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• Publicado : 25 de febrero de 2012

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1. Find the coefficient of a3b4 in the expansion of (5a + b)7.
Working:||
(Total 4 marks)

2. If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for
(a) log2 5;
(b) loga 20.
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(Total 4 marks)

3. Find the sum of the infinite geometric series

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(Total 4 marks)

4. Find the coefficient of a5b7 in the expansion of (a + b)12.
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(Total4 marks)

5. Let log10P = x , log10Q = y and log10R = z. Express in terms of x , y and z.
Working:||
(Total 4 marks)

6. Use the binomial theorem to complete this expansion.
(3x + 2y)4 = 81x4 + 216x3 y +...
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7. Consider the binomial expansion
(a) By substituting x = 1 into both sides, or otherwise, evaluate

(b) Evaluate .
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(Total 4 marks)

8. Consider the expansion of
(a) How many terms are there in thisexpansion?
(b) Find the constant term in this expansion.
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(Total 6 marks)

9. Consider the following statements
A: log10 (10x) > 0.
B: –0.5 £ cos (0.5x) £ 0.5.
C: – £ arctan x £ .
(a) Determine which statements are true forall real numbers x. Write your answers (yes or no) in the table below.
Statement|(a) Is the statement true for all real numbers x? (Yes/No)|(b) If not true, example|
A|||
B|||
C|||

(b) If a statement is not true for all x, complete the last column by giving an example of one value of x for which the statement is false.
Working:|
(Total 6 marks)

10. Find the coefficient of x3 inthe expansion of (2 – x)5.
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(Total 6 marks)

11. Find the term containing x10 in the expansion of (5 + 2x2)7.
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(Total 6 marks)

12. Given that log5 x = y, express each of the following in terms of y.
(a)log5 x2
(b) log5
(c) log25 x
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(Total 6 marks)

13. Complete the following expansion.
(2 + ax)4 = 16 + 32ax + …
(Total 6 marks)

14. Let p = log10 x, q = log10 y and r = log10 z.
Write the expression log10 in terms of p, q and r.
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(Total 6 marks)

15. Let a = log x, b = log y, and c = log z.