includes a clear and explicit description of the aim, as well as a rationale. The plan of action is not explicitly explained.
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1 A The introduction includes a clear and explicit description of the aim, as well as a rationale. The plan of action is not explicitly explained. B Constraints relative to this specific study are appropriately defined. C The Mathematical exploration relates to personal interest. C A specific model is chosen. A/B Useful explanation, appropriately supported by the diagram. B The variable P used in the formula is explained at this point. The definition (fluid density) is made at the next paragraph. Mathematics SL and HL teacher support material 1
2 E Research has been conducted on the literature of the domain of the study, in order to provide the equations relevant to the problem. B The (differential) operator is not defined in the equations provided. It is implicitly explained at the next line. A Any particular reason for choosing these values? A, B Interesting explanations on the method and process that will be used. C Research has been conducted on different models and a choice is made. E Very good understanding of the complexity of the modelling. Mathematics SL and HL teacher support material 2
3 B How was this equation determined any particular reason? E Appropriate use of mathematics to calculate the area under the curve. A The task would benefit from relevant explanations, in order to explain the process to readers who are not familiar with the problem or mathematics involved. B The results provided are correct to three significant figures. E The vertex lines on the axis of symmetry, a point cannot be an axis of symmetry (improper terminology). A, B, C Although the explanations are not correctly expressed, the symmetry of the quadratic function is used in order to avoid repetition of calculations. This helps making the work concise. Mathematics SL and HL teacher support material 3
4 C Personal example. A Appropriate explanations. B, E Technology is used in order to determine this function. B, E The diagram displays the function modelling the aerofoil, It is correctly presented with title, labels, units. The use of the space is not optimal. Mathematics SL and HL teacher support material 4
5 E Interesting idea. E Appropriate use of mathematics, beyond the scope of the Math HL syllabus. E Correct use of calculus. B The data presented in table are expressed in decimetre. This value (5cm) corresponds to the first row. A Extended research has been conducted. D Critical reflection on the research made and its applications to the current problem. E Good understanding of the subject is demonstrated. Mathematics SL and HL teacher support material 5
6 B Good use of technology, in order to generate (correct) data. Mathematics SL and HL teacher support material 6
7 E Good reasoning, supported by appropriate explanations B, E Correct and appropriate data are generated. Mathematics SL and HL teacher support material 7
8 A, B, E Final results for the drag force are produced. The lines of reasoning are consistent and easy to follow through. B Appropriate display of the results. Mathematics SL and HL teacher support material 8
9 E The method used to find the model is similar to that used in Physics. B, E The data manipulated are displayed and the linear relationship is visible. The unit of the y-axis is not properly expressed (confusing notation). The line of best fit is also displayed. Mathematics SL and HL teacher support material 9
10 B...function... D Critical analysis of the function obtained. D Critical analysis of the results obtained for the lift force. D Very good and interesting analysis of the results in the light of further research. Mathematics SL and HL teacher support material 10
11 B Interesting display of the data which offers a visual representation of the data presented in the table. B The use of arrows needs to be explained. B The values used below correspond to those for a thickness factor h equal to 1.32 (see table p.8). B It is important to mention that this function is an estimation as more calculations are necessary to prove it. Mathematics SL and HL teacher support material 11
12 D Critical analysis of the initial assumptions/ simplifications made for the investigation. B, D Interesting suggestion for possible and realistic improvements. Mathematics SL and HL teacher support material 12
13 Mathematics SL and HL teacher support material 13
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