Do not use a calculator in this question.

A curve has equation \(\displaystyle y=\frac{6+\sqrt{x}}{3+\sqrt{x}}\), where \(x\ge0\). Find the exact value of \(y\) when \(x=6\). Give your answer in the form \(a+b\sqrt{c}\), where \(a\), \(b\) and \(c\) are integers.

Do not use a calculator in this question.

The variables \(x\) and \(y\) are related by the equation \(y=kx^2\). It is given that \(y=1-\sqrt2\) when \(x=1+\sqrt2\). Find the exact value of \(k\), giving your answer in the form \(a+b\sqrt c\), where \(a\), \(b\) and \(c\) are integers.

Do not use a calculator in this question.

The point \((1-\sqrt5,p)\) lies on the curve

\(y=\frac{10+2\sqrt5}{x^2}.\)

Find the exact value of \(p\), simplifying your answer.

Diagrams \(A\) to \(D\) show four different graphs. In each case the whole graph is shown and the scales on the two axes are the same.

Place ticks in the boxes in the table to indicate which descriptions, if any, apply to each graph. There may be more than one tick in any row or column of the table.

Diagrams \(A\) to \(D\) show four different graphs. In each case the whole graph is shown and the scales on the two axes are the same.

Place ticks in the boxes in the table to indicate which descriptions, if any, apply to each graph. There may be more than one tick in any row or column of the table.