ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. Suggested grade boundaries for this paper: A* A B C D E 74 66 58 50 42 34 1. Find . (4) January 2008 2. Find ‚ giving each term in its simplest form. (4) January 2009 3. Expand and simplify (7 + 2)(7 – 2). (2) January 2009 4. y = 5x3 − + 2x − 3. (a)
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Write your name here Surname Other names Centre Number Candidate Number Edexcel GCSE Mathematics A Paper 2 (Calculator) Foundation Tier Thursday 8 November 2012 – Afternoon Time: 1 hour 45 minutes Paper Reference 1MA0/2F You must have: Ruler graduated in centimetres and millimetres‚ protractor‚ pair of compasses‚ pen‚ HB pencil‚ eraser‚ calculator. Tracing paper may be used. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the
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maximum possible revenue? (c) What is the maximum revenue the agent can obtain? (d) What restrictions‚ if any‚ need to be placed on the domain of n? | | | 3. | The graphs shown are graphs of: I : y = f(x)II : y = f /(x)III : y = f //(x)By studying the graphs‚ answerthe following questions. (a) Describe the behaviour ofy = f(x) for x where (i) x < 0 (ii) 0 < x < 6 (iii) x > 6 (b) Find the values of thex – intercepts of y = f(x). (c) Determine the expression forthe
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defined as the following: A medium in which communication occurs. However‚ there may be many misperceptions that mathematics is a language. One may argue that one can utilize numbers to represent certain letters in the alphabet‚ for example‚ a= 1‚ b = 2‚ c = 3. It is just using numbers‚ to represent a language. However‚ this is not mathematics. Numbers themselves can be a language‚ however numbers are just symbols. Numbers are not mathematics. Do we use mathematics to communicate? No. This is because mathematics
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resource has not been fully used. In other words‚ the slack value associated with that resource constraint is positive. We can conclude that the shadow price associated with that constraint: A. will have a positive value. B. will have a negative value. C. will have a value of zero. D. could have positive‚ negative‚ or zero value. D . Use the following information for problems 2 – 5: Aunt Anastasia operates a small business; she produces seasonal ceramic objects to sell to tourists
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Coursework 2 Mathematical Finance Group 27 Q1. Hedging in Complete and Incomplete market Solution: Complete market Suppose we have m states. A complete market A is one with the marketed subspace Span(A.1‚A.2‚ ⋯‚ A.n) includes all possible payoffs over the m states‚ i.e.‚ if it contains all possible m-dimensional vectors. Incomplete market Suppose we have m states. An incomplete market corresponds to a market with fewer linear independent
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the following in scientific notation. a 8000000 b 13400000000 c 0.00003451 5. a 1 Move the decimal point after the first significant figure. a 8 000 000 = 8 ⋅ 106 2 The decimal point has been moved 6 places left. 6. b 1 Move the decimal point after the first significant figure. b 13 400 000 000 = 1.34 ⋅ 1010 2 The decimal point has been moved 10 places left. 7. c 1 Move the decimal point after the first significant figure. c 0.000 034 51 = 3.451 ⋅ 10-5 2 The decimal point has been moved
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THE IMPORTANCE OF MATHEMATICS W. T. Gowers It is with some disbelief that I stand here and prepare to address this gathering on the subject of the importance of mathematics. For a start‚ it is an extraordinary honour to be invited to give the keynote address at a millennium meeting in Paris. Secondly‚ giving a lecture on the significance of mathematics demands wisdom‚ judgment and maturity‚ and there are many mathematicians far better endowed than I am with these qualities‚ including several
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Check your answers if you have time at the end. Turn over P40658A ©2012 Pearson Education Ltd. 6/6/6/4/6/3 *P40658A0120* FORMULAE SHEET – FOUNDATION TIER Area of a trapezium = 1 (a + b)h 2 Pythagoras’ Theorem a2 + b2 = c2 c a b h a b hyp opp adj = hyp cos opp = hyp sin opp = adj tan opp hyp adj hyp tan or sin cos adj Volume of prism = area of cross section opp adj cross section h lengt Circumference of circle
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C is for Ceramics Betcha didn’t know that! Joshua Bilchik Brookline High School 7 June 2013 Ceramics—with its brilliant colours‚ innovative designs‚ and varied forms is among the most enduring and fascinating of the decorative arts. Artistic expression has been hugely prevalent in society since the early man drew paintings on a cave wall. It is ever-present in the world‚ and its magical lure has impacted societies forever. Nothing ever begins a perfect form‚ and just as ceramics has evolved
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