Binomial expansion question and answer
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( If you change your mind about an answer, cross it out and put your new answer and any working underneath. 1. Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 – 3x)5, giving each term in its simplest form. (4) (Total 4 marks) _____ 2. Find the first 4 terms, in ascending powers of x, of the binomial expansion of
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(c) Substitute x = into the binomial expansion in part (a) and hence obtain an approximation to (23. Give your answer to 5 decimal places. (3) January 2010. 2. f (x) = , ( x ( < . Find the first three non-zero terms of the binomial expansion of f(x) in ascending powers of x. Give each coefficient as a simplified fraction. (6) June 2011 3. Figure 1
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A significant number of candidates failed to answer part (a) correctly, due to the unfamiliarity with the formula for Common incorrect answers for b included 1, 4, 10, 36! or 91390. In part (b), most candidates were able to write down the binomial expansion of (1 + x)n.
[DOC File]January 2006 - 6672 Pure P2 - Question paper
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(a) Write down the binomial expansion, in ascending powers of x, of (1 + 6x)4, giving each coefficient as an integer. (3) (b) Use your binomial expansion to find the exact value of 6014. (2) 2. Figure 1. Figure 1 shows the graph of y = f(x), –5 ( x ( 5. The point M (2, 4) is the maximum turning point of the graph.
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A handful of candidates ignored their binomial expansion and gave the answer 2, using their flawed logic of “twice 2” being equal to “2 squared”. Other less common errors included either giving an answer of following on from or following on from not multiplying either coefficient by 2.
[DOC File]Use the following to answer questions 1-12:
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113. Use the binomial theorem to prove the following:. Ans: In (a b)n use n 100, a 1, b 2. 114. Find the coefficient of x7y5 in the expansion of (3x y)12. Ans: . 115. Find the coefficient of x5y6 in the expansion of (2x y)11. Ans: 116. Find the coefficient of x8 in the expansion of (x2 2)13. Ans: . 117.
[DOC File]S1 SAMPLE EXAM QUESTIONS – BINIOMIAL DISTRIBUTION
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State whether or not the binomial distribution provides an appropriate model for the number of sandwiches suitable for vegetarians eaten by these four friends. Explain your answer. (2) total:11 marks. George Monoux Sixth Form College 1. 2. (a) (i) Binomial n = 8 p = 0.3 B1 B1. Binomial. 8, 0.3. P(2 or fewer) = 0.552 B1. 0.552 (0.551, 0.5525)
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( If you change your mind about an answer, cross it out and put your new answer and any working underneath. 1. (a) Find the binomial expansion of, in ascending powers of x up to and including the term in x2. Give each coefficient as a simplified fraction. (5) (b) Hence, or otherwise, find the expansion of,
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Give your answer to 7 decimal places. (2) January 2008. 3. f(x) = , (x( < . (a) Find the binomial expansion of f(x) in ascending powers of x, up to and including the term in x3. Give each coefficient in its simplest form. (6) Use your answer to part (a) to find the binomial expansion in ascending powers of x, up to and including the term in x3, of
[DOC File]June 2005 - 6672 Pure P2 - Question paper
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(a) Write down the first three terms, in ascending powers of x, of the binomial expansion of (1 + px)12, where p is a non-zero constant. (2) Given that, in the expansion of (1 + px)12, the coefficient of x is (–q) and the coefficient of x2 is 11q, (b) find the value of p and the value of q. (4) 3.
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