These are 14 practice pages on geometric sequences. 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 ratio (Level 1) the number of terms (Level 1) the first term and the common ratio 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 first term and Sn (Level 1) the common ratio 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 r the nth term and r n and nth term the first term and r 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. Answer keys are included.

Students will use the power, quotient and power rules of exponents to find the value of each of 10 exponential expressions. The problems are challenging and include negative bases of the exponents. Students search for their answers consecutively in a table whose cells contain a numbers and a word to find an aphorism. Student recording sheet and answer keys are included.

This trigonometry practice consists of 12 problems (12 given diagrams) in which students will practice finding missing side and angle measures in right triangles using the sine, cosine, and tangent ratios. The problems are divided into four groups of three (four cases). In the first group of problems students need to find the opposite side in the right triangle. The second group of problems is finding the adjacent side. The third case is finding the hypotenuse. And the four case is finding the measure of a missing angle. Practice sheets give enough room for students to show work. Answer keys are included.

These are 12 challenging problems on solving systems of two quadratic inequalities in one variable. Students can solve each system by using a sign chart, by using a double number – line or by representing the solution of each inequality on one and the same number line. Then students determine where the solutions of the two inequalities overlap and find the combined solution set of the system. The practice sheets give room for students to show work. This resource can be used as an independent/class/extra/advanced practice, enrichment or homework assignment. Answer keys are included.

This is a fun and collaborative matching activity for your students to practice expanding binomials using the binomial theorem. Students have to find a specific term in a binomial expansion working through 12 expressions. Student find the indicated term and then they look for their answer on a picture with kids holding blanks with the answers written on them. Students match the answer with the problem (record the letter of the problem near or upon the picture with the kid holding the answer of that problem). Students can work independently or in pairs. Student recording sheets and answer keys are included.

These product can be used to introduce laws of exponents or for engaging practice after teaching a lesson on exponent rules. There are 121 laws of exponents problems in all divided into 17 sections(from A to Q). In each section each “rule” is written and includes 1 to 4 worked out examples and 3 to 8 similar to them problems for students to try to solve them by their own. Students will apply A) product rule with same base B) product rule with same exponents C) quotient rule with same base D) quotient rule with same exponents E) power rule F) power rule with radicals G) negative exponents rules Students will also multiply and divide negative and fractional exponents, exponents with different bases and different power indicators, exponents with variables and in the last section students will perform adding and subtracting exponents. The practice sheets give room for students to show work. Answer keys are included.

This trigonometry activity consists of a total of 24 problems in which students will practice finding missing side and angle measures in right triangles using the sine, cosine, and tangent ratios. The problems are divided into six sections of four similar problems. The product is intended to be used for groups of maximum four members (there is a problem for each partner of the group in a section) . Solving similar problems in each section encourages the partners to help each other with methods. Moreover, this group activity may easily turn into a competition between groups. The product can be also used as an independent practice with four similar forms (form A, form B and forms C and D) if preferred. I have included a modified worksheet so the product can be used in this way. Here is the description of the problems in each section: Section 1&2 – given the hypotenuse and an acute angle. Section 3 – given an acute angle and its opposite side. Section 4 – given an acute angle and its adjacent side. Section 5 – given a leg and the hypotenuse. Section 6 – given the two legs. Students have to find the missing sides or/and angles. Answer keys are included.

This activity practices converting between polar and rectangular coordinates. Students will work on 12 problems. The first six problems are converting given rectangular coordinates into polar coordinates. The next six problems are converting points in polar coordinates to rectangular form. 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 problems right. The practice sheets give enough room for students to show work. Answer key is included.

This is an engaging and collaborative partner activity in which students will use the formulas for arc length and sector area. There are 12 sections as in each partners are given a central angle θ in degrees and the radius r of a circle. In each odd section Partner A has to find the area of the subtended sector and Partner B has to calculate the length of the intercepted arc. And in each even section Partner A has to find the length of the intercepted arc and Partner B has to compute the area of the formed sector. This is a cute way to help students remember the formulas for arc length and sector area. Student may convert the degrees into radians and use the formulas A=0.5θ r^2 and s=rθ (θ must be in radians) or they can use the formulas A=(θ/360) πr^2 and s=(θ/360) 2πr ( here θ must be in degrees). The given central angle θ is <90 degrees ; 90<θ<180; 180<θ<270 and 270<θ<360 degrees. The activity instructions don’t require that students round to the nearest tenth/hundredth/thousandth so they may leave their answers with pi or they may use the pi button on their calculator to obtain the answers, depends on teacher’s decision. The activity sheets can be used as response sheets. Recording sheet where students to show their detailed calculations is provided as well. 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 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.