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Functional Question Higher (Algebra 4) For the week beginning ….

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Two gas supply companies have different ways of charging for the gas they supply. Alpha gasCO Fixed Charge £9.60 Price per kilowatt hour of gas First 5 kilowatt hours free then £1.30 for every kilowatt hour over 5. Beta gasCO Fixed Charge No fixed charge Price per kilowatt hour of gas £1.50 for every kilowatt hour. Find the number of kilowatt hours after which Alpha gasCo becomes cheaper than Beta gasCo. You might want to use some graph paper. You must show your method clearly. Answer................................... kilowatt hours (Total 4 marks)

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9.60 + (x – 5) × 1.30 Alt: M1 for graph of Alpha parcels M1 – Method mark = 1.50x M1 for graph of Beta M1 – Method mark 3.10 = 0.20x A1 - Accuracy marks are awarded when following on from a correct method x = 15.5 A1 answer. Accept 16 but not 15. T&I gets M1 iff taken as far as 15. A1 for both schemes at 15 A1 for both schemes at 16 A1 conclusion A1 - Accuracy marks are awarded when following on from a correct method [4]

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Common Mistakes – what did the examiners say? This question was intended to give students a choice of methods and as such was considered a ‘using and applying mathematics’ question. Graph paper was supplied in case a graphical method was adopted. Pleasingly, many different methods were seen, although the main method was Trial and Improvement or writing out tables of costs for each kwh. Graphs when used were usually correct. Algebra was rarely seen but a few candidates used a logical method based on the difference in cost of each kwh and the difference in costs of 5 kwh for both schemes. This was essentially the algebraic method without letters. The main errors were careless arithmetic. About half of candidates scored full marks.

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