# Can we list all $p/q$ between $0$ and $1$ if $2 \le q \le 5$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
1. $F$ 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 $F$.
2. $T$ 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 $y > 10$.