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Mathematics and Statistics  annotated exemplars level 2 AS91256
Apply coordinate geometry methods in solving problems (2.1)
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This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.
Low Excellence
Commentary  

For Excellence, the student is required to apply coordinate geometry methods, using extended abstract thinking, in solving problems. This involves one or more of devising a strategy to investigate or solve a problem, identifying relevant concepts in context, developing a chain of logical reasoning or proof, or forming a generalisation, and also using correct mathematical statements, or communicating mathematical insight. This student’s evidence is a response to the TKI task ‘Triangle and Circle Logo’. This student has developed a proof to show that the midpoints of a quadrilateral form a parallelogram (1). Correct mathematical statements have been used in the response. For a more secure Excellence, the student could improve the communication of the thinking for the general case, for example by explaining more clearly what they are doing at each step of the proof. 
High Merit
Commentary  

For Merit, the student needs to apply coordinate geometry methods, using relational thinking, in solving problems. This involves one or more of selecting and carrying out a logical sequence of steps, connecting different concepts or representations, demonstrating understanding of concepts, or forming and using a model and also relating findings to a context, or communicating thinking using appropriate mathematical statements. This student’s evidence is a response to the TKI task ‘Triangle and Circle Logo’. This student has demonstrated an understanding of concepts by finding the midpoints of the first quadrilateral (1) and showing that these form a parallelogram (2). Thinking has been communicated using appropriate mathematical statements. This student has also started to consider the general case by finding the midpoints of the general quadrilateral (3). To reach Excellence the student could to prove the general case. 
Low Merit
Commentary  

For Merit, the student needs to apply coordinate geometry methods, using relational thinking, in solving problems. This involves one or more of selecting and carrying out a logical sequence of steps, connecting different concepts or representations, demonstrating understanding of concepts, or forming and using a model and also relating findings to a context, or communicating thinking using appropriate mathematical statements. This student’s evidence is a response to the TKI task ‘Triangle and Circle Logo’. This student has connected different concepts by finding the equation of the mirror line (1), the equation of the perpendicular line (2), the point of intersection (3) and the coordinates of the reflected point (2). The findings have been related to the context. For a more secure Merit, the student could to improve the strength of the communication in the response, for example by explaining each step of the process. 
High Achieved
Commentary  

For Achieved, the student needs to apply coordinate geometry methods in solving problems. This involves selecting and using methods, demonstrating knowledge of geometric concepts and terms, and communicating using appropriate representations. This student’s evidence is a response to the TKI task ‘Triangle and Circle Logo’. This student has selected and used gradients (1) perpendicular lines (2), equations of lines (3) and intersection of lines (4). This student has also demonstrated knowledge of geometric concepts and used appropriate representations in the response. For Merit, the student could solve the problem by finding the coordinates of the reflected point. 
Low Achieved
Commentary  

For Achieved, the student needs to apply coordinate geometry methods in solving problems. This involves selecting and using methods, demonstrating knowledge of geometric concepts and terms, and communicating using appropriate representations. This student’s evidence is a response to the TKI task ‘Triangle and Circle Logo’. This student has selected and used gradients (1) perpendicular lines (2) and has found an equation of a line (3). This student has also demonstrated knowledge of geometric concepts and used appropriate representations in the response. For a more secure Achieved, the student could strengthen the communication and could find the equation of the line perpendicular to the mirror line. 
High Not Achieved
Commentary  

For Achieved, the student needs to apply coordinate geometry methods in solving problems. This involves selecting and using methods, demonstrating knowledge of geometric concepts and terms, and communicating using appropriate representations. This student’s evidence is a response to the TKI task ‘Triangle and Circle Logo’. This student has found the gradient of the mirror line (1). The equation of the mirror line has been found but the working is incorrect because the wrong gradient has been used (2). To reach Achieved, the student could select and use one further method correctly, for example by finding the gradient of the perpendicular line or the correct equation of the mirror line. 