\(F\) is the set of all the fractions \(\dfrac{p}{q}\) which lie between \(0\) and \(1\), where \(p\) and \(q\) are positive integers having no common factor and \(2 \le q \le 5\). List all the members of \(F\) and indicate the smallest and the largest members. Find the mean value of the members of \(F\).
\(T\) is the set of all right-angled triangles with sides of length \(x\), \((x+1)\) and \(y\), where \(x\) and \(y\) are integers. If \((x+1)\) is the length of the hypotenuse, find an expression for \(y\) in terms of \(x\), giving your answer in its simplest form. Hence find a member of \(T\) for which \(y > 10\).
Thinking about Algebra
Question
