determining the greatest common factor. Versions A and B contain 15 problems each and version C has 10 more challenging examples. The product can be used as an extra practice, enrichment or homework assignment. It can be also used as a group activity - competition between groups of 2 or 3 as the members of the group will chose who which version to solve. The practice sheets give enough room for students to show work. Answer keys are included.

This is a fun game on factoring trinomials. The half of the problems are with the leading coefficient a=1 and the other half have a≠1. Students are given 12 problems and 12 pictures of dragons ( there is a picture of a dragon corresponding on each trinomial). The problems are multiple-choice format with four options each ( there is a name of a dragon corresponding on each possible answer). Students have to factor the trinomials given and find out the names of all dragons. The names are funny as they begin with Dr or the dragons may have names like “ The Lazy” , “The Clever”… The game arouses students’ imagination and makes students enjoy while solving the problems. Student recoring sheet and answer keys are provided.