AQA GCSE higher specimen paper 1: Question 28

When performing live calculations of examples of questions for the students, I shall begin by writing down an approach to how they should tackle the problem. This will only take a minute and I’ve found doing this will give the student a checklist to refer to so they can ensure that they’re on the right track when answering the questions. It’s something that has worked for me throughout my mathematical education so I don’t see why it would be any different for the students I will be teaching. Following this, using the online lesson space, I will show a clear step by step process to produce my answer, and whilst doing so I shall explain everything I am doing at a comfortable pace to ensure the student fully understands what I am doing. The questions i shall give my students will be based on slight variants of current questions found in past papers since i believe this to be the best way of preparing them for the exam. So, the question I will answer comes from a higher tier AQA GCSE past paper. It’s a question which tests the students’ knowledge of circle theorems, and straight-line coordinate geometry. To tackle this problem, the student must first understand the problem, then using the boundary conditions given in the question, find coordinate P. Following this, the gradient of the line connecting point P and the origin must be determined. After that, using the rules of lines acting as tangents against circles, the gradient of the line PQ can be found using the idea of reciprocals. The equation of the line can then be found, and once this has been done, point Q can be found by finding the x coordinate when y is 0. Once all these processes have been completed the answer for Q should be found to have the coordinates (10, 0).