Binomial Theorem Teacher Resources
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A week's worth of teaching on the Binomial Theorem. Lesson examples and a plethora of worksheets included. Learners find coefficients of specific terms within binomial expansions using notation of factorials and then apply these skills in using the Binomial Theorem to find solutions to practical applications.
In this video on the Binomial Theorem, Sal tries to give an intuition behind why combinations are part of its definition. By looking at the expansion of (a + b)3 and carefully looking at where each value originates from, one can see how we are really asking a question about combinatorics.
A comprehensive lesson plan that explores and researches Pascal's triangle and relates its properties to the Binomial Theorem through a variety of lessons. Have the class practice expanding polynomials using the theorem. A few other formulas and functions related to this theorem will be explored.
Practice applying the binomial theorem on this worksheet. It contains five multiple choice and five free response problems. The solutions are provided.
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.
In this binomial expansions practice worksheet, students utilize the theorem to determine the nth term in the expansion for 10 problems, then expand it completely for an additional 6 problems.
In this algebra worksheet, students identify the coefficient and different terms of a binomial. They use binomial expansion to find their answer. There are 7 questions with an answer key.
In this algebra worksheet, students expand binomials and identify different terms. They expand the function using the binomial theorem. There are forty-four questions with an answer key.
For this Binomial Theorem worksheet, students solve 10 different problems that include applying the Binomial Theorem in each.
Sal shows two ways to quickly calculate the coefficients of a binomial expansion. With the first method, he shows the relationship between PascalÕs triangle and the coefficients, and in the second method, he shows an even faster way for one to write the coefficients without calculating previous rows of coefficients.
In this binomial theorem worksheet, learners expand given binomials. They write an equation to identify the nth term of a sequence. This one-page worksheet contains 15 problems.
Continuing his discussion of the Poisson Distribution (or Process) from the previous video, Sal takes students through the derivation of the traffic problem he had begun. The math gets gritty in this video as Sal takes out the graphic calculator to solve the problem.
A good review worksheet on simplifying rational expressions, solving equations with factorials, solving problems on permutations and combinations, and using the Binomial Theorem.
In this sequences and series worksheet, 11th graders solve and complete 9 different problems that include various sequences and series. First, they evaluate each given expression using the binomial theorem. Then, students use Pascal's Triangle to expand each binomial.
In this Algebra II worksheet, 11th graders apply the binomial theorem to expand a binomial and determine a specific term of the expansion. The one page worksheet contains four problems. Answers are provided.
In this algebra worksheet, students factor and expand equations using binomial expansion. They identify coefficients of different terms. There are forty-four questions with an answer key.
In this advanced algebra semester review learning exercise, students answer 63 questions spiraling a review of topics including combinations, systems of equations, absolute value, parent graphs, conics, complex numbers, and binomial theorem.
In this binomial theorem worksheet, students identify the coefficients of a binomial expansion. They determine the designated term of an expansion. This two-page worksheet contains 13 problems.
Students examine the patterns in Pascal's Triangle. In this recognizing lesson, students view a model of Pascal's Triangle and describe the patterns of the multiples. Students identify the shapes that are made within Pascal's Triangle.
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.