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[DOCX File]ME-A1 Working with combinatorics Y11
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The binomial expansion is introduced, Pascal’s triangle is constructed and related identities are proved. The material studied provides the basis for more advanced work, where the binomial expansion is extended to cases for rational values of 𝑛, and applications in calculus are explored. A student: uses concepts of permutations and combinations to solve problems involving counting or ...
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[DOC File]LESSON 1 REVIEW OF SOLVING NONLINEAR INEQUALITIES
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We will use the Binomial Expansion theorem in order to find the four terms in the expansion of . Binomial Expansion Theorem Let n be a positive integer. Let a and b be real numbers, then , where . Thus, by the Binomial Expansion theorem, we have that = = = = = Answer: 17. By the Factor Theorem, is a factor of . This factorization can be found ...
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[DOC File]BINOMIAL EXPANSION INVESTIGATION - Weebly
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Pascal’s Triangle/Binomial Theorem Investigation Goal: To explore an aspect of math with which you are not deeply familiar OR that you aren’t sure how it may connect to something that interests you. In this investigation you will explore PASCAL’S TRIANGLE. What relationships can you discover? Part A: Pascal’s Triangle. 1. The triangle of numbers below forms part of the famous “Pascal ...
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Activity overview:
The binomial expansion of (p + q)n can be used to represent these situations. Example: A student takes a multiple choice quiz with 5 questions. Each question has 4 choices. She hasn't studied and will guess on every question. In order to pass this quiz, she must get 4 of the questions correct. Given that she is guessing, assume and. Also, n = 5 because there are 5 questions. Pascal’s ...
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[DOC File]Binomial Theorem Worksheet - Weebly
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You should be able to: “Build” Pascal’s Triangle to include the coefficients up to a stated value of “n”. Example: Create Pascal’s Triangle to show the coefficients of (a + b)5
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[DOC File]Binomial Expansion - Teachnet UK-home
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Example 1. Expand in ascending powers of x, up to and including the term in x2. State the set of values for which the expansion is valid. The following expansion was used in C2 to write binomial expansions, unfortunately we have a negative, fractional power. Therefore we have to use the following one instead. Therefore: = For the expansion to be valid the modulus of the ax term in the bracket ...
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[DOC File]Chapter : Binomial Distribution
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So, the values P(X = x) for x = 0, 1, 2, …, n can be obtained by considering the terms in the binomial expansion of (q + p)n, noting that q + p = 1. (q + p)n = nC0 qn p0 + nC1 qn-1 p1 + … + nCr qn-r pr + … + nCn q0 pn ( 1 = P(X = 0) + P(X = 1) + … + P(X = r) + … + P(X = n)
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[DOC File]Expanding and factoring with Algebra Tiles
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Binomial Expansion We can use the method of area model to multiply two binomials as well. Consider the example (x + 3)(x + 2). We create a rectangular area with height (x + 3) units and width (x + 2) units.
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[DOC File]THE BINOMIAL EXPANSION
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Example. Find the binomial expansion of √(1 – 3x) up to and including the term in x3. By substituting x = 0.01 in the expansion, use it to find an approximation to √97 Ex 3A p 25 EXPANSION OF (a + bx)n FOR ANY a AND b Example Ex 3B p 28 USE OF PARTIAL FRACTIONS TO SIMPLIFY EXPANSIONS. Example Now use the binomial expansion: Ex 3C p 30. Mixed Ex 3D p 31. C4 Chapter 3. 8 JMcC. …
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[DOC File]Probability Unit Vocab
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For example, 3x2 – 2x. binomial expansion* - for any power of “ n”, the binomial (a + x) can be expanded. This . is particularly useful when “x” is very much less than “a” so that . the first few terms provide a good approximation of the value of . the expression. (a + x)n = an + nan – 1x +an – 2 x 2 + . . . + x n. combinations – an arrangement of choices in which the order ...
binomial expansion question and answer

Binomial expansion example