Functional QuestionFoundation(Algebra 4)

For the week beginning ….

(a)     The basic monthly charge for a mobile phone contract is £35. This includes:Option 1: 300 free minutes of calls and 100 free texts orOption 2: 100 free minutes of calls and unlimited free texts. All other calls are charged at 6p per minute. Extra texts are charged at 10p each. On average, each month, Matt makes 500 minutes of calls and sends 250 texts. Which option should he choose? You must show your working. (5)

(b)     Viki has a different mobile phone contract. She never sends texts. The graph shows how the total monthly charge is calculated for her mobile phone contract for up to 500 minutes of calls.

(i)      Write down the basic monthly charge and the number of free minutes of calls.Basic monthly charge               £ ...............Number of free minutes of calls   ............... (2)(ii)     Work out the charge per minute for the other calls.Answer ...................................... pence(3)(Total 10 marks) 

(a)     (500 – 300) × 6 or 200 × 6 or (£) 12 or 1200 (250 – 100) × 10 or 150 × 10 or (£) 15 or 1500Option 1 M1 – Method mark          (£) 27 or 62     or      24 or 59 A1 - Accuracy marks are awarded when following on from a correct method           (500 – 100) × 6 or 400 × 6 Option 2 M1 – Method mark          (£) 27 and 24    or    62 and 59 A1 - Accuracy marks are awarded when following on from a correct method           Option 2 (cheaper) B1 - Marks awarded independent of method follow through mark

b)     (i)      £ 25B1 - Marks awarded independent of method                   150B1 - Marks awarded independent of method          (ii)     Attempt to read one coordinate between 150 and 500 ± £1eg,   250, 30  (500, £41.50 - 43.50 inclusive)Allow 350, 42.5 (± 1)Not (150, 25)M1 – Method mark                   Correct statementeg,   £1 for 20 mins       £2 for 40 mins       £5 for 100 mins       £10 for 200 minsTheir £17.50 (± 1) for 350 mins or (Their change –25) and (their mins – 150)0.05 M1 dep - A method mark dependent on a previous method mark beingawarded.                   5£0.05 A1 - Accuracy marks are awarded when following on from a correct method [10] 

This open ended question was an excellent discriminator of the candidates. The standard of presentation varied enormously as did the quality of the responses. In part (a) many candidates realised that it did not matter whether or not the monthly charge was included in the calculations and managed to reach the comparison stage. Common errors included not taking into account the number of free minutes or trying to justify answers in general terms rather than considering the costs. In part (b)(i) common errors were to give £42 for the basic monthly charge and 500 free minutes, the readings from the end of the graph. Although most candidates made a start on part (b)(ii) fully correct answers were rare. Many candidates, having correctly identified an amount of minutes with the cost were unable to divide correctly to obtain the cost per minute, for example £5 for 100 minutes often led to 20 p per minute.

Common Mistakes – what did the examiners say?