Hello teachers friends! My name is Niki.I have been teaching mathematics for over 20 years. My subjects are Algebra through Calculus 3 along with Geometry, Trig and Differential Equations. My passion is to create engaging fun and rigorous math resources of high quality for teachers and students. My products include partner and group activities, matching and sorting activities, multiple-choice games, rigorous worksheets & lessons, challenging independent practice, homework assignments, etc.
Hello teachers friends! My name is Niki.I have been teaching mathematics for over 20 years. My subjects are Algebra through Calculus 3 along with Geometry, Trig and Differential Equations. My passion is to create engaging fun and rigorous math resources of high quality for teachers and students. My products include partner and group activities, matching and sorting activities, multiple-choice games, rigorous worksheets & lessons, challenging independent practice, homework assignments, etc.
This is a collaborative activity to practice evaluating indefinite integrals by using Integration by Parts. It aims to develop and consolidate student’s skills in both integration and differentiation as well.
Partners work through 16 sections (or less if preferred) 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 (saving time) 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 answers.
A purpose of this activity is to aid learners gain a better understanding of integration.
I hope it will be helpful for your calculus students.
Typed answer keys are included
In this engaging and self-checking activity students will practice integration of trig functions using the following trig substitutions:
▸ t = tan(x/2)
▸ t = sinx or t = cosx
▸ t = tanx
There are 12 task cards – recording sheets with space provided for students to show their work. Students have 4 indefinite integrals for each type trig substitution. They are instructed which one trig substitution(s) to apply so to solve the problems easily. After finding the integral, students must fill in the missing function f(x) in a corresponding empty rectangle for the answer given coded at the bottom of the worksheet card.
The product can be used as an independent practice or for class work to organize students in cooperative learning groups. It is also great for extra integration practice or enrichment.
Answer keys are included. Typed solutions to problems A, D, E and H are provided to be possibly used as a guide.
NOTE: There are also included worksheet cards with only the problems given (without answers) so the cards can be used as worksheets, homework assignment and even as an assessment.
In this fun Valentine’s themed activity, students will practice evaluating definite integrals using u- substitution.
Activity Directions: Students are instructed to evaluate 12 definite integrals using u- substitution. The corrected values are recorded on twelve of 13 hearts on a given picture. Every time students arrive at a correct answer, they will “win the heart” having this answer written on it. Students are also asked to find the only one heart who can NOT be won.
The product can possibly be used as a partner or a group activity (group of 2 and 3).
Student recording sheets and answer keys are provided.
I hope you and your students enjoy!
♡ Happy Valentine’s Day! ♡
This is an engaging practice that investigates infinite limits both graphically and algebraically. Students are asked to graph 8 functions and evaluate 24 limits (right and left-hand limits included) based on these graphs. Then students are asked to prove 11 equalities that is to check whether 11 infinite limits are evaluated correctly.
Students are provided with rooms to show work and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem.
All the graphs are presented in the answer keys.
The resource can be used for class work, as an individual practice or homework assignment.
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 is a complete rigorous lesson on Advanced Techniques of Integration for students enrolled in AP Calculus BC or Calculus 2.
( The resource contains 47 problems - 17 with full typed solutions and 30 with answer keys)
Lesson Objective:
Find indefinite integrals and evaluating definite integrals using integration by parts.
It includes
A. Detailed Guided Notes (5 pages) including derivation of Integration by Parts formula and 7 worked out examples with indefinite and definite integrals as
4 examples perform Integration by Parts once
3 examples including repeated Integration by Parts( twice and for third time).
The students are guided through the process of picking u, du, v, and dv.
B. 20 Classifies Practice Problems ( 10 come with full typed solutions and other 10 are similar to them for students to try their own. Students are given the answers. )
C. 12 Assignment Problems with answer keys ( 6 indefinite and 6 definite integrals ).
D. 2 versions Multiple Choice Exit Tickets /Quizzes/ Assessments ( with answer keys)
In this activity students will evaluate 16 definite integrals using their properties and the following techniques of integration:
► integration by substitutions (u-substitution & trig substitutions)
► integration by parts
► completing the square
► trigonometric integrals & using trig identities
► partial fractions decomposition and long division
The resource contains multiple - choice questions - definite integrals to be calculated. Problems range in difficulty as the problems of the second part of the quiz are more complex. Students will need their correct answers to find out the configuration of a hidden constellation. Here’s how:
Students are given a figure with shapes of a circle, called “stars”. Sixteen of them are labeled with the correct answers of students’ questions and form the configuration of the constellation Draco. Students connect the “stars” of the constellation with straight lines in a specified sequence. At last, they try to identify the constellation.
A recording sheet is included for students to show how the answers are obtained. An answer key is included.
The product can be used for class work, independent or grouped (groups of 2 or 4). It could be splitted into two parts. The quiz can be used as an assessment as well.
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.
In this fun Valentine’s themed activity, students will practice evaluating definite integrals using the properties of integrals and the table of basic integrals.
Activity Directions: Students are instructed to evaluate 12 definite integrals using the table of basic integrals. The corrected values are recorded on twelve of 13 hearts on a given picture. Every time students arrive at a correct answer, they will “win the heart” having this answer written on it. Students are also asked to find the only one heart who can NOT be won.
The product can possibly be used as a partner or a group activity (groups of 2 or 3).
Student recording sheets and answer keys are provided.
I hope you and your students enjoy!
♡ Happy Valentine’s Day! ♡
This bundle contains 5 PDF format items printable. These are fun partner and group activities. Students will make compound words, search for common root between two equations, “throw” in a “bucket” extraneous solutions, draw and color balls and flowers on a picture while solving rational equations.
The resource covers the following topics:
Solving rational equations resulting in linear equations
Solving rational equations resulting in quadratic equations
using three types methods for solving:
Cross Multiplying
Multiplying by the LCD
Factoring to find the LCD
• The activities include monomial, binomial, and trinomial denominators.
• Extraneous solutions are included.
Answer keys are included.
Students will practice condensing logarithms with this multiple-choice game. On each page there are two problems each in a table. In the table there are given a picture of a parrot, a logarithmic expression that students have to condense and four answer choices. Name of parrot species corresponds to each answer choice. If students solve the problem correctly they will find out what parrot species is this one on the picture.
The problem are 12 and vary in difficulty. The distractors are well thought.
Answer key is provided.
This resource contains 16 indefinite integrals with their detailed solutions (typed). Students will use Integration by Parts to find the integrals.
The packet has 2 worksheets:
The first worksheet has the students evaluating 8 indefinite integrals
The second worksheet is finding also 8 indefinite integrals as some examples are a bit more challenging.
These are 6 practice/review tickets on indefinite integrals. Each ticket contains 9 various challenging problems. For each ticket there are included one problem or two on the following topics:
basic integration
integration using u – substitution
integration by parts
integration using suitable substitution
integration by partial fractions decomposition
There are included rational, radical, exponential, logarithmic, trigonometric and inverse trigonometric functions.
The product can be possibly used as an independent practice/quizzes 6 different forms, as a group activity (groups of 2 to 6 members), homework assignment or assessment.
Recording sheet is provided. Answer keys are included.
This is an engaging and collaborative partner activity for analyzing and sketching graphs of polynomial and rational functions using calculus. Students will use limits, first and second derivatives to provide information about function behavior and then sketch the graph of the function.
Activity Directions: Students are given five sections to work through. In each section partners are given two functions of the same type to identify their features (intercepts, asymptotes, intervals of increase and decrease, local maximum and minimum points, intervals of concave up and concave down, inflection points). After finding all the important parameters students are asked to draw a graph of the function.
▸The functions of a section differ only by coefficients so partners obtain similar results and graphs with the same shape.
Students are provided recording/response sheets with a number of steps of the general algorithm for investigation of functions, rooms to record their results and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem so sketching to become easier.
This product can be also used as a group activity, for collaborative learning, for enrichment and extra practice, as independent practice and homework assignment.
Detailed typed answer keys are included. All the graphs are drawn as well.
BONUS: I have included 4 additional sections for extra practice or enrichment.
(These are without answer keys.)
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.
This is an engaging and fascinating activity for studying the intervals of concavity of given functions. The functions included are polynomials, rational, radical, exponential, logarithmic and trigonometric. They are specially selected so that each function has more than one points of inflection. If students solve all the 16 problems correctly, they will find out 16 math calculus terms (each consisting of two words). Some of the terms might not be still popular and students will learn them.
Activity Directions: Partners are instructed to identify the intervals where 8 functions given concave up and the intervals where another 8 functions concave down. They look for their answers in a given table and search for a math calculus term corresponding to each of their answers(there is a word corresponding to an interval).
The problems are written on task cards.
This product can be possibly used as an independent practice, as a partner or a group activity (groups of 4).
Student recording sheet and answer keys are provided.
These are 6 Christmas themed task or station cards grouped with 10 to 15 similar problems per card. There are a total of 81 carefully chosen problems concerning the following applications of the derivatives:
❄finding critical points (Card A - 15 problems)
❄ determining intervals of increasing and decreasing (Card B - 15 problems)
❄ finding local extrema (Card C - 15 problems)
❄ finding absolute extrema on the specified intervals (Card D - 10 problems)
❄ finding inflection points (Card E - 14 problems)
❄ determining intervals of concavity (Card F - 12 problems)
The functions included are rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions).
The cards can be used individually or with groups. Student recording sheets are included.
Detailed answer keys/solutions (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.
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 an engaging and challenging practice aiming to improve students skills on integration by substitution. There are given total of 13 integrals. The integrands are functions involving radicals, rational and exponential functions.
For the first 8 problems students are asked to use a given substitution to find an integral. For the next 5 problems students will need to show more flexible thinking as this time they are required to find a suitable substitution to evaluate an integral.
The problems require the use of u-substitution, integration by parts and integration by partial fractions and long division. Make sure these problems are appropriate for your students - download the preview and look at the thumbnails to see problem examples.
The practice worksheets have enough room for students to show their work.
Full solutions (handwritten clearly) are included.