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May 2000: Paper 2 #1

May 2000: Paper 2 #1. The cost of sending documents from Australia to the United States of America using Immediate Courier is recorded in the table below. 80. Cost of shipping (in AUD). 70. 60. 50. 40. 30.

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May 2000: Paper 2 #1

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  1. May 2000: Paper 2 #1 The cost of sending documents from Australia to the United States of America using Immediate Courier is recorded in the table below.

  2. 80 Cost of shipping (in AUD) 70 60 50 40 30 This means when the weight is between 0.5 and 1 (including 1 but not including 0.5) the cost is 30 AUD. This means when the weight is between 0 and 0.5 (including 0.5 but not including 0) the cost is 20 AUD. Doesn't include 0.5 Exactly 1 still cost 30 Exactly 0.5 still cost 20 20 Doesn't include 0 10 1 2 3 4 Weight of package (in kg) (a) On graph paper, using a scale of 2 cm to represent 1 kg on the horizontal axis and 2 cm to represent 10 AUD on the vertical axis, draw and label the graph representing this information. Continue graphing the function in the same manner, each time "stepping" up when using the next weight interval.

  3. The cost of sending documents from Australia to the United States of America using Speedy Courier is given by the formula C = 34 + 8W, where C is the cost in Australian dollars, W is the weight in kilograms. (b) (i) Copy and complete the table below 38 50 58 66 To complete the table, plug in the values of W into the equation above. If W = 0.5, then C = 34 + 8(0.5) = 38 If W = 2, then C = 34 + 8(2) = 50 If W = 3, then C = 34 + 8(3) = 58 If W = 4, then C = 34 + 8(4) = 66

  4. 80 Cost of shipping (in AUD) 70 60 50 40 30 20 10 1 2 3 4 Weight of package (in kg) (ii) On the same set of axes as in part (a), draw the graph representing Speedy Courier costs.

  5. 80 Cost of shipping (in AUD) 68 70 62 60 Thus, a 2 kg package cost 50 AUD to ship using either company. 50 40 30 20 Thus, the difference is 68 – 62 = 6 AUD 10 1 2 3 4 Weight of package (in kg) • Use your graph to find…(Again, this means show the lines on the graph) (i) The weight for which the cost is the same for both companies (ii) The difference in cost to send a parcel weighing 3.5 kg.

  6. W1 (in kgs) W2 (in kgs) Cost for W1 (in AUD) Cost for W2 (in AUD) Total Cost (in AUD) 4.0 1.5 74 46 120 3.5 2.0 68 50 118 3.0 2.5 62 54 116 2.5 3.0 56 58 114 2.0 3.5 50 62 112 1.5 4.0 40 66 106 (d) Kim spent 106 AUD to send 2 packages of documents with a combined weight of 5.5 kgs. Given that he used both courier services, calculate the weight of documents he sent through each one. Since we know there is a limit of 4 kgs for any one package and Kim used both courier services, we can use trial and error to calculate the weight of documents he sent through each one. Let W1 = weight of package sent through Immediate Courier and W2 = weight of package sent through Speedy Courier. Thus, Kim sent a 1.5 kg package through Immediate Courier and a 4.0 kg package through Speedy Courier.

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