Moderate -0.8 This is a straightforward gradient calculation using the formula (y₂-y₁)/(x₂-x₁), followed by rationalizing the denominator—a standard algebraic manipulation. While the surds add minor computational complexity beyond a basic gradient question, this remains a routine C1 exercise requiring only recall of standard techniques with no problem-solving insight needed.
2 The point \(P\) has coordinates \(( \sqrt { 3 } , 2 \sqrt { 3 } )\) and the point \(Q\) has coordinates \(( \sqrt { 5 } , 4 \sqrt { 5 } )\). Show that the gradient of \(P Q\) can be expressed as \(n + \sqrt { 15 }\), stating the value of the integer \(n\). [0pt]
[5 marks]
2 The point $P$ has coordinates $( \sqrt { 3 } , 2 \sqrt { 3 } )$ and the point $Q$ has coordinates $( \sqrt { 5 } , 4 \sqrt { 5 } )$. Show that the gradient of $P Q$ can be expressed as $n + \sqrt { 15 }$, stating the value of the integer $n$.\\[0pt]
[5 marks]
\hfill \mbox{\textit{AQA C1 2015 Q2 [5]}}